A Generic Approach to Free Form Surface Generation

[+] Author and Article Information
J. Cotrina-Navau

Dept. de Telemàtica, Universitat Polytecnica de Catalunya, Spain e-mail: jcotrina@mat.upc.es

N. Pla-Garcia, M. Vigo-Anglada

Dept. de Lleng. i Sist. Informàtics, Universitat Politecnica de Catalunya, Spain

J. Comput. Inf. Sci. Eng 2(4), 294-301 (Mar 26, 2003) (8 pages) doi:10.1115/1.1559579 History: Received September 01, 2002; Revised January 01, 2003; Online March 26, 2003
Copyright © 2002 by ASME
Your Session has timed out. Please sign back in to continue.


Catmull,  E., and Clark,  J., 1978, “Recursively Generated b-spline Surfaces on Arbitrary Topological Meshes,” Comput.-Aided Des., 10(6), pp. 350–355.
Doo,  D., and Sabin,  M., 1978, “Behavior of Recursive Division Surfaces Near Extraordinary Points,” Comput.-Aided Des., 10(6), pp. 356–360.
Loop,  C., and DeRose,  T., 1989, “A Multisided Generalization of Bézier Surfaces,” ACM Trans. Graphics, 8(3), pp. 204–234.
Seidel,  H., 1991, “Symmetric Recursive Algorithms for Surfaces: B-patches and the de Boor Algorithm for Polynomials Over Triangles,” Constructive Approx., 7 , pp. 257–279.
Gregory,  J., and Zhou,  J., 1994, “Filling Polygonal Holes with Bicubic Patches,” Computer Aided Geometric Design, 11 , pp. 391–410.
Loop,  C., 1994, “A G1 Triangular Spline Surface of Arbitrary Topological Type,” Computer Aided Geometric Design, 11 , pp. 303–330.
Peters,  J., 1995, “Biquartic C1-surface Splines Over Irregular Meshes,” Comput.-Aided Des., 27(12), pp. 895–903.
Rief,  U., 1995, “Biquadratic g-Spline Surfaces,” Computer Aided Geometric Design, 12 , pp. 193–205.
Sederberg, T., Zheng, J., Sewell, D., and Sabin, M., 1998, “Non Uniform Recursive Subdivision Surfaces,” Proceedings of SIGGRAPH’98, pages 387–394.
Zheng,  J., Wang,  G., and Liang,  Y., 1992, “Curvature Continuity Between Adjacent Rational Bézier Patches,” Computer Aided Geometric Design, 9 , pp. 312–335.
Zheng,  J., Wang,  G., and Liang,  Y., 1995, “GCn Continuity Conditions for Adjacent Rational Parametric Surfaces,” Computer Aided Geometric Design, 12 , pp. 111–129.
Höllig,  K., and Mögerle,  H., 1990, “G-splines,” Computer Aided Geometric Design, 7 , pp. 197–207.
Prautzsch,  H., 1997, “Freeform splines,” Computer Aided Geometric Design, 14 , pp. 201–206.
Grimm, C., and Hughes, J., 1995, “Modeling Surfaces of Arbitrary Topology Using Manifolds,” SIGGRAPH, pp. 359–368.
Cotrina,  J., and Pla,  N., 2000, “Modelling Surfaces from Planar Irregular Meshes,” Computer Aided Geometric Design, 17 , pp. 1–15.
Cotrina,  J., and Pla,  N., 2000, “Modelling Surfaces of Arbitrary Topology,” Computer Aided Geometric Design, 17 , pp. 643–671.
Cotrina, J., Vigo, M., and Pla, N., 2001, “N-sided Patches with B-spline Boundaries,” Technical Report LSI-01-55-R, Dept. de Lleng. i Sist. Inf., Univ. Politec. de Catalunya, Nov.
Marshall, C., 1971, Applied Graph Theory, Wiley, New York.
White A., 1973, Graphs, Groups and Surfaces, North Holland Publishing Company.
do Carmo, M., 1976, Differential Geometry of Curves and Surfaces, Prentice-Hall, Inc.
Berger, M., and Gostiaux, B., 1988, “Differential Geometry: Manifolds, Curves and Surfaces,” Graduate texts in mathematics, 115. Springer-Verlag.
Floater,  M., 1997, “Parameterization and Smooth Approximation of Surface Triangulations,” Computer Aided Geometric Design, 14 , pp. 231–250.


Grahic Jump Location
Defining the manifold W. (a) The mesh M. (b) The sub-mesh M02. (c) The sub-mesh M12. (d) The charts and the transition function.
Grahic Jump Location
Control points for the same mesh of Fig. 2
Grahic Jump Location
Uniform embedding approach process
Grahic Jump Location
Surfaces obtained applying the uniform embedding approach
Grahic Jump Location
Regular star approach process. (a) Original mesh with some irregular vertices. (b) Preprocessed mesh, where irregular vertices have been isolated. (c) A continuous plane regular star and a transition function ϕ⁁r,lk.
Grahic Jump Location
A nice homeomorphism constructed using the regular star approach
Grahic Jump Location
N-Sided patch approach process. (a) Example of an input mesh surrounding a 5-sided hole. (b) The parametric space defined by the plane mesh for the same example. One of the charts (associated to a face) is drawn.
Grahic Jump Location
A 6-sided and a 5-sided patch obtained using the n-sided patch approach
Grahic Jump Location
Surfaces obtained applying the regular star approach



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In