Question

im trying to make a hole into a triangle in 3D space using XNA.
I want to convert this problem to 2D space.
But i dont know how to rotate the triangle that all the points have Z = 0.
Point1 has the coordinats X=0,Y=0,Z=0.
Anyone know a solution?
LG
Jens

Answer 1

Given P1, P2, P3 the points of the triangle.

Let’s note:

• a = P2 - P1
• b = P3 - P1
• n = Vector3.CrossProduct(a, b).Normalized() -> n is the normal of the triangle

The triangle is in the Z = 0 plane if and only of, n.z = 0
Then, just use:

• d = Vector3.CrossProduct(n, z).Normalized() -> it is the axis of your rotation
• angle = (float)System.Math.Acos(Vector3.DotProduct(n, z)) -> it is the angle of your rotation

The code is:

Vector3 a = P2 - P1;
Vector3 b = P3 - P1;
Vector3 n = Vector3.Cross(a, b);
n.Normalize();
Vector3 d = Vector3.Cross(n, Vector3.UnitZ);
d.Normalize();
float angle = (float)System.Math.Acos(Vector3.Dot(n, Vector3.UnitZ));

Vector3 newpoint2 = P1 + Vector3.Transform(a, Matrix.CreateFromAxisAngle(d, angle));
Vector3 newpoint3 = P1 + Vector3.Transform(b, Matrix.CreateFromAxisAngle(d, angle));