"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", blockquote: "blockquote", code: "code", h2: "h2", h3: "h3", h4: "h4", img: "img", li: "li", math: "math", mfrac: "mfrac", mi: "mi", mn: "mn", mo: "mo", mrow: "mrow", mstyle: "mstyle", msub: "msub", mtable: "mtable", mtd: "mtd", mtr: "mtr", p: "p", path: "path", pre: "pre", semantics: "semantics", span: "span", svg: "svg", ul: "ul", ..._provideComponents(), ...props.components }; return _jsxs(_Fragment, { children: [_jsxs(_components.blockquote, { children: ["\n", _jsx(_components.p, { children: "春节番外篇！" }), "\n"] }), "\n", _jsxs(_components.h2, { id: "作业-0", children: [_jsx(_components.a, { className: "heading-link", href: "#作业-0", 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" }) }) }), "作业 0"] }), "\n", _jsxs(_components.blockquote, { children: ["\n", _jsx(_components.p, { children: "更新于 2026 年 1 月。" }), "\n"] }), "\n", _jsxs(_components.p, { children: ["在 ", _jsx(_components.code, { className: "language-auto", children: "M1 Mac" }), " 上安装些许困难，最终参考了稀土掘金的教程解决了，抛弃了虚拟机的方案，直接在本机部署环境一劳永逸，还算快的。"] }), "\n", _jsxs(_components.blockquote, { children: ["\n", _jsxs(_components.p, { children: [_jsx(_components.a, { href: "https://juejin.cn/post/7144284278023684133#heading-10", target: "_blank", rel: "noopener noreferrer", children: "https://juejin.cn/post/7144284278023684133#heading-10" }), "。"] }), "\n"] }), "\n", _jsx(_components.p, { children: "按照该步骤：" }), "\n", _jsxs(_components.ul, { children: ["\n", _jsxs(_components.li, { children: ["安装 ", _jsx(_components.code, { className: "language-auto", children: "homebrew" }), "、", _jsx(_components.code, { className: "language-auto", children: "gcc" }), "、", _jsx(_components.code, { className: "language-auto", children: "cmake" }), " 即可。这里我之前都装过了。"] }), "\n", _jsxs(_components.li, { children: ["用 ", _jsx(_components.code, { className: "language-auto", children: "homebrew" }), " 安装 ", _jsx(_components.code, { className: "language-auto", children: "Eigen" }), "。"] }), "\n", _jsxs(_components.li, { children: ["编译过程注意 ", _jsx(_components.code, { className: "language-auto", children: "eigen" }), " 库安装的位置可能是和作者不一样的，比如我就是：", _jsx(_components.code, { className: "language-auto", children: "/opt/homebrew/Cellar/eigen/5.0.1" }), "。"] }), "\n", _jsxs(_components.li, { children: [_jsx(_components.code, { className: "language-auto", children: "CMakeLists.txt" }), " 也报了错，原因是 ", _jsx(_components.code, { className: "language-auto", children: "CMake" }), " 的版本太老了，问了 Gemini 这样改成功跑通了："] }), "\n"] }), "\n", _jsx(_components.pre, { children: _jsxs(_components.code, { className: "language-auto code-highlight", children: [_jsx(_components.span, { className: "code-line", children: "cmake_minimum_required (VERSION 2.8.11...3.27)\n" }), _jsx(_components.span, { className: "code-line", children: "project (homework0)\n" }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsx(_components.span, { className: "code-line", children: "find_package(Eigen3 REQUIRED)\n" }), _jsx(_components.span, { className: "code-line", children: "include_directories(\"/opt/homebrew/Cellar/eigen/5.0.1/include\")\n" }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsx(_components.span, { className: "code-line", children: "add_executable (main main.cpp)\n" })] }) }), "\n", _jsxs(_components.blockquote, { children: ["\n", _jsxs(_components.p, { children: [_jsx(_components.code, { className: "language-auto", children: "2.8.11...3.27" }), " 表示兼容前面的版本，这里的 ", _jsx(_components.code, { className: "language-auto", children: "include_directories(\"/opt/homebrew/Cellar/eigen/5.0.1/include\")" }), " 改成自己的位置，可以自己找一下。"] }), "\n"] }), "\n", _jsx(_components.p, { children: "最后按照作业中的要求正常编译就好了：" }), "\n", _jsx(_components.pre, { className: "language-sh", children: _jsxs(_components.code, { className: "language-sh code-highlight", children: [_jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token function", children: "mkdir" }), " build\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token builtin class-name", children: "cd" }), " build\n"] }), _jsxs(_components.span, { className: "code-line", children: ["cmake ", _jsx(_components.span, { className: "token punctuation", children: ".." }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token function", children: "make" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["./main ", _jsx(_components.span, { className: "token comment", children: "# 运行程序" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token comment", children: "# 下面是输出的结果（表明程序跑通了🎉(*^▽^*)）" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "Example of cpp \n" }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "1" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "0.5" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "1.41421" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "3.14159" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "0.5" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "Example of vector \n" }), _jsx(_components.span, { className: "code-line", children: "Example of output \n" }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "1" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "2" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "3" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["Example of ", _jsx(_components.span, { className: "token function", children: "add" }), " \n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "2" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "2" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "3" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "Example of scalar multiply \n" }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "3" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "6" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "9" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "2" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "4" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "6" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "Example of matrix \n" }), _jsx(_components.span, { className: "code-line", children: "Example of output \n" }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "1" }), " ", _jsx(_components.span, { className: "token