*Kerry Millen*

The traditional method is to use barycenter coordinates (Example 1). By using parameterized triangle line segments, an interpolated point may be found (Example 2).

Platform: .NET Framework 1.1+

(Example 1) private Point getPointBaryCenter(Point p1, Point p2, Point p3) { return new Point((p1.X + p2.X + p3.X) / 3, (p1.Y + p2.Y + p3.Y) / 3); } (Example 2) private Point getInterpPt(Point p1, Point p2, Point p3) { return new Point((p1.X >> 1) + ((p2.X + p3.X) >> 2), (p1.Y >> 1) + ((p2.Y + p3.Y) >> 2)); } An explanation of how this works follows. (p1, p2, and p3 are points of a triangle) Get an interpolated pt some distance (t) between p1 and p2 and call it p12. t is any number > 0 and < 1 p12 = p1 + t * (p2 - p1) Get an interpolated pt some distance (t) between p1 and p3 and call it p13. p13 = p1 + t * (p3 - p1) Get an interpolated pt some distance (t) between p12 and p13 and call it pT. (if 0 < t < 1, this point must be inside the triangle) pT = p12 + t * (p13 - p12) Substitute 0.5 for t and reduce (t can be any value). 0.5 * p1 + 0.25 * (p2 + p3) (p1 >> 1) + ((p2 + p3) >> 2) My evaluation of this method found it to be between 2.5% and 4.4% faster than the barycenter method.

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