Smooth spline surfaces over irregular meshes

ABSTRACT

An algorithm for creating smooth spline surfaces over irregular meshes is presented. The algorithm is a generalization of quadratic B-splines; that is, if a mesh is (locally) regular, the resulting surface is equivalent to a B-spline. Otherwise, the resulting surface has a degree 3 or 4 parametric polynomial representation. A construction is given for representing the surface as a collection of tangent plane continuous triangular Be´zier patches. The algorithm is simple, efficient, and generates aesthetically pleasing shapes.

REFERENCES

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Curve, surface, solid, and object representations

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.2 Approximation
          Subjects: Spline and piecewise polynomial approximation

  J. Computer Applications
  J.6 COMPUTER-AIDED ENGINEERING
      Subjects: Computer-aided design (CAD)

General Terms:
Theory, Verification

Keywords:
B-spline surfaces, arbitrary topology, computer-aided geometric design, geometric continuity, irregular meshes, triangular patches