Interpolation by geometric algorithm

Takashi Maekawa*, Yasunori Matsumoto, Ken Namiki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

85 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)313-323
Number of pages11
JournalCAD Computer Aided Design
Issue number4
Publication statusPublished - 2007 Apr
Externally publishedYes


  • B-spline curves and surfaces
  • Catmull-Clark subdivision surface
  • Geometric algorithm
  • Geometric modeling
  • Loop subdivision surface
  • Surface interpolation

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering


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