Showing papers on "Constrained Delaunay triangulation published in 2015"
TL;DR: The essential algorithms and techniques used to develop TetGen are presented, including an efficient tetrahedral mesh data structure, a set of enhanced local mesh operations, and filtered exact geometric predicates, which can robustly handle arbitrary complex 3D geometries and is fast in practice.
Abstract: TetGen is a Cpp program for generating good quality tetrahedral meshes aimed to support numerical methods and scientific computing. The problem of quality tetrahedral mesh generation is challenged by many theoretical and practical issues. TetGen uses Delaunay-based algorithms which have theoretical guarantee of correctness. It can robustly handle arbitrary complex 3D geometries and is fast in practice. The source code of TetGen is freely available.This article presents the essential algorithms and techniques used to develop TetGen. The intended audience are researchers or developers in mesh generation or other related areas. It describes the key software components of TetGen, including an efficient tetrahedral mesh data structure, a set of enhanced local mesh operations (combination of flips and edge removal), and filtered exact geometric predicates. The essential algorithms include incremental Delaunay algorithms for inserting vertices, constrained Delaunay algorithms for inserting constraints (edges and triangles), a new edge recovery algorithm for recovering constraints, and a new constrained Delaunay refinement algorithm for adaptive quality tetrahedral mesh generation. Experimental examples as well as comparisons with other softwares are presented.
1,290 citations
TL;DR: CGALmesh provides guarantees on approximation quality and on the size and shape of the mesh elements and provides four optional mesh optimization algorithms to further improve the mesh quality.
Abstract: CGALmesh is the mesh generation software package of the Computational Geometry Algorithm Library (CGAL). It generates isotropic simplicial meshes—surface triangular meshes or volume tetrahedral meshes—from input surfaces, 3D domains, and 3D multidomains, with or without sharp features. The underlying meshing algorithm relies on restricted Delaunay triangulations to approximate domains and surfaces and on Delaunay refinement to ensure both approximation accuracy and mesh quality. CGALmesh provides guarantees on approximation quality and on the size and shape of the mesh elements. It provides four optional mesh optimization algorithms to further improve the mesh quality. A distinctive property of CGALmesh is its high flexibility with respect to the input domain representation. Such a flexibility is achieved through a careful software design, gathering into a single abstract concept, denoted by the oracle, all required interface features between the meshing engine and the input domain. We already provide oracles for domains defined by polyhedral and implicit surfaces.
69 citations
26 Oct 2015
TL;DR: This work presents an efficient algorithm to convert an arbitrary manifold triangle mesh M into a Delaunay mesh, and shows that the constructed DM has O(Kn) vertices, where n is the number of vertices in M and K is a model-dependent constant.
Abstract: Delaunay meshes (DM) are a special type of triangle mesh where the local Delaunay condition holds everywhere. We present an efficient algorithm to convert an arbitrary manifold triangle mesh M into a Delaunay mesh. We show that the constructed DM has O(Kn) vertices, where n is the number of vertices in M and K is a model-dependent constant. We also develop a novel algorithm to simplify Delaunay meshes, allowing a smooth choice of detail levels. Our methods are conceptually simple, theoretically sound and easy to implement. The DM construction algorithm also scales well due to its O(nK log K) time complexity. Delaunay meshes have many favorable geometric and numerical properties. For example, a DM has exactly the same geometry as the input mesh, and it can be encoded by any mesh data structure. Moreover, the empty geodesic circumcircle property implies that the commonly used cotangent Laplace-Beltrami operator has non-negative weights. Therefore, the existing digital geometry processing algorithms can benefit the numerical stability of DM without changing any codes. We observe that DMs can improve the accuracy of the heat method for computing geodesic distances. Also, popular parameterization techniques, such as discrete harmonic mapping, produce more stable results on the DMs than on the input meshes.
54 citations
TL;DR: A simple and flexible algorithm for finding zeros of a complex function is presented, based on sampling the function at nodes of a regular or a self-adaptive mesh and on the analysis of the function sign changes, which creates a set of candidate points.
Abstract: A simple and flexible algorithm for finding zeros of a complex function is presented. An arbitrary-shaped search region can be considered and a very wide class of functions can be analyzed, including those containing singular points or even branch cuts. The proposed technique is based on sampling the function at nodes of a regular or a self-adaptive mesh and on the analysis of the function sign changes. As a result, a set of candidate points is created, where the signs of the real and imaginary parts of the function change simultaneously. To verify and refine the results, an iterative algorithm is applied. The validity of the presented technique is supported by the results obtained in numerical tests involving three different types of functions.
