Intrinsic Parameterizations of Surface Meshes

By Mathieu Desbrun, Mark Meyer, Pierre Alliez. Computer graphics forum (Print), 2002

720 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/9af118b015b76188a8f4112083c2539e87ca92b9

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

Inter-surface mapping (2004, background): “.2 Distortion metric Many paramet ation distor n measures have been proposed, including angle-preservation (conformal map) [Eck et al 1995; Hormann et al 1999a; Levy et al 2002; Desbrun et al 2002], areapreservatio thalic map) [Desbrun et al 2002], and stretch minimization [Sander et al 2001].”
Cross-parameterization and compatible remeshing of 3D models (2004, methodology): “In this case, standard planar parameterization techniques (e.g. [Desbrun et al. 2002, Levy et al. 2002, Sheffer and de Sturler 2000]) can be used to construct the cross-parameterization.”
The Intrinsic Dimension of Images and Its Impact on Learning (2021, background): “In applications, such as crystallography, computer graphics, and ecology, practitioners depend on data having low intrinsic dimension (Valle & Oganov, 2010; Desbrun et al., 2002; Laughlin, 2014).”
Anisotropic polygonal remeshing (2003, methodology): “We use the discrete conformal parameterization recently presented in [L·evy et al. 2002; Desbrun et al. 2002] as the solution of choice for mapping the 3D surface to a 2D domain: based on a simple variational formulation, this parameterization automatically provides an angle-preserving mapping,…”
GPGPU: general purpose computation on graphics hardware (2004, background): “Background The need for an unstructured sparse matrix solver arises in many simulations involving discretization of linear and non-linear partial differential equations (PDEs) over arbitrary meshes (e.g., [M¨uller et al. 2002; Desbrun et al. 2002; Kobbelt et al. 1998]).”
Fundamentals of spherical parameterization for 3D meshes (2003, background): “Most of the recent works on the subject of parameterization (e.g. [Desbrun et al. 2002; Floater 1997; Levy et al. 2002; Sander et al. 2001; Sheffer and de Sturler 2001]) have focused on defining the distortion, and showing how to minimize it.”
Mean value coordinates for closed triangular meshes (2005, methodology): “Mesh parameterization methods [Hormann and Greiner 2000; Desbrun et al. 2002; Khodakovsky et al. 2003; Schreiner et al. 2004; Floater and Hormann 2005] and freeform deformation methods [Sederberg and Parry 1986; Coquillart 1990; MacCracken and Joy 1996; Kobayashi and Ootsubo 2003] also make heavy…”
Deep Learning 3D Shape Surfaces Using Geometry Images (2016, methodology): “Although, methods for conformal (angle preserving) mesh parametrization abound [4,12,25], there is relatively less work on authalic (area preserving) mesh parametrization.”
Accelerated quadratic proxy for geometric optimization (2016, background): “As linear energies [Lévy et al. 2002; Desbrun et al. 2002] generally cannot avoid flipped elements, many papers focus on non-linear energies [Degener et al. 2003]; MIPS [Hormann and Greiner 2000] uses a non-linear energy that explodes for flipped elements and optimizes one vertex at a time; [Fu et…”
Non-commercial Research and Educational Use including without Limitation Use in Instruction at Your Institution, Sending It to Specific Colleagues That You Know, and Providing a Copy to Your Institution's Administrator. All Other Uses, Reproduction and Distribution, including without Limitation Comm (2005, neutral): “(1) is an excellent predictor of observed NMR spectra in anisotropic liquids.”
Surface Parameterization: a Tutorial and Survey (2005, methodology): “[10] both independently developed a third method to compute discrete conformal mappings which has the advantage of being linear.”
ABF++: fast and robust angle based flattening (2005, methodology): “This is particularly noticeable when comparing the results of ABF to linear, free-boundary techniques [Desbrun et al. 2002; L ´ evy et al. 2002].”
Mesh Manifold Based Riemannian Motion Planning for Omnidirectional Micro Aerial Vehicles (2021, methodology): “One important property needed for this planner is a surface flattening method that provides a bijective one-to-one mapping H. Algorithms such as Tutte Barycentric Mapping [22], Discrete Authalic Parametrization [23] and Floater Mean Value Coordinates [24] provide such a mapping.”
Numerical Computation of Surface Conformal Mappings (2012, positive): “Discrete intrinsic parameterization by minimizing Dirichlet energy was introduced by [19].”
Mesh parameterization: theory and practice (2007, methodology): “One way to enforce hard constraints is by adding them into a regular parameterization formulation using Lagrange multipliers [Desbrun et al., 2002].”
Generalized Barycentric Coordinates on Irregular Polygons (2002, methodology): “Solving the resulting linear system of equations (using a conjugate gradient solver to exploit sparsity) will provide a quick and safe way to obtain a parameterization of an arbitrary mesh [DMA02].”