A geometric consistency theorem for a symbolic perturbation scheme
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
Robust adaptive floating-point geometric predicates
Proceedings of the twelfth annual symposium on Computational geometry
Anisotropic polygonal remeshing
ACM SIGGRAPH 2003 Papers
Direct Anisotropic Quad-Dominant Remeshing
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
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
Spectral quadrangulation with orientation and alignment control
ACM SIGGRAPH Asia 2008 papers
ACM SIGGRAPH 2009 papers
Harmonic functions for quadrilateral remeshing of arbitrary manifolds
Computer Aided Geometric Design - Special issue: Geometry processing
ACM SIGGRAPH 2010 papers
A wave-based anisotropic quadrangulation method
ACM SIGGRAPH 2010 papers
Technical Section: Meshless quadrangulation by global parameterization
Computers and Graphics
Dual loops meshing: quality quad layouts on manifolds
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Hexagonal Global Parameterization of Arbitrary Surfaces
IEEE Transactions on Visualization and Computer Graphics
All-hex meshing using singularity-restricted field
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
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
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The most popular and actively researched class of quad remeshing techniques is the family of parametrization based quad meshing methods. They all strive to generate an integer-grid map, i.e. a parametrization of the input surface into R2 such that the canonical grid of integer iso-lines forms a quad mesh when mapped back onto the surface in R3. An essential, albeit broadly neglected aspect of these methods is the quad extraction step, i.e. the materialization of an actual quad mesh from the mere "quad texture". Quad (mesh) extraction is often believed to be a trivial matter but quite the opposite is true: numerous special cases, ambiguities induced by numerical inaccuracies and limited solver precision, as well as imperfections in the maps produced by most methods (unless costly countermeasures are taken) pose significant challenges to the quad extractor. We present a method to sanitize a provided parametrization such that it becomes numerically consistent even in a limited precision floating point representation. Based on this we are able to provide a comprehensive and sound description of how to perform quad extraction robustly and without the need for any complex tolerance thresholds or disambiguation rules. On top of that we develop a novel strategy to cope with common local fold-overs in the parametrization. This allows our method, dubbed QEx, to generate all-quadrilateral meshes where otherwise holes, non-quad polygons or no output at all would have been produced. We thus enable the practical use of an entire class of maps that was previously considered defective. Since state of the art quad meshing methods spend a significant share of their run time solely to prevent local fold-overs, using our method it is now possible to obtain quad meshes significantly quicker than before. We also provide libQEx, an open source C++ reference implementation of our method and thus significantly lower the bar to enter the field of quad meshing.