Robust and numerically stable Bézier clipping method for ray tracing NURBS surfaces

Abstract

Raytracing has become a popular method for generating realistic images and movies. The progress in hardware development shows that the real time raytracing on a single PC might be possible in the ongoing future. Obviously, that new generation of raytracing based applications will require more visualization precision and flexibility. Most of the modern raytracing based applications only deal with triangles as basic primitives, which brings limitations to an application and may cause visual artifacts to appear. NURBS surface representation is common for most of 3D modeling tools because of its compactness and useful geometric properties of NURBS surfaces. Using the direct raytracing NURBS surfaces, one can achieve better quality of rendered images. Although, many such approaches have already been presented, almost all of them suffer from numerical problems or do not work in some special cases. This paper presents a modified Bézier clipping method for finding ray -NURBS surface intersection points, which is fast, robust, and numerically stable.

Direct Isosurface Visualization of Hex-Based High-Order Geometry and Attribute Representations

“…While Bézier clipping is an elegant way to visualize Bézier surfaces, it has problems at silhouette pixels. A discussion of its problems and proposed solutions can be found in [11]. Once these pairs of entry and exit points are computed, a numerical root-solving technique, such as the NewtonRaphson method or bisection method, is applied to f i ðtÞ for each pair.…”

An Border-Stable Approach to NURBS Surface Rendering for Ray Tracing

“…NURBS surface representation is common for most of 3D modelling tools because of its compactness and the useful geometric properties of NURBS surfaces. Using the direct ray tracing of NURBS surfaces, one can achieve better quality of rendered images [1]. There are many approaches to solving this problem.…”

“…Efremov, V. Havran and H.P. Seidel [1] and [2] proposed the method for NURBS surface visualization in ray tracing using following method: object's every NURBS surface is transformed into equivalent rational set of Bezier surface and exactly this set is mapped. To solve rational Bezier surface problem Bezier cutting method, that is described in [7], is used.…”

“…To solve rational Bezier surface problem Bezier cutting method, that is described in [7], is used. And, also [1] and [2] proposes some modifications that improve the activity and effectiveness of Bezier cutting method.…”

Quality control automated laser-ultrasonic method for solder joints of nozzles of chambers in liquid rocket engines

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