Differential coordinates for interactive mesh editing

By Yaron Lipman, Olga Sorkine-Hornung, Daniel Cohen-Or, David Levin, C. Rössl, Hans-Peter Seidel. Proceedings Shape Modeling Applications, 2004., 2004

326 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mechanics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/46979ebb9ed2d8027d593169e0a72aca8e8a51ae

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Citations in the corpus

Differential Representations for Mesh Processing (2006, methodology): “It is important to note that all the above-mentioned methods [45,47,49] are fast: the size of the system matrices involved in the reconstruction is n × n, where n is the number of vertices in the ROI.”
On Linear Variational Surface Deformation Methods (2008, methodology): “In contrast, the Laplacian editing papers [41], [49], [60]”
Mesh-based inverse kinematics (2005, methodology): “Other editing methods use intrinsic representations such as Laplacian (also called differential) coordinates [Alexa 2003; Lipman et al. 2004; Sorkine et al. 2004] or pyramid coordinates [Sheffer and Kraevoy 2004].”
Spatial adaption of robot trajectories based on laplacian trajectory editing (2015, background): “Yet the straightforward approach suffers from two drawbacks, a large computational complexity due to a matrix inversion involved (Eck et al. 1995; Kobbelt et al. 2000) and the inadequate treatment of large deformations (Lipman et al. 2004; Zhou et al. 2005).”
Laplacian mesh optimization (2006, methodology): “In particular, several methods try to preserve all original vertex Laplacians while imposing new positions for a few vertices [Lipman et al. 2004; Sorkine et al. 2004; Yu et al. 2004], which allows detail preserving modeling.”
Articulated mesh animation from multi-view silhouettes (2008, methodology): “We convert our template mesh to Laplacian coordinates [Alexa 2003; Lipman et al. 2004] in order to represent the iteratively”
Linear rotation-invariant coordinates for meshes (2005, methodology): “In the past years several mesh editing techniques were introduced [Zorin et al. 1997; Kobbelt et al. 1998; Guskov et al. 1999; Lee 1999; Bendels and Klein 2003; Botsch and Kobbelt 2004; Lipman et al. 2004; Sheffer and Kraevoy 2004; Sorkine et al. 2004; Yu et al. 2004; Zayer et al. 2005].”
Drag Your GAN: Interactive Point-based Manipulation on the Generative Image Manifold (2023, background): “Conventionalapproaches[Botsch and Sorkine 2007] typically convert images into meshes, and then deform the mesh subject to geometric constraints such as rigidity [Igarashi et al. 2005; Sorkine and Alexa 2007] and Laplacian smoothness [Lipman et al. 2004, 2005; Sorkine et al. 2004].”
Subspace gradient domain mesh deformation (2006, methodology): “Existing techniques convert this nonlinear term into a linear one by either heuristically approximating [Lipman et al. 2004; Zhou et al. 2005] or linearizing [Sorkine et al.”