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Due to its minimal twist, the rotation minimizing frame (RMF) is widely used in computer graphics, including sweep or blending surface modeling, motion design and control in computer animation and robotics, streamline visualization, and tool path planning in CAD/CAM. We present a novel simple and efficient method for accurate and stable computation of RMF(More)
Isogeometric Analysis uses NURBS representations of the domain for performing numerical simulations. The first part of this paper presents a variational framework for generating NURBS parameteriza-tions of swept volumes. The class of these volumes covers a number of interesting free-form shapes, such as blades of turbines and propellers, ship hulls or wings(More)
Isogeometric analysis based on NURBS (Non-Uniform Rational B-Splines) as basis functions preserves the exact geometry but suffers from the drawback of a rectangular grid of control points in the parameter space, which renders a purely local refinement impossible. This paper demonstrates how this difficulty can be overcome by using T-splines instead.(More)
We show how to divide the edge graph of a Voronoi diagram into a tree that corresponds to the medial axis of an (augmented) planar domain. Division into base cases is then possible, which, in the bottom-up phase, can be merged by trivial concatenation. The resulting construction algorithm--similar to Delaunay triangulation methods--is not bisector-based and(More)
Given a closed triangular mesh, we construct a smooth free–form surface which is described as a collection of rational tensor–product and triangular surface patches. The surface is obtained by a special manifold surface construction, which proceeds by blending together geometry functions for each vertex. The transition functions between the charts, which(More)
The construction of classical hierarchical B–splines can be suitably modified in order to define locally supported basis functions that form a partition of unity. We will show that this property can be obtained by reducing the support of basis functions defined on coarse grids, according to finer levels in the hierarchy of splines. This truncation not only(More)