45 citations
TL;DR: How the near-wall mesh quality is controlled and improved by the new method while the computational time is maintained to be comparable to the original Delaunay graph mapping method is shown.
41 citations
TL;DR: This work proposes a new approach to anisotropic mesh generation, relying on the notion of an isotropic Delaunay meshes, a mesh in which the star of each vertex consists of simplices that are Delaunays for the metric associated to vertex $v$.
Abstract: Anisotropic meshes are triangulations of a given domain in the plane or in higher dimensions, with elements elongated along prescribed directions. Anisotropic triangulations are known to be well suited for interpolation of functions or solving PDEs. Assuming that the anisotropic shape requirements for mesh elements are given through a metric field varying over the domain, we propose a new approach to anisotropic mesh generation, relying on the notion of anisotropic Delaunay meshes. An anisotropic Delaunay mesh is defined as a mesh in which the star of each vertex $v$ consists of simplices that are Delaunay for the metric associated to vertex $v$. This definition works in any dimension and allows us to define a simple refinement algorithm. The algorithm takes as input a domain and a metric field and provides, after completion, an anisotropic mesh whose elements are sized and shaped according to the metric field.
31 citations
TL;DR: This work proposes a new approach to generate an anisotropic mesh that approximates S with elements shaped according to the metric field, which relies on the well-established concepts of restricted Delaunay triangulation and Delaunays refinement and comes with theoretical guarantees.
Abstract: Anisotropic simplicial meshes are triangulations with elements elongated along prescribed directions. Anisotropic meshes have been shown well suited for interpolation of functions or solving PDEs. They can also significantly enhance the accuracy of a surface representation. Given a surface S endowed with a metric tensor field, we propose a new approach to generate an anisotropic mesh that approximates S with elements shaped according to the metric field. The algorithm relies on the well-established concepts of restricted Delaunay triangulation and Delaunay refinement and comes with theoretical guarantees. The star of each vertex in the output mesh is Delaunay for the metric attached to this vertex. Each facet has a good aspect ratio with respect to the metric specified at any of its vertices. The algorithm is easy to implement. It can mesh various types of surfaces like implicit surfaces, polyhedra, or isosurfaces in 3D images. It can handle complicated geometries and topologies, and very anisotropic metric fields.
30 citations
TL;DR: This paper presents a fully automatic Delaunay based sculpting algorithm for approximating the shape of a finite set of points S in R 2 and introduces the notion of directed boundary samples which characterizes the two dimensional objects based on the alignment of their boundaries in the cavities.
Abstract: In this paper, we present a fully automatic Delaunay based sculpting algorithm for approximating the shape of a finite set of points S in R 2 . The algorithm generates a relaxed Gabriel graph ( R G G ) that consists of most of the Gabriel edges and a few non-Gabriel edges induced by the Delaunay triangulation. Holes are characterized through a structural pattern called as body-arm formed by the Delaunay triangles in the void regions. R G G is constructed through an iterative removal of Delaunay triangles subjected to circumcenter (of triangle) and topological regularity constraints in O ( n log n ) time using O ( n ) space. We introduce the notion of directed boundary samples which characterizes the two dimensional objects based on the alignment of their boundaries in the cavities. Theoretically, we justify our algorithm by showing that under given sampling conditions, the boundary of R G G captures the topological properties of objects having directed boundary samples. Unlike many other approaches, our algorithm does not require tuning of any external parameter to approximate the geometric shape of point set and hence human intervention is completely eliminated. Experimental evaluations of the proposed technique are done using L 2 error norm measure, which is the symmetric difference between the boundaries of reconstructed shape and the original shape. We demonstrate the efficacy of our automatic shape reconstruction technique by showing several examples and experiments with varying point set densities and distributions.
28 citations
TL;DR: Theoretically, the proposed Delaunay-based surface reconstruction algorithm is justified by establishing a topological guarantee on the 3D shape-hull with the help of topological rules and the effectiveness of the approach is demonstrated with experimental results on models with sharp features and sparsely distributed point clouds.
