Hybrid GPU Local Delaunay Triangulation through Points Consolidation

2012 ◽  
pp. 91-113
Author(s):  
Carlos Buchart ◽  
Aiert Amundarain ◽  
Diego Borro
Keyword(s):  
Hybrid Methods ◽  
Graphics Hardware ◽  
Reconstruction Method ◽  
Delaunay Triangulations ◽  
Multiple Points ◽  
Parallel Reconstruction ◽  
Free Set ◽  
Point Projection ◽  
Set Of Points ◽  
Interesting Solution

This chapter describes a surface reconstruction method that mixes interpolating and approximating features and its implementation in graphics hardware. Hybrid methods are useful in areas such sculpting, medicine, and cultural heritage, where details must be preserved. Such cases may also contain noise (due to sampling inaccuracies) or duplicated points (in the case of the scan is done from multiple points of view), where hybrid methods provide an interesting solution. The proposed method makes use of a point projection operator to create a regular distributed and noise free set of points, which is reconstructed using local Delaunay triangulations. Both points projection and triangulation methods are studied in its basic serial version, but aiming to design parallel versions (more specifically GPU implementations) that increase their performance. The adaptations required for the parallel reconstruction are discussed, and several implementation details are given.

Inflectional Convex Space Curves

1984 ◽  
Vol 36 (3) ◽  
pp. 537-549 ◽  
Author(s):  
Tibor Bisztriczky
Keyword(s):  
Convex Hull ◽  
Convex Space ◽  
Intersection Point ◽  
List Type ◽  
Multiple Points ◽  
Space Curves ◽  
Euclidean Three Space ◽  
Set Of Points ◽  
Three Space ◽  
Regular Closed

Let Φ be a regular closed C2 curve on a sphere S in Euclidean three-space. Let H(S)[H(Φ) ] denote the convex hull of S[Φ]. For any point p ∈ H(S), let O(p) be the set of points of Φ whose osculating plane at each of these points passes through p.1. THEOREM ([8]). If Φ has no multiple points and p ∈ H(Φ), then |0(p) | ≧ 3[4] when p is [is not] a vertex of Φ.2. THEOREM ( [9]). a) If the only self intersection point of Φ is a doublepoint and p ∈ H(Φ) is not a vertex of Φ, then |O(p)| ≧ 2.b) Let Φ possess exactly n vertices. Then(1)|O(p)| ≦ nforp ∈ H(S) and(2)if the osculating plane at each vertex of Φ meets Φ at exactly one point, |O(p)| = n if and only if p ∈ H(Φ) is not vertex.

AN EFFICIENT AND SIMPLE QUAD EDGE CONVERSION OF POLYGONAL MAINFOLD OBJECTS

2001 ◽  
Vol 01 (02) ◽  
pp. 251-271
Author(s):  
KWANG-MAN OH ◽  
JEONG-DAN CHOI ◽  
CHAN-SU LEE ◽  
CHAN-JONG PARK ◽  
EE-TAEK LEE
Keyword(s):  
Data Structure ◽  
High Performance ◽  
Graphics Hardware ◽  
Delaunay Triangulations ◽  
Computer Aided Geometric Design ◽  
Real Time Processing ◽  
Time Processing ◽  
Level Of Details ◽  
Efficient Data ◽  
Processing Techniques

This paper presents an efficient and simple quad edge conversion method of polygonal (manifold) objects. In a wide variety of applications such as scientific visualization, virtual reality and computer aided geometric design, polygonal objects are expected to be visualized and manipulated within a given time constraint. To achieve these expectations, it is necessary to introduce an efficient data structure as well as high performance graphics hardware and real-time processing techniques such as simplification and level of details. The quad edge data structure is very efficient for handling polygonal objects even though it was originally designed to handle the subdivisions of manifold objects such as Delaunay triangulations and Voronoi diagrams. It, however, has not been used widely because there is no efficient algorithm for quad edge conversion of conventional polygonal objects. In this paper, we propose a new incremental quad edge conversion algorithm that processes the triangles one by one. Since quad edge has only the splice as a topological operator, the quad edge conversion of each triangle is done by applying three splice operations, a splice per vertex. As an applicaion for the quad edge, a simplification of conventional polygonal objects is implemented. It includes the removing, moving, replacing, and inserting of vertices and edges.

