In this paper (part three of the trilogy) we use low degree G and G continuous regular algebraic spline curves de ned within parallelograms, to interpolate an ordered set of data points in the plane. We explicitly characterize curve families whose members have the required interpolating properties and possess a minimal number of in ection points. The regular algebraic spline curves considered h...

A novel technique is presented to facilitate the implementation of hierarchical b-splines and their interfacing with conventional finite element implementations. The discrete interpretation of the two-scale relation, as common in subdivision schemes, is used to establish algebraic relations between the basis functions and their coefficients on different levels of the hierarchical b-spline basis...

The recurrence algorithm is given for the calculation of NUAH B-splines in the space Sn+1 = span{sinh t, cosh t, t , · · · , t, t, 1} (n ≥ 3). The case of NUAH B-spline bases of low order with multiple knot sequences is studied. The limiting cases of UAH Bsplines are recovered when shape parameters α′s → 0and + ∞. Then the corresponding NUAH B-spline curve is defined and its main properties suc...

Specifications The purpose of Abstract Specifications1 is to create and document a conceptual model sufficient enough to allow for the creation of Implementation Specifications. One OGC abstract specification, the Spatial Schema, gives a standard for geographic information by specifying geometry and topology separately as a UML (Unified Modeling Language)2 package dependency tree. The geometry ...

We use a combination of both symbolic and numerical techniques to construct a degree bounded C-continuous, rational B-spline -approximations of real algebraic surface-surface intersection curves. The algebraic surfaces could be either in implicit or rational parametric form. At singular points we use the classical Newton power series factorizations to determine the distinct branches of the spac...

In this paper, a Crank–Nicolson finite difference scheme based on cubic B-spline quasi-interpolation has been derived for the solution of coupled Burgers equations with Caputo–Fabrizio derivative. The first- and second-order spatial derivatives have approximated by first second quasi-interpolation. discrete obtained in way constitutes system algebraic associated bi-pentadiagonal matrix. We show...

We study the algebraic and facial structures of hyperbolic programs, and examine natural relaxations of hyperbolic programs, the relaxations themselves being hyperbolic programs.