Abstract: Given a finite set of points S ? R 2 , we define a proximity graph called as shape-hull graph ( SHG ( S ) ) that contains all Gabriel edges and a few non-Gabriel edges of Delaunay triangulation of S . For any S , SHG ( S ) is topologically regular with its boundary (referred to as shape-hull ( SH )) homeomorphic to a simple closed curve. We introduce the concept of divergent concavity for simple, closed, planar curves based on the alignment of curves in concave portions and discuss various measures to characterize curves having divergent concavity. Under sufficiently dense sampling, we prove that SH ( S ) , where S is sampled from a divergent concave curve Σ D , represents a piece-wise linear approximation of Σ D . We extend this result to provide a sculpting algorithm for closed surface reconstruction from a set of raw samples. The surface is constructed through a repeated elimination of Delaunay tetrahedra subjected to circumcenter and topological constraints. Theoretically, we justify our algorithm by establishing a topological guarantee on the 3D shape-hull with the help of topological rules. We demonstrate the effectiveness of our approach with experimental results on models with sharp features and sparsely distributed point clouds. Compared to existing sculpting approaches for surface reconstruction that require either a parameter tuning or several stages, our approach is simple, non-parametric, single stage and reconstructs topologically correct piece-wise linear approximation for divergent concave surfaces. Delaunay-based surface reconstruction algorithm has been proposed.It is a non-parametric and single stage approach.Theoretical guarantee has been discussed.
25 citations
TL;DR: A non-structured discretization method in which the subsurface with rolling terrain is divided into numbers of Delaunay triangular cells and each mesh has the uniform physical property distributions for gravity and magnetic anomalies.
21 citations
TL;DR: A layout preservation is introduced, which extracts placement and routing behaviors from an existing layout into a crossing graph via constrained Delaunay triangulation, and later this crossing graph can be migrated into multiple layouts with placement and routed reconnection.
Abstract: Analog layout generation in the advanced CMOS design is challenging by its increasing layout constraints and performance requirements This situation becomes more intricate by the growing parasitic variability and manufacturing reliability To facilitate the feasibility of template-based layout migration, this paper first introduces a layout preservation, which extracts placement and routing behaviors from an existing layout into a crossing graph via constrained Delaunay triangulation And later this crossing graph can be migrated into multiple layouts with placement and routing reconnection The proposed approach also provides a refinement for wire to optimize the performance metrics This approach is applied to a variable-gain amplifier, a folded-cascode operational amplifier, and a low dropout regulator The experimental results demonstrate more possibility on layout migration, such that averagely more than 75% routing of migrated layout is generated by our approach Additionally, it exhibits the productivity with qualified performance on different designs
TL;DR: A randomized algorithm for inserting a segment into a CDT in expected time linear in the number of edges the segment crosses is given, and it is demonstrated with a performance comparison that for segments that cross many edges, the algorithm is faster than gift-wrapping.
Abstract: The most commonly implemented method of constructing a constrained Delaunay triangulation (CDT) in the plane is to first construct a Delaunay triangulation, then incrementally insert the input segments one by one. For typical implementations of segment insertion, this method has a ? ( k n 2 ) worst-case running time, where n is the number of input vertices and k is the number of input segments.We give a randomized algorithm for inserting a segment into a CDT in expected time linear in the number of edges the segment crosses. We demonstrate with a performance comparison that for segments that cross many edges, our algorithm is faster than gift-wrapping. We also show that a simple algorithm for segment location, which precedes segment insertion, is fast enough never to be a bottleneck in CDT construction. A result of Agarwal, Arge, and Yi implies that randomized incremental construction of CDTs by our segment insertion algorithm takes expected O ( n log ? n + n log 2 ? k ) time. We show that this bound is tight by deriving a matching lower bound. Although there are CDT construction algorithms guaranteed to run in O ( n log ? n ) time, incremental CDT construction is easier to program and competitive in practice.Lastly, we partly extend the analysis (albeit not the linear-time insertion algorithm) to randomized incremental CDT construction in three dimensions.
TL;DR: The dual of the digital Voronoi diagram constructed by flooding the plane from the data points gives a geometrically and topologically correct dual triangulation, providing the proof of correctness for recently developed GPU algorithms that outperform traditional CPU algorithms for constructing two-dimensional Delaunay triangulations.
Abstract: We prove that the dual of the digital Voronoi diagram constructed by flooding the plane from the data points gives a geometrically and topologically correct dual triangulation. This provides the proof of correctness for recently developed GPU algorithms that outperform traditional CPU algorithms for constructing two-dimensional Delaunay triangulations.
