Fundamentals of spherical parameterization for 3D meshes

By Craig Gotsman, Xianfeng David Gu, Alla Sheffer. ACM Transactions on Graphics, 2003

341 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/3e82eeaa150a4511003fb84f1add52d165f9d35c

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

Laplace-Beltrami Eigenfunctions Towards an Algorithm That "Understands" Geometry (2006, methodology): “For instance, Colin-de-verdière’s number [3] was used in [12] to construct valid spherical embeddings of genus 0 meshes.”
Face transfer with multilinear models (2005, methodology): “Despite rapid advances in automatic parameterization of meshes (e.g., [Praun and Hoppe 2003; Gotsman et al. 2003]), it took consid- erable experimentation to place many facial scans into detailed correspondence.”
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.”
Surface Parameterization: a Tutorial and Survey (2005, methodology): “A theorem by Colin de Verdière, described in [24], guarantees a valid embedding into the sphere if certain conditions on the eigenvalues of the matrix formed by the left hand sides of the equation hold.”
Spring Embedders and Force Directed Graph Drawing Algorithms (2012, methodology): “Gotsman et al. [34] describe a method for producing such an embedding using a generalization to spherical space of planar methods for expressing convex combinations of points.”
Numerical Computation of Surface Conformal Mappings (2012, background): “Conformal mappings for topological spheres are discussed in [27] and [31].”
Recent Advances in Remeshing of Surfaces (2008, background): “Another way to minimize seams due to cutting is to first parameterize the mesh to a sphere [27], which is then mapped in a highly structured way to the square.”
Technical Section: Discrete Laplace-Beltrami operators for shape analysis and segmentation (2009, methodology): “Spec tral methods have recently gained much interest in computer graphics [62], with applications that include mesh compression [30], parametrization [ 25 , 43], segmentation [31, 35] , remeshing [17], filtering [34, 57], correspondence [27], ma tching and retrieval [28, 49, 52], manifold learning [”
Deep Learning 3D Shape Surfaces Using Geometry Images (2016, methodology): “We use the spherical parametrization suggested in [10] for initialization due to its speed and ease of implementation.”
Robust 3D Shape Correspondence in the Spectral Domain (2006, background): “Recently, they have found several applications in geometry processing as well, including mesh segmentation [22], spherical parameterization [16], and surface reconstruction [19].”
Segmentation of 3D meshes through spectral clustering (2004, background): “[7] recently to solve the spherical parameterization problem.”
Polynomial splines over hierarchical T-meshes (2008, background): “The reader is referred to [10,12,19] for some references on this topic.”
Periodic global parameterization (2006, methodology): “2002] after cutting the model using the method of Sheffer and Hart [2002]. The cuts were used to generate disk topology and reduce the stretch.”