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THB-splines: The truncated basis for hierarchical splines
It is shown that 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 by reducing the support of basis functions defined on coarse grids, according to finer levels in the hierarchy of splines.
A hierarchical approach to adaptive local refinement in isogeometric analysis
Abstract Adaptive local refinement is one of the key issues in isogeometric analysis. In this article we present an adaptive local refinement technique for isogeometric analysis based on extensions
Adaptive isogeometric analysis by local h-refinement with T-splines
Isogeometric analysis based on non-uniform rational B-splines (NURBS) as basis functions preserves the exact geometry but suffers from the drawback of a rectangular grid of control points in the
Computation of rotation minimizing frames
This work presents a novel simple and efficient method for accurate and stable computation of RMF of a curve in 3D, which uses two reflections to compute each frame from its preceding one to yield a sequence of frames to approximate an exact RMF.
An algebraic approach to curves and surfaces on the sphere and on other quadrics
Abstract An explicit representation for any irreducible rational Bezier curve and Bezier surface patch on the unit sphere is given. The extension to general quadrics (ellipsoids, hyperboloids,
THB-splines: An effective mathematical technology for adaptive refinement in geometric design and isogeometric analysis
Local refinement with hierarchical B-spline structures is an active topic of research in the context of geometric modeling and isogeometric analysis. By exploiting a multilevel control structure, we
Least-Squares Fitting of Algebraic Spline Surfaces
An algorithm for fitting implicitly defined algebraic spline surfaces to given scattered data is presented, by simultaneously approximating points and associated normal vectors, which is computationally simple, as the result is obtained by solving a system of linear equations.
Strongly stable bases for adaptively refined multilevel spline spaces
The problem of constructing a normalized hierarchical basis for adaptively refined spline spaces is addressed and the theory is applied to hierarchically refined tensor-productspline spaces, under certain reasonable assumptions on the given knot configuration.
Computing roots of polynomials by quadratic clipping
An algorithm is presented which is able to compute all roots of a given univariate polynomial within a given interval and it is shown that the new technique compares favorably with the classical technique of Bezier clipping.
Computer-Aided Design With Spatial Rational B-Spline Motions
Using rational motions it is possible to apply many fundamental B-spline techniques to the design of motions. The present paper summarizes the basic theory of rational motions and introduces a linear