Determining the convex hull of convex polygons with congruent corresponding angles

摘要

The convex hull of two polygons having congruent corresponding angles with the same orientation can be determined by analyzing the relationship of each vertex of one of the polygons relative to its adjacent vertices. More particularly a line may be defined between a selected vertex on one of the polygons and its corresponding vertex on the other polygon. If the vertices adjacent to the selected vertex both fall on the same side of the line, then a line connecting the selected vertex with its corresponding vertex lies on the convex hull of the two polygons. If, on the other hand, the vertices adjacent to the selected vertex are located on different sides of the line, then the line connecting the selected vertex with its corresponding vertex does not lie on the convex hull.