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We present a method for using ray tracing to render spline surfacesÂ¿one that is suitable for any object generated from control vertices via tensor-product B-splines. The method derives from kajiya's work on ray tracing procedurally defined surfaces1 and makes use of two preprocessing steps. One involves the controlvertex refinement recurrences due to Riesenfeld et. al.2, and the second generates a tree of nested bounding boxes. Intersection testing involves running Kajiya's algorithm on the tree, followed by two to three (on the average) iterations of Newton's method.