The Experts below are selected from a list of 10041 Experts worldwide ranked by ideXlab platform
Jenő Szirmai - One of the best experts on this subject based on the ideXlab platform.
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Interior Angle sums of geodesic triAngles in $S^2 \times R$ and $H^2 \times R$ geometries
arXiv: Metric Geometry, 2019Co-Authors: Jenő SzirmaiAbstract:In the present paper we study $S^2 \times R$ and $H^2 \times R$ geometries, which are homogeneous Thurston 3-geometries. We analyse the Interior Angle sums of geodesic triAngles in both geometries and prove, that in $S^2 \times R$ space it can be larger or equal than $\pi$ and in $H^2 \times R$ space the Angle sums can be less or equal than $\pi$. In our work we will use the projective model of $S^2 \times R$ and $H^2 \times R$ geometries described by E. Molnar in \cite{M97}.
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Interior Angle sums of geodesic triAngles in s 2 times r and h 2 times r geometries
arXiv: Metric Geometry, 2019Co-Authors: Jenő SzirmaiAbstract:In the present paper we study $S^2 \times R$ and $H^2 \times R$ geometries, which are homogeneous Thurston 3-geometries. We analyse the Interior Angle sums of geodesic triAngles in both geometries and prove, that in $S^2 \times R$ space it can be larger or equal than $\pi$ and in $H^2 \times R$ space the Angle sums can be less or equal than $\pi$. In our work we will use the projective model of $S^2 \times R$ and $H^2 \times R$ geometries described by E. Molnar in \cite{M97}.
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$$\mathbf {Nil}$$ Nil Geodesic TriAngles and Their Interior Angle Sums
Bulletin of the Brazilian Mathematical Society New Series, 2018Co-Authors: Jenő SzirmaiAbstract:In this paper we study the Interior Angle sums of geodesic triAngles in $$\mathbf {Nil}$$ Nil geometry and prove that these can be larger, equal or less than $$\pi $$ π . We use for the computations the projective model of $$\mathbf {Nil}$$ Nil introduced by Molnár (Beitr. Algebra Geom. 38(2):261–288, 1997 ).
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$$\mathbf {}$$ Geodesic TriAngles and Their Interior Angle Sums
Bulletin of the Brazilian Mathematical Society New Series, 2018Co-Authors: Jenő SzirmaiAbstract:In this paper we study the Interior Angle sums of geodesic triAngles in \(\mathbf {Nil}\) geometry and prove that these can be larger, equal or less than \(\pi \). We use for the computations the projective model of \(\mathbf {Nil}\) introduced by Molnar (Beitr. Algebra Geom. 38(2):261–288, 1997).
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mathbf geodesic triAngles and their Interior Angle sums
Bulletin of the Brazilian Mathematical Society New Series, 2018Co-Authors: Jenő SzirmaiAbstract:In this paper we study the Interior Angle sums of geodesic triAngles in \(\mathbf {Nil}\) geometry and prove that these can be larger, equal or less than \(\pi \). We use for the computations the projective model of \(\mathbf {Nil}\) introduced by Molnar (Beitr. Algebra Geom. 38(2):261–288, 1997).
Bedrich Benes - One of the best experts on this subject based on the ideXlab platform.
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Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement
IEEE Transactions on Visualization and Computer Graphics, 2017Co-Authors: Dong-ming Yan, David Bommes, Pierre Alliez, Bedrich BenesAbstract:Surface remeshing is a key component in many geometry processing applications. The typical goal consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper the desired application (e.g., the minimum Interior Angle is above an application-dependent threshold). Our algorithm is designed to address all three optimization goals simultaneously by targeting prescribed bounds on approximation error $\delta$ , minimal Interior Angle $\theta$ and maximum mesh complexity $N$ (number of vertices). The approximation error bound $\delta$ is a hard constraint, while the other two criteria are modeled as optimization goals to guarantee feasibility. Our optimization framework applies carefully prioritized local operators in order to greedily search for the coarsest mesh with minimal Interior Angle above $\theta$ and approximation error bounded by $\delta$ . Fast runtime is enabled by a local approximation error estimation, while implicit feature preservation is obtained by specifically designed vertex relocation operators. Experiments show that for reasonable Angle bounds ( $\theta \leq 35^\circ$ ) our approach delivers high-quality meshes with implicitly preserved features (no tagging required) and better balances between geometric fidelity, mesh complexity and element quality than the state-of-the-art.
