Optimized GPU evaluation of arbitrary degree NURBS curves and surfaces

Krishnamurthy, Adarsh; Khardekar, Rahul; McMains, Sara

doi:10.1016/j.cad.2009.06.015

Cited by 31 publications

(31 citation statements)

References 14 publications

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“…Krishnamurthy used different parametric resolution for discrete LOD, Vertex Buffer Object (VBO) is used to avoid transferring the evaluated data back from GPU to CPU for rendering [7,8]. However, the method requires re-evaluating NURBS surface with different parametric resolutions and regenerating the connectivity index data by CPU.…”

Section: Gpu Based Lod Rendering Of Nurbs Surfacesmentioning

confidence: 98%

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GPU Based Evaluation and LOD Rendering of NURBS Surfaces

Dunming¹,

Zhao²,

Hu³

2012

Computer-Aided Design and Applications

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This paper proposes a new GPU method for the evaluation and LOD (Level of Detail) rendering of NURBS surfaces. Compared with the existing evaluation method of basis function, the approach simplifies the process by just one-pass and saves the graphics memory with only one texture array. The wavelet based LOD rendering method also saves the time to re-evaluate and re-transfer the data for rendering.

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Section: Gpu Based Lod Rendering Of Nurbs Surfacesmentioning

confidence: 98%

“…Then GPU was used to evaluate NURBS surfaces of arbitrary order [7,8]. Packing of the knots and basis function data was optimized to reduce the data to be transferred.…”

Section: Gpu Based Evaluation Of Nurbs Surfacesmentioning

confidence: 99%

GPU Based Evaluation and LOD Rendering of NURBS Surfaces

Dunming¹,

Zhao²,

Hu³

2012

Computer-Aided Design and Applications

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“…Additionally, [34] utilizes a selective distribution of threads (one GPU thread per control point for evaluation of bi-cubic Bézier patches and one GPU thread per patch for subsequent processing). In [38], the authors present a more generic evaluation (based on nonuniform rational B-splines) approach in which the operations are distributed between CPU and GPU, so that inherently serial operations are carried out by the CPU.…”

Section: Related Workmentioning

confidence: 99%

High-Performance Computation of Bézier Surfaces on Parallel and Heterogeneous Platforms

Palomar

Gómez-Luna

Cheikh³

et al. 2017

Int J Parallel Prog

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Bézier surfaces are mathematical tools employed in a wide variety of applications. Some works in the literature propose parallelization strategies to improve performance for the computation of Bézier surfaces. These approaches, however, are mainly focused on graphics applications and often are not directly applicable to other domains. In this work, we propose a new method for the computation of Bézier surfaces, together with approaches to efficiently map the method onto different platforms (CPUs, discrete and integrated GPUs). Additionally, we explore CPU-GPU cooperation mechanisms for computing Bézier surfaces using two integrated heterogeneous systems with different characteristics. An exhaustive performance evaluation-including different data-types, rendering and several hardware platforms-is performed. The results show that our method achieves speedups as high as 3.12x (double-precision) and 2.47x (single-precision) on CPU, and 3.69x (double-precision) and 13.14x (single-precision) on GPU compared to other methods in the literature. In heterogeneous platforms, the CPU-GPU cooperation increases the performance up to 2.09x with respect to the GPU-only version. Our method and the 123Int J Parallel Prog associated parallelization approaches can be easily employed in domains other than computer-graphics (e.g., image registration, bio-mechanical modeling and flow simulation), and extended to other Bézier formulations and Bézier constructions of higher order than surfaces.

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“…Once all the slices have been classified, we can get the complete voxelized representation of the CAD model. We make use of the method developed by Krishnamurthy et al (2009) to directly evaluate and render the NURBS surfaces in the model using the GPU. The B-rep model is first decomposed into its component surfaces.…”

Section: Gpu-accelerated Point Membership Classificationmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

Direct immersogeometric fluid flow analysis using B-rep CAD models

Hsu

Wang

et al. 2016

Computer Aided Geometric Design

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We present a new method for immersogeometric fluid flow analysis that directly uses the CAD boundary representation (B-rep) of a complex object and immerses it into a locally refined, non-boundary-fitted discretization of the fluid domain. The motivating applications include analyzing the flow over complex geometries, such as moving vehicles, where the detailed geometric features usually require time-consuming, labor-intensive geometry cleanup or mesh manipulation for generating the surrounding boundary-fitted fluid mesh. The proposed method avoids the challenges associated with such procedures. A new method to perform point membership classification of the background mesh quadrature points is also proposed. To faithfully capture the geometry in intersected elements, we implement an adaptive quadrature rule based on the recursive splitting of elements. Dirichlet boundary conditions in intersected elements are enforced weakly in the sense of Nitsche's method. To assess the accuracy of the proposed method, we perform computations of the benchmark problem of flow over a sphere represented using B-rep. Quantities of interest such as drag coefficient are in good agreement with reference values reported in the literature. The results show that the density and distribution of the surface quadrature points are crucial for the weak enforcement of Dirichlet boundary conditions and for obtaining accurate flow solutions. Also, with sufficient levels of surface quadrature element refinement, the quadrature error near the trim curves becomes insignificant. Finally, we demonstrate the effectiveness of our immersogeometric method for high-fidelity industrial scale simulations by performing an aerodynamic analysis of an agricultural tractor directly represented using B-rep. AbstractWe present a new method for immersogeometric fluid flow analysis that directly uses the CAD boundary representation (B-rep) of a complex object and immerses it into a locally refined, non-boundary-fitted discretization of the fluid domain. The motivating applications include analyzing the flow over complex geometries, such as moving vehicles, where the detailed geometric features usually require time-consuming, labor-intensive geometry cleanup or mesh manipulation for generating the surrounding boundary-fitted fluid mesh. The proposed method avoids the challenges associated with such procedures. A new method to perform point membership classification of the background mesh quadrature points is also proposed. To faithfully capture the geometry in intersected elements, we implement an adaptive quadrature rule based on the recursive splitting of elements. Dirichlet boundary conditions in intersected elements are enforced weakly in the sense of Nitsche's method. To assess the accuracy of the proposed method, we perform computations of the benchmark problem of flow over a sphere represented using B-rep. Quantities of interest such as drag coefficient are in good agreement with reference values reported in the literature. The results show that the ...

show abstract

Optimized GPU evaluation of arbitrary degree NURBS curves and surfaces

Cited by 31 publications

References 14 publications

GPU Based Evaluation and LOD Rendering of NURBS Surfaces

GPU Based Evaluation and LOD Rendering of NURBS Surfaces

High-Performance Computation of Bézier Surfaces on Parallel and Heterogeneous Platforms

Direct immersogeometric fluid flow analysis using B-rep CAD models

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