TL;DR: A fast unstructured mesh generation algorithm based on conforming centroidal Voronoi Delaunay triangulation (CfCVDT) algorithm that is capable of generating high quality body/interface fitted meshes for complicate domains/interfaces.
TL;DR: An almost tight upper bound of O(n2+ε), for any ε > 0, is obtained on the maximum number of discrete changes that the Delaunay triangulation DT(P) of P experiences during this motion.
Abstract: Let P be a collection of n points in the plane, each moving along some straight line at unit speed. We obtain an almost tight upper bound of O(n2+e), for any e > 0, on the maximum number of discrete changes that the Delaunay triangulation DT(P) of P experiences during this motion. Our analysis is cast in a purely topological setting, where we only assume that (i) any four points can be co-circular at most three times, and (ii) no triple of points can be collinear more than twice; these assumptions hold for unit speed motions.
07 Sep 2015
TL;DR: This paper proposes an efficient policy to deal with moving points in the manifold estimation process and tests its effectiveness with four sequences of the KITTI dataset and shows the effectiveness in comparison with state-of-the-art approaches.
Abstract: As incremental Structure from Motion algorithms become effective, a good sparse point cloud representing the map of the scene becomes available frame-by-frame. From the 3D Delaunay triangulation of these points, state-of-the-art algorithms build a manifold rough model of the scene. These algorithms integrate incrementally new points to the 3D reconstruction only if their position estimate does not change. Indeed, whenever a point moves in a 3D Delaunay triangulation, for instance because its estimation gets refined, a set of tetrahedra have to be removed and replaced with new ones to maintain the Delaunay property; the management of the manifold reconstruction becomes thus complex and it entails a potentially big overhead. In this paper we investigate different approaches and we propose an efficient policy to deal with moving points in the manifold estimation process. We tested our approach with four sequences of the KITTI dataset and we show the effectiveness of our proposal in comparison with state-of-the-art approaches.
TL;DR: In this paper, the bend structures of linear features are identified by using a constrained Delaunay triangulation (CDT in abbreviation) model and represented by binary bend-structure trees.
Abstract: In this article, a new morphing method is proposed for two linear features at different scales, based on their entire structures (MLBES in abbreviation). First, the bend structures of the linear features are identified by using a constrained Delaunay triangulation (CDT in abbreviation) model and represented by binary bend-structure trees. By matching the independent bends represented by the bend-structure trees, corresponding independent bends are obtained. These corresponding independent bends are further used to match their child bends based on hierarchical bend structures so that corresponding bends are obtained. On this basis, the two linear features are split into pairs of corresponding subpolylines by the start and end points of the corresponding bends. Second, structures of the corresponding subpolylines are identified by the Douglas-Peucker algorithm and represented by binary line generalization trees (BLG-trees in abbreviation). The corresponding subpolylines are split into smaller corresponding subpolylines by matching the nodes of the BLG-trees. Third, the corresponding points are identified by using the linear interpolation algorithm for every pair of corresponding subpolylines. Finally, straight-line trajectories are employed to generate a family of intermediate-scale linear features. By comparison with other methods, it is found that MLBES is accurate and efficient.
TL;DR: A tightly coupled parallelization technique is devised to boost the performance of the 4-dimensional mesher, thereby taking advantage of the multi-core and many-core platforms already available in the market.
Abstract: In this paper, we present a Delaunay refinement algorithm for 4-dimensional ($$\hbox {3D}+t$$3D+t) segmented images. The output mesh is proved to consist of sliver-free simplices. Assuming that the hyper-surface is a closed smooth manifold, we also guarantee faithful geometric and topological approximation. We implement and demonstrate the effectiveness of our method on publicly available segmented cardiac images. Finally, we devise a tightly coupled parallelization technique to boost the performance of our 4-dimensional mesher, thereby taking advantage of the multi-core and many-core platforms already available in the market.
TL;DR: The proofs for the 2-manifold tests that are used during the growing of the surface reconstruction from a sparse cloud of points are detailed: it is shown that the tetrahedron-based test and the test for adding (or subtracting) one tetrahedral to (or from) the list are equivalent to standard tests based on triangles.
Abstract: This is a companion paper of a previous work on the surface reconstruction from a sparse cloud of points, which are estimated by Structure-from-Motion. The surface is a 2-manifold sub-complex of the 3D Delaunay triangulation of the points. It is computed as the boundary of a list of tetrahedra, which grows in the set of Delaunay tetrahedra. Here we detail the proofs for the 2-manifold tests that are used during the growing: we show that the tetrahedron-based test and the test for adding (or subtracting) one tetrahedron to (or from) the list are equivalent to standard tests based on triangles.
