I've implemented a Seperating Axis test for two triangles. The test seems to work in all cases, except if the two triangles happen to be on the same plane. For the seprating axis, i'm testing the normals for both triangles, then the 9 axis i get from crossing the sides of the triangles.
My best guess is that because the two triangles lie on the same plane, the cross product of their normals returns a zero vector? But how would you go about fixing that?
Any idea why it would fail only when the triangles are on the same plane? If it's any help, i've attached my code:
public static bool Intersects(Triangle triangle1, Triangle triangle2) {
Vector3 t1_v0 = triangle1.p0.ToVector();
Vector3 t1_v1 = triangle1.p1.ToVector();
Vector3 t1_v2 = triangle1.p2.ToVector();
Vector3 t1_f0 = t1_v1 - t1_v0; // B - A
Vector3 t1_f1 = t1_v2 - t1_v1; // C - B
Vector3 t1_f2 = t1_v0 - t1_v2; // A - C
Vector3 t2_v0 = triangle2.p0.ToVector();
Vector3 t2_v1 = triangle2.p1.ToVector();
Vector3 t2_v2 = triangle2.p2.ToVector();
Vector3 t2_f0 = t2_v1 - t2_v0; // B - A
Vector3 t2_f1 = t2_v2 - t2_v1; // C - B
Vector3 t2_f2 = t2_v0 - t2_v2; // A - C
Vector3[] axisToTest = new[] {
Vector3.Cross(t1_f0, t1_f1),
Vector3.Cross(t2_f0, t1_f1),
Vector3.Cross(t2_f0, t1_f0),
Vector3.Cross(t2_f0, t1_f1),
Vector3.Cross(t2_f0, t1_f2),
Vector3.Cross(t2_f1, t1_f0),
Vector3.Cross(t2_f1, t1_f1),
Vector3.Cross(t2_f1, t1_f2),
Vector3.Cross(t2_f2, t1_f0),
Vector3.Cross(t2_f2, t1_f1),
Vector3.Cross(t2_f2, t1_f2),
};
foreach(Vector3 axis in axisToTest) {
if (!TriangleTriangleSAT(triangle1, triangle2, axis)) {
return false;
}
}
return true;
}
protected static bool TriangleTriangleSAT(Triangle triangle1, Triangle triangle2, Vector3 raw_axis) {
Vector3 axis = Vector3.Normalize(raw_axis);
Vector2 range1 = GetTriangleInterval(triangle1, axis);
Vector2 range2 = GetTriangleInterval(triangle2, axis);
float min1 = range1.X;
float max1 = range1.Y;
float min2 = range2.X;
float max2 = range2.Y;
if (max1 < min2 || max2 < min1) {
return false;
}
/*if (range1.Y < range2.X || range2.Y < range1.X) {
return false;
}*/
return true;
}
protected static Vector2 GetTriangleInterval(Triangle triangle, Vector3 axis) {
Vector3[] vertices = new Vector3[] {
triangle.p0.ToVector(),
triangle.p1.ToVector(),
triangle.p2.ToVector()
};
float min = Vector3.Dot(axis, vertices[0]);
float max = min;
for (int i = 0; i < vertices.Length ; ++i) {
float value = Vector3.Dot(axis, vertices[i]);
min = Min(min, value);
max = Max(max, value);
}
return new Vector2(min, max);
}