Multi-core parallel reconstruction method for cone-beam computed tomography

2009 ◽  
Author(s):  
Mingjun Li ◽  
Dinghua Zhang ◽  
Kuidong Huang ◽  
Qingchao Yu ◽  
Shunli Zhang
Keyword(s):  
Computed Tomography ◽  
Cone Beam Computed Tomography ◽  
Cone Beam ◽  
Reconstruction Method ◽  
Parallel Reconstruction

A Level Set Method for the Construction of Boundary Conforming Voronoi Regions and Delaunay Triangulations Governed by a Spatial Distribution of Metrics

2014 ◽  
Vol 14 (3) ◽  
Author(s):  
Ü. Keskin ◽  
J. Peiró
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Domain Boundary ◽  
Metric Tensor ◽  
Delaunay Triangulations ◽  
Voronoi Region ◽  
Voronoi Regions ◽  
Boundary Conforming ◽  
Speed Of Propagation ◽  
Set Of Points

A Voronoi region can be interpreted as the shape achieved by a crystal that grows from a seed and stops growing when it reaches either the domain boundary or another crystal. This analogy is exploited here to devise a method for the generation of anisotropic boundary-conforming Voronoi regions for a set of points. This is achieved by simulating the propagation of crystals as evolving fronts modeled by a level set method. The techniques to detect the collision of fronts (crystals), formation of interfaces between seeds, and treatment of boundaries as additional (inner or outer) restricting seeds are described in detail. The generation of anisotropic Voronoi regions consistent with a user-prescribed Riemannian metric is achieved by re-interpreting the metric tensor in terms of the speed of propagation normal to the boundary of the crystal. This re-interpretation offers a better means of restricting metric fields for mesh generation.

Packing a Square Lattice with a Rectangle-Free Set of Points

1987 ◽  
Vol 60 (4) ◽  
pp. 229 ◽  
Author(s):  
N. S. Mendelsohn
Keyword(s):  
Square Lattice ◽  
Free Set ◽  
Set Of Points

Atom Probe Reconstruction With a Locally Varying Emitter Shape

2018 ◽  
Vol 25 (2) ◽  
pp. 280-287 ◽  
Author(s):  
Daniel Beinke ◽  
Guido Schmitz
Keyword(s):  
Atom Probe Tomography ◽  
Local Density ◽  
Atom Probe ◽  
Radial Symmetry ◽  
Reconstruction Technique ◽  
Reconstruction Method ◽  
New Approach ◽  
Surrounding Matrix ◽  
Projection Approach ◽  
Point Projection

AbstractAn improved reconstruction method for atom probe tomography is presented. In this approach, the curvature of the field emitter is variable, in contrast to the conventional reconstruction technique. The information about the tip shape at different stages of the reconstruction is directly extracted from the local density of events on the detector. To this end, the detector and the tip surface are split into different segments. According to the density distribution of events observed on the detector, the size of the corresponding segment on the tip surface is calculated, yielding an emitter profile which is not necessarily spherical. The new approach is demonstrated for emitter structures with radial symmetry that contain a spherical precipitate with a substantially lower or higher evaporation field compared to the surrounding matrix. A comparison to the conventional point projection approach is made.

scholarly journals Competitive Online Routing on Delaunay Triangulations

2017 ◽  
Vol 27 (04) ◽  
pp. 241-253
Author(s):  
Prosenjit Bose ◽  
Jean-Lou De Carufel ◽  
Stephane Durocher ◽  
Perouz Taslakian
Keyword(s):  
Delaunay Triangulation ◽  
Shortest Path ◽  
Competitive Ratio ◽  
Routing Algorithm ◽  
Source Node ◽  
Point Sets ◽  
Target Node ◽  
Delaunay Triangulations ◽  
Online Routing ◽  
Set Of Points

