Deformable curve and surface finite-elements for free-form shape design
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Free-form shape design using triangulated surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Texture mapping progressive meshes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Fair Triangle Mesh Generation with Discrete Elastica
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
A finite element method for surface restoration with smooth boundary conditions
Computer Aided Geometric Design
A remeshing approach to multiresolution modeling
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Generalized surface flows for mesh processing
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Discrete quadratic curvature energies
Computer Aided Geometric Design
Technical Section: A simple and flexible framework to adapt dynamic meshes
Computers and Graphics
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
ACM Transactions on Mathematical Software (TOMS)
Two Step Time Discretization of Willmore Flow
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Spin transformations of discrete surfaces
ACM SIGGRAPH 2011 papers
Robust modeling of constant mean curvature surfaces
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Geometric fairing of irregular meshes for free-form surface design
Computer Aided Geometric Design
Shape-Up: Shaping Discrete Geometry with Projections
Computer Graphics Forum
Can Mean-Curvature Flow be Modified to be Non-singular?
Computer Graphics Forum
Consistent volumetric discretizations inside self-intersecting surfaces
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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We present a formulation of Willmore flow for triangulated surfaces that permits extraordinarily large time steps and naturally preserves the quality of the input mesh. The main insight is that Willmore flow becomes remarkably stable when expressed in curvature space -- we develop the precise conditions under which curvature is allowed to evolve. The practical outcome is a highly efficient algorithm that naturally preserves texture and does not require remeshing during the flow. We apply this algorithm to surface fairing, geometric modeling, and construction of constant mean curvature (CMC) surfaces. We also present a new algorithm for length-preserving flow on planar curves, which provides a valuable analogy for the surface case.