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We propose a framework for 3D geometry processing that provides direct access to surface curvature to facilitate advanced shape editing, filtering, and synthesis algorithms. The central idea is to map a given surface to the curvature domain by evaluating its principle curvatures, apply filtering and editing operations to the curvature distribution, and… (More)

The emergence of large-scale freeform shapes in architecture poses big challenges to the fabrication of such structures. A key problem is the approximation of the design surface by a union of patches, so-called panels, that can be manufactured with a selected technology at reasonable cost, while meeting the design intent and achieving the desired aesthetic… (More)

Given a set of points in a Hilbert space that can be separated from the origin. The slab support vector machine (slab SVM) is an optimization problem that aims at finding a slab (two parallel hyperplanes whose distance—the slab width—is essentially fixed) that encloses the points and is maximally separated from the origin. Extreme cases of the slab SVM… (More)

Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual… (More)

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