Finite Elements in Analysis and Design
Globally smooth parameterizations with low distortion
ACM SIGGRAPH 2003 Papers
Mathematical Programming: Series A and B
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Periodic global parameterization
ACM Transactions on Graphics (TOG)
Designing quadrangulations with discrete harmonic forms
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
N-symmetry direction field design
ACM Transactions on Graphics (TOG)
Conformal equivalence of triangle meshes
ACM SIGGRAPH 2008 papers
Spectral quadrangulation with orientation and alignment control
ACM SIGGRAPH Asia 2008 papers
Quadrilateral mesh simplification
ACM SIGGRAPH Asia 2008 papers
ACM SIGGRAPH 2009 papers
Localized quadrilateral coarsening
SGP '09 Proceedings of the Symposium on Geometry Processing
A wave-based anisotropic quadrangulation method
ACM SIGGRAPH 2010 papers
Almost Isometric Mesh Parameterization through Abstract Domains
IEEE Transactions on Visualization and Computer Graphics
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Simple quad domains for field aligned mesh parametrization
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
Quadrangular parameterization for reverse engineering
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Bounded distortion mapping spaces for triangular meshes
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
OpenFlipper: an open source geometry processing and rendering framework
Proceedings of the 7th international conference on Curves and Surfaces
An RBF-Based Reparameterization Method for Constrained Texture Mapping
IEEE Transactions on Visualization and Computer Graphics
The hardness of the closest vector problem with preprocessing
IEEE Transactions on Information Theory
Shape-Up: Shaping Discrete Geometry with Projections
Computer Graphics Forum
Computing Extremal Quasiconformal Maps
Computer Graphics Forum
All-hex meshing using singularity-restricted field
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
QEx: robust quad mesh extraction
ACM Transactions on Graphics (TOG)
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Quadrilateral remeshing approaches based on global parametrization enable many desirable mesh properties. Two of the most important ones are (1) high regularity due to explicit control over irregular vertices and (2) smooth distribution of distortion achieved by convex variational formulations. Apart from these strengths, state-of-the-art techniques suffer from limited reliability on real-world input data, i.e. the determined map might have degeneracies like (local) non-injectivities and consequently often cannot be used directly to generate a quadrilateral mesh. In this paper we propose a novel convex Mixed-Integer Quadratic Programming (MIQP) formulation which ensures by construction that the resulting map is within the class of so called Integer-Grid Maps that are guaranteed to imply a quad mesh. In order to overcome the NP-hardness of MIQP and to be able to remesh typical input geometries in acceptable time we propose two additional problem specific optimizations: a complexity reduction algorithm and singularity separating conditions. While the former decouples the dimension of the MIQP search space from the input complexity of the triangle mesh and thus is able to dramatically speed up the computation without inducing inaccuracies, the latter improves the continuous relaxation, which is crucial for the success of modern MIQP optimizers. Our experiments show that the reliability of the resulting algorithm does not only annihilate the main drawback of parametrization based quad-remeshing but moreover enables the global search for high-quality coarse quad layouts - a difficult task solely tackled by greedy methodologies before.