3个平面的三维交点 - C＃ [英] Point of intersection of three planes 3D - C#

问题描述

有没有人有任何C＃算法找到交集的三个平面（每个面由三个点定义的点：（X1，Y1，Z1），（X2，Y2，Z2），（X3，Y3，Z3）每个平面的不同）。 斧+由+ CZ + D = 0 ，其中：

Does anyone have any C# algorithm for finding the point of intersection of the three planes (each plane is defined by three points: (x1,y1,z1), (x2,y2,z2), (x3,y3,z3) for each plane different). The plane defined by the equation: ax + by + cz + d = 0, where:

A = y1 (z2 - z3) + y2 (z3 - z1) + y3 (z1 - z2)

B = z1 (x2 - x3) + z2 (x3 - x1) + z3 (x1 - x2)

C = x1 (y2 - y3) + x2 (y3 - y1) + x3 (y1 - y2)

D = -(x1 (y2 z3 - y3 z2) + x2 (y3 z1 - y1 z3) + x3 (y1 z2 - y2 z1))

非常感谢你！

Thank you very much!

推荐答案

这是相当繁琐的，因为在许多情况下，飞机可以是平行的或在一些配置中，它们不相交于一点。

It's quite fiddly because in many cases the planes can be parallel or in some configuration where they don't intersect at a single point.

然而，当他们这样做，该公式可以在这里找到：

However, when they do, the formula can be found here:

http://geomalgorithms.com/a05-_intersect-1.html

我宁愿认为这是不够的信息，为您;但也许这将让你开始。

I rather think that won't be enough information for you; but maybe it will get you started.

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