作为组合剪切矩阵的基本转换? [英] Shear Matrix as a combination of basic transformation?

问题描述

我知道旋转，缩放，平移等的变换矩阵.我也知道剪切变换的矩阵.现在，我需要剪切矩阵-

I know the transformation matrices for rotation, scaling, translation etc. I also know the matrix for shear transformation. Now, I need to have the shear matrix--

[1 Sx 0]
[0 1  0]
[0 0  1]

其他上述转换形式的组合.尝试搜索，尝试过集思广益，但无法罢工！谢谢！

in the form of a combination of other aforesaid transformations. Tried searching, tried brainstorming, but unable to strike! Thanks!

推荐答案

对于剪切角theta的x剪切操作将旋转和缩放比例减小为 如下:

The x-shear operation for a shearing angle thetareduces to rotations and scaling as follows:

(a)逆时针旋转theta/2.

(b)用x-scaling factor = sin(theta/2)和y-scaling factor = cos(theta/2)缩放.

(c)顺时针旋转45 degree.

(d)用x-scaling factor = sqrt(2)/sin(theta)和y-scaling factor= sqrt(2)缩放.

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