3. 二维变换矩阵
x' a11 a12 a13 x a11x a12y a13z
y' = a21 a22 a23 y = a21x a22y a23z
z' a31 a32 a33 w a31x a32y a33z
3.1二维平移变换矩阵
P =(x, y, 1)
P*=(x*,y*,1)
1 0 tx
T = 0 1 ty
0 0 1
P*= T(tx,ty)P
3.1二维比例变换矩阵
sx 0 0
S = 0 sy 0
0 0 1
P*= S(sx,sy)P
3.2二维旋转变换矩阵
以原点为中心
cos(r) -sin(r) 0
R = sin(r) cos(r) 0
0 0 1
P*= R(r)P
3.3反射变换矩阵
X 轴对称
1 0 0
RX= 0 -1 0
0 0 1
Y 轴对称
-1 0 0
RY= 0 1 0
0 0 1
原点对称
-1 0 0
RO= 0 -1 0
0 0 1
3.4 错切变换矩阵
X 轴错切
1 s 0
SX= 0 1 0
0 0 1
x* = x+sy; y* = y
Y 轴错切
1 0 0
SY= s 1 0
0 0 1
x* = x; y* = sx+y
4. 三维变换
平移 比例 错切 可对照二维做扩展
旋转：
绕X轴
0 0 0 1
0 cos(r) -sin(r) 0
RX= 0 sin(r) cos(r) 0
0 0 0 1
绕Y轴
0 cos(r) sin(r 1
0 1 0 0
RY= 0 -sin(r) cos(r) 0
0 0 0 1
绕Z轴
cos(r) -sin(r) 0 0
RZ= sin(r) cos(r) 0 0
0 0 1 0
0 0 0 1