Add design shear

content/atlas.md

@@ -32,6 +32,8 @@ date: 2024-02-28
 
 * [Code Framework Learn](computer_sci/code_frame_learn/MOC.md)
 
+* [Design](design/design_moc.md)
+
 🦺 I also need some tool to help me:
 
 * [Git](toolkit/git/git_MOC.md)

content/design/design_moc.md

@@ -0,0 +1,10 @@
+---
+title: Design - MOC
+tags:
+  - MOC
+  - design
+date: 2024-03-22
+---
+# Transform
+
+* [Shear](design/transform/shear.md)

content/design/transform/shear.md

@@ -0,0 +1,74 @@
+---
+title: Shear
+tags:
+  - basic
+  - "#design"
+date: 2024-03-22
+---
+
+# Detail
+
+在二维图像处理中，shear操作是指将图像沿水平或垂直方向进行**错切**，从而改变图像的形状。shear操作可以用仿射变换矩阵来表示，如下所示为一个Horizontal Shear：
+
+$$
+\begin{bmatrix}
+1 & \tan(\theta) \\
+0 & 1
+\end{bmatrix}
+$$
+$$
+\begin{bmatrix}
+x' \\
+y'
+\end{bmatrix} = 
+\begin{bmatrix}
+x + my \\
+y
+\end{bmatrix} = 
+\begin{bmatrix}
+1 & m \\
+0 & 1 \\
+\end{bmatrix} 
+\begin{bmatrix}
+x \\
+y
+\end{bmatrix}
+$$
+
+上述矩阵的效果如图：
+
+![](design/transform/attachments/Pasted%20image%2020240322111022.png)
+
+同时还有Vertical Shear
+
+
+$$
+\begin{bmatrix}
+1 & 0 \\
+\tan(\theta) & 1
+\end{bmatrix}
+$$
+$$
+\begin{bmatrix}
+x' \\
+y'
+\end{bmatrix} = 
+\begin{bmatrix}
+x \\
+mx + y
+\end{bmatrix} = 
+\begin{bmatrix}
+1 & 0 \\
+m & 1 \\
+\end{bmatrix} 
+\begin{bmatrix}
+x \\
+y
+\end{bmatrix}
+$$
+![](design/transform/attachments/Pasted%20image%2020240322111458.png)
+
+
+# Reference
+
+* https://en.wikipedia.org/wiki/Shear_mapping