2D Shape Manipulation Using Equilateral Triangle Mesh

2012 ◽  
Author(s):  
Yong Jie Shi ◽  
Dan Xu
Keyword(s):  
Equilateral Triangle ◽  
Triangle Mesh ◽  
Shape Manipulation

Research on hole filling algorithm in triangle mesh models

2009 ◽  
Vol 29 (8) ◽  
pp. 2035-2037 ◽  
Author(s):  
Jian-lei TIAN ◽  
Xu-min LIU ◽  
Yong GUAN
Keyword(s):  
Triangle Mesh ◽  
Hole Filling ◽  
Mesh Models

scholarly journals Dual Zero-Watermarking Scheme for Two-Dimensional Vector Map Based on Delaunay Triangle Mesh and Singular Value Decomposition

2019 ◽  
Vol 9 (4) ◽  
pp. 642 ◽  
Author(s):  
Xu Xi ◽  
Xinchang Zhang ◽  
Weidong Liang ◽  
Qinchuan Xin ◽  
Pengcheng Zhang
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Two Dimensional ◽  
Triangle Mesh ◽  
Vector Map ◽  
Vector Maps ◽  
Feature Sequence ◽  
Zero Watermarking ◽  
Value Decomposition ◽  
Watermarking Scheme

Digital watermarking is important for the copyright protection of electronic data, but embedding watermarks into vector maps could easily lead to changes in map precision. Zero-watermarking, a method that does not embed watermarks into maps, could avoid altering vector maps but often lack of robustness. This study proposes a dual zero-watermarking scheme that improves watermark robustness for two-dimensional (2D) vector maps. The proposed scheme first extracts the feature vertices and non-feature vertices of the vector map with the Douglas-Peucker algorithm and subsequently constructs the Delaunay Triangulation Mesh (DTM) to form a topological feature sequence of feature vertices as well as the Singular Value Decomposition (SVD) matrix to form intrinsic feature sequence of non-feature vertices. Next, zero-watermarks are obtained by executing exclusive disjunction (XOR) with the encrypted watermark image under the Arnold scramble algorithm. The experimental results show that the scheme that synthesizes both the feature and non-feature information improves the watermark capacity. Making use of complementary information between feature and non-feature vertices considerably improves the overall robustness of the watermarking scheme. The proposed dual zero-watermarking scheme combines the advantages of individual watermarking schemes and is robust against such attacks as geometric attacks, vertex attacks and object attacks.

scholarly journals GERBERT OF AURILLAC: ASTRONOMY AND GEOMETRY IN TENTH CENTURY EUROPE

2013 ◽  
Vol 23 ◽  
pp. 467-471 ◽  
Author(s):  
COSTANTINO SIGISMONDI
Keyword(s):  
Rational Approximation ◽  
Equilateral Triangle ◽  
Tenth Century ◽  
The Sun ◽  
Astronomical Observations ◽  
The North ◽  
Celestial Pole ◽  
Gerbert Of Aurillac

Gerbert of Aurillac was the most prominent personality of the tenth century: astronomer, organ builder and music theoretician, mathematician, philosopher, and finally pope with the name of Silvester II (999–1003). Gerbert introduced firstly the arabic numbers in Europe, invented an abacus for speeding the calculations and found a rational approximation for the equilateral triangle area, in the letter to Adelbold here discussed. Gerbert described a semi-sphere to Constantine of Fleury with built-in sighting tubes, used for astronomical observations. The procedure to identify the star nearest to the North celestial pole is very accurate and still in use in the XII century, when Computatrix was the name of Polaris. For didactical purposes the Polaris would have been precise enough and much less time consuming, but here Gerbert was clearly aligning a precise equatorial mount for a fixed instrument for accurate daytime observations. Through the sighting tubes it was possible to detect equinoxes and solstices by observing the Sun in the corresponding days. The horalogium of Magdeburg was probably a big and fixed-mount nocturlabe, always pointing the star near the celestial pole.

Dual-Primal Mesh Optimization for Polygonized Implicit Surfaces With Sharp Features

2002 ◽  
Vol 2 (4) ◽  
pp. 277-284 ◽  
Author(s):  
Yutaka Ohtake ◽  
Alexander G. Belyaev
Keyword(s):  
Adaptive Mesh ◽  
Implicit Surfaces ◽  
Marching Cubes ◽  
Triangle Mesh ◽  
Implicit Surface ◽  
Weighted Vertex ◽  
Visualization Toolkit ◽  
Object Oriented Approach ◽  
Speed And Accuracy ◽  
Dual Mesh

A new method for improving polygonizations of implicit surfaces with sharp features is proposed. The method is based on the observation that, given an implicit surface with sharp features, a triangle mesh whose triangles are tangent to the implicit surface at certain inner triangle points gives a better approximation of the implicit surface than the standard Marching Cubes mesh [Lorensen, W.E., and Cline, H.E., 1987, Computer Graphics (Proceedings of SIGGRAPH ’87), 21(3), pp. 163–169] (in our experiments we use VTK Marching Cubes [Schroeder, W., Martin, K., and Lorensen, W., 1998, The Visualization Toolkit: An Object-Oriented Approach to 3-D Graphics, Prentice Hall]). First, given an initial triangle mesh, its dual mesh composed of the triangle centroids is considered. Then the dual mesh is modified such that its vertices are placed on the implicit surface and the mesh dual to the modified dual mesh is considered. Finally the vertex positions of that “double dual” mesh are optimized by minimizing a quadratic energy measuring a deviation of the mesh normals from the implicit surface normals computed at the vertices of the modified dual mesh. In order to achieve an accurate approximation of fine surface features, these basic steps are combined with adaptive mesh subdivision and curvature-weighted vertex resampling. The proposed method outperforms approaches based on the mesh evolution paradigm in speed and accuracy.

Optimized triangle mesh reconstruction from unstructured points

2003 ◽  
Vol 19 (1) ◽  
pp. 23-37 ◽  
Author(s):  
Yong-Jin Liu ◽  
Matthew Ming-Fai Yuen
Keyword(s):  
Triangle Mesh ◽  
Mesh Reconstruction
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