Spot noise texture synthesis for data visualization
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Imaging vector fields using line integral convolution
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Modifying a Sparse Cholesky Factorization
SIAM Journal on Matrix Analysis and Applications
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
Multiple-Rank Modifications of a Sparse Cholesky Factorization
SIAM Journal on Matrix Analysis and Applications
Discrete multiscale vector field decomposition
ACM SIGGRAPH 2003 Papers
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Discrete exterior calculus
An intuitive framework for real-time freeform modeling
ACM SIGGRAPH 2004 Papers
Geometry-Aware Bases for Shape Approximation
IEEE Transactions on Visualization and Computer Graphics
ACM SIGGRAPH 2005 Papers
Discrete one-forms on meshes and applications to 3D mesh parameterization
Computer Aided Geometric Design
Appearance-space texture synthesis
ACM SIGGRAPH 2006 Papers
Edge subdivision schemes and the construction of smooth vector fields
ACM SIGGRAPH 2006 Papers
Vector field design on surfaces
ACM Transactions on Graphics (TOG)
Introduction to discrete differential geometry: the geometry of plane curves
ACM SIGGRAPH 2006 Courses
Discrete differential forms for computational modeling
ACM SIGGRAPH 2006 Courses
ACM SIGGRAPH 2006 Courses
Stable, circulation-preserving, simplicial fluids
ACM Transactions on Graphics (TOG)
Designing quadrangulations with discrete harmonic forms
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
A Discrete Laplace–Beltrami Operator for Simplicial Surfaces
Discrete & Computational Geometry
Efficient linear system solvers for mesh processing
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Generalized Streak Lines: Analysis and Visualization of Boundary Induced Vortices
IEEE Transactions on Visualization and Computer Graphics
N-symmetry direction field design
ACM Transactions on Graphics (TOG)
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
SBIM '07 Proceedings of the 4th Eurographics workshop on Sketch-based interfaces and modeling
A photometric approach for estimating normals and tangents
ACM SIGGRAPH Asia 2008 papers
Spectral quadrangulation with orientation and alignment control
ACM SIGGRAPH Asia 2008 papers
MLS-based scalar fields over triangle meshes and their application in mesh processing
Proceedings of the 2009 symposium on Interactive 3D graphics and games
Procedural noise using sparse Gabor convolution
ACM SIGGRAPH 2009 papers
ACM SIGGRAPH 2009 papers
Technical Section: Dynamic harmonic fields for surface processing
Computers and Graphics
Feature-aligned shape texturing
ACM SIGGRAPH Asia 2009 papers
Motion field texture synthesis
ACM SIGGRAPH Asia 2009 papers
Geometry-aware direction field processing
ACM Transactions on Graphics (TOG)
Height and Tilt Geometric Texture
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Spectral conformal parameterization
SGP '08 Proceedings of the Symposium on Geometry Processing
Slit map: conformal parameterization for multiply connected surfaces
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Editing operations for irregular vertices in triangle meshes
ACM SIGGRAPH Asia 2010 papers
A local-frame based method for vector field construction on raw point cloud
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part I
Differential domain analysis for non-uniform sampling
ACM SIGGRAPH 2011 papers
ACM SIGGRAPH 2011 papers
Prominent Field for Shape Processing and Analysis of Archaeological Artifacts
International Journal of Computer Vision
Freeform vector graphics with controlled thin-plate splines
Proceedings of the 2011 SIGGRAPH Asia Conference
Irregular vertex editing for architectural geometry design
Proceedings of the 2011 Symposium on Simulation for Architecture and Urban Design
Computer Graphics Forum
Analytic Tangent Irradiance Environment Maps for Anisotropic Surfaces
Computer Graphics Forum
Efficient texture mapping by homogeneous patch discovery
Proceedings of the Eighth Indian Conference on Computer Vision, Graphics and Image Processing
Fast flow visualization on CUDA based on texture optimization
AMT'12 Proceedings of the 8th international conference on Active Media Technology
On the equilibrium of simplicial masonry structures
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Globally optimal direction fields
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Context-based coherent surface completion
ACM Transactions on Graphics (TOG)
An operator approach to tangent vector field processing
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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Tangent vector fields are an essential ingredient in controlling surface appearance for applications ranging from anisotropic shading to texture synthesis and non-photorealistic rendering. To achieve a desired effect one is typically interested in smoothly varying fields that satisfy a sparse set of user-provided constraints. Using tools from Discrete Exterior Calculus, we present a simple and efficient algorithm for designing such fields over arbitrary triangle meshes. By representing the field as scalars over mesh edges (i.e., discrete 1-forms), we obtain an intrinsic, coordinate-free formulation in which field smoothness is enforced through discrete Laplace operators. Unlike previous methods, such a formulation leads to a linear system whose sparsity permits efficient pre-factorization. Constraints are incorporated through weighted least squares and can be updated rapidly enough to enable interactive design, as we demonstrate in the context of anisotropic texture synthesis.