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Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement
IEEE Transactions on Visualization and Computer Graphics, 2017Co-Authors: Dong-ming Yan, David Bommes, Pierre Alliez, Bedrich BenesAbstract:The typical goal of surface remeshing consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper the desired application. In this paper, we design an algorithm to address all three optimization goals simultaneously. The user specifies desired bounds on approximation error , minimal Interior Angle and maximum mesh complexity N (number of vertices). Since such a desired mesh might not even exist, our optimization framework treats only the approximation error bound as a hard constraint and the other two criteria as optimization goals. More specifically, we iteratively perform carefully prioritized local operators, whenever they do not violate the approximation error bound and improve the mesh otherwise. Our optimization framework greedily searches for the coarsest mesh with minimal Interior Angle above and approximation error bounded by . Fast runtime is enabled by a local approximation error estimation, while implicit feature preservation is obtained by specifically designed vertex relocation operators. Experiments show that our approach delivers high-quality meshes with implicitly preserved features and better balances between geometric fidelity, mesh complexity and element quality than the state-of-the-art.
Yuliang Wang - One of the best experts on this subject based on the ideXlab platform.
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On vanishing and localizing of transmission eigenfunctions near singular points: a numerical study
Inverse Problems, 2017Co-Authors: Eemeli Blåsten, Hongyu Liu, Yuliang WangAbstract:This paper is concerned with the intrinsic geometric structure of Interior transmission eigenfunctions arising in wave scattering theory. We numerically show that the aforementioned geometric structure can be very delicate and intriguing. The major findings can be roughly summarized as follows. We say that a point on the boundary of the inhomogeneity is singular if the surface tangent is discontinuous there. The Interior transmission eigenfunction then vanishes near a singular point where the Interior Angle is less than π, whereas the Interior transmission eigenfunction localizes near a singular point if its Interior Angle is bigger than π. Furthermore, we show that the vanishing and blowup orders are inversely proportional to the Interior Angle of the singular point: the sharper the corner, the higher the convergence order. Our results are first of its type in the spectral theory for transmission eigenvalue problems, and the existing studies in the literature concentrate more on the intrinsic properties of the transmission eigenvalues instead of the transmission eigenfunctions. Due to the finiteness of computing resources, our study is by no means exclusive and complete. We consider our study only in a certain geometric setup including corner, curved corner and edge singularities. Nevertheless, we believe that similar results hold for more general singularities and rigorous theoretical justifications are much desirable. Our study enriches the spectral theory for transmission eigenvalue problems. We also discuss its implication to inverse scattering theory.
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On vanishing and localizing near cusps of transmission eigenfunctions: a numerical study
arXiv: Numerical Analysis, 2017Co-Authors: Eemeli Blåsten, Hongyu Liu, Yuliang WangAbstract:This paper is concerned with the intrinsic geometric structure of Interior transmission eigenfunctions arising in wave scattering theory. We numerically show that the aforementioned geometric structure can be much delicate and intriguing. The major findings can be roughly summarized as follows. If there is a cusp on the support of the underlying potential function, then the Interior transmission eigenfunction vanishes near the cusp if its Interior Angle is less than $\pi$, whereas the Interior transmission eigenfunction localizes near the cusp if its Interior Angle is bigger than $\pi$. Furthermore, we show that the vanishing and blowup orders are inversely proportional to the Interior Angle of the cusp: the sharper the Angle, the higher the convergence order. Our results are first of its type in the spectral theory for transmission eigenvalue problems, and the existing studies in the literature concentrate more on the intrinsic properties of the transmission eigenvalues instead of the transmission eigenfunctions. Due to the limitedness of the computing resources, our study is by no means exclusive and complete. We consider our study only in a certain geometric setup including corner, curved corner and edge singularities. Nevertheless, we believe that similar results hold for more general cusp singularities and rigorous theoretical justifications are much desirable. Our study enriches the spectral theory for transmission eigenvalue problems. We also discuss its implication to inverse scattering theory.
Dong-ming Yan - One of the best experts on this subject based on the ideXlab platform.
