Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
MAPS: multiresolution adaptive parameterization of surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Dynamic generators of topologically embedded graphs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Globally smooth parameterizations with low distortion
ACM SIGGRAPH 2003 Papers
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Optimal Global Conformal Surface Parameterization
VIS '04 Proceedings of the conference on Visualization '04
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Periodic global parameterization
ACM Transactions on Graphics (TOG)
Rotational symmetry field design on surfaces
ACM SIGGRAPH 2007 papers
Rectangular multi-chart geometry images
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Designing quadrangulations with discrete harmonic forms
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
A continuum theory for unstructured mesh generation in two dimensions
Computer Aided Geometric Design
N-symmetry direction field design
ACM Transactions on Graphics (TOG)
Conformal equivalence of triangle meshes
ACM SIGGRAPH 2008 papers
IEEE Transactions on Visualization and Computer Graphics
ACM SIGGRAPH 2009 papers
Geometry-aware direction field processing
ACM Transactions on Graphics (TOG)
Metric-Driven RoSy Field Design and Remeshing
IEEE Transactions on Visualization and Computer Graphics
A local/global approach to mesh 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
ACM SIGGRAPH 2010 papers
Almost Isometric Mesh Parameterization through Abstract Domains
IEEE Transactions on Visualization and Computer Graphics
Global parametrization by incremental flattening
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
QEx: robust quad mesh extraction
ACM Transactions on Graphics (TOG)
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The quality of a global parametrization is determined by a number of factors, including amount of distortion, number of singularities (cones), and alignment with features and boundaries. Placement of cones plays a decisive role in determining the overall distortion of the parametrization; at the same time, feature and boundary alignment also affect the cone placement. A number of methods were proposed for automatic choice of cone positions, either based on singularities of cross-fields and emphasizing alignment, or based on distortion optimization. In this paper we describe a method for placing cones for seamless global parametrizations with alignment constraints. We use a close relation between variation-minimizing cross-fields and related 1-forms and conformal maps, and demonstrate how it leads to a constrained optimization problem formulation. We show for boundary-aligned parametrizations metric distortion may be reduced by cone chains, sometimes to an arbitrarily small value, and the trade-off between the distortion and the number of cones can be controlled by a regularization term. Constrained parametrizations computed using our method have significantly lower distortion compared to the state-of-the art field-based method, yet maintain feature and boundary alignment. In the most extreme cases, parametrization collapse due to alignment constraints is eliminated.