"use strict"; const {Fragment: _Fragment, jsx: _jsx, jsxs: _jsxs} = arguments[0]; const {useMDXComponents: _provideComponents} = arguments[0]; function _createMdxContent(props) { const _components = { a: "a", annotation: "annotation", code: "code", h1: "h1", img: "img", li: "li", math: "math", mfrac: "mfrac", mi: "mi", mn: "mn", mo: "mo", mrow: "mrow", mstyle: "mstyle", msub: "msub", msubsup: "msubsup", msup: "msup", mtable: "mtable", mtd: "mtd", mtr: "mtr", p: "p", path: "path", pre: "pre", semantics: "semantics", span: "span", strong: "strong", svg: "svg", ul: "ul", ..._provideComponents(), ...props.components }; return _jsxs(_Fragment, { children: [_jsxs(_components.h1, { id: "更多渲染模式", children: [_jsx(_components.a, { className: "heading-link", href: "#更多渲染模式", children: _jsx(_components.svg, { xmlns: "http:www.w3.org/2000/svg", fill: "#ab2b65", viewBox: "0 0 20 20", className: "w-5 h-5", children: _jsx(_components.path, { fillRule: "evenodd", clipRule: "evenodd", d: "M9.493 2.853a.75.75 0 00-1.486-.205L7.545 6H4.198a.75.75 0 000 1.5h3.14l-.69 5H3.302a.75.75 0 000 1.5h3.14l-.435 3.148a.75.75 0 001.486.205L7.955 14h2.986l-.434 3.148a.75.75 0 001.486.205L12.456 14h3.346a.75.75 0 000-1.5h-3.14l.69-5h3.346a.75.75 0 000-1.5h-3.14l.435-3.147a.75.75 0 00-1.486-.205L12.045 6H9.059l.434-3.147zM8.852 7.5l-.69 5h2.986l.69-5H8.852z" }) }) }), "更多渲染模式"] }), "\n", _jsx(_components.p, { children: "以第一篇第一个模型为例：" }), "\n", _jsx(_components.pre, { className: "language-python", children: _jsxs(_components.code, { className: "language-python code-highlight", children: [_jsxs(_components.span, { className: "code-line", children: ["xml ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token triple-quoted-string string", children: "\"\"\"\n" })] }), _jsx(_components.span, { className: "code-line", children: _jsx(_components.span, { className: "token triple-quoted-string string", children: "\n" }) }), _jsx(_components.span, { className: "code-line", children: _jsx(_components.span, { className: "token triple-quoted-string string", children: " \n" }) }), _jsx(_components.span, { className: "code-line", children: _jsx(_components.span, { className: "token triple-quoted-string string", children: " \n" }) }), _jsx(_components.span, { className: "code-line", children: _jsx(_components.span, { className: "token triple-quoted-string string", children: " \n" }) }), _jsx(_components.span, { className: "code-line", children: _jsx(_components.span, { className: "token triple-quoted-string string", children: " \n" }) }), _jsx(_components.span, { className: "code-line", children: _jsx(_components.span, { className: "token triple-quoted-string string", children: " \n" }) }), _jsx(_components.span, { className: "code-line", children: _jsx(_components.span, { className: "token triple-quoted-string string", children: " \n" }) }), _jsx(_components.span, { className: "code-line", children: _jsx(_components.span, { className: "token triple-quoted-string string", children: " \n" }) }), _jsx(_components.span, { className: "code-line", children: _jsx(_components.span, { className: "token triple-quoted-string string", children: " \n" }) }), _jsx(_components.span, { className: "code-line", children: _jsx(_components.span, { className: "token triple-quoted-string string", children: "\n" }) }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token triple-quoted-string string", children: "\"\"\"" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["model ", _jsx(_components.span, { className: "token operator", children: "=" }), " mujoco", _jsx(_components.span, { className: "token punctuation", children: "." }), "MjModel", _jsx(_components.span, { className: "token punctuation", children: "." }), "from_xml_string", _jsx(_components.span, { className: "token punctuation", children: "(" }), "xml", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["data ", _jsx(_components.span, { className: "token operator", children: "=" }), " mujoco", _jsx(_components.span, { className: "token punctuation", children: "." }), "MjData", _jsx(_components.span, { className: "token punctuation", children: "(" }), "model", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token comment", children: "# 基本渲染" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token keyword", children: "with" }), " mujoco", _jsx(_components.span, { className: "token punctuation", children: "." }), "Renderer", _jsx(_components.span, { className: "token punctuation", children: "(" }), "model", _jsx(_components.span, { className: "token punctuation", children: ")" }), " ", _jsx(_components.span, { className: "token keyword", children: "as" }), " renderer", _jsx(_components.span, { className: "token punctuation", children: ":" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" mujoco", _jsx(_components.span, { className: "token punctuation", children: "." }), "mj_forward", _jsx(_components.span, { className: "token punctuation", children: "(" }), "model", _jsx(_components.span, { className: "token punctuation", children: "," }), " data", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "update_scene", _jsx(_components.span, { className: "token punctuation", children: "(" }), "data", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" media", _jsx(_components.span, { className: "token punctuation", children: "." }), "show_image", _jsx(_components.span, { className: "token punctuation", children: "(" }), "renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "render", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] })] }) }), "\n", _jsx(_components.img, { src: "https://obsidian2flowershow-inkem.flowershow.me/I-%E9%99%84%E4%BB%B6/Pasted%20image%2020250913111617.png", alt: "Pasted image 20250913111617", className: "internal", "data-fs-resolved-file-path": "/I-附件/Pasted image 20250913111617.png" }), "\n", _jsx(_components.p, { children: _jsx(_components.strong, { children: "透明渲染与框架可视化" }) }), "\n", _jsx(_components.pre, { className: "language-python", children: _jsxs(_components.code, { className: "language-python code-highlight", children: [_jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token comment", children: "# 创建场景选项对象" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["scene_option ", _jsx(_components.span, { className: "token operator", children: "=" }), " mujoco", _jsx(_components.span, { className: "token punctuation", children: "." }), "MjvOption", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token comment", children: "# 设置可视化选项" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["scene_option", _jsx(_components.span, { className: "token punctuation", children: "." }), "frame ", _jsx(_components.span, { className: "token operator", children: "=" }), " mujoco", _jsx(_components.span, { className: "token punctuation", children: "." }), "mjtFrame", _jsx(_components.span, { className: "token punctuation", children: "." }), "mjFRAME_GEOM ", _jsx(_components.span, { className: "token comment", children: "# 显示几何体框架" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["scene_option", _jsx(_components.span, { className: "token punctuation", children: "." }), "flags", _jsx(_components.span, { className: "token punctuation", children: "[" }), "mujoco", _jsx(_components.span, { className: "token punctuation", children: "." }), "mjtVisFlag", _jsx(_components.span, { className: "token punctuation", children: "." }), "mjVIS_TRANSPARENT", _jsx(_components.span, { className: "token punctuation", children: "]" }), " ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token boolean", children: "True" }), " ", _jsx(_components.span, { className: "token comment", children: "# 启用透明度" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token comment", children: "# 渲染" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token keyword", children: "with" }), " mujoco", _jsx(_components.span, { className: "token punctuation", children: "." }), "Renderer", _jsx(_components.span, { className: "token punctuation", children: "(" }), "model", _jsx(_components.span, { className: "token punctuation", children: ")" }), " ", _jsx(_components.span, { className: "token keyword", children: "as" }), " renderer", _jsx(_components.span, { className: "token punctuation", children: ":" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "update_scene", _jsx(_components.span, { className: "token punctuation", children: "(" }), "data", _jsx(_components.span, { className: "token punctuation", children: "," }), " scene_option", _jsx(_components.span, { className: "token operator", children: "=" }), "scene_option", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" frame ", _jsx(_components.span, { className: "token operator", children: "=" }), " renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "render", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" media", _jsx(_components.span, { className: "token punctuation", children: "." }), "show_image", _jsx(_components.span, { className: "token punctuation", children: "(" }), "frame", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] })] }) }), "\n", _jsx(_components.img, { src: "https://obsidian2flowershow-inkem.flowershow.me/I-%E9%99%84%E4%BB%B6/Pasted%20image%2020250913111719.png", alt: "Pasted image 20250913111719", className: "internal", "data-fs-resolved-file-path": "/I-附件/Pasted image 20250913111719.png" }), "\n", _jsx(_components.p, { children: _jsx(_components.strong, { children: "深度渲染" }) }), "\n", _jsx(_components.p, { children: "深度渲染图像中每个像素值表示场景某点与摄像机的距离，常用于机器人视觉、3D 