number", children: "2" }), " ", _jsx(_components.span, { className: "token number", children: "3" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "4" }), " ", _jsx(_components.span, { className: "token number", children: "5" }), " ", _jsx(_components.span, { className: "token number", children: "6" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "7" }), " ", _jsx(_components.span, { className: "token number", children: "8" }), " ", _jsx(_components.span, { className: "token number", children: "9" }), "\n"] })] }) }), "\n", _jsxs(_components.h3, { id: "作业代码实现", children: [_jsx(_components.a, { className: "heading-link", href: "#作业代码实现", 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" }) }) }), "作业代码实现"] }), "\n", _jsx(_components.pre, { children: _jsxs(_components.code, { className: "language-c++ code-highlight", children: [_jsx(_components.span, { className: "code-line", children: "#include\n" }), _jsx(_components.span, { className: "code-line", children: "#include\n" }), _jsx(_components.span, { className: "code-line", children: "#include\n" }), _jsx(_components.span, { className: "code-line", children: "#include\n" }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsx(_components.span, { className: "code-line", children: "int main(){\n" }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsx(_components.span, { className: "code-line", children: " // Basic Example of cpp\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << \"Example of cpp \\n\";\n" }), _jsx(_components.span, { className: "code-line", children: " float a = 1.0, b = 2.0;\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << a << std::endl;\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << a/b << std::endl;\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << std::sqrt(b) << std::endl;\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << std::acos(-1) << std::endl;\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << std::sin(30.0/180.0*acos(-1)) << std::endl;\n" }), _jsx(_components.span, { className: "code-line", children: " // 30/180 * pib = 1/6 pi\n" }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsx(_components.span, { className: "code-line", children: " // Example of vector\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << \"Example of vector \\n\";\n" }), _jsx(_components.span, { className: "code-line", children: " // vector definition\n" }), _jsx(_components.span, { className: "code-line", children: " Eigen::Vector3f v(1.0f,2.0f,3.0f);\n" }), _jsx(_components.span, { className: "code-line", children: " Eigen::Vector3f w(1.0f,0.0f,0.0f);\n" }), _jsx(_components.span, { className: "code-line", children: " // vector output\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << \"Example of output \\n\";\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << v << std::endl;\n" }), _jsx(_components.span, { className: "code-line", children: " // vector add\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << \"Example of add \\n\";\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << v + w << std::endl;\n" }), _jsx(_components.span, { className: "code-line", children: " // vector scalar multiply\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << \"Example of scalar multiply \\n\";\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << v * 3.0f << std::endl;\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << 2.0f * v << std::endl;\n" }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsx(_components.span, { className: "code-line", children: " // Example of matrix\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << \"Example of matrix \\n\";\n" }), _jsx(_components.span, { className: "code-line", children: " // matrix definition\n" }), _jsx(_components.span, { className: "code-line", children: " Eigen::Matrix3f i,j;\n" }), _jsx(_components.span, { className: "code-line", children: " i << 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0;\n" }), _jsx(_components.span, { className: "code-line", children: " j << 2.0, 3.0, 1.0, 4.0, 6.0, 5.0, 9.0, 7.0, 8.0;\n" }), _jsx(_components.span, { className: "code-line", children: " // matrix output\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << \"Example of output \\n\";\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << i << std::endl;\n" }), _jsx(_components.span, { className: "code-line", children: " // matrix add i + j\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << \"Example of matrix add \\n\";\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << i + j << std::endl;\n" }), _jsx(_components.span, { className: "code-line", children: " // matrix scalar multiply i * 2.0\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << \"Example of matrix scalar multiply i * 2.0\" << std::endl;\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << i * 2.0f << std::endl;\n" }), _jsx(_components.span, { className: "code-line", children: " // matrix multiply i * j\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << \"Example of matrix multiply multiply i * j\" << std::endl;\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << i * j << std::endl;\n" }), _jsx(_components.span, { className: "code-line", children: " // matrix multiply vector i * v\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << \"Example of matrix multiply vector i * v\" << std::endl;\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << i * v << std::endl;\n" }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << \"Homework start output\" << std::endl;\n" }), _jsx(_components.span, { className: "code-line", children: " Eigen::Vector3f P(2.0f, 1.0f, 1.0f);\n" }), _jsx(_components.span, { className: "code-line", children: " Eigen::Matrix3f R, T;\n" }), _jsx(_components.span, { className: "code-line", children: " float theta = 1.0/4.0 * acos(-1);\n" }), _jsx(_components.span, { className: "code-line", children: " // std::cout << \"theta: \" << theta << std::endl;\n" }), _jsx(_components.span, { className: "code-line", children: " R << cos(theta), -sin(theta), 0.0, cos(theta), sin(theta), 0.0, 0.0, 0.0, 1.0;\n" }), _jsx(_components.span, { className: "code-line", children: " T << 0.0, 0.0, 1.0, 0.0, 0.0, 2.0, 0.0, 0.0, 1.0;\n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << \"旋转变换后 