Computing the padded shape-inside boundary for a polygon is moderately straightforward when the padded boundary is the same shape as the original boundary. In this case all of the edges are simply inset by the shape-padding distance. Edges that meet at a reflex vertex must be connected by a circular arc which we will approximate with a regular polygon segment. The attached screenshot demonstrates this case. As you can see, the intersection of each pair of inset padded edges becomes a vertex of the padded shape, except when the original common vertex was a reflex vertex. In the screenshot the original boundary's reflex vertex is labeled "4" and the approximation to the circular arc that joins inset edges 3-4 and 4-5 is labeled "[4" and "4]".