thejinchao.github.io/assets/transform_02.html-CX7S70bP.js

import{_ as x,c as j,a,b as m,d as l,o as c}from"./app-Bj0iHonY.js";const t="/assets/transform_axis-DnM_BPj4.svg",n="/assets/transform_axis_move-Ck2kYwSA.svg",e="/assets/transform_axis_roate-Bm4Ra9LF.svg",i={};function u(r,s){return c(),j("div",null,s[0]||(s[0]=[a('<h1 id="几何变换-二" tabindex="-1"><a class="header-anchor" href="#几何变换-二"><span>几何变换（二）</span></a></h1><hr><h2 id="_4-仿射变换" tabindex="-1"><a class="header-anchor" href="#_4-仿射变换"><span>4. 仿射变换</span></a></h2><h3 id="_4-1-齐次坐标-homogeneous-coordinates" tabindex="-1"><a class="header-anchor" href="#_4-1-齐次坐标-homogeneous-coordinates"><span>4.1 齐次坐标(Homogeneous Coordinates)</span></a></h3><h4 id="_4-1-1-定义" tabindex="-1"><a class="header-anchor" href="#_4-1-1-定义"><span>4.1.1 定义</span></a></h4>',5),m("p",null,[l("齐次坐标就是将一个原本是n维的向量或者一个n维的点用一个n+1维坐标来表示，例如二维点"),m("mjx-container",{class:"MathJax",jax:"CHTML",style:{position:"relative"}},[m("mjx-math",{class:"MJX-TEX","aria-hidden":"true"},[m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c5B"})]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D465 TEX-I"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2C"})]),m("mjx-mi",{class:"mjx-i",space:"2"},[m("mjx-c",{class:"mjx-c1D466 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这样可以保证矢量的“平移不变性”，也就是一个矢量经过平移变换，仍然保持和原先一致。")],-1),m("mjx-container",{class:"MathJax",jax:"CHTML",display:"true",style:{position:"relative"}},[m("mjx-math",{display:"true",style:{"margin-left":"0","margin-right":"0"},class:"MJX-TEX","aria-hidden":"true"},[m("mjx-mrow",null,[m("mjx-mo",{class:"mjx-n"},[m("mjx-stretchy-v",{style:{height:"3.845em","vertical-align":"-1.672em"},class:"mjx-c5B"},[m("mjx-beg",null,[m("mjx-c")]),m("mjx-ext",null,[m("mjx-c")]),m("mjx-end",null,[m("mjx-c")]),m("mjx-mark")])]),m("mjx-mtable",{style:{"min-width":"3.848em"}},[m("mjx-table",null,[m("mjx-itable",null,[m("mjx-mtr",null,[m("mjx-mtd",{style:{"padding-right":"0.5em","padding-bottom":"0.2em"}},[m("mjx-mn",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c31"})]),m("mjx-tstrut")]),m("mjx-mtd",{style:{"padding-left":"0.5em","padding-right":"0.5em","padding-bottom":"0.2em"}},[m("mjx-mn",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c30"})]),m("mjx-tstrut")]),m("mjx-mtd",{style:{"padding-left":"0.5em","padding-bottom":"0.2em"}},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D461 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