On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
Anisotropic polygonal remeshing
ACM SIGGRAPH 2003 Papers
Parameterization of triangle meshes over quadrilateral domains
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Geometric modeling with conical meshes and developable surfaces
ACM SIGGRAPH 2006 Papers
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
Geometry of multi-layer freeform structures for architecture
ACM SIGGRAPH 2007 papers
Designing quadrangulations with discrete harmonic forms
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
N-symmetry direction field design
ACM Transactions on Graphics (TOG)
Interactive procedural street modeling
ACM SIGGRAPH 2008 papers
Spectral quadrangulation with orientation and alignment control
ACM SIGGRAPH Asia 2008 papers
ACM SIGGRAPH 2009 papers
Geometry-aware direction field processing
ACM Transactions on Graphics (TOG)
ACM SIGGRAPH 2010 papers
Paneling architectural freeform surfaces
ACM SIGGRAPH 2010 papers
Quadrangular parameterization for reverse engineering
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Modeling Polyhedral Meshes with Affine Maps
Computer Graphics Forum
Shape-Up: Shaping Discrete Geometry with Projections
Computer Graphics Forum
All-hex meshing using singularity-restricted field
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Technical note: Modeling flow features with user-guided streamline parameterization
Computer-Aided Design
Smooth surfaces from rational bilinear patches
Computer Aided Geometric Design
Discrete line congruences for shading and lighting
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
Animation-aware quadrangulation
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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We present a novel method to approximate a freeform shape with a planar quadrilateral (PQ) mesh for modeling architectural glass structures. Our method is based on the study of conjugate direction fields (CDF) which allow the presence of ±κ/4(κ ε Z) singularities. Starting with a triangle discretization of a freeform shape, we first compute an as smooth as possible conjugate direction field satisfying the user's directional and angular constraints, then apply mixed-integer quadrangulation and planarization techniques to generate a PQ mesh which approximates the input shape faithfully. We demonstrate that our method is effective and robust on various 3D models.