任意三角形网格的基于二元四次箱样条分片C^1曲面(英文)

Piecewise C^1 Surfaces Based on Bivariate Quartic Box-Splines for Arbitrary Triangular Meshes

提出一种以任意三角剖分为控制网格的二元箱样条曲面算法.二元三方向剖分是方向最少的三角剖分,建立在其上的二元三向四次箱样条在CAGD等领域有着广泛的应用.其规范的箱样条曲面计算仅适用于控制点的价数均为6的网格.从规范的算法出发,提出了一种任意价数控制网格的曲面计算算法,并对算法的连续性等进行了详细的分析.生成的曲面具有保凸性,且是分片C1连续的.该算法可进行3D离散点全局或局部插值,并可应用于3D曲面重构等领域.

For arbitrary triangular control meshes, a surface algorithm based-on bivariate box-spline is developed. Bivariate 3-direction is a triangulation with the least directions. Box spline built on it is widely applied in CAGD. Its standard surface algorithm is only for normal control mesh in which every point has valence 6. Starting with bivariate 3-directional quartic box-splines, the paper proposes an algorithm for arbitrary triangular control meshes. The analysis of its properties especially continuity are presented in detail. The constructed surfaces by the algorithm are convex preserving, and they are piecewise C^1. The algorithm can be easily applied for global or local interpolation, which is indispensable in 3D surface reconstruction from scattered points.