用于计算左手坐标的叉积变化的方法？ [英] Does the method for computing the cross-product change for left handed coordinates?

问题描述

用于计算左手坐标的叉积变化的方法是什么？

解决方案

向量（x1，x2，x3）和（y1​​，y2，y3）是

  z1 = x2 * y3  -  x3 * y2 
 z2 = x3 * y1  -  x1 * y3 
 z3 = x1 * y2  - x2 * y1 
  

它被设计成三个向量 x ， y 和 z 具有与坐标系本身相同的旋向性。该属性不依赖于坐标系的旋向性 - 对于左手坐标系，矢量满足左手规则。你不需要改变公式的任何内容。

有用的链接：

• Righthanded和Lefthanded坐标系统和交叉产品
>

• 维基百科文章中的相关部分

Does the method for computing the cross-product change for left handed coordinates?

解决方案

The formula for the cross product of the vectors (x1, x2, x3) and (y1, y2, y3) is

z1 = x2 * y3 - x3 * y2
z2 = x3 * y1 - x1 * y3
z3 = x1 * y2 - x2 * y1

It is designed in a way that the three vectors x, y and z in the given order have the same handedness as the coordinate system itself. This property does not depend on the handedness of the coordinate system -- for a left-handed coordinate system the vectors fulfil the left-hand rule. You don't need to change anything about the formula.

Useful links:

• Righthanded and Lefthanded Systems of Coordinates and the Cross Product
• Relevant section from the Wikipedia article

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