Method for generating high-quality tetrahedral meshes of geological models by utilizing CGAL

Wang, Bowen; Mei, Gang; Xu, Nengxiong

doi:10.1016/j.mex.2020.101061

Cited by 9 publications

(4 citation statements)

References 25 publications

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“…Image metrics, namely Dice coefficient, mean surface distance (MSD) and Hausdorff distance, were calculated between the transformed images and the canonical bone 52 . Mesh metrics, namely tet-collapse 53 and volume-skew 54 were calculated for the canonical and individual meshes. Briefly, tet-collapse measures the ratio of height and face area and is zero for a fully collapse tetrahedron and one for an optimal tetrahedron.…”

Section: Methodsmentioning

confidence: 99%

A computational framework for canonical holistic morphometric analysis of trabecular bone

Bachmann

Dunmore

Skinner

et al. 2022

Sci Rep

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Bone is a remarkable, living tissue that functionally adapts to external loading. Therefore, bone shape and internal structure carry information relevant to many disciplines, including medicine, forensic science, and anthropology. However, morphometric comparisons of homologous regions across different individuals or groups are still challenging. In this study, two methods were combined to quantify such differences: (1) Holistic morphometric analysis (HMA) was used to quantify morphometric values in each bone, (2) which could then be mapped to a volumetric mesh of a canonical bone created by a statistical free-form deformation model (SDM). Required parameters for this canonical holistic morphometric analysis (cHMA) method were identified and the robustness of the method was evaluated. The robustness studies showed that the SDM converged after one to two iterations, had only a marginal bias towards the chosen starting image, and could handle large shape differences seen in bones of different species. Case studies were performed on metacarpal bones and proximal femora of different primate species to confirm prior study results. The differences between species could be visualised and statistically analysed in both case studies. cHMA provides a framework for performing quantitative comparisons of different morphometric quantities across individuals or groups. These comparisons facilitate investigation of the relationship between spatial morphometric variations and function or pathology, or both.

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Section: Methodsmentioning

confidence: 99%

A computational framework for canonical holistic morphometric analysis of trabecular bone

Bachmann

Dunmore

Skinner

et al. 2022

Sci Rep

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“…(3) The proposed method achieves a balance between computational efficiency and computational accuracy. The widely recognized computational geometry library CGAL utilizes rational number arithmetic for exact computations, ensuring high robustness by avoiding rounding errors in floating-point arithmetic [43,52]. However, the reliance on rational number arithmetic introduces complexity to the computation process.…”

Section: Resultsmentioning

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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“…Consequently, these factors contribute to increased difficulty in generating tetrahedral mesh in such complex areas. The accurate representation of intersecting faults within the mesh becomes challenging due to limited and fragmented data, requiring specialized techniques and methodologies to overcome these obstacles to achieve a reliable and precise mesh generation process [ 20 , 21 ]. The fault model describes the contact relationship and geometry between faults, and the construction of the fault model is based on the establishment of a 3D geological model to provide constraints for the generation of the ground level [ 22 , 23 ].…”

Section: Introductionmentioning

confidence: 99%

Generation of 3D finite element mesh of layered geological bodies in intersecting fault zones

Chen,

Yang,

et al. 2024

PLoS ONE

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As the geological fault surface divides the 3D space of stratified ores and rocks into complex spatial surface domains, it is necessary to fully consider the spatial relationship between intersecting fault zones and geological bodies in the process of 3D modeling, and how to accurately establish the 3D finite element mesh of geological bodies in intersecting fault zones is a difficult point in modeling complex geological structure. The laminated geological body in intersecting fault zone is a multifaceted domain grid model consisting of a ground-level grid, a geological fault plane grid, and a range grid. By analyzing the spatial relationship between the geological interfaces of the intersecting fault zones, a closed manifold processing method is proposed to establish the closed manifold spatial surface model of the intersecting fault zones, based on which the closed spatial surface model is tetrahedrally divided to establish a 3D solid model. Finally, the 3D solid model is imported into Ansys to generate a 3D finite element mesh. VC++ is used as the development platform for programming, to realize the generation and closed manifold processing of ground level and geological fault surfaces, and use TetGen library to generate finite element mesh based on irregular tetrahedron. Taking an intersecting fault zone in an open-pit mine as an example, the 3D finite element mesh of laminated geological bodies in the intersecting fault zone is established successfully. This method provides an effective and feasible solution for generating accurate 3D finite element meshes in complex stratigraphic spaces based on closed manifold processing.

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Method for generating high-quality tetrahedral meshes of geological models by utilizing CGAL

Cited by 9 publications

References 25 publications

A computational framework for canonical holistic morphometric analysis of trabecular bone

A computational framework for canonical holistic morphometric analysis of trabecular bone

Simple and Robust Boolean Operations for Triangulated Surfaces

Generation of 3D finite element mesh of layered geological bodies in intersecting fault zones

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