Interpolation by geometric algorithm

被引：79

作者：

Maekawa, Takashi ^{[1
]}

Matsumoto, Yasunori ^{[1
]}

Namiki, Ken ^{[1
]}

机构：

[1] Yokohama Natl Univ, Dept Mech Engn, Yokohama, Kanagawa 2408501, Japan

来源：

COMPUTER-AIDED DESIGN | 2007年 / 39卷 / 04期

基金：

日本学术振兴会;

关键词：

geometric algorithm; surface interpolation; loop subdivision surface; Catmull-Clark subdivision surface; B-spline curves and surfaces; geometric modeling;

D O I：

10.1016/j.cad.2006.12.008

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We present a novel geometric algorithm to construct a smooth surface that interpolates a triangular or a quadrilateral mesh of arbitrary topological type formed by n vertices. Although our method can be applied to B-spline surfaces and subdivision surfaces of all kinds, we illustrate our algorithm focusing on Loop subdivision surfaces as most of the meshes are in triangular form. We start our algorithm by assuming that the given triangular mesh is a control net of a Loop subdivision surface. The control points are iteratively updated globally by a simple local point-surface distance computation and an offsetting procedure without solving a linear system. The complexity of our algorithm is O(mn) where n is the number of vertices and at is the number of iterations. The number of iterations m depends on the fineness of the mesh and accuracy required. (c) 2007 Elsevier Ltd. All rights reserved.

引用

页码：313 / 323

页数：11

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