Joint-dependent local deformations for hand animation and object grasping
Proceedings on Graphics interface '88
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Smooth surface reconstruction from noisy range data
Proceedings of the 1st international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
An intuitive framework for real-time freeform modeling
ACM SIGGRAPH 2004 Papers
Colorization using optimization
ACM SIGGRAPH 2004 Papers
Simplifying Flexible Isosurfaces Using Local Geometric Measures
VIS '04 Proceedings of the conference on Visualization '04
Mean value coordinates for closed triangular meshes
ACM SIGGRAPH 2005 Papers
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Image deformation using moving least squares
ACM SIGGRAPH 2006 Papers
Subspace gradient domain mesh deformation
ACM SIGGRAPH 2006 Papers
Harmonic coordinates for character articulation
ACM SIGGRAPH 2007 papers
Automatic rigging and animation of 3D characters
ACM SIGGRAPH 2007 papers
Handle-aware isolines for scalable shape editing
ACM SIGGRAPH 2007 papers
Discrete laplace operators: no free lunch
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
GPU-assisted positive mean value coordinates for mesh deformations
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
On Linear Variational Surface Deformation Methods
IEEE Transactions on Visualization and Computer Graphics
Diffusion curves: a vector representation for smooth-shaded images
ACM SIGGRAPH 2008 papers
Geometric skinning with approximate dual quaternion blending
ACM Transactions on Graphics (TOG)
Bounded biharmonic weights for real-time deformation
ACM SIGGRAPH 2011 papers
Stretchable and Twistable Bones for Skeletal Shape Deformation
Proceedings of the 2011 SIGGRAPH Asia Conference
Freeform vector graphics with controlled thin-plate splines
Proceedings of the 2011 SIGGRAPH Asia Conference
A topological hierarchy for functions on triangulated surfaces
IEEE Transactions on Visualization and Computer Graphics
Topology-based smoothing of 2D scalar fields with C1-continuity
EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
A vectorial solver for free-form vector gradients
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Two-layer sparse compression of dense-weight blend skinning
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Bijective composite mean value mappings
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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Functions that optimize Laplacian-based energies have become popular in geometry processing, e.g. for shape deformation, smoothing, multiscale kernel construction and interpolation. Minimizers of Dirichlet energies, or solutions of Laplace equations, are harmonic functions that enjoy the maximum principle, ensuring no spurious local extrema in the interior of the solved domain occur. However, these functions are only C0 at the constrained points, which often causes smoothness problems. For this reason, many applications optimize higher-order Laplacian energies such as biharmonic or triharmonic. Their minimizers exhibit increasing orders of continuity but lose the maximum principle and show oscillations. In this work, we identify characteristic artifacts caused by spurious local extrema, and provide a framework for minimizing quadratic energies on manifolds while constraining the solution to obey the maximum principle in the solved region. Our framework allows the user to specify locations and values of desired local maxima and minima, while preventing any other local extrema. We demonstrate our method on the smoothness energies corresponding to popular polyharmonic functions and show its usefulness for fast handle-based shape deformation, controllable color diffusion, and topologically-constrained data smoothing. © 2012 Wiley Periodicals, Inc.