Heterogeneous spline surface intersections

Briseid, Sverre; Dokken, Tor; Hagen, Trond Runar

doi:10.1145/1925059.1925085

Cited by 2 publications

(3 citation statements)

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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%

“…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]. Additionally, Alcantara et al [26] employ the hash constructed on GPU to determine the intersection of two animated mesh surfaces in real time.…”

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%