### Plane Normal and Points on Plane

Question: I have an origin point and a normal vector and wish to determine three points to create a reference plane. How can I calculate the third point using normal and origin?

Answer: This is very elementary geometry. If you have an origin point and a normal vector, you can easily calculate three points in a plane. Conversely, if you have three points in a plane, it is easy to calculate the normal vector.

Let 'x' denote the vector cross product.

Given an origin point P and a normal vector N:

• Select an arbitrary vector V that is not collinear with N, e.g. the X or Y axis.
• Set U = N x V to obtain a vector that is perpendicular to N.
• Set V = N x U to obtain another vector perpendicular to both N and V.
• Set Q = P + U and R = P + V to obtain three points P, Q and R in the plane.

Given three points P, Q and R in the plane:

• Set V = Q - P and W = R - P to obtain two perpendicular vectors in the plane.
• Set N = V x W to obtain the plane normal.

I published a number of posts demonstrating this. The most useful ones for you might be the ones describing the GetCurveNormal method: