Research On Triangular Bézier Surface Subdivisional Programme

In the applications of geometric modeling based on triangular patches, in order to meet the needs of the complexity of model surfaces'shape and make storage and data interchange much easier, the study on the subdivision of triangular surface is paid much attention to in recent years. However, triangular surface is not the tensor product surface, and general methods for subdivision of curve and surface are difficult to be applied to triangular patches directly. The research on subdivision of triangular surface is relatively not much. So the efficient subdivision algorithm needs further studies, especially, the study of triangular surfaces subdivision by means of structure new function has never seen before.This thesis investigates the smooth joining of triangular surfaces, particularly the subdivision of triangular Bézier surface, and proposes a subdivision algorithm of triangular Bézier surface. The algorithm subdivides triangular Bézier surface by structuring a new tensor product named duality Bernstein function. It is proved that the new triangular Bézier surface converges to the former triangular Bézier surface, and that the blossom algorithm is more effective than structuring new function on the subdivision of triangular surface. The experiment manifests the algorithm is practicable and effective. Based on this, a study on GC1 smooth joining condition about the two new triangular Bézier surfaces by duality Bernstein function is conducted. The GC1 smooth joining condition only has relations with the points on commonality boundary and the second line control vertices on boundary which are new points.Finally, a summary of this thesis is given as well as the possible new directions of the subdivision of triangular surface.