http://groups.csail.mit.edu/graphics/classes/6.837/F03/lectures/04_transformations.ppt
Maps points (x, y) in one coordinate system to points (x', y') in another coordinate system
x' = ax + by + c
y' = dx + ey + f
For example, IFS:
Can be combined
Are these operations invertible?
Yes, except scale = 0
恒等 平移 旋转 等比缩放
可逆，除非等比缩放系数为0
Classes of Transformations 变换分类
Rigid Body / Euclidean Transforms 刚体、欧式变换
Similitudes / Similarity Transforms 相似性变换
Linear 线性变换
Affine 放射
Projective 投影
保持不变量的对象
点点之间
距离
线线之间
角度
平行关系
保距变换
保角变换
平行变换
Rigid-Body / Euclidean Transforms
Preserves distances
Preserves angles
Rigid / Euclidean
Translation Identity Rotation
Similitudes / Similarity Transforms
Linear Transformations
L(p + q) = L(p) + L(q)
L(ap) = a L(p)
shear
vt. 剪；修剪；剥夺
vi. 剪；剪切；修剪
切力 切变
Affine Transformations
Projective Transformations
preserves lines
