# Geometric Scaling of a Triangle

Expanding or shrinking a polygon board outline is a common but mathematically intensive task. Any polygon can be divided into a number of triangles, which can be individually scaled.To use this calculator enter 3 adjacent points from a polygon, and the center point will be the projected point of the new polygon. This also calculates the segment lengths and angles of the original triangle.

The algorithm uses the law of cosines to compute the angles of the original triangle. It also computes the angles for lines which bisect each angle, by averaging the angles of the two adjacent segments. Using a little trig it computes the distance from the old point to the new point. This distance with the bisecting angle is sufficient to compute the (x,y) differential to the new point. The differential is added to the old coordinate location to generate the new one.

 Points of Original Triangle Expansion Point 1 , (x,y) Point 2 , (x,y) Point 3 , (x,y) Lengths L1, L2, L3 Angles a1, a2, a3 Point 1B , (x,y) Point 2B , (x,y) Point 3B , (x,y)