Expand fill of convex polygon

Question

I have a convex polygon P1 of N points. This polygon could be any shape or proportion (as long as it is still convex).

I need to compute an

Answer 1

For each line segment of the original, find the midpoint m and (unit length) outward normal u of the segment. The corresponding segment of the expanded polygon will then lie on the line through m+n*u (where you want to expand the original by n) with normal u. To find the vertices of the expanded polygon you then need to find the intersection of pairs of successive lines.