Spherical parametrization and remeshing

By Emil Praun, Hugues Hoppe. ACM Transactions on Graphics, 2003

511 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/49049f76cfb877c6e521a87ee80aaecfad49ec15

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

Polynomial splines over hierarchical T-meshes (2008, background): “The reader is referred to [10,12,19] for some references on this topic.”
Stereographic wavelet frames on the sphere (2005, background): “Spherical wavelet frames offer a way to model efficiently functions that are deformations of a spherical base and could thus be of interest in computer graphics [9, 16].”
Möbius voting for surface correspondence (2009, methodology): “Previous methods that have mapped meshes to spheres [Praun and Hoppe 2003; Sheffer et al. 2004] or planes [Hormann et al.”
Technologies for 3D mesh compression: A survey (2005, methodology): “Table 3 Bitrates of progressive mesh coding algorithms, which are of the form ''geometry bitrate in bpv:connectivity bitrate in bpv (quantization resolutions in bits)'' O (v log 2 v):N/A Popovic and Hoppe [46] O (v log 2 v):N/A Taubin et al. [47] 7–10:20–40 (6) Pajarola and Rossignac [49] 7:12–15 (8”
Convolutional neural networks on surfaces via seamless toric covers (2017, methodology): “For classification tasks, Sinha et al. [2016] parameterize the entire surface using geometry images [Praun and Hoppe 2003] combined with spherical area-preserving parameterizations.”
Ambient Occlusion and Edge Cueing for Enhancing Real Time Molecular Visualization (2006, background): “Following [24], Ms2 is a gnomonic projection over an octahedron, which is unfolded into a square.”
Recent Advances in Remeshing of Surfaces (2008, background): “A number of algorithms for spherical parameterization exist, e.g., [1, 27, 64 ].”
Surface Parameterization: a Tutorial and Survey (2005, unknown): “[62] has been generalized to the spherical case by Praun and Hoppe [58].”
PolyCube-Maps (2004, methodology): “There exist several methods that construct a seamless parameterization of a mesh over a triangulated base complex [Eck et al. 1995; Lee et al. 1998; Khodakovsky et al. 2003; Praun and Hoppe 2003] and use it for remeshing and mesh compression.”
SurfNet: Generating 3D Shape Surfaces Using Deep Residual Networks (2017, background): “This spherical parametrization is converted to a ﬂat and regular geometry image by ﬁrst projecting onto an octahedron and then cutting it along 4 of its 8 edges (see [23]).”
Deep Learning 3D Shapes Using Alt-az Anisotropic 2-Sphere Convolution (2018, methodology): “Spherical parameterization methods (Peng & Timalsena (2016); Praun & Hoppe (2003); Gu et al. (2004)) map a genus-0 3D shape onto a sphere bijectively which provides a global framework for the spherical convolution.”
Image-Based 3D Object Reconstruction: State-of-the-Art and Trends in the Deep Learning Era (2019, methodology): “Spherical parameterizations and geometry images [62], [63], [64] are the most commonly used parameterizations.”
Deep Learning 3D Shape Surfaces Using Geometry Images (2016, methodology): “Different cuts lead to variation in geometry image boundaries [22], and hence, learning them requires the CNN to learn maps between image boundaries in addition to image pixels.”
Mesh parameterization: theory and practice (2007, methodology): “These methods obtain an initial guess by simplifying the model until it becomes a tetrahedron (or at least, convex), trivially embed it on the sphere, and then progressively add back the vertices [Shapiro and Tal, 1998; Praun and Hoppe, 2003].”