Homogeneous bounding boxes as tools for intersection algorithms of rational bezier curves and surfaces

In the divide-and-conquer algorithm for detecting intersections of parametric rational Bezier 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 Bezier curve (surface) with weights of mixed signs. This replacement of the conventional bounding box by the homogeneous one does not increase the computation time.