14 Dec 2015
TL;DR: This paper proposes a node placement algorithm based on iterative Delaunay triangulation, which is to first obtain Delauny triangles for some initial seed nodes, to truly achieve complete coverage yet with significantly smaller computation time.
Abstract: This paper studies the sensor placement problem for ensuring complete coverage in an area with obstacles. Instead of using the simplistic disk coverage model, we adopt our recently proposed confident information coverage model for field attribute monitoring applications. We propose a node placement algorithm based on iterative Delaunay triangulation, which is to first obtain Delaunay triangles for some initial seed nodes. Among all Delaunay triangles, we propose algorithms to find a valid one yet with the largest coverage hole for placing a new node. The Delaunay triangulation process is then repeated, until all the Delaunday triangles can be completely covered. Simulation results show that our algorithm has comparable performance in terms of the number of placed nodes, compared with a peer algorithm based on a grid approach to discretize the continuous field. However, our algorithm can truly achieve complete coverage yet with significantly smaller computation time.
TL;DR: This work considers higher-order triangular-distance Delaunay graphs, namely k-TD, which contains an edge between two points if the interior of the smallest homothet of ?
Abstract: We consider an extension of the triangular-distance Delaunay graphs (TD-Delaunay) on a set P of points in general position in the plane In TD-Delaunay, the convex distance is defined by a fixed-oriented equilateral triangle ?, and there is an edge between two points in P if and only if there is an empty homothet of ? having the two points on its boundary We consider higher-order triangular-distance Delaunay graphs, namely k-TD, which contains an edge between two points if the interior of the smallest homothet of ? having the two points on its boundary contains at most k points of P We consider the connectivity, Hamiltonicity and perfect-matching admissibility of k-TD Finally we consider the problem of blocking the edges of k-TD
14 Sep 2015
TL;DR: Algorithms to compute the Delaunay triangulation of a point set L using only (squared) distance comparisons (i.e., predicates of degree 2) are proposed and a new perturbation scheme is introduced to compute a perturbed set L′ close to L such that theDelaunay Triangulation and the witness complex coincide.
Abstract: We propose algorithms to compute the Delaunay triangulation of a point set L using only (squared) distance comparisons (i.e., predicates of degree 2). Our approach is based on the witness complex, a weak form of the Delaunay complex introduced by Carlsson and de Silva. We give conditions that ensure that the witness complex and the Delaunay triangulation coincide and we introduce a new perturbation scheme to compute a perturbed set L′ close to L such that the Delaunay triangulation and the witness complex coincide. Our perturbation algorithm is a geometric application of the Moser-Tardos constructive proof of the Lovasz local lemma.
TL;DR: The effect of using several optimal triangulations for P is investigated, and careful edge flipping in the constrained Delaunay triangulation leads to an axis competitive to 'high quality axes' requiring ?
30 Apr 2015-The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences
TL;DR: In this paper, the authors proposed an approach to derive a tide-coordinate shoreline from two extracted instantaneous shorelines corresponding to a nearly low tide and high tide events by using the Modification of Normalized Difference Water Index (MNDWI) and kmeans clustering method.
Abstract: . Due to both natural and anthropogenic causes, the coastal lines keeps changing dynamically and continuously their shape, position and extend over time. In this paper we propose an approach to derive a tide-coordinate shoreline from two extracted instantaneous shorelines corresponding to a nearly low tide and high tide events. First, all the multispectral images are panshaperned to meet the 15 meters spatial resolution of the panchromatic images. Second, by using the Modification of Normalized Difference Water Index (MNDWI) and the kmeans clustering method we extract the raster shoreline for each image acquisition time. Third, each raster shoreline is smoothed and vectorized using a penalized least square method. Fourth, a 2D constrained Delaunay triangulation is built from the two extracted instantaneous shorelines with their respective heights interpolated from a Tidal gauche station. Finally, the desired tide-coordinate shoreline is interpolated from the previous triangular intertidal surface. The results show that an automatic tide-coordinated extraction method can be efficiently implemented using free available remote sensing imagery data (Landsat 8) and open source software (QGIS and Orfeo toolbox) and python scripting for task automation and software integration.
