Accelerating geometric queries using the GPU

Abstract

Figure 1: Geometric operations such as silhouette curve extraction and minimum distance/closest point computations between NURBS surfaces and complex CAD models accelerated using the GPU. AbstractWe present practical algorithms for accelerating geometric queries on models made of NURBS surfaces using programmable Graphics Processing Units (GPUs). We provide a generalized framework for using GPUs as co-processors in accelerating CAD operations. By attaching the data corresponding to surface-normals to a surface bounding-box structure, we can calculate view-dependent geometric features such as silhouette curves in real time. We make use of additional surface data linked to surface bounding-box hierarchies on the GPU to answer 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 than the commercial solid modeling kernel ACIS.

An efficient approach to directly compute the exact Hausdorff distance for 3D point sets

“…Recently, Krishnamurthy et al [28,38,39] developed a GPU algorithm that computes the Hausdorff distance between NURBS surfaces. Interactive speeds are obtained by performing GPU traversal of a boundingbox hierarchy and selectively culling pairs of bounding boxes that could not contribute to the Hausdorff distance.…”

GPU-Accelerated Minimum Distance and Clearance Queries

“…We present a short outline of our algorithms that were explained in detail in [2], [6], [26], [27]. In our NURBS evaluation paper [27] we developed a method to directly evaluate a mesh of points on a NURBS surface using the GPU.…”

“…While rendering, we interpret these values stored in the texture as vertex coordinates using a Vertex Buffer Object (VBO) and display the VBO as a mesh directly on the screen. In our NURBS modeling work [2], [6], we construct surface AABBs that enclose a surface patch having four adjacent surface points as corners (Fig. 4).…”

“…In this paper, we provide a hybrid CPU/GPU framework to accelerate minimum distance computations, which is expanded from our previous conference presentation [2]. Our main contributions include:…”

GPU Algorithm for Outer Boundaries of a Triangle Set

“…MPFR 라이브러리에서는 임의 정밀도의 부동소숫점 수 치 연산을 지원해 준다 [23] . [6] 는 삼각형 집합에 의한 3차 원 배치의 한 공간 셀을 O(n 2+ε ) 시간에 구하는 알 고리즘을 제안하였고, de Berg 등 [9,10] [13] . Li와 McMains는 3차원 그리드를 만들 고, 두 다면체의 합 삼각형들이 포함되는 그리드 셀을 찾아 Minkowski sum 경계를 구하는 GPU 알 고리즘을 제안하였다 [14] .…”