Coons Surface Reconstruction Through Bézier Triangular Geodesic Network

Surface reconstruction on triangular domain plays an important role in CAGD,CG and free-form surface modeling.In this paper,we study the reconstruction of Coons surface through Bézier triangular geodesic network.The Bézier triangular geodesic network includes triangular geodesic,triangular geodesic network around a point and triangular geodesic network with arbitrary topology.In the problem of Coons surface reconstruction through Bézier triangular geodesic,the necessary and sufficient conditions and a class of sufficient conditions for the three curves to be a geodesic on the surface are given,and the compatibility constraints of tangent vector and torsion vector at the corners of triangular geodesic are analyzed.Based on the rational Hermite polynomial basis represented by barycentric coordinates,three interpolation operators with two adjacent boundary lines as geodesics are designed.On this basis,four Coons surface construction schemes with interpolating three curves as surface boundary geodesic are given.In the Coons surface reconstruction through Bézier triangular geodesic network around a point,the intersection geodesic constraint and vertex surrounding constraint of Bézier triangular geodesic network around a point are discussed.By using the reconstruction method of Coons surface patches through triangular geodesic,the combined Coons surface interpolation three curves network is designed as triangular geodesic network.The three curves network with Coons surface interpolation for arbitrary topological structure is designed as triangular geodesic network.The innovation of this paper is mainly reflected in two aspects.First,the necessary and sufficient conditions and a class of sufficient conditions for three curves to be a surface geodesic are given.Second,four formats of interpolation surface construction are designed.These formats combine Hermite basis based on barycentric coordinate representation and Coons method.The construction is simple and easy to implement.The constructed surface is in polynomial form,which is compatible with the primary flow CAD system.The interpolation surface constructed in this paper has good applicability and application prospect.