Abstract

In a recent publication on the voxelization of rational curves (Comput. Graphics 27(1) (2003) 83), a difference bound is used to maximize the parameter step, thus speeding up the voxelization. In fact, evaluation of difference bounds has found wide applications in computations of parametric curves and surfaces, as well as in error estimation, in general. While any correctly derived bound can be used for these purposes, a larger bound greatly improves computational efficiency. To respond to the strong interest shown by the graphics community, this short paper proposes very large difference bounds for rational Bézier curves and surfaces. The focus is on the derivation and mathematical proof of the bound evaluation, in the form of two theorems.

Author Keywords: Rational Bézier curves and surfaces; Difference bound; Error estimation

Article Outline

1. Introduction

2. Bound evaluation for rational Bézier curves

3. Bound evaluation for rational Bézier surfaces

4. Conclusion

References

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