Applications of Laguerre geometry in CAGD
Computer Aided Geometric Design
Computational Line Geometry
Making papercraft toys from meshes using strip-based approximate unfolding
ACM SIGGRAPH 2004 Papers
The Visual Computer: International Journal of Computer Graphics
Degree elevation and developable Bézier surfaces
Computer Aided Geometric Design
Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes
International Journal of Computer Vision
Geometric modeling with conical meshes and developable surfaces
ACM SIGGRAPH 2006 Papers
Paper craft models from meshes
The Visual Computer: International Journal of Computer Graphics
Geometry of multi-layer freeform structures for architecture
ACM SIGGRAPH 2007 papers
Focal surfaces of discrete geometry
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Developable surfaces from arbitrary sketched boundaries
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Papercraft Models using Generalized Cylinders
PG '07 Proceedings of the 15th Pacific Conference on Computer Graphics and Applications
Piecewise developable surface approximation of general NURBS surfaces, with global error bounds
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Procedural modeling of structurally-sound masonry buildings
ACM SIGGRAPH Asia 2009 papers
ACM SIGGRAPH 2010 papers
ACM SIGGRAPH 2010 papers
Paneling architectural freeform surfaces
ACM SIGGRAPH 2010 papers
Triangle surfaces with discrete equivalence classes
ACM SIGGRAPH 2010 papers
Computer-generated residential building layouts
ACM SIGGRAPH Asia 2010 papers
ACM SIGGRAPH 2011 papers
Industrial design using interpolatory discrete developable surfaces
Computer-Aided Design
Shape space exploration of constrained meshes
Proceedings of the 2011 SIGGRAPH Asia Conference
Darboux cyclides and webs from circles
Computer Aided Geometric Design
Rationalization of Triangle-Based Point-Folding Structures
Computer Graphics Forum
Computer Graphics Forum
Structural optimization of 3D masonry buildings
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Discrete line congruences for shading and lighting
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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Motivated by applications in architecture and manufacturing, we discuss the problem of covering a freeform surface by single curved panels. This leads to the new concept of semi-discrete surface representation, which constitutes a link between smooth and discrete surfaces. The basic entity we are working with is the developable strip model. It is the semi-discrete equivalent of a quad mesh with planar faces, or a conjugate parametrization of a smooth surface. We present a B-spline based optimization framework for efficient computing with D-strip models. In particular we study conical and circular models, which semi-discretize the network of principal curvature lines, and which enjoy elegant geometric properties. Together with geodesic models and cylindrical models they offer a rich source of solutions for surface panelization problems.