Three-Dimensional Delaunay Mesh Generation

Cheng, Siu-Wing; Poon, Sheung-Hung

doi:10.1007/s00454-006-1252-5

Cited by 40 publications

(47 citation statements)

References 21 publications

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“…Though energies between particles are computed in 3D world space, particles move strictly in parametric space (10), avoiding the error-prone projection onto the surface that results from 3D movements. Taking these steps in parameter space only requires a change of coordinates (7), (9). From each surface we can obtain parametric derivatives du and dv, which we use to construct the metric tensor M and Jacobian J needed for the inverse transformation.…”

Section: Particle System Formulationmentioning

confidence: 99%

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Particle Systems for Adaptive, Isotropic Meshing of CAD Models

Bronson¹,

Levine²,

Whitaker³

2010

Proceedings of the 19th International Meshing Roundtable

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We present a particle-based approach for generating adaptive triangular surface and tetrahedral volume meshes from computer-aided design models. Input shapes are treated as a collection of smooth, parametric surface patches that can meet non-smoothly on boundaries. Our approach uses a hierarchical sampling scheme that places particles on features in order of increasing dimensionality. These particles reach a good distribution by minimizing an energy computed in 3D world space, with movements occurring in the parametric space of each surface patch. Rather than using a pre-computed measure of feature size, our system automatically adapts to both curvature as well as a notion of topological separation. It also enforces a measure of smoothness on these constraints to construct a sizing field that acts as a proxy to piecewise-smooth feature size. We evaluate our technique with comparisons against other popular triangular meshing techniques for this domain.

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Section: Particle System Formulationmentioning

confidence: 99%

“…A notion of local feature size for piecewisesmooth shapes has been defined [8] by coupling local feature size for the smooth regions with a topological condition called gap size [9]. Computing this measure robustly is a significant challenge.…”

Section: Introductionmentioning

confidence: 99%

Particle Systems for Adaptive, Isotropic Meshing of CAD Models

Bronson¹,

Levine²,

Whitaker³

2010

Proceedings of the 19th International Meshing Roundtable

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“…An early algorithm by Chew [9] for generating guaranteedquality triangular meshes uses Delaunay vertex deletion to obtain a better bound on the minimum angle than is achieved by similar algorithms that do not use vertex deletion, and the same principle has been exploited by mesh generators that generate better-quality tetrahedra by occasionally deleting vertices from a three-dimensional Delaunay triangulation [7,Section 14.5]. Another application of Delaunay vertex deletion is interactive data cleaning, in which a user desires to remove outlier vertices from a triangulation used to interpolate data.…”

Section: Introductionmentioning

confidence: 99%

Vertex Deletion for 3D Delaunay Triangulations

Buchin¹,

Devillers²,

Mulzer³

et al. 2013

Lecture Notes in Computer Science

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Abstract. We show how to delete a vertex q from a three-dimensional Delaunay triangulation DT(S) in expected O(C ⊗ (P )) time, where P is the set of vertices neighboring q in DT(S) and C ⊗ (P ) is an upper bound on the expected number of tetrahedra whose circumspheres enclose q that are created during the randomized incremental construction of DT(P ). Experiments show that our approach is significantly faster than existing implementations if q has high degree, and competitive if q has low degree.

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“…At its base level, topology is dependent on mesh generation, a relatively recent field of research which began to emerge in the 1970s. Cheng's discussion of Delaunay mesh generation [72] features a brief introduction to the history of generation techniques dating back to the 1970s. Some early advances in automatic unstructured grid generation were made in the early 1970s by Frederick [94] and George [95], but for the most part, unstructured grids remained experimental whilst triangulation became the predominant method, following…”

Section: Topology and Retopologymentioning

confidence: 99%

“…Computerised 3D design programs are often split into two main categories: CAD/CAM programs used in design and manufacturing industries, and artistic or animation programs used primarily in the film and gaming industries [71,72]. Whilst the software packages used in each sector may share some common features, their development occurred independently of each other, and to some extent, they have remained independent over the years [71].…”

Section: An Introduction To Cad and 3d Modellingmentioning

confidence: 99%

Design of asymmetric shape-transition hypersonic inlets

Jones¹

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P a g e | i AbstractScramjet engines suffer performance penalties at off-design conditions, due to the fact that the engine is designed for one particular set of flight characteristics. Thermal compression has been suggested as one way of addressing poor off-design performance.For thermal compression to occur in the combustor, the incoming airflow must be of a non-uniform pressure distribution. This paper investigates the generation of a non-uniform compression field at the combustor entrance by designing an asymmetric inlet with uneven compression ratios.A complicating factor is that scramjet engines must be carefully body-integrated onto the vehicle forebody to maximise air capture and reduce drag. Any attempt at designing an inlet suitable for thermal compression must body-integrated.One challenge in designing an asymmetric inlet is the current selection of 3D surface modelling tools available to designers. The secondary goal of this project is to improve the current surface generation method for CFD analysis by identifying a new tool to carry out the design process. Ideally, the modelling process should be rapid and user-friendly.The tools selected for this project were 3DReshaper®, Blender™ andMeshLab.This project follows through the design of an asymmetric inlet using a combination of these tools, with a view to providing a non-uniform pressure distribution at the combustor entrance. The ease and usability of the modelling method was evaluated, and found to provide no real improvement over the current method. One tool, Rhinoceros®, has been identified as having potential for future investigation, due to its mesh-to-NURBS surface conversion functionality.The inlet design was tested in an Eilmer4 CFD simulation, and was found to be successful in generating non-uniform pressure distribution at Abstract P a g e | ii the outlet (Figure i). However, an unanticipated shock effect was noted in the inlet, which reduced the effectiveness of the non-uniformity. This effect was due to a shock reflection off the cowl closure point, indicating that a greater understanding of cowl placement is necessary when designing this type of inlet.Figure i -Non-uniform pressure distribution at the inlet exit due to asymmetric inlet shape.Several avenues for future research have been identified. Foremost is an investigation into the cowl closure behaviour contributing to the unwanted shock in the inlet. In addition, testing of new modelling techniques to overcome the problems identified with Blender™ and 3DReshaper® is recommended. Creating a stronger, quicker, easier design process will enable iterative designs to be created and assist in resolving the reflected shock issue. Once this has been completed, a full system analysis can be carried out to determine whether this type of thermal compression inlet has any positive effect on scramjet engine performance.

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Three-Dimensional Delaunay Mesh Generation

Cited by 40 publications

References 21 publications

Particle Systems for Adaptive, Isotropic Meshing of CAD Models

Particle Systems for Adaptive, Isotropic Meshing of CAD Models

Vertex Deletion for 3D Delaunay Triangulations

Design of asymmetric shape-transition hypersonic inlets

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