Point of intersection of three planes 3D - C#

问题

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))

Thank you very much!

回答1:

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.

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

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

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

来源：https://stackoverflow.com/questions/14981410/point-of-intersection-of-three-planes-3d-c-sharp