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

• Applied computing

  • Arts and humanities

    • Architecture (buildings)

      • Computer-aided design

  • Physical sciences and engineering

    • Engineering

      • Computer-aided design

• Computing methodologies

  • Computer graphics

    • Shape modeling

      • Parametric curve and surface models

      • Volumetric models

• Mathematics of computing

  • Mathematical analysis

    • Functional analysis

      • Approximation

    • Numerical analysis

      • Computations on polynomials