Simple and Robust Boolean Operations for Triangulated Surfaces

Mei, Gang; Tipper, John C.

doi:10.48550/arxiv.1308.4434

Cited by 7 publications

(3 citation statements)

References 25 publications

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“…In [Xu and Keyser 2013], the topology of the resulting surface is guaranteed correct thanks to a clever use of orientation predicates with no need of exact constructions. Instead of walking on the surface, [Mei and Tipper 2013] uses a temporary octree to quickly find the candidate pairs of intersecting triangles. ] exploit CGAL's exact kernel to partition the space into cells, each labeled with winding numbers w.r.t.…”

Section: Surface and Volume-based Methodsmentioning

confidence: 99%

Interactive and Robust Mesh Booleans

Cherchi¹,

Pellacini²,

Attene³

et al. 2022

Preprint

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Section: Surface and Volume-based Methodsmentioning

confidence: 99%

Interactive and Robust Mesh Booleans

Cherchi¹,

Pellacini²,

Attene³

et al. 2022

Preprint

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“…There is extensive literature for Booleans on meshes [12,13,14,1,2,15,9]. The trilemma for different approaches are essentially performance, accuracy, and algorithmic stability.…”

Section: Related Workmentioning

confidence: 99%

Fast Exact Booleans for Iterated CSG using Octree-Embedded BSPs

Nehring-Wirxel,

Trettner,

Kobbelt

2021

Preprint

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We present octree-embedded BSPs, a volumetric mesh data structure suited for performing a sequence of Boolean operations (iterated CSG) efficiently. At its core, our data structure leverages a plane-based geometry representation and integer arithmetics to guarantee unconditionally robust operations. These typically present considerable performance challenges which we overcome by using custom-tailored fixedprecision operations and an efficient algorithm for cutting a convex mesh against a plane. Consequently, BSP Booleans and mesh extraction are formulated in terms of mesh cutting. The octree is used as a global acceleration structure to keep modifications local and bound the BSP complexity. With our optimizations, we can perform up to 2.5 million mesh-plane cuts per second on a single core, which creates roughly 40-50 million output BSP nodes for CSG. We demonstrate our system in two iterated CSG settings: sweep volumes and a milling simulation.

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“…To address this issue, researchers have employed different approaches. One method involves using rational numbers to represent point coordinates, enabling accurate representation of point locations and ensuring topological correctness of the calculation results [34]. For instance, Hu et al [32] combined exact rational number calculations with geometric tolerance to robustly solve problems such as self-intersections and gaps in Boolean operations.…”

Section: Introductionmentioning

confidence: 99%

Simple and Robust Boolean Operations for Triangulated Surfaces

et al. 2023

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Boolean operations on geometric models are important in numerical simulation and serve as essential tools in the fields of computer-aided design and computer graphics. The accuracy of these operations is heavily influenced by finite precision arithmetic, a commonly employed technique in geometric calculations, which introduces numerical approximations. To ensure robustness in Boolean operations, numerical methods relying on rational numbers or geometric predicates have been developed. These methods circumvent the accumulation of rounding errors during computation, thus preserving accuracy. Nonetheless, it is worth noting that these approaches often entail more intricate operation rules and data structures, consequently leading to longer computation times. In this paper, we present a straightforward and robust method for performing Boolean operations on both closed and open triangulated surfaces. Our approach aims to eliminate errors caused by floating-point operations by relying solely on entity indexing operations, without the need for coordinate computation. By doing so, we ensure the robustness required for Boolean operations. Our method consists of two main stages: (1) Firstly, candidate triangle intersection pairs are identified using an octree data structure, and then parallel algorithms are employed to compute the intersection lines for all pairs of triangles. (2) Secondly, closed or open intersection rings, sub-surfaces, and sub-blocks are formed, which is achieved entirely by cleaning and updating the mesh topology without geometric solid coordinate computation. Furthermore, we propose a novel method based on entity indexing to differentiate between the union, subtraction, and intersection of Boolean operation results, rather than relying on inner and outer classification. We validate the effectiveness of our method through various types of Boolean operations on triangulated surfaces.

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Simple and Robust Boolean Operations for Triangulated Surfaces

Cited by 7 publications

References 25 publications

Interactive and Robust Mesh Booleans

Interactive and Robust Mesh Booleans

Fast Exact Booleans for Iterated CSG using Octree-Embedded BSPs

Simple and Robust Boolean Operations for Triangulated Surfaces

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