Point projection for Non-Uniform Rational B-Splines (NURBS) surfaces is a fundamental operator in Computer-Aided modeling (CAD) modeling. This operator takes as input a query point and a NURBS surface in ℝ3, and outputs the UV parameter values whose corresponding 3D point (one on the surface) has the minimum distance between the query point and a variable point on the surface. Existing projection methods consistently employ an iterative searching strategy, which suffers from efficiency issues, especially for tasks involving enormous query points such as 3D CAD model quality testing. This paper proposes a parallel, subdivision-based strategy to increase query speed. It uses geometric subdivision to quickly cull out potential parameter regions where a query point’s corresponding UV parameters reside, then utilizes the Gauss- Newton method to quickly march to the precise UV values. All steps are done completely on GPU: the geometric subdivision is shared across all query points, and the Gauss-Newton marching is done in parallel as well. Experimental results show that a significant increase of at least 11x can be attained using the proposed method.
As an effective method for the fusion of the digital economy and the real economy, the 3d geometric modeling kernel has received extensive attentions in various fields recently. However, under the rapid development, the safety and quality problems of modeling kernel are constantly occurring, which brings bad user experience to application software developer. Therefore, based on analyzing the specific requirements of modeling kernel function at different modules, we propose a third party test and evaluation method for 3d geometric modeling kernel, which could test and quantify the code security, interface completeness, functional and performance quality level of 3d geometric modeling kernel, so as to assist correct and effective decision-making. Finally, the rationality of 3d geometric modeling kernel test and evaluation method is verified by testing a open source kernel.
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