Geometric rounding and feature separation in meshes

Milenkovic, Victor; Sacks, Elisha

doi:10.1016/j.cad.2018.10.003

Cited by 6 publications

(3 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In these cases exact or implicit coordinates must be converted to inexact floating point values and the necessary approximation may invalidate the model by introducing degenerate or intersecting elements. A provably correct and efficient solution to this problem is still elusive and existing algorithms are either impractical [Devillers et al 2018] or do not guarantee to produce a correct result in all the cases [Milenkovic and Sacks 2019]. However, existing heuristics proved to fail only in an extremely small percentage of practical cases .…”

Section: Exact and Approximated Methodsmentioning

confidence: 99%

Interactive and Robust Mesh Booleans

Cherchi¹,

Pellacini²,

Attene³

et al. 2022

Preprint

View full text Add to dashboard Cite

Section: Exact and Approximated Methodsmentioning

confidence: 99%

Interactive and Robust Mesh Booleans

Cherchi¹,

Pellacini²,

Attene³

et al. 2022

Preprint

View full text Add to dashboard Cite

“…The first snap rounding algorithm for 3D geometry was proposed by Fortune [Fortune 1999], but its requirements on the input make it impractical. A more practical solution was proposed later in [Milenkovic and Sacks 2019], though no guarantees are given. Recently, a 3D snap rounding algorithm for general input has been proposed in [Devillers et al 2018].…”

Section: Snap Roundingmentioning

confidence: 99%

Convex polyhedral meshing for robust solid modeling

Diazzi

Attene

2021

ACM Trans. Graph.

View full text Add to dashboard Cite

We introduce a new technique to create a mesh of convex polyhedra representing the interior volume of a triangulated input surface. Our approach is particularly tolerant to defects in the input, which is allowed to self-intersect, to be non-manifold, disconnected, and to contain surface holes and gaps. We guarantee that the input surface is exactly represented as the union of polygonal facets of the output volume mesh. Thanks to our algorithm, traditionally difficult solid modeling operations such as mesh booleans and Minkowski sums become surprisingly robust and easy to implement, even if the input has defects. Our technique leverages on the recent concept of indirect geometric predicate to provide an unprecedented combination of guaranteed robustness and speed, thus enabling the practical implementation of robust though flexible solid modeling systems. We have extensively tested our method on all the 10000 models of the Thingi10k dataset, and concluded that no existing method provides comparable robustness, precision and performances.

show abstract

“…One of the primary challenges encountered in implementing Boolean operations is the utilization of finite precision arithmetic. In geometric calculations, floating-point arithmetic is commonly employed for computing point coordinates [29][30][31]. Nonetheless, owing to the finite precision nature of floating-point arithmetic, the introduction of rounding errors and loss of precision becomes inevitable [32,33].…”

Section: Introductionmentioning

confidence: 99%

Simple and Robust Boolean Operations for Triangulated Surfaces

et al. 2023

View full text Add to dashboard Cite

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.

show abstract

Geometric rounding and feature separation in meshes

Cited by 6 publications

References 14 publications

Interactive and Robust Mesh Booleans

Interactive and Robust Mesh Booleans

Convex polyhedral meshing for robust solid modeling

Simple and Robust Boolean Operations for Triangulated Surfaces

Contact Info

Product

Resources

About