I have a 3D Plane defined by two 3D Vectors:
- P = a Point which lies on the Plane
- N = The Plane’s surface Normal
And I want to calculate any vector that lies on the plane.
I have a 3D Plane defined by two 3D Vectors: P = a Point
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I have a 3D Plane defined by two 3D Vectors:
And I want to calculate any vector that lies on the plane.
Take any vector, v, not parallel to N, its vector cross product with N ( w1 = v x N ) is a vector that is parallel to the plane.
You can also take w2 = v – N (v.N)/(N.N) which is the projection of v into plane.
A point in the plane can then be given by x = P + a w, In fact all points in the plane can be expressed as
x = P + a w2 + b ( w2 x N )
So long as the v from which w2 is “suitable”.. cant remember the exact conditions and too lazy to work it out 😉
If you want to determine if a point lies in the plane rather than find a point in the plane, you can use
x.N = P.N
for all x in the plane.