An Algorithm for Rendering Vertexes and Edges of Polyhedron with High Order Geometric Continuity

摘要

The surface rendering for simultaneously connecting with several neighboring surfaces with high order geometric continuous is quite complicated in the computer graphics and CAGD. This paper proposed a new simple geometric algorithm for generating and rendering the smooth connecting surfaces for the vertexes and edges of the polyhedron. The rectangular Bezier surfaces are generated to connect the two adjacent planes, and the triangular Bezier surfaces are generated to connect its several neighboring surfaces with high order geometric continuity. The control net points of the connecting surfaces are calculated by the geometric drawing method according to the geometric continuity connection condition or the share common plane condition. All the surfaces and planes can be connected smoothly with G~2 geometry continuity in the polyhedron. The algorithm can be popularized to the situation of higher order geometric continuous connection easily.