R*P:\\n\" << R * P << std::endl; \n" }), _jsx(_components.span, { className: "code-line", children: " std::cout << \"平移变换后 T*R*P:\\n\" << T * R * P << std::endl;\n" }), _jsx(_components.span, { className: "code-line", children: " return 0;\n" }), _jsx(_components.span, { className: "code-line", children: "}\n" })] }) }), "\n", _jsx(_components.p, { children: "作业最后算出的结果是：" }), "\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: _jsx(_components.mn, { children: "1" }) }) }) }), _jsx(_components.mtr, { children: _jsx(_components.mtd, { children: _jsx(_components.mstyle, { scriptlevel: "0", displaystyle: "false", children: _jsx(_components.mn, { children: "2" }) }) }) }), _jsx(_components.mtr, { children: _jsx(_components.mtd, { children: _jsx(_components.mstyle, { scriptlevel: "0", displaystyle: "false", children: _jsx(_components.mn, { children: "1" }) }) }) })] }), _jsx(_components.mo, { fence: "true", children: "]" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\begin{bmatrix}\n1 \\\\\n2 \\\\\n1\n\\end{bmatrix}" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "3.6em", verticalAlign: "-1.55em" } }), _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: _jsx(_components.span, { className: "mord", children: "1" }) })] }), _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: "2" }) })] }), _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: "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", _jsxs(_components.blockquote, { children: ["\n", _jsx(_components.p, { children: "手算一下就可以很简单地验证。" }), "\n"] }), "\n", _jsxs(_components.h2, { id: "作业-1", children: [_jsx(_components.a, { className: "heading-link", href: "#作业-1", 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" }) }) }), "作业 1"] }), "\n", _jsxs(_components.p, { children: ["做这个作业也是一上来就遇到报错了，发现是因为没有安装 ", _jsx(_components.code, { className: "language-auto", children: "opencv@2" }), " 的原因，但发现 ", _jsx(_components.code, { className: "language-auto", children: "opencv2" }), " 已经停止维护了😅，不过根据我上一次的经验，我还是跑通了！"] }), "\n", _jsxs(_components.p, { children: ["安装好 ", _jsx(_components.code, { className: "language-auto", children: "opencv" }), " 后需要修改 ", _jsx(_components.code, { className: "language-auto", children: "main.cpp" }), " 中的引入代码，因为现在已经是 ", _jsx(_components.code, { className: "language-auto", children: "opencv4" }), " 了："] }), "\n", _jsx(_components.pre, { children: _jsx(_components.code, { className: "language-c++ code-highlight", children: _jsx(_components.span, { className: "code-line", children: "#include \n" }) }) }), "\n", _jsxs(_components.blockquote, { children: ["\n", _jsxs(_components.p, { children: ["这里建议亲自根据 ", _jsx(_components.code, { className: "language-auto", children: "brew info opencv" }), " 去调查一下文件目录再写入，只需要保证是从 ", _jsx(_components.code, { className: "language-auto", children: "/include" }), " 这个位置开始就对了，比如我这里实际目录的结构是 ", _jsx(_components.code, { className: "language-auto", children: "/opt/homebrew/Cellar/eigen/5.0.1/include/opencv4/opencv2/opencv.hpp" }), "。"] }), "\n"] }), "\n", _jsxs(_components.p, { children: ["首先更改 ", _jsx(_components.code, { className: "language-auto", children: "CMakeLists.txt" }), "："] }), "\n", _jsx(_components.pre, { className: "language-sh", children: _jsxs(_components.code, { className: "language-sh code-highlight", children: [_jsxs(_components.span, { className: "code-line", children: ["cmake_minimum_required ", _jsx(_components.span, { className: "token punctuation", children: "(" }), "VERSION ", _jsx(_components.span, { className: "token number", children: "2.8" }), ".11", _jsx(_components.span, { className: "token punctuation", children: ".." }), ".3.27", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["project ", _jsx(_components.span, { className: "token punctuation", children: "(" }), "homework0", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: ["find_package", _jsx(_components.span, { className: "token punctuation", children: "(" }), "OpenCV REQUIRED", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: ["message", _jsx(_components.span, { className: "token punctuation", children: "(" }), "STATUS ", _jsxs(_components.span, { className: "token string", children: ["\"Eigen3 include dirs: ", _jsx(_components.span, { className: "token variable", children: "${EIGEN3_INCLUDE_DIRS}" }), "\""] }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["message", _jsx(_components.span, { className: "token punctuation", children: "(" }), "STATUS ", _jsxs(_components.span, { className: "token string", children: ["\"OpenCV include dirs: ", _jsx(_components.span, { className: "token variable", children: "${OpenCV_INCLUDE_DIRS}" }), "\""] }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["set", _jsx(_components.span, { className: "token punctuation", children: "(" }), "CMAKE_CXX_STANDARD ", _jsx(_components.span, { className: "token number", children: "17" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: ["include_directories", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token string", children: "\"/opt/homebrew/Cellar/eigen/5.0.1/include\"" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["include_directories", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token string", children: "\"/opt/homebrew/Cellar/opencv/4.13.0_3/include\"" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: ["add_executable", _jsx(_components.span, { className: "token punctuation", children: "(" }), "Rasterizer main.cpp rasterizer.hpp rasterizer.cpp Triangle.hpp Triangle.cpp", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["target_include_directories", _jsx(_components.span, { className: "token punctuation", children: "(" }), "Rasterizer PRIVATE \n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token variable", children: "${EIGEN3_INCLUDE_DIRS}" }), " \n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token variable", children: "${OpenCV_INCLUDE_DIRS}" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["target_link_libraries", _jsx(_components.span, { className: "token punctuation", children: "(" }), "Rasterizer ", _jsx(_components.span, { className: "token variable", children: "${OpenCV_LIBRARIES}" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] })] }) }), "\n", _jsxs(_components.p, { children: ["然后在 ", _jsx(_components.code, { className: "language-auto", children: "代码框架" }), " 目录进行编译即可："] }), "\n", _jsx(_components.pre, { className: "language-sh", children: _jsx(_components.code, { className: "language-sh code-highlight", children: _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token function", children: "mkdir" }), " build ", _jsx(_components.span, { className: "token operator", children: "&&" }), " ", _jsx(_components.span, { className: "token builtin class-name", children: "cd" }), " build ", _jsx(_components.span, { className: "token operator", children: "&&" }), " cmake ", _jsx(_components.span, { className: "token punctuation", children: ".." }), " ", _jsx(_components.span, { className: "token operator", children: "&&" }), " ", _jsx(_components.span, { className: "token function", children: "make" }), "\n"] }) }) }), "\n", _jsxs(_components.p, { children: ["在 ", _jsx(_components.code, { className: "language-auto", children: "/build" }), " 下运行："] }), "\n", _jsx(_components.pre, { className: "language-sh", children: _jsx(_components.code, { className: "language-sh code-highlight", children: _jsx(_components.span, { className: "code-line", children: "./Rasterizer\n" }) }) }), "\n", _jsx(_components.p, { children: "紧接着会在终端中输出，并打开一个窗口！" }), "\n", _jsxs(_components.blockquote, { children: ["\n", _jsx(_components.p, { children: "终于可以开始写作业了，太棒了！🚀" }), "\n"] }), "\n", _jsxs(_components.h3, { id: "代码实现过程", children: [_jsx(_components.a, { className: "heading-link", href: "#代码实现过程", 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" }) }) }), "代码实现过程"] }), "\n", _jsx(_components.p, { children: "作业要求：" }), "\n", _jsx(_components.pre, { children: _jsxs(_components.code, { className: "language-auto code-highlight", children: [_jsx(_components.span, { className: "code-line", children: "get_model_matrix(float rotation_angle): \n" }), _jsx(_components.span, { className: "code-line", children: "逐个元素地构建模型变换矩阵并返回该矩阵。在此函数中，你只需要实现三维中绕 z 轴旋转的变换矩阵，而不用处理平移与缩放。\n" })] }) }), "\n", _jsxs(_components.h3, { id: "模型变换", children: [_jsx(_components.a, { className: "heading-link", href: "#模型变换", 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" }) }) }), "模型变换"] }), "\n", _jsxs(_components.p, { children: ["绕 ", _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: "0.6833em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0715em" }, children: "Z" })] }) })] }), " 轴的旋转矩阵为："] }), "\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 center center center", columnspacing: 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-sin(rotation_angle), 0.0, 0.0,\n" }), _jsx(_components.span, { className: "code-line", children: " sin(rotation_angle), cos(rotation_angle), 0.0, 0.0,\n" }), _jsx(_components.span, { className: "code-line", children: " 0.0, 0.0, 1.0, 0.0,\n" }), _jsx(_components.span, { className: "code-line", children: " 0.0, 0.0, 0.0, 1.0;\n" }), _jsx(_components.span, { className: "code-line", children: " model = rotate_matrix * model;\n" }), _jsx(_components.span, { className: "code-line", children: " // TODO: Implement this function\n" }), _jsx(_components.span, { className: "code-line", children: " // Create the model matrix for rotating the triangle around the Z axis.\n" }), _jsx(_components.span, { className: "code-line", children: " // Then return it.\n" }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsx(_components.span, { className: "code-line", children: " return model;\n" }), _jsx(_components.span, { className: "code-line", children: "}\n" })] }) }), "\n", _jsxs(_components.p, { children: ["惊奇的发现按下 ", _jsx(_components.code, { className: "language-auto", children: "AD" }), " 键后屏幕中原本平直的白线可以发生旋转了，虽然不知道发生了什么但是大为震撼！"] }), "\n", _jsxs(_components.blockquote, { children: ["\n", _jsx(_components.p, { children: "果然还是太菜了，画条线就给我激动坏了 hhh，果然 CG 给我带来的多巴胺还是要比调用 API 来获得图像要多的多。" }), "\n"] }), "\n", _jsxs(_components.blockquote, { children: ["\n", _jsxs(_components.p, { children: [_jsx(_components.code, { className: "language-auto", children: "./Rasterizer -r 20 image.png" }), " ：旋转后的输出："] }), "\n"] }), "\n", _jsx(_components.img, { src: "https://ccccooh.oss-cn-hangzhou.aliyuncs.com/img/202602181659515.png", alt: "image.png", className: "internal" }), "\n", _jsxs(_components.h3, { id: "投影变换", children: [_jsx(_components.a, { className: "heading-link", href: "#投影变换", 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" }) }) }), "投影变换"] }), "\n", _jsxs(_components.blockquote, { children: ["\n", _jsxs(_components.p, { children: ["这里先要猜测已经做好了 ", _jsx(_components.code, { className: "language-auto", children: "viewing" }), " 变换，我已经得到一个 ", _jsx(_components.code, { className: "language-auto", children: "fructum" }), "，然后按照课堂所学返回一个透视投影的变换矩阵就好了。"] }), "\n"] }), "\n", _jsxs(_components.h4, { id: "公式推导", children: [_jsx(_components.a, { className: "heading-link", href: "#公式推导", 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" }) }) }), "公式推导"] }), "\n", _jsxs(_components.p, { children: ["根据课堂内容，", _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: "M" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "p" }), _jsx(_components.mi, { children: "e" }), _jsx(_components.mi, 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}), _jsx(_components.span, { className: "mord", children: _jsx(_components.span, { className: "mord", children: "0" }) })] }), _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", children: "0" }) })] }), _jsxs(_components.span, { style: { top: "-2.41em" }, 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", children: "n" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.1076em" }, children: "f" })] })] }), _jsxs(_components.span, { style: { top: "-1.21em" }, 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: "2.15em" }, 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: "2.65em" }, children: _jsxs(_components.span, { style: { top: "-4.65em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "6.8em" } }), _jsx(_components.span, { style: { width: "0.875em", height: "4.8em" }, children: _jsx(_components.svg, { xmlns: "http://www.w3.org/2000/svg", width: "0.875em", height: "4.8em", viewBox: "0 0 875 4800", children: _jsx(_components.path, { d: "M76,0c-16.7,0,-25,3,-25,9c0,2,2,6.3,6,13c21.3,28.7,42.3,60.3,\n63,95c96.7,156.7,172.8,332.5,228.5,527.5c55.7,195,92.8,416.5,111.5,664.5\nc11.3,139.3,17,290.7,17,454c0,28,1.7,43,3.3,45l0,1209\nc-3,4,-3.3,16.7,-3.3,38c0,162,-5.7,313.7,-17,455c-18.7,248,-55.8,469.3,-111.5,664\nc-55.7,194.7,-131.8,370.3,-228.5,527c-20.7,34.7,-41.7,66.3,-63,95c-2,3.3,-4,7,-6,11\nc0,7.3,5.7,11,17,11c0,0,11,0,11,0c9.3,0,14.3,-0.3,15,-1c5.3,-5.3,10.3,-11,15,-17\nc242.7,-294.7,395.3,-681.7,458,-1161c21.3,-164.7,33.3,-350.7,36,-558\nl0,-1344c-2,-159.3,-10,-310.7,-24,-454c-53.3,-528,-210,-949.7,\n-470,-1265c-4.7,-6,-9.7,-11.7,-15,-17c-0.7,-0.7,-6.7,-1,-18,-1z" }) }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "2.15em" }, children: _jsx(_components.span, {}) }) })] }) }) })] })] })] })] }) }), "\n", _jsxs(_components.p, { children: ["函数 ", _jsx(_components.code, { className: "language-auto", children: "get_projection_matrix" }), " 给出的参数是（四个浮点参数）："] }), "\n", _jsxs(_components.ul, { children: ["\n", _jsxs(_components.li, { children: [_jsx(_components.code, { className: "language-auto", children: "eye_fov" }), "：视角。"] }), "\n", _jsxs(_components.li, { children: [_jsx(_components.code, { className: "language-auto", children: "aspect_ratio" }), "：宽高比。"] }), "\n", _jsxs(_components.li, { children: [_jsx(_components.code, { className: "language-auto", children: "zNear" }), "：", _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: "n" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "n" })] }) }) }), _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: "n" })] }) })] })] }), "\n", _jsxs(_components.li, { children: [_jsx(_components.code, { className: "language-auto", children: "zFar" }), "：", _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" })] }) })] })] }), "\n"] }), "\n", _jsxs(_components.p, { children: ["这里的 ", _jsx(_components.code, { className: "language-auto", children: "eye_fov" }), " 需要看完第五讲的内容才能理解，如果已知 ", _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: "n" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "n" })] }) }) }), _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: "n" })] }) })] }), " 就能利用 ", _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: "e" }), _jsx(_components.mi, { children: "y" }), _jsx(_components.mi, { children: "e" }), _jsx(_components.mi, { mathvariant: "normal", children: "_" }), _jsx(_components.mi, { children: "f" }), _jsx(_components.mi, { children: "o" }), _jsx(_components.mi, { children: "v" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "eye\\_fov" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: 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className: "mord mathnormal mtight", style: { marginRight: "0.0269em" }, children: "w" }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "i" }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "d" }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "t" }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "h" })] }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.345em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] })] })] }), _jsxs(_components.span, { style: { top: "-2.25em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3.008em" } }), _jsxs(_components.span, { className: "mord", children: [_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: "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: "0.9322em" }, children: [_jsxs(_components.span, { style: { top: "-2.655em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) }) })] }), _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: "-3.4461em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", children: "h" }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "e" }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "i" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0359em" }, children: "g" }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "t" }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "h" })] }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.345em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] })] })] }), _jsxs(_components.span, { style: { top: "-0.81em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3.008em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0278em" }, children: "r" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mord", children: "−" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0197em" }, children: "l" })] })] }), _jsxs(_components.span, { style: { top: "0.63em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3.008em" } }), _jsxs(_components.span, { className: "mord", children: [_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" } }), _jsx(_components.span, { className: "mord", children: "−" }), _jsx(_components.span, { className: "mord mathnormal", children: "b" })] })] })] }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "4.07em" }, children: _jsx(_components.span, {}) }) })] }) }) }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] })] }) })] }) }), "\n", _jsxs(_components.p, { children: ["我们要做的就是把 ", _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: _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "M" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "p" }), _jsx(_components.mi, { children: "e" }), _jsx(_components.mi, { children: "r" }), _jsx(_components.mi, { children: "s" }), _jsx(_components.mi, { children: "p" })] })] }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "M_{persp}" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.9694em", verticalAlign: "-0.2861em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.109em" }, children: "M" }), _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: "-0.109em", 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", children: "p" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0278em" }, children: "er" }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "s" }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "p" })] }) })] }) }), _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, {}) }) })] }) })] })] }) })] }), " 计算出来并返回就好了，将上面三个矩阵乘起来得到："] }), "\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.mrow, { children: [_jsx(_components.mo, { fence: "true", children: 