Discrete box splines and refinement algorithms books

Discrete box splines we start by introducing some notation. The algorithms of jetter and mccool 14, 20 evaluate boxsplines approx imately by sampling in the. Morkenknot line refinement algorithms for tensor product bspline surfaces. An application of multivariate b splines to computer aided geometric design. The bernstein indices on an element form a discrete finitedimensional space. The relevant theory of discrete b splines with associated new algorithms is extended to provide a framework for understanding and implementing general subdivision schemes for nonuniform b splines. On discrete simplex splines and subdivision sciencedirect. Some further properties of discrete box splines are given in section 4. The methods in comparison are truncated hierarchical bsplines with two different refinement strategies, tsplines with the refinement strategy introduced by scott et al.

Three simple algorithms for calculating bivariate box splines and their linear. Forb88 hierarchical bspline refinement, computer graphics 22 1988, 205. Algebraic properties of discrete box splines springerlink. Discrete fracture analysis using locally refined tsplines. Computer aided geometric design vol 1, issue 2, pages 97.

Refinable smooth surfaces for locally quaddominant meshes with tgons. The new derived polygon corresponding to an arbitrary refinement of the knot vector for an existing b spline curve, including multiplicities, is shown to be formed by successive evaluations of the. Find the top 100 most popular items in amazon books best sellers. Discrete box splines and refinement algorithms sciencedirect. Discrete analogoues of multivariate simplex splines are introduced. Ahu68 an algorithm for generating splinelike curves, ibm j. On leave from the university of oslo, institutt for informatikk, box 1080. Graphs, algorithms, and optimization discrete mathematics. The central objective of this paper is to discuss linear independence of translates of discrete box splines which we introduced earlier as. Discrete box splines and refinement algorithms 3 2.

It is based on the notion of discrete simplex splines, which is proven to be an extension of the ideas underlying the definitions of discrete cube splines, also called box splines, and discrete cone splines 3, 7. Their study yields a subdivision scheme for simplex splines. Pettersen, polynomial splines over locally refined boxpartitions. Bivariate box splines and smooth pp functions on a three direction mesh, j. Compactly supported smooth piecewise polynomial functions provide an efficient tool for the approximation of curves and surfaces and. Three simple algorithms for calculating bivariate box splines and their linear combinations are given. The authors present the graph theory in a rigorous, but informal style. Barl11 convergence of discrete and penalized least squares spherical splines. Pettersen, polynomial splines over locally refined boxpartitions, comput. Discrete bsplines and subdivision techniques in computer. Since they are locally polynomial, they are easy to evaluate. Discover the best programming algorithms in best sellers. Appears in 4 books from 19741993 references to this book.

The oslo algorithm is a recursive method for updating the b spline. The uspline algorithm guarantees that each uspline basis function is. We conclude the paper with some examples in section 5, remarks in section 6, and a proof of control mesh convergence in section 7. Compactly supported smooth piecewise polynomial functions provide an efficient tool for the approximation of curves and surfaces and other smooth functions of one and several arguments. The refined net as well as the bezier net are generated by filling and averaging procedures. Fast and stable evaluation of boxsplines via the bbform uf cise. Truncated hierarchical catmullclark subdivision with local re. Dael88 bivariate interpolation with quadratic box splines, math. Algebraic properties of discrete box splines, 1984. Triangular spline algorithms computer aided geometric design. The second edition of this popular book presents the theory of graphs from an algorithmic viewpoint. Adaptive isogeometric methods with hierarchical splines. A bivariate c1 subdivision scheme based on cubic halfbox splines. We discuss shape preserving properties, the construction of nonrectangular box spline surfaces, applications of box splines to surface modelling and problems related to an imbedding of box spline surfaces within a tensor product surface.