Spline Surface Intersections Optimized for GPUs

Briseid, Sverre; Dokken, Tor; Hagen, Trond Runar; Nygaard, Jens Olav

doi:10.1007/11758549_32

Cited by 9 publications

(5 citation statements)

References 4 publications

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“…Run a preprocess to detect the intersection regions and intersection types, using Sinha's theorem [25], bounding box test, and normal cone test [23], [24], and so on; 2. for those regions with transversal intersections, exploit fast and appropriate methods, such as SISL method [33], and so on; 3. for those regions with singular intersections, for example, tangential intersections and selfintersections, employ the proposed GPU accelerated AA-based method. Finally, though our method is developed for B-spline surface intersection, it can naturally be extended to deal with NURBS intersection.…”

Section: Resultsmentioning

confidence: 99%

“…Currently, the widely employed method in practical applications is the hybrid method of decomposition and tracing, which first identifies all intersection branches by decomposition, and then traces out the curve for each intersection branch [23], [24]. To reduce the computation complexity of recursive decomposition, Sinha et al [25] develop a theorem to detect the topology of transversal intersections.…”

Section: Surface Intersectionmentioning

confidence: 99%

“…To reduce the computation complexity of recursive decomposition, Sinha et al [25] develop a theorem to detect the topology of transversal intersections. Moreover, Briseid et al [23] make a pioneering work which accelerates the recursive decomposition algorithm for detecting the topology of intersection by GPU. Furthermore, it is updated to use a heterogeneous system including a multicore CPU and a modern programming model for a GPU [24].…”

Section: Surface Intersectionmentioning

confidence: 99%

See 2 more Smart Citations

Affine Arithmetic-Based B-Spline Surface Intersection with GPU Acceleration

Lin

Yang

Liao

et al. 2014

IEEE Trans. Visual. Comput. Graphics

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Because the B-spline surface intersection is a fundamental operation in geometric design software, it is important to make the surface intersection operation robust and efficient. As is well known, affine arithmetic is robust for calculating the surface intersection because it is able to not only find every branch of the intersection, but also deal with some singular cases, such as surface tangency. However, the classical affine arithmetic is defined only for the globally supported polynomials, and its computation is very time consuming, thus hampering its usefulness in practical applications, especially in geometric design. In this paper, we extend affine arithmetic to calculate the range of recursively and locally defined B-spline basis functions, and we accelerate the affine arithmetic-based surface intersection algorithm by using a GPU. Moreover, we develop efficient methods to thin the strip-shaped intersection regions produced by the affine arithmetic-based intersection algorithm, calculate the intersection points, and further improve their accuracy. The many examples presented in this paper demonstrate the robustness and efficiency of this method.

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Section: Resultsmentioning

confidence: 99%

Section: Surface Intersectionmentioning

confidence: 99%

Section: Surface Intersectionmentioning

confidence: 99%

See 1 more Smart Citation

Affine Arithmetic-Based B-Spline Surface Intersection with GPU Acceleration

Lin

Yang

Liao

et al. 2014

IEEE Trans. Visual. Comput. Graphics

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“…To overcome the image-space resolution for spline intersections, researchers at SINTEF adapted the serial subdivision algorithm to use the GPU. They accelerate the computations by using the GPU to test for intersections and iteratively subdivide the spline patches until a prescribed accuracy is attained [22], [23].…”

Section: Related Workmentioning

confidence: 99%

GPU-Accelerated Minimum Distance and Clearance Queries

Krishnamurthy

McMains

Haller

2011

IEEE Trans. Visual. Comput. Graphics

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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.

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“…[Hoff et al 2001] use the GPU to perform fast proximity queries on 2D shapes using a pixel grid to perform distance computations, but their technique does not extend to 3D shapes. Recently, researchers at SINTEF accelerate spline intersections by using the GPU to test for intersections and iteratively subdivide the spline patches until a prescribed accuracy is attained [Briseid et al 2006;Dokken et al 2005].…”

Section: Related Workmentioning

confidence: 99%

Accelerating geometric queries using the GPU

Krishnamurthy

McMains

Halle

2009

2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling

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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.

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Spline Surface Intersections Optimized for GPUs

Cited by 9 publications

References 4 publications

Affine Arithmetic-Based B-Spline Surface Intersection with GPU Acceleration

Affine Arithmetic-Based B-Spline Surface Intersection with GPU Acceleration

GPU-Accelerated Minimum Distance and Clearance Queries

Accelerating geometric queries using the GPU

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