坐标变换

采用一定的数学方法将一种坐标系的坐标变换为另一种坐标系的坐标的过程。

基本变换

共有五种，除平移外均以坐标原点为基准点，即变换前后坐标原点不变。　　下面给出五种基本变换的中英文名称和矩阵描述。

平移 offset

二维...................三维　　▏1....0....0▕ ........▏1....0....0....0▕　　▏0....1....0▕ ........▏0....1....0....0▕　　▏x.....y....1▕ ........▏0....0....1....0▕　　...........................▏x.....y....z....1▕

变倍 scale

二维...................三维　　▏x....0....0▕ ........▏x....0....0....0▕　　▏0....y....0▕ ........▏0....y....0....0▕　　▏0....0....1▕ ....... ▏0....0....z....0▕　　..........................▏0....0....0....1▕

旋转 rotate

二维　　▏cos(θ)..-sin(θ)..0▕　　▏sin(θ)...cos(θ)..0▕　　▏0..........0..........1▕　　三维　　绕Z轴.................................绕Y轴................................绕X轴　　▏cos(θ)..-sin(θ)..0..0▕........▏cos(θ)..0..-sin(θ)..0▕........▏1..0.........0...........0▕　　▏sin(θ)...cos(θ)..0..0▕........▏0..........1..........0..0▕........▏0..cos(θ)..-sin(θ)..0▕　　▏0..........0..........1..0▕........▏sin(θ)...0..cos(θ)..0▕........▏0..sin(θ)...cos(θ)..0▕　　▏0..........0..........0..1▕........▏0..........0..........0..1▕........▏0..0..........0..........1▕

切变 shear

二维　　沿X轴.................沿Y轴　　▏1....k....0▕ ........▏1....0....0▕　　▏0....1....0▕ ........▏k....1....0▕　　▏0....0....1▕ ........▏0....0....1▕　　三维　　沿X轴......................沿Y轴.......................沿Z轴　　▏1....k.....l.....0▕........▏1....0....0....0▕........▏1....0....0....0▕　　▏0....1....0....0▕........▏k.....1....l.....0▕........▏0....1....0....0▕　　▏0....0....1....0▕........▏0....0....1....0▕........▏k.....l.....1....0▕　　▏0....0....0....1▕........▏0....0....0....1▕........▏0....0....0....1▕

反射 reflect

反射变换的实质是负变倍，实际上叫做“镜像”更为贴切。　　二维　　基于X轴..............基于Y轴　　▏1....0....0▕ ........▏-1...0....0▕　　▏0...-1....0▕ ........▏0....1....0▕　　▏0....0....1▕ ........▏0....0....1▕　　三维　　基于Y-X平面............基于X-Z平面............基于Z-Y平面　　▏1....0....0....0▕........▏1....0....0....0▕........▏-1....0....0....0▕　　▏0....1....0....0▕........▏0...-1....0....0▕........▏0....1....0....0▕　　▏0....0...-1....0▕........▏0....0....1....0▕........▏0....0....1....0▕　　▏0....0....0....1▕........▏0....0....0....1▕........▏0....0....0....1▕