MATLAB: Reflection of a fixed point on a 3D plain.

Question

Suppose we have a plane of the form:

Ax + By + Cz + D = 0,

where the coefficients "A", "B", "C", and "D" are known values.

We also have a known point x

x = [x1 y1 z1 ]

How can I find the point s that is the reflection of point x on the given plane. By reflection I don’t mean mirroring. I mean that the plane works as a boundary condition and point s is on the same side with point x (with regard to the given plane) ?

Answer 1

You have straight line ( vector), intersection point P, normal vector of a plane and you want to find vector

Find cross product of vectors and (axis of rotation)

Calculate angle between and

Use this rotation matrix to rotate your original vector about cross(,)

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