# 圖學

> ## 圖學 \#
>
> 應該是啦... 不是就算了 \[毆]

## transform matrix

參考資料：<https://www.siggraph.org/education/materials/HyperGraph/modeling/mod_tran/2dconc.htm>

* Scale：`Sx` 為 x 軸倍率，`Sy` 為 y 軸倍率

  ```
    | Sx    0   0 |
    |  0   Sy   0 |
    |  0    0   1 |
  ```
* Rotate：`a` 為旋轉弳度

  ```
    |  cos(a)   sin(a)   0 |
    | -sin(a)   cos(a)   0 |
    |       0        0   1 |
  ```
* Translate（移動）：`Tx` 為 x 軸移動量，`Ty` 為 y 軸移動量

  ```
    |  1    0   0 |
    |  0    1   0 |
    | Tx   Ty   1 |
  ```

### 組合技

如果需要一次（依序）做多個 transform，就（依序）對多個 transform matrix 做矩陣乘法。 注意：矩陣乘法沒有交換律。

* 原地選轉：

  ```
    |                       cos(a)                         sin(a)   0 |
    |                      -sin(a)                         cos(a)   0 |
    | Tx(1 - cos(a)) + Ty * sin(a)   Ty(1 - cos(a)) - Tx * sin(a)   1 |
  ```

  1. 移動到原點
  2. 旋轉
  3. 移動回原始位置


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