Curvature analysis and visualization for functions defined on Euclidean spaces or surfaces
Computer Aided Geometric Design
Applications of Laguerre geometry in CAGD
Computer Aided Geometric Design
A Laguerre geometric approach to rational offsets
Computer Aided Geometric Design
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Variational shape approximation
ACM SIGGRAPH 2004 Papers
Geometric modeling with conical meshes and developable surfaces
ACM SIGGRAPH 2006 Papers
Geometry of multi-layer freeform structures for architecture
ACM SIGGRAPH 2007 papers
Developable surface fitting to point clouds
Computer Aided Geometric Design
Parametric polynomial minimal surfaces of degree six with isothermal parameter
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Design of self-supporting surfaces
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
A new material practice: integrating design and material behavior
Proceedings of the 2012 Symposium on Simulation for Architecture and Urban Design
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Meshes with planar quadrilateral faces are desirable discrete surface representations for architecture. The present paper introduces new classes of planar quad meshes, which discretize principal curvature lines of surfaces in so-called isotropic 3-space. Like their Euclidean counterparts, these isotropic principal meshes meshes are visually expressing fundamental shape characteristics and they can satisfy the aesthetical requirements in architecture. The close relation between isotropic geometry and Euclidean Laguerre geometry provides a link between the new types of meshes and the known classes of conical meshes and edge offset meshes. The latter discretize Euclidean principal curvature lines and have recently been realized as particularly suited for freeform structures in architecture, since they allow for a supporting beam layout with optimal node properties. We also present a discrete isotropic curvature theory which applies to all types of meshes including triangle meshes. The results are illustrated by discrete isotropic minimal surfaces and meshes computed by a combination of optimization and subdivision.