# Interpolation by geometric algorithm

Takashi Maekawa, Yasunori Matsumoto, Ken Namiki

62 引用 (Scopus)

### 抄録

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 (m n) where n is the number of vertices and m is the number of iterations. The number of iterations m depends on the fineness of the mesh and accuracy required.

元の言語 English 313-323 11 CAD Computer Aided Design 39 4 https://doi.org/10.1016/j.cad.2006.12.008 Published - 2007 4 1 Yes

### Fingerprint

Subdivision Surfaces
Geometric Algorithms
Interpolation
Interpolate
Triangular
Mesh
Iteration
B-spline Surface
Triangular Mesh
Smooth surface
Control Points
Linear Systems
Arbitrary
Splines
Linear systems

### ASJC Scopus subject areas

• Computer Graphics and Computer-Aided Design
• Industrial and Manufacturing Engineering
• Geometry and Topology

### これを引用

Interpolation by geometric algorithm. / Maekawa, Takashi; Matsumoto, Yasunori; Namiki, Ken.

：: CAD Computer Aided Design, 巻 39, 番号 4, 01.04.2007, p. 313-323.

Maekawa, Takashi ; Matsumoto, Yasunori ; Namiki, Ken. / Interpolation by geometric algorithm. ：: CAD Computer Aided Design. 2007 ; 巻 39, 番号 4. pp. 313-323.
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