In the divide-and-conquer algorithm for detecting intersections of parametric rational Bézier curves (surfaces), we use bounding boxes in recursive rough checks. In this paper, we replace the conventional bounding box with a homogeneous bounding box, which is projectively defined. We propose a new rough check algorithm based on it. One characteristic of the homogeneous bounding box is that it contains a rational Bézier curve (surface) with weights of mixed signs. This replacement of the conventional bounding box by the homogeneous one does not increase the computation time.
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Yamada, A., Yamaguchi, F. Homogeneous bounding boxes as tools for intersection algorithms of rational bézier curves and surfaces. The Visual Computer 12, 202–214 (1996). https://doi.org/10.1007/BF01782323
- Computer graphics
- Rational Bézier curves and surfaces
- Intersection detection
- Projective spaces