Triangle Surface Modeling Algorithm Via Blending

This thesis focuses on the curve and surface modeling problem in CAGD/CAM field. Using the so-called blending approach, we discuss some triangle surface modeling techniques, including the techniques of the quadratic polynomial blending surface based on the triangular, the methods of quadratic triangular Bezier blending surface, and the cubic triangular Bezier blending surface.In this paper, we first review the research history, classification, and significance of the free-form curve and shape modeling. Then we discuss some key technologies in the recent triangular-based of CAGD field, and give motivation and research significance of triangle surface modeling via blending approach.We discuss a quadratic polynomial-based triangular blending surfaces modeling, and give the G0,G1 continuity blending scheme. With these blending formats, the blending surface can reach the G0,G1 continuity.Then, we discuss the quadratic of Triangular Bezier blending surfaces, and introduce two different ways to design the blending surfaces in the special definition of regional. The proposed triangular Bezier surface blending scheme can reach the G1 continuity without any continuity conditions.After much analysis, we introduce a way to construct the cubic triangle Bezier blending surfaces with a parameter using two cubic triangular Bezier patches. The blending surfaces can reach the G1 continuity. And the introduced parameter "k" can control the shape of the cubic triangular Bezier blending surface.