Computing Discrete Minimal Surfaces and Their Conjugates

By Ulrich Pinkall, Konrad Polthier. 1993

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Geometric Deep Learning: Going beyond Euclidean data (2016, neutral): “ubiquitously used in computer graphics [70].”
Learning Category-Specific Mesh Reconstruction from Image Collections (2018, background): “In particular, enforcing smooth surface has been extensively studied by the Computer Graphics community [20,25].”
Learning shape correspondence with anisotropic convolutional neural networks (2016, methodology): “Isotropic Laplacians were computed using the cotangent formula [Mac49, Duf59, PP93, MDSB03]; anisotropic Laplacians were computed according to (30).”
Geometric deep learning (2016, background): “…of the LBO is given as an n × n matrix L = A − 1 W , where α ij , β ij denote the angles ∠ ikj, ∠ jhi of the triangles sharing the edge ij , and A = diag( a 1 , . . . , a n ) with a i = jk : ijk ∈ F A ijk being the local area element at vertex i and A ijk denoting the area of triangle ijk [68].”
On Linear Variational Surface Deformation Methods (2008, methodology): “as proposed in [18], [45], and [51] and employed, for”
Recent Advances in Mesh Morphing (2002, background): “Harmonic maps are often described as the function u among all functions mapping to a given domain Ω that minimize the Direchlet energy Pinkall and Polthier 53 show how to discretize this problem for triangles, so that weights are derived per vertex and neighbor leading to a system of linear equation”
Discrete conformal maps and ideal hyperbolic polyhedra (2010, background): “It is also interesting from the theoretical point of view, because the second derivative of ET,Θ,λ at u is the well known finite-element approximation of the Dirichlet energy (the cotan-formula) for a triangulation with edge lengths ̃̀ [6] [28]: 3.”
Interactive and anisotropic geometry processing using the screened Poisson equation (2011, background): “Previous work has shown that the filtering of mesh geometry can be expressed in terms of the solution to a Poisson equation [Pinkall and Polthier 1993; Taubin 1995; Desbrun et al. 1999] and that geometry-awareness can be incorporated by anisotropically weighting the Laplace operator [Clarenz et al.”
Blended intrinsic maps (2011, methodology): “Following [Lipman and Funkhouser 2009], we first conformally map the two surfaces to the extended complex plane using mid-edge uniformization [Pinkall and Polthier 1993].”