Let [Formula: see text] be a graph, [Formula: see text] be a source node and [Formula: see text] be a target node. The sequence of adjacent nodes (graph walk) visited by a routing algorithm is a [Formula: see text]-competitive route if its length in [Formula: see text] is at most [Formula: see text] times the length of the shortest path from [Formula: see text] to [Formula: see text] in [Formula: see text]. We present a [Formula: see text]-competitive online routing algorithm on the Delaunay triangulation of an arbitrary given set of points in the plane. This improves the competitive ratio on Delaunay triangulations from the previous best of [Formula: see text]. We also present a [Formula: see text]-competitive online routing algorithm for Delaunay triangulations of point sets in convex position.

Low-energy point-reflection EM

1995 ◽  
Vol 53 ◽  
pp. 610-611
Author(s):  
J. C. H. Spence ◽  
X. Zhang ◽  
J. M. Zuo ◽  
U. Weierstall ◽  
E. Munro ◽  
...  
Keyword(s):  
Low Voltage ◽  
High Vacuum ◽  
Ultra High Vacuum ◽  
Experimental Point ◽  
Crystalline Substrate ◽  
Point Reflection ◽  
Reflection Geometry ◽  
Optical Analog ◽  
Point Projection ◽  
Atomically Flat

The limited penetration of the low-voltage point-projection microscope (PPM) may be avoided by using the reflection geometry to image clean surfaces in ultra-high vacuum. Figure 1 shows the geometry we are using for experimental point-reflection (PRM) imaging. A nanotip field-emitter at about 100 - 1000 volts is placed above a grounded atomically flat crystalline substrate, which acts as a mirror and anode. Since most of the potential is dropped very close to the tip, trajectories are reasonably straight if the sample is in the far-field of the tip. A resolution of 10 nm is sought initially. The specular divergent RHEED beam then defines a virtual source S' below the surface, resulting in an equivalent arrangement to PPM (or defocused CBED). Shadow images of surface asperities are then expected on the distant detector, out of focus by the tip-to-sample distance. These images can be interpreted as in-line electron holograms and so reconstructed (see X. Zhang et al, these proceedings). Optical analog experiments confirm the absence of foreshortening when the detector is parallel to the surface.

Fresnel interference in point-projection imaging of purple membrane

1995 ◽  
Vol 53 ◽  
pp. 846-847
Author(s):  
X. Zhang ◽  
J. Spence ◽  
W. Qian ◽  
D. Taylor ◽  
K. Taylor
Keyword(s):  
Detection Efficiency ◽  
Mean Free Path ◽  
Purple Membrane ◽  
Unit Cell Dimension ◽  
Experimental Point ◽  
Membrane Thickness ◽  
Low Energies ◽  
Channel Plate ◽  
Point Projection ◽  
Inelastic Mean Free Path

Experimental point-projection shadow microscope (PPM) images of uncoated, unstained purple membrane (PM, bacteriorhodopsin, a membrane protein from Halobacterium holobium) were obtained recently using 100 volt electrons. The membrane thickness is about 5 nm and the hexagonal unit cell dimension 6 nm. The images show contrast around the edges of small holes, as shown in figure 1. The interior of the film is opaque. Since the inelastic mean free path for 100V electrons in carbon (about 6 Å) is much less than the sample thickness, the question arises that how much, if any, transmission of elastically scattered electrons occurs. A large inelastic contribution is also expected, attenuated by the reduced detection efficiency of the channel plate at low energies. Quantitative experiments using an energy-loss spectrometer are planned. Recently Shedd has shown that at about 100V contrast in PPM images of thin gold films can be explained as Fresnel interference effects between different pinholes in the film, separated by less than the coherence width.

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