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neochaojin
2025-02-24 16:53:23 +08:00
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commit e5181f6061
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docs/note/graphics/math/transform_04.md
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@@ -188,8 +188,11 @@ $$
$$ $$
一般来说，当针对一个空间点做矩阵转换时，如果$\boldsymbol{M}[u_x, u_y, u_z, 1]^T=[v_x,v_y,v_z,1]^T$，那么 一般来说，当针对一个空间点做矩阵转换时，如果$\boldsymbol{M}[u_x, u_y, u_z, 1]^T=[v_x,v_y,v_z,1]^T$，那么
$$ $$
(k\boldsymbol{M})[u_x, u_y, u_z, 1]^T=k[v_x,v_y,v_z,1]^T=[kv_x,kv_y,kv_z,k]^T=[v_x,v_y,v_z,1]^T \begin{aligned}
$$ (k\boldsymbol{M})[u_x, u_y, u_z, 1]^T&=k[v_x,v_y,v_z,1]^T\\
&=[kv_x,kv_y,kv_z,k]^T\\
&=[v_x,v_y,v_z,1]^T
\end{aligned}$$
可知$k\boldsymbol{M}$在针对空间点转换矩阵中等同于$\boldsymbol{M}$，所以为了表达方便，经常将上面得到的这个矩阵乘以-1，得到 可知$k\boldsymbol{M}$在针对空间点转换矩阵中等同于$\boldsymbol{M}$，所以为了表达方便，经常将上面得到的这个矩阵乘以-1，得到
$$ $$
\boldsymbol{M}_{\text{persp}\rightarrow\text{ccv}}=\begin{bmatrix} \boldsymbol{M}_{\text{persp}\rightarrow\text{ccv}}=\begin{bmatrix}