四参数转换使用的公式

tk posted @ Feb 24, 2012 09:05:41 AM in 业余 with tags LaTeX Tex , 4118 阅读

设四参数转换尺度为 $k$ ，旋转角为 $\theta$ ，坐标系位移量分别为 $\Delta X$ ， $\Delta Y$ 则单点转换公式为

$\begin{bmatrix} X_1\\Y_1 \end{bmatrix} = \begin{bmatrix} \Delta X\\ \Delta Y \end{bmatrix} + \begin{bmatrix} k \cdot \cos\theta & - k \cdot \sin\theta \\ k \cdot \sin\theta & k \cdot \cos\theta \end{bmatrix} \begin{bmatrix} X_0\\Y_0 \end{bmatrix}$

变换后的矩阵形式为

$\begin{bmatrix} 1&0 & X_0 &-Y_0 \\ 0&1 &Y_0 & X_0 \end{bmatrix} \begin{bmatrix} \Delta X \\ \Delta Y \\ k \cdot \cos\theta \\ k \cdot \sin\theta \end{bmatrix} = \begin{bmatrix} X_1 \\ Y_1 \end{bmatrix}$

这就是类似 $BX=A$ 的平差式

所以可知

$X=\bigl(B^TB\bigr)^{-1}B^TA$

PS:实验下学 $\LaTeX{}$ 怎么写公式

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tisyang 说:
Mar 08, 2012 11:32:08 PM

$LaTeX{}$
For a test

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