MODELING WITH CUBIC A-PATCHES

被引：58

作者：

BAJAJ, CL

CHEN, JD

XU, GL

机构：

[1] Department of Computer Sciences, Purdue University, West Lafayette

来源：

ACM TRANSACTIONS ON GRAPHICS | 1995年 / 14卷 / 02期

关键词：

ALGORITHMS; ALGEBRAIC SURFACES; COMPUTER-AIDED GEOMETRIC DESIGN; FREEFORM SURFACE; GEOMETRIC CONTINUITY;

D O I：

10.1145/221659.221662

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We present a sufficient criterion for the Bernstein-Bezier (BB) form of a trivariate polynomial within a tetrahedron, such that the real zero contour of the polynomial defines a smooth and single-sheeted algebraic surface patch. We call this an A-patch. We present algorithms to build a mesh of cubic A-patches to interpolate a given set of scattered point data in three dimensions, respecting the topology of any surface triangulation T of the given point set. In these algorithms we first specify ''normals'' on the data points, then build a simplicial hull consisting of tetrahedra surrounding the surface triangulation T, and finally construct cubic A-patches within each tetrahedron. The resulting surface constructed is C-1 (tangent plane) continuous and single sheeted in each of the tetrahedra. We also show how to adjust the free parameters of the A-patches to achieve both local and global shape control.

引用

页码：103 / 133

页数：31

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