重建、避障等应用中。" }), "\n", _jsx(_components.pre, { className: "language-python", children: _jsxs(_components.code, { className: "language-python code-highlight", children: [_jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token keyword", children: "with" }), " mujoco", _jsx(_components.span, { className: "token punctuation", children: "." }), "Renderer", _jsx(_components.span, { className: "token punctuation", children: "(" }), "model", _jsx(_components.span, { className: "token punctuation", children: ")" }), " ", _jsx(_components.span, { className: "token keyword", children: "as" }), " renderer", _jsx(_components.span, { className: "token punctuation", children: ":" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 启用深度渲染模式" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "enable_depth_rendering", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 更新场景" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "update_scene", _jsx(_components.span, { className: "token punctuation", children: "(" }), "data", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 深度渲染模式下render返回深度的浮点数组，单位为米" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" depth ", _jsx(_components.span, { className: "token operator", children: "=" }), " renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "render", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 令最近点的深度为0" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" depth ", _jsx(_components.span, { className: "token operator", children: "-=" }), " depth", _jsx(_components.span, { className: "token punctuation", children: "." }), _jsx(_components.span, { className: "token builtin", children: "min" }), _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 按近射线平均距离的2倍缩放" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" depth ", _jsx(_components.span, { className: "token operator", children: "/=" }), " ", _jsx(_components.span, { className: "token number", children: "2" }), _jsx(_components.span, { className: "token operator", children: "*" }), "depth", _jsx(_components.span, { className: "token punctuation", children: "[" }), "depth ", _jsx(_components.span, { className: "token operator", children: "<=" }), " ", _jsx(_components.span, { className: "token number", children: "1" }), _jsx(_components.span, { className: "token punctuation", children: "]" }), _jsx(_components.span, { className: "token punctuation", children: "." }), "mean", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 缩放到[0, 255]" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" pixels ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token number", children: "255" }), _jsx(_components.span, { className: "token operator", children: "*" }), "np", _jsx(_components.span, { className: "token punctuation", children: "." }), "clip", _jsx(_components.span, { className: "token punctuation", children: "(" }), "depth", _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "1" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 显示深度图" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" media", _jsx(_components.span, { className: "token punctuation", children: "." }), "show_image", _jsx(_components.span, { className: "token punctuation", children: "(" }), "pixels", _jsx(_components.span, { className: "token punctuation", children: "." }), "astype", _jsx(_components.span, { className: "token punctuation", children: "(" }), "np", _jsx(_components.span, { className: "token punctuation", children: "." }), "uint8", _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] })] }) }), "\n", _jsx(_components.img, { src: "https://obsidian2flowershow-inkem.flowershow.me/I-%E9%99%84%E4%BB%B6/Pasted%20image%2020250913113307.png", alt: "Pasted image 20250913113307", className: "internal", "data-fs-resolved-file-path": "/I-附件/Pasted image 20250913113307.png" }), "\n", _jsxs(_components.p, { children: ["在最后的深度缩放中，", _jsx(_components.code, { className: "language-auto", children: "[depth <= 1]" }), " 筛选出 1 米以内的近距离像素，并通过 ", _jsx(_components.code, { className: "language-auto", children: "mean()" }), " 计算近距离像素的平均距离作为缩放因子的依据。此时如果大多数像素的距离越近，缩放因子将越大，远距离像素抑制更明显，从而突出近距离细节。"] }), "\n", _jsx(_components.p, { children: _jsx(_components.strong, { children: "分割渲染" }) }), "\n", _jsx(_components.p, { children: "分割渲染根据场景中不同的几何体给像素划分不同的颜色区域并分离背景，常用于物体计数和识别、场景理解和分析等。" }), "\n", _jsx(_components.pre, { className: "language-python", children: _jsxs(_components.code, { className: "language-python code-highlight", children: [_jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token keyword", children: "with" }), " mujoco", _jsx(_components.span, { className: "token punctuation", children: "." }), "Renderer", _jsx(_components.span, { className: "token punctuation", children: "(" }), "model", _jsx(_components.span, { className: "token punctuation", children: ")" }), " ", _jsx(_components.span, { className: "token keyword", children: "as" }), " renderer", _jsx(_components.span, { className: "token punctuation", children: ":" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 禁用深度渲染" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "disable_depth_rendering", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 启用分割渲染" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "enable_segmentation_rendering", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 更新场景" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "update_scene", _jsx(_components.span, { className: "token punctuation", children: "(" }), "data", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 分割渲染模式下render返回双通道分割信息" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" seg ", _jsx(_components.span, { className: "token operator", children: "=" }), " renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "render", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 第一个通道seg[:, :, 0]包含对象ID" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 第二个通道seg[:, :, 1]包含对象类型（刚体、关节、站点等）" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" geom_ids ", _jsx(_components.span, { className: "token operator", children: "=" }), " seg", _jsx(_components.span, { className: "token punctuation", children: "[" }), _jsx(_components.span, { className: "token punctuation", children: ":" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token punctuation", children: ":" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0" }), _jsx(_components.span, { className: "token punctuation", children: "]" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 无穷大映射到-1" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" geom_ids ", _jsx(_components.span, { className: "token operator", children: "=" }), " geom_ids", _jsx(_components.span, { className: "token punctuation", children: "." }), "astype", _jsx(_components.span, { className: "token punctuation", children: "(" }), "np", _jsx(_components.span, { className: "token punctuation", children: "." }), "float64", _jsx(_components.span, { className: "token punctuation", children: ")" }), " ", _jsx(_components.span, { className: "token operator", children: "+" }), " ", _jsx(_components.span, { className: "token number", children: "1" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 缩放到[0, 1]" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" geom_ids ", _jsx(_components.span, { className: "token operator", children: "=" }), " geom_ids ", _jsx(_components.span, { className: "token operator", children: "/" }), " geom_ids", _jsx(_components.span, { className: "token punctuation", children: "." }), _jsx(_components.span, { className: "token builtin", children: "max" }), _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" pixels ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token number", children: "255" }), _jsx(_components.span, { className: "token operator", children: "*" }), "geom_ids\n"] }), _jsx(_components.span, { className: "code-line", children: " \n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 显示分割图" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" media", _jsx(_components.span, { className: "token punctuation", children: "." }), "show_image", _jsx(_components.span, { className: "token punctuation", children: "(" }), "pixels", _jsx(_components.span, { className: "token punctuation", children: "." }), "astype", _jsx(_components.span, { className: "token punctuation", children: "(" }), "np", _jsx(_components.span, { className: "token punctuation", children: "." }), "uint8", _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] })] }) }), "\n", _jsx(_components.img, { src: "https://obsidian2flowershow-inkem.flowershow.me/I-%E9%99%84%E4%BB%B6/Pasted%20image%2020250913145758.png", alt: "Pasted image 20250913145758", className: "internal", "data-fs-resolved-file-path": "/I-附件/Pasted image 20250913145758.png" }), "\n", _jsxs(_components.h1, { id: "相机矩阵", children: [_jsx(_components.a, { className: "heading-link", href: "#相机矩阵", children: _jsx(_components.svg, { xmlns: "http:www.w3.org/2000/svg", fill: "#ab2b65", viewBox: "0 0 20 20", className: "w-5 h-5", children: _jsx(_components.path, { fillRule: "evenodd", clipRule: "evenodd", d: "M9.493 2.853a.75.75 0 00-1.486-.205L7.545 6H4.198a.75.75 0 000 1.5h3.14l-.69 5H3.302a.75.75 0 000 1.5h3.14l-.435 3.148a.75.75 0 001.486.205L7.955 14h2.986l-.434 3.148a.75.75 0 001.486.205L12.456 14h3.346a.75.75 0 000-1.5h-3.14l.69-5h3.346a.75.75 0 000-1.5h-3.14l.435-3.147a.75.75 0 00-1.486-.205L12.045 6H9.059l.434-3.147zM8.852 7.5l-.69 5h2.986l.69-5H8.852z" }) }) }), "相机矩阵"] }), "\n", _jsxs(_components.p, { children: [_jsx(_components.strong, { children: "相机矩阵" }), "能够建立起三维世界坐标系中的点和相机二维像素坐标系中的点之间的映射关系，广泛应用于计算机图形学渲染、三维重建、深度估计等场景。"] }), "\n", _jsx(_components.p, { children: "相机矩阵的建立涉及四个坐标系：" }), "\n", _jsxs(_components.ul, { children: ["\n", _jsx(_components.li, { children: "世界坐标系（黄）：固定的参考坐标系，描述所有物体和相机在三维场景中的绝对位姿" }), "\n", _jsx(_components.li, { children: "相机坐标系（红）：以相机光心为原点、光轴为 z 轴的坐标系，描述所有物体相对于相机的位置" }), "\n", _jsx(_components.li, { children: "图像坐标系（绿）：以相机光心沿光轴正方向一个焦距处为原点，位于成像所在平面的坐标系" }), "\n", _jsx(_components.li, { children: "像素坐标系（黑）：原点位于图像左上角的平面坐标系" }), "\n"] }), "\n", _jsx(_components.img, { src: "https://obsidian2flowershow-inkem.flowershow.me/I-%E9%99%84%E4%BB%B6/Pasted%20image%2020250914164103.png", alt: "Pasted image 20250914164103", className: "internal", "data-fs-resolved-file-path": "/I-附件/Pasted image 20250914164103.png" }), "\n", _jsxs(_components.p, { children: ["对于世界坐标系中一点 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "P" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "X" }), _jsx(_components.mi, { children: "w" })] }), _jsx(_components.mo, { separator: "true", children: "," }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "Y" }), _jsx(_components.mi, { children: "w" })] }), _jsx(_components.mo, { separator: "true", children: "," }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "Z" }), _jsx(_components.mi, { children: "w" })] }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "P(X_w,Y_w,Z_w)" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.1389em" }, children: "P" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0785em" }, children: "X" }), _jsx(_components.span, { className: "msupsub", children: 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"0.1667em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.2222em" }, children: "Y" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.1514em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.2222em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0269em" }, children: "w" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mpunct", children: "," }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0715em" }, children: "Z" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.1514em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0715em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0269em" }, children: "w" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mclose", children: ")" })] }) })] }), "，相机矩阵将其映射为像素坐标系中的点 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "p" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "x" }), _jsx(_components.mo, { separator: "true", children: "," }), _jsx(_components.mi, { children: "y" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "p(x, y)" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "p" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathnormal", children: "x" }), _jsx(_components.span, { className: "mpunct", children: "," }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0359em" }, children: "y" }), _jsx(_components.span, { className: "mclose", children: ")" })] }) })] }), "。"] }), "\n", _jsx(_components.p, { children: _jsx(_components.strong, { children: "世界坐标系→相机坐标系" }) }), "\n", _jsxs(_components.p, { children: ["先考虑将 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "P" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "P" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6833em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.1389em" }, children: "P" })] }) })] }), " 相对于世界坐标系的表示转换为相对于相机坐标系的表示，此处引用【机器人学导论】简明学习笔记 2——空间描述和变换内容。"] }), "\n", _jsx(_components.p, { children: "对于姿态相同、位置不同的坐标系之间的变换，有：" }), "\n", _jsx(_components.img, { src: "https://obsidian2flowershow-inkem.flowershow.me/I-%E9%99%84%E4%BB%B6/Pasted%20image%2020250915112230.png", alt: "Pasted image 20250915112230", className: "internal", "data-fs-resolved-file-path": "/I-附件/Pasted image 20250915112230.png" }), "\n", _jsx(_components.p, { children: "对于位置相同、姿态不同的坐标系之间的变换，我们先通过姿态描述引入旋转矩阵：" }), "\n", _jsx(_components.img, { src: "https://obsidian2flowershow-inkem.flowershow.me/I-%E9%99%84%E4%BB%B6/Pasted%20image%2020250915112409.png", alt: "Pasted image 20250915112409", className: "internal", "data-fs-resolved-file-path": "/I-附件/Pasted image 20250915112409.png" }), "\n", _jsx(_components.p, { children: "旋转矩阵可以进一步用于在位置相同、姿态不同的坐标系之间转换坐标：" }), "\n", _jsx(_components.img, { src: "https://obsidian2flowershow-inkem.flowershow.me/I-%E9%99%84%E4%BB%B6/Pasted%20image%2020250915112631.png", alt: "Pasted image 20250915112631", className: "internal", "data-fs-resolved-file-path": "/I-附件/Pasted image 20250915112631.png" }), "\n", _jsx(_components.p, { children: "将平移变换与旋转变换组合，我们得到用于描述任意坐标系下坐标的一般变换方法：" }), "\n", _jsx(_components.img, { src: "https://obsidian2flowershow-inkem.flowershow.me/I-%E9%99%84%E4%BB%B6/Pasted%20image%2020250916114001.png", alt: "Pasted image 20250916114001", className: "internal", "data-fs-resolved-file-path": "/I-附件/Pasted image 20250916114001.png" }), "\n", _jsxs(_components.p, { children: ["假设上图中 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mo, { stretchy: "false", children: "{" }), _jsx(_components.mi, { children: "A" }), _jsx(_components.mo, { stretchy: "false", children: "}" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\{A\\}" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "{" }), _jsx(_components.span, { className: "mord mathnormal", children: "A" }), _jsx(_components.span, { className: "mclose", children: "}" })] }) })] }), " 为世界坐标系，", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mo, { stretchy: "false", children: "{" }), _jsx(_components.mi, { children: "B" }), _jsx(_components.mo, { stretchy: "false", children: "}" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\{B\\}" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "{" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0502em" }, children: "B" }), _jsx(_components.span, { className: "mclose", children: "}" })] }) })] }), " 为相机坐标系，则已知 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "P" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "P" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6833em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.1389em" }, children: "P" })] }) })] }), " 在世界坐标系的位置向量 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msup, { children: [_jsx(_components.mrow, {}), _jsx(_components.mi, { children: "A" })] }), _jsx(_components.mi, { children: "P" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "^AP" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8413em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, {}), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8413em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "A" }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.1389em" }, children: "P" })] }) })] }), "，相机坐标系在世界坐标系的位置向量 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: 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_jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msubsup, { children: [_jsx(_components.mrow, {}), _jsx(_components.mi, { children: "A" }), _jsx(_components.mi, { children: "B" })] }), _jsx(_components.mi, { children: "R" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "^B_AR" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.1167em", verticalAlign: "-0.2753em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, {}), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.8413em" }, children: [_jsxs(_components.span, { style: { top: "-2.4247em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "A" }) })] }), _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0502em" }, children: "B" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2753em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0077em" }, children: "R" })] }) })] }), "，我们有 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "P" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "P" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6833em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.1389em" }, children: "P" })] }) })] }), " 在相机坐标系的位置向量"] }), "\n", _jsx(_components.span, { className: "katex-display", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", display: "block", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msup, { children: [_jsx(_components.mrow, {}), _jsx(_components.mi, { children: "B" })] }), _jsx(_components.mi, { children: "P" }), _jsxs(_components.msubsup, { children: [_jsx(_components.mo, { children: "=" }), _jsx(_components.mi, { children: "A" }), _jsx(_components.mi, { children: "B" })] }), _jsx(_components.mi, { children: "R" }), _jsxs(_components.msup, { children: [_jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "A" })] }), _jsx(_components.mi, { children: "P" }), _jsxs(_components.msup, { children: 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children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "A" }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.1389em" }, children: "P" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3283em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.1389em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0502em" }, children: "B" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0278em" }, children: "O" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0077em" }, children: "R" }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "G" })] }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mclose", children: ")" })] })] })] }) }), "\n", _jsx(_components.p, { children: "用矩阵将相机坐标系的位姿整合起来可以表示为" }), "\n", 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_jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsxs(_components.span, { className: "minner", children: [_jsx(_components.span, { className: "mopen delimcenter", style: { top: "0em" }, children: _jsx(_components.span, { className: "delimsizing size3", children: "[" }) }), _jsx(_components.span, { className: "mord", children: _jsxs(_components.span, { className: "mtable", children: [_jsx(_components.span, { className: "col-align-c", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "1.45em" }, children: [_jsxs(_components.span, { style: { top: "-3.61em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord", children: _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0785em" }, children: "I" }) })] }), _jsxs(_components.span, { style: { top: "-2.41em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord", children: _jsx(_components.span, { className: "mord", children: "0" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.95em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "arraycolsep", style: { width: "0.5em" } }), _jsx(_components.span, { className: "arraycolsep", style: { width: "0.5em" } }), _jsx(_components.span, { className: "col-align-c", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "1.45em" }, children: [_jsxs(_components.span, { style: { top: "-3.61em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord", children: "−" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0715em" }, children: "C" })] })] }), _jsxs(_components.span, { style: { top: "-2.41em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord", children: _jsx(_components.span, { className: "mord", children: "1" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.95em" }, children: _jsx(_components.span, {}) }) })] }) })] }) }), _jsx(_components.span, { className: "mclose delimcenter", style: { top: "0em" }, children: _jsx(_components.span, { className: "delimsizing size3", children: "]" }) })] })] })] })] }) }), "\n", _jsxs(_components.p, { children: ["其中 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mn, { children: "3" }), _jsx(_components.mo, { children: "×" }), _jsx(_components.mn, { children: "3" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "3\\times3" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7278em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord", children: "3" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6444em" } }), _jsx(_components.span, { className: "mord", children: "3" })] })] })] }), " 矩阵 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "R" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "R" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6833em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0077em" }, children: "R" })] }) })] }), " 描述相机的姿态，", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mn, { children: "3" }), _jsx(_components.mo, { children: "×" }), _jsx(_components.mn, { children: "1" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "3\\times1" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7278em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord", children: "3" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6444em" } }), _jsx(_components.span, { className: "mord", children: "1" })] })] })] }), " 向量 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "t" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "R" }), _jsx(_components.mi, { children: "C" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "t=-RC" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6151em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "t" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7667em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord", children: "−" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0077em" }, children: "R" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0715em" }, children: "C" })] })] })] }), " 描述相机相对于世界坐标系的平移，", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "C" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "C" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6833em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0715em" }, children: "C" })] }) })] }), " 即相机的位置（图中的 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msup, { children: [_jsx(_components.mrow, {}), _jsx(_components.mi, { children: "A" })] }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "P" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "B" }), _jsx(_components.mi, { children: "O" }), _jsx(_components.mi, { children: "R" }), _jsx(_components.mi, { children: "G" })] })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "^AP_{BORG}" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.9913em", verticalAlign: "-0.15em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, {}), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8413em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "A" }) })] }) }) }) }) })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.1389em" }, children: "P" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3283em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.1389em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0502em" }, children: "B" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0278em" }, children: "O" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0077em" }, children: "R" }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "G" })] }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] })] }) })] }), "）。"] }), "\n", _jsx(_components.p, { children: "在实际代码中，我们分别提取相机的姿态信息和位置信息为矩阵再相乘（即上式右端的形式）得到齐次变换矩阵。" }), "\n", _jsx(_components.p, { children: _jsx(_components.strong, { children: "相机坐标系→图像坐标系" }) }), "\n", _jsx(_components.img, { src: "https://obsidian2flowershow-inkem.flowershow.me/I-%E9%99%84%E4%BB%B6/Pasted%20image%2020250916160722.png", alt: "Pasted image 20250916160722", className: "internal", "data-fs-resolved-file-path": "/I-附件/Pasted image 20250916160722.png" }), "\n", _jsxs(_components.p, { children: ["对于 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "P" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "P" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6833em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.1389em" }, children: "P" })] }) })] }), " 在相机坐标系中的位置 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mo, { stretchy: "false", children: "(" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "X" }), _jsx(_components.mi, { children: "C" })] }), _jsx(_components.mo, { separator: "true", children: "," }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "Y" }), _jsx(_components.mi, { children: "C" })] }), _jsx(_components.mo, { separator: "true", children: "," }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "Z" }), _jsx(_components.mi, { children: "C" })] }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "(X_C, Y_C, Z_C)" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0785em" }, children: "X" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { 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_jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3283em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.2222em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0715em" }, children: "C" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mpunct", children: "," }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0715em" }, children: "Z" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3283em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0715em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0715em" }, children: "C" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mclose", children: ")" })] }) })] }), " 及其在图像坐标系上的投影点 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "p" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "x" }), _jsx(_components.mo, { separator: "true", children: "," }), _jsx(_components.mi, { children: "y" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "p (x, y)" })] }) }) }), _jsx(_components.span, { className: 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children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "f" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "f" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8889em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.1076em" }, children: "f" })] }) })] }), "，根据相似三角形原理有"] }), "\n", _jsx(_components.span, { className: "katex-display", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", display: "block", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.mfrac, { children: [_jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "Z" }), _jsx(_components.mi, { children: "C" })] }), _jsx(_components.mi, { children: "f" })] }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.mfrac, { children: [_jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "X" }), _jsx(_components.mi, { children: "c" })] }), _jsx(_components.mi, { children: "x" })] }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.mfrac, { children: [_jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "Y" }), _jsx(_components.mi, { children: "C" })] }), _jsx(_components.mi, { children: "y" })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\frac{Z_C}f=\\frac{X_c}x=\\frac{Y_C}y" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "2.2408em", verticalAlign: 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"-3.677em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord", children: _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0715em" }, children: "Z" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3283em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0715em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0715em" }, children: "C" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8804em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "2.0463em", verticalAlign: "-0.686em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "1.3603em" }, children: [_jsxs(_components.span, { style: { top: "-2.314em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord", children: _jsx(_components.span, { className: "mord mathnormal", children: "x" }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.677em" }, children: [_jsx(_components.span, { className: 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"vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.686em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "2.2408em", verticalAlign: "-0.8804em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "1.3603em" }, children: [_jsxs(_components.span, { style: { top: "-2.314em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord", children: _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0359em" }, children: "y" }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.677em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord", 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children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "arraycolsep", style: { width: "0.5em" } }), _jsx(_components.span, { className: "arraycolsep", style: { width: "0.5em" } }), _jsx(_components.span, { className: "col-align-c", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "2.05em" }, children: [_jsxs(_components.span, { style: { top: "-4.21em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord", children: _jsx(_components.span, { className: "mord", children: "0" }) })] }), _jsxs(_components.span, { style: { top: "-3.01em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord", children: _jsx(_components.span, { className: "mord", children: "0" }) })] }), _jsxs(_components.span, { style: { top: "-1.81em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord", children: _jsx(_components.span, { className: "mord", children: "1" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "1.55em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "arraycolsep", style: { width: "0.5em" } }), _jsx(_components.span, { className: "arraycolsep", style: { width: "0.5em" } }), _jsx(_components.span, { className: "col-align-c", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "2.05em" }, children: [_jsxs(_components.span, { style: { 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})] }) }), _jsx(_components.span, { className: "mclose", children: _jsx(_components.span, { className: "delimsizing mult", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "2.05em" }, children: _jsxs(_components.span, { style: { top: "-4.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "5.6em" } }), _jsx(_components.span, { style: { width: "0.667em", height: "3.6em" }, children: _jsx(_components.svg, { xmlns: "http://www.w3.org/2000/svg", width: "0.667em", height: "3.6em", viewBox: "0 0 667 3600", children: _jsx(_components.path, { d: "M347 1759 V0 H0 V84 H263 V1759 v0 v1759 H0 v84 H347z\nM347 1759 V0 H263 V1759 v0 v1759 h84z" }) }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "1.55em" }, children: _jsx(_components.span, {}) }) })] }) }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsxs(_components.span, { className: "minner", children: [_jsx(_components.span, { className: "mopen", children: _jsx(_components.span, { className: "delimsizing mult", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "2.05em" }, children: _jsxs(_components.span, { style: { top: "-4.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "5.6em" } }), _jsx(_components.span, { style: { width: "0.667em", height: "3.6em" }, children: _jsx(_components.svg, { xmlns: "http://www.w3.org/2000/svg", width: "0.667em", height: "3.6em", viewBox: "0 0 667 3600", children: _jsx(_components.path, { d: "M403 1759 V84 H666 V0 H319 V1759 v0 v1759 v84 h347 v-84\nH403z M403 1759 V0 H319 V1759 v0 v1759 v84 h84z" }) }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "1.55em" }, children: _jsx(_components.span, {}) }) })] }) }) }), _jsx(_components.span, { className: "mord", children: _jsx(_components.span, { className: "mtable", children: _jsx(_components.span, { className: "col-align-c", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "2.05em" }, children: [_jsxs(_components.span, { style: { top: "-4.21em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord", children: _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: 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_jsxs(_components.span, { style: { top: "-3.01em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord", children: _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.2222em" }, children: "Y" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3283em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.2222em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0715em" }, children: "C" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }) })] }), _jsxs(_components.span, { style: { top: "-1.81em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord", children: _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0715em" }, children: "Z" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3283em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0715em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0715em" }, children: "C" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "1.55em" }, children: _jsx(_components.span, {}) }) })] }) }) }) }), _jsx(_components.span, { className: "mclose", children: _jsx(_components.span, { className: "delimsizing mult", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "2.05em" }, children: _jsxs(_components.span, { style: { top: "-4.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "5.6em" } }), _jsx(_components.span, { style: { width: "0.667em", height: "3.6em" }, children: _jsx(_components.svg, { xmlns: "http://www.w3.org/2000/svg", width: "0.667em", height: "3.6em", viewBox: "0 0 667 3600", children: _jsx(_components.path, { d: "M347 1759 V0 H0 V84 H263 V1759 v0 v1759 H0 v84 H347z\nM347 1759 V0 H263 V1759 v0 v1759 h84z" }) }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "1.55em" }, children: _jsx(_components.span, {}) }) })] }) }) })] })] })] })] }) }), "\n", _jsx(_components.p, { children: _jsx(_components.strong, { children: "图像坐标系→像素坐标系" }) }), "\n", _jsx(_components.img, { src: "https://obsidian2flowershow-inkem.flowershow.me/I-%E9%99%84%E4%BB%B6/Pasted%20image%2020250916162524.png", alt: "Pasted image 20250916162524", className: "internal", "data-fs-resolved-file-path": "/I-附件/Pasted image 20250916162524.png" }), "\n", _jsxs(_components.p, { children: ["图像坐标系的原点位于图像中心，单位通常为毫米，而像素坐标系的原点位于图像左上角，单位为像素。对于图像坐标系原点的平移量 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mo, { stretchy: "false", children: "(" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "u" }), _jsx(_components.mi, { children: "O" })] }), _jsx(_components.mo, { separator: "true", children: "," }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "v" }), _jsx(_components.mi, { children: "O" })] }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "(u_O, v_O)" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "u" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3283em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0278em" }, children: "O" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mpunct", children: "," }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0359em" }, children: "v" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3283em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0359em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0278em" }, children: "O" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mclose", children: ")" })] }) })] }), " 和每个像素的物理大小 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "d" }), _jsx(_components.mi, { children: "x" })] }), _jsx(_components.mo, { children: "×" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "d" }), _jsx(_components.mi, { children: "y" })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "d_x\\times d_y" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8444em", verticalAlign: "-0.15em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "d" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.1514em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "x" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.9805em", verticalAlign: "-0.2861em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "d" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.1514em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0359em" }, children: "y" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2861em" }, children: _jsx(_components.span, {}) }) })] }) })] })] })] })] }), "，", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "p" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "p" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.625em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "p" })] }) })] }), " 在像素坐标系下的坐标计算如下"] }), "\n", _jsx(_components.span, { className: "katex-display", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", display: "block", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mo, { fence: "true", children: "{" }), _jsxs(_components.mtable, { rowspacing: "0.16em", columnalign: "center", columnspacing: "1em", children: [_jsx(_components.mtr, { children: _jsx(_components.mtd, { children: _jsx(_components.mstyle, { scriptlevel: "0", displaystyle: "false", children: _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "u" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mi, { children: "x" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "d" }), _jsx(_components.mi, { children: "x" 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className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: ":" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token triple-quoted-string string", children: "\"\"\"计算3x4相机矩阵\n" })] }), _jsx(_components.span, { className: "code-line", children: _jsx(_components.span, { className: "token triple-quoted-string string", children: " \n" }) }), _jsx(_components.span, { className: "code-line", children: _jsx(_components.span, { className: "token triple-quoted-string string", children: " 相机矩阵用于将世界坐标投影到像素坐标\n" }) }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token triple-quoted-string string", children: " \"\"\"" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 更新场景以确保相机参数正确" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "update_scene", _jsx(_components.span, { className: "token punctuation", children: "(" }), "data", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: " \n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 获取立体相机的平均位置和方向" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" pos ", _jsx(_components.span, { className: "token operator", children: "=" }), " np", _jsx(_components.span, { className: "token punctuation", children: "." }), "mean", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: "[" }), "camera", _jsx(_components.span, { className: "token punctuation", children: "." }), "pos ", _jsx(_components.span, { className: "token keyword", children: "for" }), " camera ", _jsx(_components.span, { className: "token keyword", children: "in" }), " renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "scene", _jsx(_components.span, { className: "token punctuation", children: "." }), "camera", _jsx(_components.span, { className: "token punctuation", children: "]" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " axis", _jsx(_components.span, { className: "token operator", children: "=" }), _jsx(_components.span, { className: "token number", children: "0" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# MuJoCo中z轴负方向为相机朝向" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" z ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token operator", children: "-" }), "np", _jsx(_components.span, { className: "token punctuation", children: "." }), "mean", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: "[" }), "camera", _jsx(_components.span, { className: "token punctuation", children: "." }), "forward ", _jsx(_components.span, { className: "token keyword", children: "for" }), " camera ", _jsx(_components.span, { className: "token keyword", children: "in" }), " renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "scene", _jsx(_components.span, { className: "token punctuation", children: "." }), "camera", _jsx(_components.span, { className: "token punctuation", children: "]" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " axis", _jsx(_components.span, { className: "token operator", children: "=" }), _jsx(_components.span, { className: "token number", children: "0" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" y ", _jsx(_components.span, { className: "token operator", children: "=" }), " np", _jsx(_components.span, { className: "token punctuation", children: "." }), "mean", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: "[" }), "camera", _jsx(_components.span, { className: "token punctuation", children: "." }), "up ", _jsx(_components.span, { className: "token keyword", children: "for" }), " camera ", _jsx(_components.span, { className: "token keyword", children: "in" }), " renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "scene", _jsx(_components.span, { className: "token punctuation", children: "." }), "camera", _jsx(_components.span, { className: "token punctuation", children: "]" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " axis", _jsx(_components.span, { className: "token operator", children: "=" }), _jsx(_components.span, { className: "token number", children: "0" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" rot ", _jsx(_components.span, { className: "token operator", children: "=" }), " np", _jsx(_components.span, { className: "token punctuation", children: "." }), "vstack", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: "(" }), "np", _jsx(_components.span, { className: "token punctuation", children: "." }), "cross", _jsx(_components.span, { className: "token punctuation", children: "(" }), "y", _jsx(_components.span, { className: "token punctuation", children: "," }), " z", _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " y", _jsx(_components.span, { className: "token punctuation", children: "," }), " z", _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" fov ", _jsx(_components.span, { className: "token operator", children: "=" }), " model", _jsx(_components.span, { className: "token punctuation", children: "." }), "vis", _jsx(_components.span, { className: "token punctuation", children: "." }), "global_", _jsx(_components.span, { className: "token punctuation", children: "." }), "fovy\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 平移矩阵 (4x4)" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" translation ", _jsx(_components.span, { className: "token operator", children: "=" }), " np", _jsx(_components.span, { className: "token punctuation", children: "." }), "eye", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token number", children: "4" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), " ", _jsx(_components.span, { className: "token comment", children: "# 单位矩阵" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" translation", _jsx(_components.span, { className: "token punctuation", children: "[" }), _jsx(_components.span, { className: "token number", children: "0" }), _jsx(_components.span, { className: "token punctuation", children: ":" }), _jsx(_components.span, { className: "token number", children: "3" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "3" }), _jsx(_components.span, { className: "token punctuation", children: "]" }), " ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token operator", children: "-" }), "pos\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 旋转矩阵 (4x4)" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" rotation ", _jsx(_components.span, { className: "token operator", children: "=" }), " np", _jsx(_components.span, { className: "token punctuation", children: "." }), "eye", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token number", children: "4" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" rotation", _jsx(_components.span, { className: "token punctuation", children: "[" }), _jsx(_components.span, { className: "token number", children: "0" }), _jsx(_components.span, { className: "token punctuation", children: ":" }), _jsx(_components.span, { className: "token number", children: "3" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0" }), _jsx(_components.span, { className: "token punctuation", children: ":" }), _jsx(_components.span, { className: "token number", children: "3" }), _jsx(_components.span, { className: "token punctuation", children: "]" }), " ", _jsx(_components.span, { className: "token operator", children: "=" }), " rot\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 焦距变换矩阵 (3x4)" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" focal_scaling ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token number", children: "1." }), _jsx(_components.span, { className: "token operator", children: "/" }), "np", _jsx(_components.span, { className: "token punctuation", children: "." }), "tan", _jsx(_components.span, { className: "token punctuation", children: "(" }), "np", _jsx(_components.span, { className: "token punctuation", children: "." }), "deg2rad", _jsx(_components.span, { className: "token punctuation", children: "(" }), "fov", _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token operator", children: "/" }), _jsx(_components.span, { className: "token number", children: "2" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), " ", _jsx(_components.span, { className: "token operator", children: "*" }), " renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "height ", _jsx(_components.span, { className: "token operator", children: "/" }), " ", _jsx(_components.span, { className: "token number", children: "2.0" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" focal ", _jsx(_components.span, { className: "token operator", children: "=" }), " np", _jsx(_components.span, { className: "token punctuation", children: "." }), "diag", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: "[" }), _jsx(_components.span, { className: "token operator", children: "-" }), "focal_scaling", _jsx(_components.span, { className: "token punctuation", children: "," }), " focal_scaling", _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "1.