TY - JOUR

T1 - Interpolation by geometric algorithm

AU - Maekawa, Takashi

AU - Matsumoto, Yasunori

AU - Namiki, Ken

N1 - Funding Information:
A portion of this work was supported from the Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research under the grant number 16560116. We wish to thank the following individuals for their help: Jun-ichi Yokoi, Takayuki Sasaki for many helpful discussions, Takuya Maekawa and Masayuki Morioka for proofreading the paper, and Ioana Boier-Martin for providing the heart Catmull–Clark models. The Igea and the Armadillo models are courtesy of Cyberware. The bunny and the laughing buddha models are courtesy of the Stanford University Computer Graphics Laboratory. The fan model is courtesy of INRIA.

PY - 2007/4

Y1 - 2007/4

N2 - 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.

AB - 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.

KW - B-spline curves and surfaces

KW - Catmull-Clark subdivision surface

KW - Geometric algorithm

KW - Geometric modeling

KW - Loop subdivision surface

KW - Surface interpolation

UR - http://www.scopus.com/inward/record.url?scp=34147179068&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34147179068&partnerID=8YFLogxK

U2 - 10.1016/j.cad.2006.12.008

DO - 10.1016/j.cad.2006.12.008

M3 - Article

AN - SCOPUS:34147179068

VL - 39

SP - 313

EP - 323

JO - CAD Computer Aided Design

JF - CAD Computer Aided Design

SN - 0010-4485

IS - 4

ER -