Fast and robust Booleans on polyhedra

Xu, Songgang; Keyser, John

doi:10.1016/j.cad.2012.10.036

Cited by 16 publications

(7 citation statements)

References 12 publications

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“…Pioneered by Requicha and Voelcker in the 70 's [1977] and defined by regularized Boolean set operations on halfspaces, CSG has become one of the most popular approaches for solid modeling, due to its guarantee of solidity and the ease of control. The most commonly used halfspaces are parameterized primitives, such as boxes, spheres, cones, cylinders, and tori, but other forms of halfspaces have been extensively studied in the research community, such as implicit functions [Nielson 2004;Pasko et al 1995], parametric surfaces [Casale and Bobrow 1989;Keyser et al 2004], and meshes [Bernstein and Fussell 2009;Douze et al 2017;Feito et al 2013;Pavić et al 2010;Smith and Dodgson 2007;Wang 2010;Xu and Keyser 2013]. CSG has been extended to support other types of constructive modeling operations such as blending [Rossignac and Requicha 1984], offseting [Rossignac and Requicha 1986], and warping [Wyvill et al 1999].…”

Section: Csgmentioning

confidence: 99%

Boundary-sampled halfspaces

Zhou

Carr

et al. 2021

ACM Trans. Graph.

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We present a novel representation of solid models for shape design. Like Constructive Solid Geometry (CSG), the solid shape is constructed from a set of halfspaces without the need for an explicit boundary structure. Instead of using Boolean expressions as in CSG, the shape is defined by sparsely placed samples on the boundary of each halfspace. This representation, called Boundary-Sampled Halfspaces (BSH), affords greater agility and expressiveness than CSG while simplifying the reverse engineering process. We discuss theoretical properties of the representation and present practical algorithms for boundary extraction and conversion from other representations. Our algorithms are demonstrated on both 2D and 3D examples.

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Section: Csgmentioning

confidence: 99%

Boundary-sampled halfspaces

Zhou

Carr

et al. 2021

ACM Trans. Graph.

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“…For example, Banerjee & Rossignac [1996] and later Xu & Keyser [2013] build exact topologies but fixed-precision floating point vertex positions, leading to self-intersections, inversions (see Figure 6) and degeneracies in the output. Campen & Kobbelt [2010a] round all input vertices aggressively to ensure exact plane intersections for a BSP-representation.…”

Section: Approaches To Robustness and Sources Of Non-robustnessmentioning

confidence: 99%

Mesh arrangements for solid geometry

et al. 2016

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“…Many techniques have been used to accelerate the intersection detection of two meshes, such as methods of BSP (binary space partitions) [3,4], OBB tree [20], Spatial hashing [8,33,38], and Octree [9]. The Octree technique is adopted in this research.…”

Section: Building Octree Of the Common Spacementioning

confidence: 99%

A CAD tool to support idea generation in the product planning phase

Bacciotti

Borgianni

Rotini

2016

Computer-Aided Design and Applications

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Boolean operation of geometric models is an essential element in computational geometry. An efficient approach is developed in this research to perform Boolean operation for triangulated meshes represented by B-rep. This approach is much fast and robust than many existing methods. The Octree technique is adapted to facilitate the division of the common space of two meshes in order to reduce the time of Octree's construction and intersection detection. Floating point arithmetic errors and singularity of intersections are then analyzed to guarantee the unique intersection between a segment and a face, and the continuity of intersections. A novel technique based on intersecting triangles is finally proposed to create required sub-meshes based on the type of Boolean operations. Some experimental results and comparisons with other methods are presented to prove that the proposed method is fast and robust.

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Fast and robust Booleans on polyhedra

Cited by 16 publications

References 12 publications

Boundary-sampled halfspaces

Boundary-sampled halfspaces

Mesh arrangements for solid geometry

A CAD tool to support idea generation in the product planning phase

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