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Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement
IEEE Transactions on Visualization and Computer Graphics, 2017Co-Authors: Dong-ming Yan, David Bommes, Pierre Alliez, Bedrich BenesAbstract:Surface remeshing is a key component in many geometry processing applications. The typical goal consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper the desired application (e.g., the minimum Interior Angle is above an application-dependent threshold). Our algorithm is designed to address all three optimization goals simultaneously by targeting prescribed bounds on approximation error $\delta$ , minimal Interior Angle $\theta$ and maximum mesh complexity $N$ (number of vertices). The approximation error bound $\delta$ is a hard constraint, while the other two criteria are modeled as optimization goals to guarantee feasibility. Our optimization framework applies carefully prioritized local operators in order to greedily search for the coarsest mesh with minimal Interior Angle above $\theta$ and approximation error bounded by $\delta$ . Fast runtime is enabled by a local approximation error estimation, while implicit feature preservation is obtained by specifically designed vertex relocation operators. Experiments show that for reasonable Angle bounds ( $\theta \leq 35^\circ$ ) our approach delivers high-quality meshes with implicitly preserved features (no tagging required) and better balances between geometric fidelity, mesh complexity and element quality than the state-of-the-art.
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Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement
IEEE Transactions on Visualization and Computer Graphics, 2017Co-Authors: Dong-ming Yan, David Bommes, Pierre Alliez, Bedrich BenesAbstract:The typical goal of surface remeshing consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper the desired application. In this paper, we design an algorithm to address all three optimization goals simultaneously. The user specifies desired bounds on approximation error , minimal Interior Angle and maximum mesh complexity N (number of vertices). Since such a desired mesh might not even exist, our optimization framework treats only the approximation error bound as a hard constraint and the other two criteria as optimization goals. More specifically, we iteratively perform carefully prioritized local operators, whenever they do not violate the approximation error bound and improve the mesh otherwise. Our optimization framework greedily searches for the coarsest mesh with minimal Interior Angle above and approximation error bounded by . Fast runtime is enabled by a local approximation error estimation, while implicit feature preservation is obtained by specifically designed vertex relocation operators. Experiments show that our approach delivers high-quality meshes with implicitly preserved features and better balances between geometric fidelity, mesh complexity and element quality than the state-of-the-art.
Ángel Plaza - One of the best experts on this subject based on the ideXlab platform.
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Properties of the longest-edge n-section refinement scheme for triangular meshes
Applied Mathematics Letters, 2012Co-Authors: José P. Suárez, Tania Moreno, Pilar Abad, Ángel PlazaAbstract:Abstract We prove that the longest-edge n -section of triAngles for n ⩾ 4 produces a sequence of triAngle meshes with minimum Interior Angle converging to zero. The so called degeneracy property of LE for n ⩾ 4 is proved.
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A new proof of the degeneracy property of the longest-edge n-section refinement scheme for triangular meshes
Applied Mathematics and Computation, 2012Co-Authors: Francisco Perdomo, Ángel PlazaAbstract:In this note, by using complex variable functions, we present a new simpler proof of the degeneracy property of the longest-edge n-section of triAngles for n P 4. This means that the longest-edge n-section of triAngles for n P 4 produces a sequence of triAngles with minimum Interior Angle converging to zero.
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On the non-degeneracy property of the longest-edge trisection of triAngles
Applied Mathematics and Computation, 2010Co-Authors: Ángel Plaza, Sergio Falcon, José P. SuárezAbstract:The longest-edge (LE) trisection of a triAngle t is obtained by joining the two equally spaced points of the longest-edge of t with the opposite vertex. In this paper we prove that for any given triAngle t with smallest Interior Angle @t>0, if the minimum Interior Angle of the three triAngles obtained by the LE-trisection of t into three new triAngles is denoted by @t"1, then @t"1>[email protected]/c"1, where c"[email protected]/3arctan(3/5)~3.1403. Moreover, we show empirical evidence on the non-degeneracy property of the triangular meshes obtained by iterative application of the LE-trisection of triAngles. If @t"n denotes the minimum Angle of the triAngles obtained after n iterative applications of the LE-trisection, then @t"n>@t/c where c is a positive constant independent of n. An experimental estimate of c~6.7052025350 is provided.