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0" }), _jsx(_components.span, { className: "token punctuation", children: "]" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: "[" }), _jsx(_components.span, { className: "token number", children: "0" }), _jsx(_components.span, { className: "token punctuation", children: ":" }), _jsx(_components.span, { className: "token number", children: "3" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token punctuation", children: ":" }), _jsx(_components.span, { className: "token punctuation", children: "]" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 图像矩阵 (3x3)" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" image ", _jsx(_components.span, { className: "token operator", children: "=" }), " np", _jsx(_components.span, { className: "token punctuation", children: "." }), "eye", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token number", children: "3" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" image", _jsx(_components.span, { className: "token punctuation", children: "[" }), _jsx(_components.span, { className: "token number", children: "0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "2" }), _jsx(_components.span, { className: "token punctuation", children: "]" }), " ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token punctuation", children: "(" }), "renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "width ", _jsx(_components.span, { className: "token operator", children: "-" }), " ", _jsx(_components.span, { className: "token number", children: "1" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), " ", _jsx(_components.span, { className: "token operator", children: "/" }), " ", _jsx(_components.span, { className: "token number", children: "2.0" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" image", _jsx(_components.span, { className: "token punctuation", children: "[" }), _jsx(_components.span, { className: "token number", children: "1" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "2" }), _jsx(_components.span, { className: "token punctuation", children: "]" }), " ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token punctuation", children: "(" }), "renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "height ", _jsx(_components.span, { className: "token operator", children: "-" }), " ", _jsx(_components.span, { className: "token number", children: "1" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), " ", _jsx(_components.span, { className: "token operator", children: "/" }), " ", _jsx(_components.span, { className: "token number", children: "2.0" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: " \n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 组合所有变换" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token keyword", children: "return" }), " image @ focal @ rotation @ translation\n"] })] }) }), "\n", _jsxs(_components.p, { children: ["焦距变换矩阵中，焦距 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "f" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "f" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8889em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.1076em" }, children: "f" })] }) })] }), " 由垂直视场角 ", _jsx(_components.code, { className: "language-auto", children: "fov" }), "（度）和图像高度 ", _jsx(_components.code, { className: "language-auto", children: "height" }), "（像素）计算而来"] }), "\n", _jsx(_components.span, { className: "katex-display", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", display: "block", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "f" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.mfrac, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { mathvariant: "normal", children: "h" }), _jsx(_components.mi, { mathvariant: "normal", children: "e" }), _jsx(_components.mi, { mathvariant: "normal", children: "i" }), _jsx(_components.mi, { mathvariant: "normal", children: "g" }), _jsx(_components.mi, { mathvariant: "normal", children: "h" }), _jsx(_components.mi, { mathvariant: "normal", children: "t" })] }), _jsx(_components.mi, { mathvariant: "normal", children: "/" }), _jsx(_components.mn, { children: "2" })] }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "tan" }), _jsx(_components.mo, { children: "⁡" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { mathvariant: "normal", children: "f" }), _jsx(_components.mi, { mathvariant: "normal", children: "o" }), _jsx(_components.mi, { mathvariant: "normal", children: "v" })] }), _jsx(_components.mi, { mathvariant: "normal", children: "/" }), _jsx(_components.mn, { children: "2" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "f=\\frac{\\mathrm{height}/2}{\\tan(\\mathrm{fov}/2)}" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8889em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.1076em" }, children: "f" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "2.363em", verticalAlign: "-0.936em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "1.427em" }, children: [_jsxs(_components.span, { style: { top: "-2.314em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mop", children: "tan" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord", children: _jsx(_components.span, { className: "mord mathrm", style: { marginRight: "0.0139em" }, children: "fov" }) }), _jsx(_components.span, { className: "mord", children: "/2" }), _jsx(_components.span, { className: "mclose", children: ")" })] })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.677em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord", children: _jsx(_components.span, { className: "mord mathrm", children: "height" }) }), _jsx(_components.span, { className: "mord", children: "/2" })] })] })] }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.936em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] })] })] })] }) }), "\n", _jsxs(_components.p, { children: ["由于 MuJoCo 渲染器以 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "z" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "z" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.044em" }, children: "z" })] }) })] }), " 轴负方向为相机朝向，因此相机坐标系的 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "x" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "x" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "x" })] }) })] }), " 轴与图像坐标系的 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "x" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "x" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "x" })] }) })] }), " 轴方向相反，焦距变换矩阵计算 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "x" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "x" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "x" })] }) })] }), " 坐标的焦距需添加负号。"] }), "\n", _jsxs(_components.p, { children: ["图像矩阵中，像素大小为 ", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mn, { children: "1" }), _jsx(_components.mi, { children: "m" }), _jsx(_components.mi, { children: "m" }), _jsx(_components.mo, { children: "×" }), _jsx(_components.mn, { children: "1" }), _jsx(_components.mi, { children: "m" }), _jsx(_components.mi, { children: "m" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "1mm\\times1mm" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7278em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord", children: "1" }), _jsx(_components.span, { className: "mord mathnormal", children: "mm" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6444em" } }), _jsx(_components.span, { className: "mord", children: "1" }), _jsx(_components.span, { className: "mord mathnormal", children: "mm" })] })] })] }), "，又计算机图形学中像素坐标索引从 0 开始，因此高宽需减一。"] }), "\n", _jsx(_components.p, { children: "通过相机矩阵，我们可以对三维空间的信息在相机获得的二维图像上进行标记：" }), "\n", _jsx(_components.pre, { className: "language-python", children: _jsxs(_components.code, { className: "language-python code-highlight", children: [_jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token keyword", children: "with" }), " mujoco", _jsx(_components.span, { className: "token punctuation", children: "." }), "Renderer", _jsx(_components.span, { className: "token punctuation", children: "(" }), "model", _jsx(_components.span, { className: "token punctuation", children: ")" }), " ", _jsx(_components.span, { className: "token keyword", children: "as" }), " renderer", _jsx(_components.span, { className: "token punctuation", children: ":" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "disable_segmentation_rendering", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 更新场景" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "update_scene", _jsx(_components.span, { className: "token punctuation", children: "(" }), "data", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 获取红色盒子的世界坐标" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" box_pos ", _jsx(_components.span, { className: "token operator", children: "=" }), " data", _jsx(_components.span, { className: "token punctuation", children: "." }), "geom_xpos", _jsx(_components.span, { className: "token punctuation", children: "[" }), "model", _jsx(_components.span, { className: "token punctuation", children: "." }), "geom", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token string", children: "'red_box'" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: "." }), _jsx(_components.span, { className: "token builtin", children: "id" }), _jsx(_components.span, { className: "token punctuation", children: "]" }), " ", _jsx(_components.span, { className: "token comment", children: "# 位置" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" box_mat ", _jsx(_components.span, { className: "token operator", children: "=" }), " data", _jsx(_components.span, { className: "token punctuation", children: "." }), "geom_xmat", _jsx(_components.span, { className: "token punctuation", children: "[" }), "model", _jsx(_components.span, { className: "token punctuation", children: "." }), "geom", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token string", children: "'red_box'" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: "." }), _jsx(_components.span, { className: "token builtin", children: "id" }), _jsx(_components.span, { className: "token punctuation", children: "]" }), _jsx(_components.span, { className: "token punctuation", children: "." }), "reshape", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token number", children: "3" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "3" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), " ", _jsx(_components.span, { className: "token comment", children: "# 旋转矩阵" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" box_size ", _jsx(_components.span, { className: "token operator", children: "=" }), " model", _jsx(_components.span, { className: "token punctuation", children: "." }), "geom_size", _jsx(_components.span, { className: "token punctuation", children: "[" }), "model", _jsx(_components.span, { className: "token punctuation", children: "." }), "geom", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token string", children: "'red_box'" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: "." }), _jsx(_components.span, { className: "token builtin", children: "id" }), _jsx(_components.span, { className: "token punctuation", children: "]" }), " ", _jsx(_components.span, { className: "token comment", children: "# 尺寸" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: " \n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 计算盒子8个角点的局部坐标" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" offsets ", _jsx(_components.span, { className: "token operator", children: "=" }), " np", _jsx(_components.span, { className: "token punctuation", children: "." }), "array", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: "[" }), _jsx(_components.span, { className: "token operator", children: "-" }), _jsx(_components.span, { className: "token number", children: "1" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "1" }), _jsx(_components.span, { className: "token punctuation", children: "]" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), " ", _jsx(_components.span, { className: "token operator", children: "*" }), " box_size", _jsx(_components.span, { className: "token punctuation", children: "[" }), _jsx(_components.span, { className: "token punctuation", children: ":" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token boolean", children: "None" }), _jsx(_components.span, { className: "token punctuation", children: "]" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" xyz_local ", _jsx(_components.span, { className: "token operator", children: "=" }), " np", _jsx(_components.span, { className: "token punctuation", children: "." }), "stack", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token builtin", children: "list" }), _jsx(_components.span, { className: "token punctuation", children: "(" }), "itertools", _jsx(_components.span, { className: "token punctuation", children: "." }), "product", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token operator", children: "*" }), "offsets", _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: "." }), "T\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 转换到世界坐标" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" xyz_global ", _jsx(_components.span, { className: "token operator", children: "=" }), " box_pos", _jsx(_components.span, { className: "token punctuation", children: "[" }), _jsx(_components.span, { className: "token punctuation", children: ":" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token boolean", children: "None" }), _jsx(_components.span, { className: "token punctuation", children: "]" }), " ", _jsx(_components.span, { className: "token operator", children: "+" }), " box_mat @ xyz_local\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 相机矩阵需要齐次坐标 [x, y, z, 1]" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" corners_homogeneous ", _jsx(_components.span, { className: "token operator", children: "=" }), " np", _jsx(_components.span, { className: "token punctuation", children: "." }), "ones", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token number", children: "4" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " xyz_global", _jsx(_components.span, { className: "token punctuation", children: "." }), "shape", _jsx(_components.span, { className: "token punctuation", children: "[" }), _jsx(_components.span, { className: "token number", children: "1" }), _jsx(_components.span, { className: "token punctuation", children: "]" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " dtype", _jsx(_components.span, { className: "token operator", children: "=" }), _jsx(_components.span, { className: "token builtin", children: "float" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" corners_homogeneous", _jsx(_components.span, { className: "token punctuation", children: "[" }), _jsx(_components.span, { className: "token punctuation", children: ":" }), _jsx(_components.span, { className: "token number", children: "3" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token punctuation", children: ":" }), _jsx(_components.span, { className: "token punctuation", children: "]" }), " ", _jsx(_components.span, { className: "token operator", children: "=" }), " xyz_global\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 获取相机矩阵" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" m ", _jsx(_components.span, { className: "token operator", children: "=" }), " compute_camera_matrix", _jsx(_components.span, { className: "token punctuation", children: "(" }), "renderer", _jsx(_components.span, { className: "token punctuation", children: "," }), " data", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 将世界坐标投影到像素空间" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" xs", _jsx(_components.span, { className: "token punctuation", children: "," }), " ys", _jsx(_components.span, { className: "token punctuation", children: "," }), " s ", _jsx(_components.span, { className: "token operator", children: "=" }), " m @ corners_homogeneous\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# x和y在像素坐标系中" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" x ", _jsx(_components.span, { className: "token operator", children: "=" }), " xs ", _jsx(_components.span, { className: "token operator", children: "/" }), " s\n"] }), _jsxs(_components.span, { className: "code-line", children: [" y ", _jsx(_components.span, { className: "token operator", children: "=" }), " ys ", _jsx(_components.span, { className: "token operator", children: "/" }), " s\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# 渲染相机视图并叠加投影的角点坐标" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" pixels ", _jsx(_components.span, { className: "token operator", children: "=" }), " renderer", _jsx(_components.span, { className: "token punctuation", children: "." }), "render", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" fig", _jsx(_components.span, { className: "token punctuation", children: "," }), " ax ", _jsx(_components.span, { className: "token operator", children: "=" }), " plt", _jsx(_components.span, { className: "token punctuation", children: "." }), "subplots", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token number", children: "1" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "1" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ax", _jsx(_components.span, { className: "token punctuation", children: "." }), "imshow", _jsx(_components.span, { className: "token punctuation", children: "(" }), "pixels", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ax", _jsx(_components.span, { className: "token punctuation", children: "." }), "plot", _jsx(_components.span, { className: "token punctuation", children: "(" }), "x", _jsx(_components.span, { className: "token punctuation", children: "," }), " y", _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token string", children: "'+'" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " c", _jsx(_components.span, { className: "token operator", children: "=" }), _jsx(_components.span, { className: "token string", children: "'w'" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), " ", _jsx(_components.span, { className: "token comment", children: "# 白色十字标记角点" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ax", _jsx(_components.span, { className: "token punctuation", children: "." }), "set_axis_off", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] })] }) }), "\n", _jsx(_components.img, { src: "https://obsidian2flowershow-inkem.flowershow.me/I-%E9%99%84%E4%BB%B6/Pasted%20image%2020250917155928.png", alt: "Pasted image 20250917155928", className: "internal", "data-fs-resolved-file-path": "/I-附件/Pasted image 20250917155928.png" })] }); } function MDXContent(props = {}) { const {wrapper: MDXLayout} = { ..._provideComponents(), ...props.components }; return MDXLayout ? _jsx(MDXLayout, { ...props, children: _jsx(_createMdxContent, { ...props }) }) : _createMdxContent(props); } return { default: MDXContent };

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