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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" }) }) }), "代码实现"] }), "\n", _jsxs(_components.h4, { id: "分部版本", children: [_jsx(_components.a, { className: "heading-link", href: "#分部版本", 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" }) }) }), "分部版本"] }), "\n", _jsx(_components.p, { children: "这是最终代码：" }), "\n", _jsx(_components.img, { src: "https://ccccooh.oss-cn-hangzhou.aliyuncs.com/img/202602191053086.png", alt: "image.png", className: "internal" }), "\n", _jsx(_components.pre, { className: "language-c", children: _jsxs(_components.code, { className: "language-c code-highlight", children: [_jsxs(_components.span, { className: "code-line", children: ["Eigen", _jsx(_components.span, { className: "token operator", children: "::" }), "Matrix4f ", _jsx(_components.span, { className: "token function", children: "get_projection_matrix" }), _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token keyword", children: "float" }), " eye_fov", _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token keyword", children: "float" }), " aspect_ratio", _jsx(_components.span, { className: "token punctuation", children: "," }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token keyword", children: "float" }), " zNear", _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token keyword", children: "float" }), " zFar", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token punctuation", children: "{" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "// Students will implement this function" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [" Eigen", _jsx(_components.span, { className: "token operator", children: "::" }), "Matrix4f projection ", _jsx(_components.span, { className: "token operator", children: "=" }), " Eigen", _jsx(_components.span, { className: "token operator", children: "::" }), "Matrix4f", _jsx(_components.span, { className: "token operator", children: "::" }), _jsx(_components.span, { className: "token function", children: "Identity" }), _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: ";" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" Eigen", _jsx(_components.span, { className: "token operator", children: "::" }), "Matrix4f M_persp2ortho ", _jsx(_components.span, { className: "token operator", children: "=" }), " Eigen", _jsx(_components.span, { className: "token operator", children: "::" }), "Matrix4f", _jsx(_components.span, { className: "token operator", children: "::" }), _jsx(_components.span, { className: "token function", children: "Identity" }), _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: ";" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" Eigen", _jsx(_components.span, { className: "token operator", children: "::" }), "Matrix4f M_ortho ", _jsx(_components.span, { className: "token operator", children: "=" }), " Eigen", _jsx(_components.span, { className: "token operator", children: "::" }), "Matrix4f", _jsx(_components.span, { className: "token operator", children: "::" }), _jsx(_components.span, { className: "token function", children: "Identity" }), _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: ";" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" Eigen", _jsx(_components.span, { className: "token operator", children: "::" }), "Matrix4f M_ortho_Translate ", _jsx(_components.span, { className: "token operator", children: "=" }), " Eigen", _jsx(_components.span, { className: "token operator", children: "::" }), "Matrix4f", _jsx(_components.span, { className: "token operator", children: "::" }), _jsx(_components.span, { className: "token function", children: "Identity" }), _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: ";" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" Eigen", _jsx(_components.span, { className: "token operator", children: "::" }), "Matrix4f M_ortho_Scale ", _jsx(_components.span, { className: "token operator", children: "=" }), " Eigen", _jsx(_components.span, { className: "token operator", children: "::" }), "Matrix4f", _jsx(_components.span, { className: "token operator", children: "::" }), _jsx(_components.span, { className: "token function", children: "Identity" }), _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: ";" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" Eigen", _jsx(_components.span, { className: "token operator", children: "::" }), "Matrix4f M_yFlip ", _jsx(_components.span, { className: "token operator", children: "=" }), " Eigen", _jsx(_components.span, { className: "token operator", children: "::" }), "Matrix4f", _jsx(_components.span, { className: "token operator", children: "::" }), _jsx(_components.span, { className: "token function", children: "Identity" }), _jsx(_components.span, { className: "token punctuation", children: "(" }), _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 keyword", children: "float" }), " n ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token operator", children: "-" }), "zNear", _jsx(_components.span, { className: "token punctuation", children: "," }), " f ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token operator", children: "-" }), "zFar", _jsx(_components.span, { className: "token punctuation", children: ";" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token keyword", children: "float" }), " fov ", _jsx(_components.span, { className: "token operator", children: "=" }), " eye_fov ", _jsx(_components.span, { className: "token operator", children: "*" }), " ", _jsx(_components.span, { className: "token function", children: "acos" }), _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 operator", children: "/" }), " ", _jsx(_components.span, { className: "token number", children: "180.0" }), _jsx(_components.span, { className: "token punctuation", children: ";" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "// 将角度转化为弧度" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token keyword", children: "float" }), " h ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token number", children: "2.0" }), " ", _jsx(_components.span, { className: "token operator", children: "*" }), " ", _jsx(_components.span, { className: "token operator", children: "-" }), "n ", _jsx(_components.span, { className: "token operator", children: "*" }), " ", _jsx(_components.span, { className: "token function", children: "tan" }), _jsx(_components.span, { className: "token punctuation", children: "(" }), "fov ", _jsx(_components.span, { className: "token operator", children: "/" }), " ", _jsx(_components.span, { className: "token number", children: "2.0" }), _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 keyword", children: "float" }), " w ", _jsx(_components.span, { className: "token operator", children: "=" }), " h ", _jsx(_components.span, { className: "token operator", children: "*" }), " aspect_ratio", _jsx(_components.span, { className: "token punctuation", children: ";" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token keyword", children: "float" }), " t ", _jsx(_components.span, { className: "token operator", children: "=" }), " h ", _jsx(_components.span, { className: "token operator", children: "/" }), " ", _jsx(_components.span, { className: "token number", children: "2.0" }), _jsx(_components.span, { className: "token punctuation", children: ";" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token keyword", children: "float" }), " b ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token operator", children: "-" }), " h ", _jsx(_components.span, { className: "token operator", children: "/" }), " ", _jsx(_components.span, { className: "token number", children: "2.0" }), _jsx(_components.span, { className: "token punctuation", children: ";" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token keyword", children: "float" }), " l ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token operator", children: "-" }), " w ", _jsx(_components.span, { className: "token operator", children: "/" }), " ", _jsx(_components.span, { className: "token number", children: "2.0" }), _jsx(_components.span, { className: "token punctuation", children: ";" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token keyword", children: "float" }), " r ", _jsx(_components.span, { className: "token operator", children: "=" }), " w ", _jsx(_components.span, { className: "token operator", children: "/" }), " ", _jsx(_components.span, { className: "token number", children: "2.0" }), _jsx(_components.span, { className: "token punctuation", children: ";" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" M_persp2ortho ", _jsx(_components.span, { className: "token operator", children: "<<" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" n", _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " n", _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " n", _jsx(_components.span, { className: "token operator", children: "+" }), "f", _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token operator", children: "-" }), "n", _jsx(_components.span, { className: "token operator", children: "*" }), "f", _jsx(_components.span, { className: "token punctuation", children: "," }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _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: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: ";" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" M_ortho_Translate ", _jsx(_components.span, { className: "token operator", children: "<<" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token number", children: "1.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token operator", children: "-" }), _jsx(_components.span, { className: "token punctuation", children: "(" }), "r", _jsx(_components.span, { className: "token operator", children: "+" }), "l", _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token operator", children: "/" }), _jsx(_components.span, { className: "token number", children: "2.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token number", children: "0.0" }), _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: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token operator", children: "-" }), _jsx(_components.span, { className: "token punctuation", children: "(" }), "t", _jsx(_components.span, { className: "token operator", children: "+" }), "b", _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token operator", children: "/" }), _jsx(_components.span, { className: "token number", children: "2.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token operator", children: "-" }), _jsx(_components.span, { className: "token punctuation", children: "(" }), "n", _jsx(_components.span, { className: "token operator", children: "+" }), "f", _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token operator", children: "/" }), _jsx(_components.span, { className: "token number", children: "2.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "1.0" }), _jsx(_components.span, { className: "token punctuation", children: ";" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" M_ortho_Scale ", _jsx(_components.span, { className: "token operator", children: "<<" }), " \n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token number", children: "2" }), _jsx(_components.span, { className: "token operator", children: "/" }), _jsx(_components.span, { className: "token punctuation", children: "(" }), "r", _jsx(_components.span, { className: "token operator", children: "-" }), "l", _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "2" }), _jsx(_components.span, { className: "token operator", children: "/" }), _jsx(_components.span, { className: "token punctuation", children: "(" }), "t", _jsx(_components.span, { className: "token operator", children: "-" }), "b", _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "2" }), _jsx(_components.span, { className: "token operator", children: "/" }), _jsx(_components.span, { className: "token punctuation", children: "(" }), "n", _jsx(_components.span, { className: "token operator", children: "-" }), "f", _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "0.0" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " ", _jsx(_components.span, { className: "token number", children: "1.0" }), _jsx(_components.span, { className: "token punctuation", children: ";" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" projection ", _jsx(_components.span, { className: "token operator", children: "=" }), " M_yFlip ", _jsx(_components.span, { className: "token operator", children: "*" }), " M_ortho_Scale ", _jsx(_components.span, { className: "token operator", children: "*" }), " M_ortho_Translate ", _jsx(_components.span, { className: "token operator", children: "*" }), " M_persp2ortho", _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: "// 构建透视投影矩阵并返回" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "// TODO: Implement this function" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "// Create the projection matrix for the given parameters." }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "// Then return it." }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token keyword", children: "return" }), " projection", _jsx(_components.span, { className: "token punctuation", children: ";" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token punctuation", children: "}" }), "\n"] })] }) }), "\n", _jsxs(_components.p, { children: ["测试过程中使用的命令 ", _jsx(_components.code, { className: "language-auto", children: "项目根目录" }), "："] }), "\n", _jsx(_components.pre, { className: "language-sh", children: _jsx(_components.code, { className: "language-sh code-highlight", children: _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token function", children: "rm" }), " ", _jsx(_components.span, { className: "token parameter variable", children: "-r" }), " build ", _jsx(_components.span, { className: "token operator", children: "&&" }), " ", _jsx(_components.span, { className: "token function", children: "mkdir" }), " build ", _jsx(_components.span, { className: "token operator", children: "&&" }), " ", _jsx(_components.span, { className: "token builtin class-name", children: "cd" }), " build ", _jsx(_components.span, { className: "token operator", children: "&&" }), " cmake ", _jsx(_components.span, { className: "token punctuation", children: ".." }), " ", _jsx(_components.span, { className: "token operator", children: "&&" }), " ", _jsx(_components.span, { className: "token function", children: "make" }), " ", _jsx(_components.span, { className: "token operator", children: "&&" }), " ./Rasterizer ", _jsx(_components.span, { className: "token operator", children: "&&" }), " ", _jsx(_components.span, { className: "token builtin class-name", children: "cd" }), " ", _jsx(_components.span, { className: "token punctuation", children: ".." }), "\n"] }) }) }), "\n", _jsxs(_components.blockquote, { children: ["\n", _jsxs(_components.p, { children: ["因为不确定 ", _jsx(_components.code, { className: "language-auto", children: "build" }), " 是会被覆盖，就每次都删除重新构建了，不过好像不需要如此多此一举？"] }), "\n"] }), "\n", _jsxs(_components.h4, { id: "合并版本", children: [_jsx(_components.a, { className: "heading-link", href: "#合并版本", 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" }) }) }), "合并版本"] }), "\n", _jsx(_components.p, { children: "上面的代码是直接施加三个变换的矩阵，我们也可以直接使用推导后得到的矩阵来简化代码。" }), "\n", _jsx(_components.p, { children: "得到的代码更加简单，但本质只是手动合并了：" }), "\n", _jsx(_components.pre, { children: _jsxs(_components.code, { className: "language-c++ code-highlight", children: [_jsx(_components.span, { className: "code-line", children: "Eigen::Matrix4f get_projection_matrix(float eye_fov, float aspect_ratio,\n" }), _jsx(_components.span, { className: "code-line", children: " float zNear, float zFar)\n" }), _jsx(_components.span, { className: "code-line", children: "{\n" }), _jsx(_components.span, { className: "code-line", children: " // Students will implement this function\n" }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsx(_components.span, { className: "code-line", children: " Eigen::Matrix4f projection = Eigen::Matrix4f::Identity();\n" }), _jsx(_components.span, { className: "code-line", children: " float n = -zNear, f = -zFar;\n" }), _jsx(_components.span, { className: "code-line", children: " float fov = eye_fov * acos(-1) / 180.0;\n" }), _jsx(_components.span, { className: "code-line", children: " // 将角度转化为弧度\n" }), _jsx(_components.span, { className: "code-line", children: " float h = 2.0 * -n * tan(fov / 2.0);\n" }), _jsx(_components.span, { className: "code-line", children: " float w = h * aspect_ratio;\n" }), _jsx(_components.span, { className: "code-line", children: " float t = h / 2.0;\n" }), _jsx(_components.span, { className: "code-line", children: " float b = - h / 2.0;\n" }), _jsx(_components.span, { className: "code-line", children: " float l = - w / 2.0;\n" }), _jsx(_components.span, { className: "code-line", children: " float r = w / 2.0;\n" }), _jsx(_components.span, { className: "code-line", children: " \n" }), _jsx(_components.span, { className: "code-line", children: " projection << \n" }), _jsx(_components.span, { className: "code-line", children: " n/r, 0.0, 0.0, 0.0,\n" }), _jsx(_components.span, { className: "code-line", children: " 0.0, n/t, 0.0, 0.0,\n" }), _jsx(_components.span, { className: "code-line", children: " 0.0, 0.0, (n+f)/(n-f), 2*n*f/(f-n),\n" }), _jsx(_components.span, { className: "code-line", children: " 0.0, 0.0, 1.0, 0.0;\n" }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsx(_components.span, { className: "code-line", children: " // TODO: Implement this function\n" }), _jsx(_components.span, { className: "code-line", children: " // Create the projection matrix for the given parameters.\n" }), _jsx(_components.span, { className: "code-line", children: " // Then return it.\n" }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsx(_components.span, { className: "code-line", children: " return projection;\n" }), _jsx(_components.span, { className: "code-line", children: "}\n" })] }) }), "\n", _jsxs(_components.p, { children: ["至此，我们的代码算是完成了。这里，对于绘制出三角形倒立的问题，我采用的解决办法是将 ", _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: "n" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "n" })] }) }) }), _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: "n" })] }) })] }), " 和 ", _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" })] }) })] }), " 取负。"] })] }); } function MDXContent(props = {}) { const {wrapper: MDXLayout} = { ..._provideComponents(), ...props.components }; return MDXLayout ? _jsx(MDXLayout, { ...props, children: _jsx(_createMdxContent, { ...props }) }) : _createMdxContent(props); } return { default: MDXContent };