We present a new and efficient algorithm to compute affine equivalences symmetries between two trigonometric curves in an arbitrary dimension. The benefits from the power of invariance polynomial gcd factoring without solving any system equations. is implemented MAPLE, extensive experimentations demonstrating efficiency method are given.

On the basis of a fully discrete trigonometric Galerkin method and two grid iterations we propose solvers for integral and pseudodifferential equations on closed curves which solve the problem with an optimal convergence order ‖uN − u‖λ ≤ cλ,μNλ−μ‖u‖μ, λ ≤ μ (Sobolev norms of periodic functions) in O(N log N) arithmetical operations.

Recently, we have introduced spaces of splines deened on triangulations lying on the sphere or on sphere-like surfaces. These spaces arose out of a new kind of Bernstein-B ezier theory on such surfaces. The purpose of this paper is to contribute to the development of a constructive theory for such spline spaces analogous to the well-known theory of polynomial splines on planar triangula-tions. ...

We present an e cient algorithm to construct C smooth meshes of quintic A-patches that interpolate or approximate the vertices of a given triangulated polyhedron P. An A-patch is a smooth and functional zero-contour patch of a trivariate polynomial in Bernstein-B ezier (BB) form de ned within a tetrahedron. A simplicial hull is constructed based on P. A quintic A-patch is then constructed withi...

The main result of this paper is a generalization of the property that, for smooth u, uxy = 0 implies (*) u(x, y) = a(x) + b(y). Any function having generalized unsymmetric mixed partial derivative identically zero is of the form (*). There is a function with generalized symmetric mixed partial derivative identically zero not of the form (*), but (*) does follow here with the additional assumpt...

We explore the subrings in trigonometric polynomial rings and their factorization properties. Consider the ring S′ of complex trigonometric polynomials over the field Q(i) (see [11]). We construct the subrings S′ 1, S′ 0 of S′ such that S′ 1 ⊆ S′ 0 ⊆ S′. Then S′ 1 is a Euclidean domain, whereas S′ 0 is a Noetherian HFD. We also characterize the irreducible elements of S′ 1, S′ 0 and discuss amo...

In this study we explore the subrings in trigonometric polynomial rings. Consider the rings T and T ′ of real and complex trigonometric polynomials over the fields R and its algebraic extension C respectively ( see [6]). We construct the subrings T0 of T and T ′ 0, T ′ 1 of T ′. Then T0 is a BFD whereas T ′ 0 and T ′ 1 are Euclidean domains. We also discuss among these rings the Condition : Let...

Consider a plane curve given parametrically by a generalized trigonometric polynomial, that is, x + iy = P n k=1 a k e ik. In this paper, we obtain an impliciti-zation of the curve, that is, an equation in x and y which captures all the points on the curve and, if any, only nitely many more points.

A new class of spline curves in polar coordinates has been presented in (SS anchez-Reyes, 1992) and independently considered in (de Casteljau, 1994). These are rational trigonometric curves in Cartesian coordinates and can be represented as NURBS. From the relationship existing with the correspondent curves in Cartesian coordinates an alternative way to derive some useful tools for modelling sp...