我想从计算机程序的一个 3D 音量中获取一个随机的 2D 切片, 用于生成噪音 。 我决定使用一个旋转矩阵, 据我理解, 必须是旋转组 SO(3) 的成员。 我如何创建这个组的任意成员?
选择三个随机值 u 1 , u 2 , u 3 0至1之间。
校对:Soup
w = sqrt(1 - u 1 sin(2pi*u 2 )
x = sqrt(1 - u 1 )cos (2pi*u 2 )
y = sqrt (u < sub >1 )sin (2pi*u 3 )
z = sqrt (u < sub >1 )cos (2pi*u 3 )
您可以使用 < a href=> http://www.flipcode.com/documents/matrfaq.html__54" rel="nofollow" 来生成合适的旋转矩阵。 | 2 2 |
| 1 - 2y - 2z 2xy - 2zw 2xz + 2yw |
| |
| 2 2 |
M = | 2xy + 2zw 1 - 2x - 2z 2yz - 2xw |
| |
| 2 2 |
| 2xz - 2yw 2yz + 2xw 1 - 2x - 2y |
| |
您可以绘制随机的 3D 矢量, 由三个独立的随机变量组成组成, 作为每个轴。 然后您可以定义此矢量为您随机的 2D 切片的正常矢量, 以及该 2D 切片与来源的距离。 我非常确定( 虽然没有正式证明), 此方法应该给可能的 2D 切片统一分布( 先前的语句基本上是非正式的 ) 。
编辑 : 第二个想法是, 您也许应该绘制一个独立的变量来表示 2D 切片 与源的距离。 否则, 您将会得到 2D 切片的分布, 而这些切片更有可能在离源的某个距离附近 。
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