SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
On Krylov Subspace Approximations to the Matrix Exponential Operator
SIAM Journal on Numerical Analysis
Interactive multi-resolution modeling on arbitrary meshes
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Multilevel Solvers for Unstructured Surface Meshes
SIAM Journal on Scientific Computing
ABF++: fast and robust angle based flattening
ACM Transactions on Graphics (TOG)
A fast multigrid algorithm for mesh deformation
ACM SIGGRAPH 2006 Papers
Discrete laplace operator on meshed surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Discrete Laplace--Beltrami operators and their convergence
Computer Aided Geometric Design
Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids
Computer-Aided Design
Shape google: Geometric words and expressions for invariant shape retrieval
ACM Transactions on Graphics (TOG)
Fragmented skull modeling using heat kernels
Graphical Models
Continuous and discrete Mexican hat wavelet transforms on manifolds
Graphical Models
wFEM heat kernel: Discretization and applications to shape analysis and retrieval
Computer Aided Geometric Design
SMI 2013: Heat diffusion kernel and distance on surface meshes and point sets
Computers and Graphics
Context-based coherent surface completion
ACM Transactions on Graphics (TOG)
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
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Studying the behavior of the heat diffusion process on a manifold is emerging as an important tool for analyzing the geometry of the manifold. Unfortunately, the high complexity of the computation of the heat kernel -- the key to the diffusion process - limits this type of analysis to 3D models of modest resolution. We show how to use the unique properties of the heat kernel of a discrete two dimensional manifold to overcome these limitations. Combining a multi-resolution approach with a novel approximation method for the heat kernel at short times results in an efficient and robust algorithm for computing the heat kernels of detailed models. We show experimentally that our method can achieve good approximations in a fraction of the time required by traditional algorithms. Finally, we demonstrate how these heat kernels can be used to improve a diffusion-based feature extraction algorithm.