SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Texture synthesis over arbitrary manifold surfaces
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Discrete multiscale vector field decomposition
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
Adaptive Smoothing Tangential Direction Fields on Polygonal Surfaces
PG '01 Proceedings of the 9th Pacific Conference on Computer Graphics and Applications
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
Direct Anisotropic Quad-Dominant Remeshing
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Jump map-based interactive texture synthesis
ACM Transactions on Graphics (TOG)
Edge subdivision schemes and the construction of smooth vector fields
ACM SIGGRAPH 2006 Papers
Vector field design on surfaces
ACM Transactions on Graphics (TOG)
Periodic global parameterization
ACM Transactions on Graphics (TOG)
Representing Higher-Order Singularities in Vector Fields on Piecewise Linear Surfaces
IEEE Transactions on Visualization and Computer Graphics
Rotational symmetry field design on surfaces
ACM SIGGRAPH 2007 papers
Design of tangent vector fields
ACM SIGGRAPH 2007 papers
Interactive procedural street modeling
ACM SIGGRAPH 2008 papers
Controlled field generation for quad-remeshing
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
ACM SIGGRAPH 2009 papers
Geometry-aware direction field processing
ACM Transactions on Graphics (TOG)
Feature aligned quad dominant remeshing using iterative local updates
Computer-Aided Design
ACM SIGGRAPH 2010 papers
A wave-based anisotropic quadrangulation method
ACM SIGGRAPH 2010 papers
Editing operations for irregular vertices in triangle meshes
ACM SIGGRAPH Asia 2010 papers
ACM SIGGRAPH 2011 papers
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
Simple quad domains for field aligned mesh parametrization
Proceedings of the 2011 SIGGRAPH Asia Conference
Boundary aligned smooth 3D cross-frame field
Proceedings of the 2011 SIGGRAPH Asia Conference
Technical Section: Meshless quadrangulation by global parameterization
Computers and Graphics
Quadrangular parameterization for reverse engineering
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
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
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Practical mixed-integer optimization for geometry processing
Proceedings of the 7th international conference on Curves and Surfaces
All-hex meshing using singularity-restricted field
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Sketch-based generation and editing of quad meshes
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Designing unreinforced masonry models
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Controlled-distortion constrained global parametrization
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Globally optimal direction fields
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
ACM Transactions on Graphics (TOG)
Animation-aware quadrangulation
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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Many algorithms in computer graphics and geometry processing use two orthogonal smooth direction fields (unit tangent vector fields) defined over a surface. For instance, these direction fields are used in texture synthesis, in geometry processing or in nonphotorealistic rendering to distribute and orient elements on the surface. Such direction fields can be designed in fundamentally different ways, according to the symmetry requested: inverting a direction or swapping two directions might be allowed or not. Despite the advances realized in the last few years in the domain of geometry processing, a unified formalism is still lacking for the mathematical object that characterizes these generalized direction fields. As a consequence, existing direction field design algorithms are limited to using nonoptimum local relaxation procedures. In this article, we formalize N-symmetry direction fields, a generalization of classical direction fields. We give a new definition of their singularities to explain how they relate to the topology of the surface. Specifically, we provide an accessible demonstration of the Poincaré-Hopf theorem in the case of N-symmetry direction fields on 2-manifolds. Based on this theorem, we explain how to control the topology of N-symmetry direction fields on meshes. We demonstrate the validity and robustness of this formalism by deriving a highly efficient algorithm to design a smooth field interpolating user-defined singularities and directions.