SGP17: Eurographics Symposium on Geometry Processing - Posters

Permanent URI for this collection

https://diglib.eg.org/handle/10.2312/2631655

Browse

Browsing SGP17: Eurographics Symposium on Geometry Processing - Posters by Subject "Computing methodologies"

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Localized Manifold Harmonics for Spectral Shape Analysis
    (The Eurographics Association, 2017) Melzi, Simone; Rodolà, Emanuele; Castellani, Umberto; Bronstein, Michael M.; Jakob Andreas Bærentzen and Klaus Hildebrandt
    The use of Laplacian eigenfunctions is ubiquitous in a wide range of computer graphics and geometry processing applications. In particular, Laplacian eigenbases allow generalizing the classical Fourier analysis to manifolds. A key drawback of such bases is their inherently global nature, as the Laplacian eigenfunctions carry geometric and topological structure of the entire manifold. In this paper, we introduce a new framework for local spectral shape analysis. We show how to efficiently construct localized orthogonal bases by solving an optimization problem that in turn can be posed as the eigendecomposition of a new operator obtained by a modification of the standard Laplacian. We study the theoretical and computational aspects of the proposed framework and showcase our new construction on the classical problems of shape approximation and correspondence.
  • Thumbnail Image
    Item
    PCR: A Geometric Cocktail for Triangulating Point Clouds Beautifully Without Angle Bounds
    (The Eurographics Association, 2017) Leitão, Gonçalo N. V.; Gomes, Abel J. P.; Jakob Andreas Bærentzen and Klaus Hildebrandt
    Reconstructing a triangulated surface from a point cloud through a mesh growing algorithm is a difficult problem, in largely because they use bounds for the admissible dihedral angle to decide on the next triangle to be attached to the mesh front. This paper proposes a solution to this problem by combining three geometric properties: proximity, co-planarity, and regularity; hence, the PCR cocktail. The PCR cocktail-based algorithm works well even for point clouds with non-uniform point density, holes, high curvature regions, creases, apices, and noise.
  • Thumbnail Image
    Item
    A Primal-to-Primal Discretization of Exterior Calculus on Polygonal Meshes
    (The Eurographics Association, 2017) Ptackova, Lenka; Velho, Luiz; Jakob Andreas Bærentzen and Klaus Hildebrandt
    Discrete exterior calculus (DEC) offers a coordinate-free discretization of exterior calculus especially suited for computations on curved spaces. We present an extended version of DEC on surface meshes formed by general polygons that bypasses the construction of any dual mesh and the need for combinatorial subdivisions. At its core, our approach introduces a polygonal wedge product that is compatible with the discrete exterior derivative in the sense that it obeys the Leibniz rule. Based on this wedge product, we derive a novel primal-primal Hodge star operator, which then leads to a discrete version of the contraction operator. We show preliminary results indicating the numerical convergence of our discretization to each one of these operators.