Modeling surfaces of arbitrary topology using manifolds
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
Globally smooth parameterizations with low distortion
ACM SIGGRAPH 2003 Papers
Anisotropic polygonal remeshing
ACM SIGGRAPH 2003 Papers
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
A simple manifold-based construction of surfaces of arbitrary smoothness
ACM SIGGRAPH 2004 Papers
Direct Anisotropic Quad-Dominant Remeshing
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Optimal Global Conformal Surface Parameterization
VIS '04 Proceedings of the conference on Visualization '04
Parameterization of triangle meshes over quadrilateral domains
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Greedy optimal homotopy and homology generators
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Harmonic functions for quadrilateral remeshing of arbitrary manifolds
Computer Aided Geometric Design - Special issue: Geometry processing
Discrete conformal mappings via circle patterns
ACM Transactions on Graphics (TOG)
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Periodic global parameterization
ACM Transactions on Graphics (TOG)
Discrete differential forms for computational modeling
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Efficient linear system solvers for mesh processing
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Stable, circulation-preserving, simplicial fluids
ACM Transactions on Graphics (TOG)
Rotational symmetry field design on surfaces
ACM SIGGRAPH 2007 papers
Design of tangent vector fields
ACM SIGGRAPH 2007 papers
Geometry of multi-layer freeform structures for architecture
ACM SIGGRAPH 2007 papers
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
A continuum theory for unstructured mesh generation in two dimensions
Computer Aided Geometric Design
Conformal equivalence of triangle meshes
ACM SIGGRAPH 2008 papers
Technical Section: A simple and flexible framework to adapt dynamic meshes
Computers and Graphics
An incremental approach to feature aligned quad dominant remeshing
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Volumetric parameterization and trivariate b-spline fitting using harmonic functions
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Controlled field generation for quad-remeshing
Proceedings of the 2008 ACM symposium on Solid and physical modeling
User-controllable polycube map for manifold spline construction
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Spectral quadrangulation with orientation and alignment control
ACM SIGGRAPH Asia 2008 papers
Quadrilateral mesh simplification
ACM SIGGRAPH Asia 2008 papers
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
Harmonic 1-form based skeleton extraction from examples
Graphical Models
Extracting lines of curvature from noisy point clouds
Computer-Aided Design
ACM SIGGRAPH 2009 papers
Volumetric parameterization and trivariate B-spline fitting using harmonic functions
Computer Aided Geometric Design
Technical Section: Dynamic harmonic fields for surface processing
Computers and Graphics
Recent Advances in Computational Conformal Geometry
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Parameterizing Singularities of Positive Integral Index
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Surface Quasi-Conformal Mapping by Solving Beltrami Equations
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
ACM SIGGRAPH Asia 2009 papers
Generalized Koebe's method for conformal mapping multiply connected domains
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Easy integral surfaces: a fast, quad-based stream and path surface algorithm
Proceedings of the 2009 Computer Graphics International Conference
Geometry-aware direction field processing
ACM Transactions on Graphics (TOG)
Efficient substitutes for subdivision surfaces
ACM SIGGRAPH 2009 Courses
Lens-shaped surfaces and C 2 subdivision
Computing - Geometric Modelling, Dagstuhl 2008
Feature aligned quad dominant remeshing using iterative local updates
Computer-Aided Design
Spectral conformal parameterization
SGP '08 Proceedings of the Symposium on Geometry Processing
Semi-regular quadrilateral-only remeshing from simplified base domains
SGP '09 Proceedings of the Symposium on Geometry Processing
Localized quadrilateral coarsening
SGP '09 Proceedings of the Symposium on Geometry Processing
Discrete surface Ricci flow: theory and applications
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
ACM SIGGRAPH 2010 papers
A wave-based anisotropic quadrangulation method
ACM SIGGRAPH 2010 papers
Lp Centroidal Voronoi Tessellation and its applications
ACM SIGGRAPH 2010 papers
Slit map: conformal parameterization for multiply connected surfaces
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Technical Section: Shape approximation by differential properties of scalar functions
Computers and Graphics
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Efficient substitutes for subdivision surfaces in feature-quality games
ACM SIGGRAPH ASIA 2010 Courses
Constructing streak surfaces for 3D unsteady vector fields
Proceedings of the 26th Spring Conference on Computer Graphics
Editable polycube map for GPU-based subdivision surfaces
I3D '11 Symposium on Interactive 3D Graphics and Games
SMI 2011: Full Paper: Template-based quadrilateral meshing
Computers and Graphics
SMI 2011: Full Paper: Shape optimization of quad mesh elements
Computers and Graphics
General planar quadrilateral mesh design using conjugate direction field
Proceedings of the 2011 SIGGRAPH Asia Conference
Connectivity editing for quadrilateral meshes
Proceedings of the 2011 SIGGRAPH Asia Conference
Global parametrization of range image sets
Proceedings of the 2011 SIGGRAPH Asia Conference
Technical Section: Meshless quadrangulation by global parameterization
Computers and Graphics
Computer-Aided Design
Computer Aided Geometric Design
Quadrangular parameterization for reverse engineering
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Minimum cuts and shortest non-separating cycles via homology covers
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Global parametrization by incremental flattening
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Dual loops meshing: quality quad layouts on manifolds
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
SMI 2012: Full Spectral computations on nontrivial line bundles
Computers and Graphics
Shape-Up: Shaping Discrete Geometry with Projections
Computer Graphics Forum
All-hex meshing using singularity-restricted field
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Design-driven quadrangulation of closed 3D curves
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
EGSR'10 Proceedings of the 21st Eurographics conference on Rendering
On the equilibrium of simplicial masonry structures
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Sketch-based generation and editing of quad meshes
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Controlled-distortion constrained global parametrization
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Integer-grid maps for reliable quad meshing
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Digital geometry processing with discrete exterior calculus
ACM SIGGRAPH 2013 Courses
QEx: robust quad mesh extraction
ACM Transactions on Graphics (TOG)
SMI 2013: Laplacians on flat line bundles over 3-manifolds
Computers and Graphics
Globally optimal cortical surface matching with exact landmark correspondence
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
ACM Transactions on Graphics (TOG)
The chain collocation method: A spectrally accurate calculus of forms
Journal of Computational Physics
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We introduce a framework for quadrangle meshing of discrete manifolds. Based on discrete differential forms, our method hinges on extending the discrete Laplacian operator (used extensively in modeling and animation) to allow for line singularities and singularities with fractional indices. When assembled into a singularity graph, these line singularities are shown to considerably increase the design flexibility of quad meshing. In particular, control over edge alignments and mesh sizing are unique features of our novel approach. Another appeal of our method is its robustness and scalability from a numerical viewpoint: we simply solve a sparse linear system to generate a pair of piecewise-smooth scalar fields whose isocontours form a pure quadrangle tiling, with no T-junctions.