An Investigation Of Recurrent Surfaces On Triangular Mesh

Surfaces on triangular mesh have drawn wide attention as an important form ofmathematical description of geometric configuration in CAGD. The triangularsurface modeling can not only solve the modeling problem of the complex productwith irregular shapes and surfaces effectively, but also serve as the foundation ofinterpolating surface on scattered data. Meanwhile, the modeling method ofrecurrence scheme is an excellent modeling tool with many special advantages.Under certain restricted conditions, some recursive curves and surfaces areequivalent to the Bézier and B-spline curves and surfaces. The generalizedrepresentation of recursive schemes are also useful in unifying the data formatting.So, the modeling of recurrent surfaces on triangular mesh can provide a new way ofthinking in the field of CAGD by making use of their advantages.The purpose of this dissertation is to investigate a specified recurrence surfaceon triangular mesh——L\W surface on triangular mesh. The main contents of thisdissertation are outlined as follows.1. The properties of L\W curves are discussed, the equivalence relationshipbetween L\W curves and some frequently-used curves are brought to light, andthe properties of L\W surfaces in rectangle region are also expounded.2. The constructing of recurrence surfaces on triangular mesh is analyzed, L\Wsurfaces in triangular region are defined and their properties are given, and themethod of constructing the L-surfaces and W-surfaces in triangular region isalso discussed.3. The rational form of L\W surfaces on triangular mesh and their properties aregiven, the method of constructing the L\W surfaces and the equivalencerelationship between L\W surfaces and B-B surfaces are presented, and theinfluence of weight factors is analyzed.4. The problem of smooth connection is taken into consideration, the conditionsof smooth connection by means of directional derivatives are discussed, and theconditions ofG1-connection between B-B surfaces are given.