22 Jun 2015
TL;DR: A novel smoothing method based on weighted Laplacian formulation is applied to resolve the heat conduction equation by finite-volume discretizations with Voronoi diagram and the computational cost is lower when using the proposed approach than when applying any of the other approaches.
Abstract: In this work, a novel smoothing method based on weighted Laplacian formulation is applied to resolve the heat conduction equation by finite-volume discretizations with Voronoi diagram. When a minimum number of vertices is obtained, the mesh is smoothed by means of a new approach to the weighted Laplacian formulation. The combination of techniques allows to solve the resulting linear system by the Conjugate Gradient Method. The new approach to the weighted Laplacian formulation within the set of techniques is compared to other 4 approaches to the weighted Laplacian formulation. Comparative analysis of the results shows that the proposed approach allows to maintain the approximation and presents smaller number of vertices than any of the other 4 approaches. Thus, the computational cost of the resolution is lower when using the proposed approach than when applying any of the other approaches and it is also lower than using only Delaunay refinements.
DOI•
07 Dec 2015TL;DR: The comparison of the methods showed that in all the analysed objects the Medial Axis (Transform) gives the smallest distortion and deviation values, which allows us to recommend it.
Abstract: The article presents a method that would compare skeletonisation methods for areal objects. The skeleton of an areal object, being its linear representation, is used, among others, in cartographic visualisation. The method allows us to compare between any skeletonisation methods in terms of the deviations of distance differences between the skeleton of the object and its border from one side and the distortions of skeletonisation from another. In the article, 5 methods were compared: Voronoi diagrams, densifi ed Voronoi diagrams, constrained Delaunay triangulation, Straight Skeleton and Medial Axis (Transform). The results of comparison were presented on the example of several areal objects. The comparison of the methods showed that in all the analysed objects the Medial Axis (Transform) gives the smallest distortion and deviation values, which allows us to recommend it.
TL;DR: This paper presents proofs that give the upper and lower bounds of mesh quality (in terms of several triangle aspect ratios) for the reconstructed mesh.
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TL;DR: This work proposes a nonparametric process to compute potential values by the local information, based on the Delaunay Triangulation or its dual Voronoi tessellation, which positively demonstrates the superiority of these parametric and non Parametric IT-based methods.
Abstract: In our physically inspired in-tree (IT) based clustering algorithm and the series after it, there is only one free parameter involved in computing the potential value of each point. In this work, based on the Delaunay Triangulation or its dual Voronoi tessellation, we propose a nonparametric process to compute potential values by the local information. This computation, though nonparametric, is relatively very rough, and consequently, many local extreme points will be generated. However, unlike those gradient-based methods, our IT-based methods are generally insensitive to those local extremes. This positively demonstrates the superiority of these parametric (previous) and nonparametric (in this work) IT-based methods.
TL;DR: Experimental results show that the new method can generate ideal tetrahedral meshes for closed implicit surfaces efficiently that are Delaunay based and has the advantage of high efficiency and nice performance at surface boundaries.
Abstract: We present a heuristic approach to tetrahedral mesh generation for implicit closed surfaces. It consists of a surface sampling step and a volume sampling step that both work in a unified optimization framework. First, high-quality isotropic samplings as well as a triangular mesh on the surface are generated. Then uniform volume samplings are determined by optimizing the point distribution inside the closed surface domain. Finally, the tetrahedral mesh is easily obtained by constrained Delaunay triangulation. Experimental results show that the new method can generate ideal tetrahedral meshes for closed implicit surfaces efficiently that are Delaunay based. Our method has the advantage of high efficiency and nice performance at surface boundaries. Copyright © 2015 John Wiley & Sons, Ltd.
01 Nov 2015
TL;DR: An algorithm for triangular mesh generation from unorganized points based on 3D Delaunay tetrahedralization and mesh-growing method that is general and applicable to various object topologies is presented.
Abstract: This paper presents an algorithm for triangular mesh generation from unorganized points based on 3D Delaunay tetrahedralization and mesh-growing method. This algorithm requires the point density to meet the well-sampled condition in smooth regions and dense sampling in sections of a great curvature and two close opposite surfaces. The principle of the algorithm is as follows. It begins with 3D Delaunay tetrahedralization of all sampling points. Then extract part of triangles belonging to the surface as the seed facets according to the rough separation characteristics which based on the angle formed by the circumscribing balls of incident tetrahedrons. Finally, the algorithm grows the seed facets from front triangles to all triangles of the surface. This paper shows several experimental results which explain this approach is general and applicable to various object topologies.