An algorithm reducing 3D Boolean operations to a 2D problem: concepts and results

Gardan, Yvon; Perrin, Estelle

doi:10.1016/0010-4485(95)00050-x

Cited by 15 publications

(10 citation statements)

References 9 publications

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“…The results show that the proposed method outperforms other four ones as well, and is several orders of magnitude faster than the former two ones. By comparing the differences of these methods, we can easily see that the reason for the larger running time of the former two methods may well be that both methods employ the CGAL library and the DCEL structure 9 . Even so, it is noteworthy that 8 Here the improvement factor refers to the ratio of time.…”

Section: ) Results Of the First Experimentmentioning

confidence: 99%

“…Boolean operation on polygons is one of the oldest and best-known problems in computer graphics, and it has attracted much attentions, due to its simple formulation and broad applications in various disciplines such as computational geometry, CAD, GIS, visual computing, motion planning [5], [8], [9], [12], [18], [29], [27], [28]. When the polygons to be operated are conic polygons (whose boundaries consist of conic segments or second degree curves), researchers have made some efforts, see, e.g., [3], [4], [10].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Simple Algorithm for Computing Several Sequences Synthesis

Wang

Qing

Feng

2000

Information Security for Global Information Infrastructures

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In this article, we devise a concise algorithm for computing BOCP. Our method is simple, easyto-implement but without loss of efficiency. Given two circular-arc polygons with m and n edges respectively, our method runs in O(m + n + (l + k) log l) time, using O(m + n + k) space, where k is the number of intersections, and l is the number of edges. Our algorithm has the power to approximate to linear complexity when k and l are small. The superiority of the proposed algorithm is also validated through empirical study.

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Section: ) Results Of the First Experimentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Simple Algorithm for Computing Several Sequences Synthesis

Wang

Qing

Feng

2000

Information Security for Global Information Infrastructures

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show abstract

“…Computing offset model of a shape represented by a Tmesh can be used for tool path generation and process planning of a sculptured surface such as mold & die (Choi et al [2]). Boolean operation between T-meshes (Cardan et al [1]) is very similar to T-mesh regularization in that it finds intersections between T-meshes and selectively collects portions as specified by the Boolean operator. Hence the algorithm described in this paper can be applied to Boolean operation between T-meshes.…”

Section: Introductionmentioning

confidence: 99%

Self-intersection Removal in Triangular Mesh Offsetting

Jung¹,

Shin²,

Choi³

2004

Computer-Aided Design and Applications

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Proposed in this paper is an efficient algorithm to remove self-intersections from the raw offset triangular mesh. The resulting regular mesh can be used in shape inflation, tool path generation, and process planning to name a few. Objective is to find the valid region -set of triangles defining the outer boundary of the offset volume from the raw offset triangular mesh. Starting with a seed triangle, the algorithm grows the valid region to neighboring triangles until it reaches triangles with self-intersection. Then the region growing process crosses over the self-intersection and moves to the adjacent valid triangle. Therefore the region growing traverses valid triangles and intersecting triangles adjacent to valid triangles only. This property makes the algorithm efficient and robust, since this method omits unnecessary traversing invalid region, which usually has very complex geometric shape and contains many meaningless self-intersections.

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“…A topologically complete set operations algorithm for planar polyhedra two-manifold objects was described by Mäntylä [7], introducing the vertex neighborhood classifier for Boolean operations. Gardan and Perrin [8] proposed an interesting method for reducing 3D Boolean operations to a 2D problem in manifold environments.…”

Section: Introductionmentioning

confidence: 99%

Boolean operations on multi-region solids for mesh generation

Pereira

Arruda

Miranda

et al. 2011

Engineering with Computers

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An algorithm for Boolean operations on nonmanifold models is proposed to allow the treatment of solids with multiple regions (internal interfaces) and degenerate portions (shells and wires), in the context of mesh generation. In a solid modeler, one of the most powerful tools to create three-dimensional objects with any level of geometric complexity is the Boolean set operators. They are intuitive and popular ways to combine solids, based on the operations applied to point sets. To assure that the resulting objects have the same dimension as the original objects, without loose or dangling parts, a regularization process is usually applied after a Boolean operation. In practice, the regularization is performed classifying the topological elements and removing internal or lowerdimensional structures. However, in many engineering applications, the adopted geometric model may contain idealized internal parts, as in the case of multi-region models, or lower-dimensional parts, as in the case of solids that contain dangling slabs that are represented as zerothickness surfaces or wireframes in the model. Therefore, the aim of this work is the development of a generic algorithm that allows the application of the Boolean set operations in a geometric modeling environment applied to finite and boundary element mesh generation. This environment adopts a non-manifold boundary representation that considers an undefined number of topological entities (group concept), and works with objects of different dimensions and with objects not necessarily plane or polyhedral (parametric curved surfaces). Numerical examples are presented to illustrate the proposed methodology.

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An algorithm reducing 3D Boolean operations to a 2D problem: concepts and results

Cited by 15 publications

References 9 publications

A Simple Algorithm for Computing Several Sequences Synthesis

A Simple Algorithm for Computing Several Sequences Synthesis

Self-intersection Removal in Triangular Mesh Offsetting

Boolean operations on multi-region solids for mesh generation

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