计算机图形学（3）

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1. 缩放矩阵是对角矩阵，对角线上每个值表示缩放的比例

2. 

2D Shear

Shear transformations produce a shape distortion.

(old coordinates are (x, y) and the new coordinates are (x', y'))

X-Direction Shear is given by the following matrix:

(1     0    0)
(SHx   1    0) 
(0     0    1)
  
                        ( 1    0    0)
(x' y' 1) = ( x y 1)  * (SHx   1    0)（这里使用齐次坐标系表示的，所以多了一个1）
                        ( 0    0    1) 
                
Which produces a shearing along x that is proportional to y:

 x' = x + SHx * y
 y' = y
 1 = 1

Y-Direction Shear is given by the following matrix:

(1    SHy   0)     
(0     1    0)   
(0     0    1)


                        (1  SHy   0)
(x' y' 1) = ( x y 1)  * (0   1    0)
                        (0   0    1) 
     
Which produces a shearing along y that is proportional to x:

x' = x 
y' = x * SHy + y
1=1

shear的过程中x和y中一定有一个是保持不变的。

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3. So if you have a location on the object which is say the center of mass plus some displacement,rotating that is equivalent to rotating the center of mass and then rotating the displacement.

旋转是线性操作，在2D中是可以交换的，但在3D中不可以。

旋转的矩阵表达可以通过极坐标系进行推理。