GPU-Accelerated Minimum Distance and Clearance Queries

Abstract

Abstract-We present practical algorithms for accelerating distance queries on models made of trimmed NURBS surfaces using programmable Graphics Processing Units (GPUs). We provide a generalized framework for using GPUs as co-processors in accelerating CAD operations. By supplementing surface data with a surface bounding-box hierarchy on the GPU, we answer distance queries such as finding the closest point on a curved NURBS surface given any point in space and evaluating the clearance between two solid models constructed using multiple NURBS surfaces. We simultaneously output the parameter values corresponding to the solution of these queries along with the model space values. Though our algorithms make use of the programmable fragment processor, the accuracy is based on the model space precision, unlike earlier graphics algorithms that were based only on image space precision. In addition, we provide theoretical bounds for both the computed minimum distance values as well as the location of the closest point. Our algorithms are at least an order of magnitude faster and about two orders of magnitude more accurate than the commercial solid modeling kernel ACIS.

Direct immersogeometric fluid flow analysis using B-rep CAD models

“…Performing this operation directly on B-reps consisting of trimmed NURBS surfaces is a compute-intensive operation. Hence, in our method, we create a highresolution voxelization of the CAD model using GPU rendering of trimmed-NURBS surfaces (Krishnamurthy et al, 2009(Krishnamurthy et al, , 2011 . This voxelization is then used to perform point membership classification on vertices of the background mesh.…”

Interactive rendering of NURBS surfaces

“…Therefore, these approaches perform a previous tessellation on the CPU. In this paper we present RPNS, Rendering pipeline for NURBS Surface, a novel solution for the direct evaluation of NURBS surfaces on the GPU without any previous decomposition to Bézier surfaces. The objective is the efficient and interactive rendering of each surface so that the final image has no cracks or holes, neither inside each surface nor between neighbor surfaces, making it possible to exploit the parallelism of the GPU to perform common operations such as sketching on surfaces or interactive rendering of deforming surfaces [16,17]. A new primitive, KSQuad, based on the regions defined by the projection on the parametric cell delimited by the different knot spans is proposed.…”

Deep learning and GPU-accelerated algorithms for computer-aided engineering

“…We extend the Theorem 3.2, to obtain a bound on the distance tranforms. For this work, we use key results from the theorems in Krishnamurthy et al [106]. This work theoretically computes the bounds for distance computation between a point and the trimmed NURBS surface tessellation.…”

“…Proof. We invoke Theorem 2 of Krishnamurthy et al [106] to obtain the maximum distance from a given point to the trimmed NURBS tessellation is given by Equation 3…”