A necessary and sufficient condition for the existence of a complete stable matching
Journal of Algorithms
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
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ACM SIGGRAPH 2003 Papers
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Curves and Surfaces for Computer Graphics
Curves and Surfaces for Computer Graphics
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Computers and Graphics
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ACM SIGGRAPH Asia 2009 papers
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Advances in Engineering Software
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ACM SIGGRAPH 2010 papers
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Computers and Graphics
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Proceedings of the Eighth Eurographics Symposium on Sketch-Based Interfaces and Modeling
Freeform vector graphics with controlled thin-plate splines
Proceedings of the 2011 SIGGRAPH Asia Conference
Slices: a shape-proxy based on planar sections
Proceedings of the 2011 SIGGRAPH Asia Conference
Transfinite surface interpolation over irregular n-sided domains
Computer-Aided Design
Quadrangular parameterization for reverse engineering
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Multi-sided attribute based modeling
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Sketch-based generation and editing of quad meshes
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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Geometry curves: A compact representation for 3D shapes
Graphical Models
A general and efficient method for finding cycles in 3D curve networks
ACM Transactions on Graphics (TOG)
ACM Transactions on Graphics (TOG)
An algorithm for triangulating multiple 3D polygons
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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We propose a novel, design-driven, approach to quadrangulation of closed 3D curves created by sketch-based or other curve modeling systems. Unlike the multitude of approaches for quad-remeshing of existing surfaces, we rely solely on the input curves to both conceive and construct the quad-mesh of an artist imagined surface bounded by them. We observe that viewers complete the intended shape by envisioning a dense network of smooth, gradually changing, flow-lines that interpolates the input curves. Components of the network bridge pairs of input curve segments with similar orientation and shape. Our algorithm mimics this behavior. It first segments the input closed curves into pairs of matching segments, defining dominant flow line sequences across the surface. It then interpolates the input curves by a network of quadrilateral cycles whose iso-lines define the desired flow line network. We proceed to interpolate these networks with all-quad meshes that convey designer intent. We evaluate our results by showing convincing quadrangulations of complex and diverse curve networks with concave, non-planar cycles, and validate our approach by comparing our results to artist generated interpolating meshes.