Projective transformations of the parameter of a Bernstein-Bézier curve

ABSTRACT

The definitions of polynomial and rational Bernstein-Bézier curves are reviewed and extended to include homogeneous parametrizations. Then the effects of a projective transformation of the parameter space are described in terms of a group representation. This representation is used to answer the following questions: (1) If the control points are held fixed, when do two different sets of weights determine the same rational curve? (2) How do we find the control points for a subdivision of the original curve?

REFERENCES

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INDEX TERMS

Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.2 Nonnumerical Algorithms and Problems
          Subjects: Geometrical problems and computations

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

General Terms:
Design, Theory