Farin points (weight points) are a useful tool for handling the weights of rational Bézier curves. They describe the weights of the Bézier points uniquely and in a geometrically intuitive way. The main problem for using Farin points for triangular or tensorproduct rational Bézier surfaces is the fact that they are not independent of each other and therefore overdefine the weights. To overcome t...

a topological index of a molecular graph g is a numeric quantity related to g which isinvariant under symmetry properties of g. in this paper we obtain the randić, geometricarithmetic,first and second zagreb indices , first and second zagreb coindices of tensorproduct of two graphs and then the harary, schultz and modified schultz indices of tensorproduct of a graph g with complete graph of ord...

Converting a quadrilateral input mesh into a C surface with one bi-3 tensorproduct spline patch per facet is a classical challenge. We give explicit local averaging formulas for the spline control points. Where the quadrilateral mesh is not regular, the patches have two internal double knots, the least number and multiplicity to always allow for an unbiased G construction.

A C++ library, named ZKCM, has been developed for the purpose of multiprecision matrix calculations, which is based on the GNU MP and MPFR libraries. It is especially convenient for writing programs involving tensorproduct operations, tracing-out operations, and singular-value decompositions. Its extension library, ZKCM QC, for simulating quantum computing has been developed using the time-depe...

Finite element derivative superconvergent points for harmonic functions under local rectangular mesh are investigated. All superconvergent points for the finite element space of any order that is contained in the tensorproduct space and contains the intermediate family can be predicted. In the case of the serendipity family, results are given for finite element spaces of order below 6. The resu...

Partition of Unity Parametrics (PUPs) are a generalization of NURBS that allow us to use arbitrary basis functions for modeling parametric curves and surfaces. One interesting problem is finding subdivision schemes for this recently developed and flexible class of parametrics. In this paper, we introduce a systematic approach for determining uniform subdivision of PUPs curves and tensorproduct ...

Parametric surfaces in various representations, such as Bézier-and B-spline-tensorproduct patches, triangular patches etc., play an important role in CAGD-applications. Connecting patches with different degree of continuity and trimming surfaces are well-known techniques to construct a variety of shapes like ship hulls, car bodies, etc. For finite element analysis, stereolithography, rendering ...

SUMMARY One possibility to use wavelet methods for numerically solving elliptic operator equations on fairly general domains is a domain decomposition approach. Employing parametric mappings to a reference cube, one is left with the problem of the construction and implementation of wavelet bases on cubes. In this paper, we review the basic construction principles of wavelets on the interval whi...

We show how to combine, into one unified spline complex, C2 tensorproduct bi-cubic NURBS and G2 bi-cubic rational splines. The G2 splines are capable of exactly representing basic shapes such as (pieces of) quadrics and surfaces of revolution, including tori and cyclides. The main challenge is to bridge the differing continuity. We transform the G2 splines to splines that are C2 in homogeneous ...

This paper is devoted to GPU kernel optimization and performance analysis of three tensorproduct operators arising in finite element methods. We provide a mathematical background to these operations and implementation details. Achieving close-to-the-peak performance for these operators requires extensive optimization because of the operators’ properties: low arithmetic intensity, tiered structu...