Patent ID: 7362326

Claim:
An apparatus for determining a convex hull of a convex hull formed by two convex polygons having congruent corresponding angles with the same orientation, comprising: a processing unit; memory for storing computer executable instructions; a vertex identification module that identifies each vertex of a first convex polygon in series about a perimeter of the first convex polygon; a line connection module that, for each vertex in the first convex polygon, identifies a corresponding vertex in a second convex polygon, each angle in the second convex polygon being congruent to a corresponding angle in the first convex polygon and oriented in a same direction as the corresponding angle in the first convex polygon; defines a line between the vertex in the first convex polygon and the corresponding vertex in the second convex polygon; determines if both an immediately preceding vertex and an immediately subsequent vertex both fall on a same side of the defined line; and if both the immediately preceding vertex and the immediately subsequent vertex fall on the same side of the defined line, determines that a line connecting the vertex in the first polygon to the corresponding vertex in the second polygon lies on perimeter of a convex hull of the polygons; and a convex hull determination module that determines the convex hull to be portions of each of the first convex polygon and the second convex polygon connected by two of the determined connecting lines, such that the two of the determined connecting lines are connected to different vertices of the first convex polygon and the second convex polygon.