X n Given a sequence of points { i}i=l on a regular quadric S: X T A X = 0 C E d, d >1 3, we study the problem of constructing a G I rational quadratic spline curve lying on 5' that interpolates { X ~ } ~ j . It is shown that a necessary condition for the existence of a nontrivial interpolant is ( X ~ A X 2 ) ( X T i A X i + I ) > 0, i = 1 , 2 , . . . , n 1. Also considered is a Hermite interpo...

When an approximant is accurate on interval, it only natural to try extend multi-dimensional domains. In the present article we make use of fact that linear rational barycentric interpolants converge rapidly toward analytic and several-times differentiable functions interpolate them two-dimensional starlike domains parametrized in polar coordinates. radial direction, engage at conformally shift...

abstract Evaluating and comparing the quality of surface interpolants is an important problem in computer graphics, computer aided geometric design and scientiic visualization. We introduce geometric uncertainty as a measure of interpolation error, level of conndence or quality of an interpolant. Geometric uncertainty can be estimated as a scalar or a vector-valued function that depends upon ge...

Mean value interpolation is a simple, fast, linearly precise method of smoothly interpolating a function given on the boundary of a domain. For planar domains, several properties of the interpolant were established in a recent paper by Dyken and the second author, including: sufficient conditions on the boundary to guarantee interpolation for continuous data; a formula for the normal derivative...

In this contribution, we study multivariate polynomial interpolation and quadrature rules on non-tensor product node sets linked to Lissajous curves and Chebyshev varieties. After classifying multivariate Lissajous curves and the interpolation nodes related to these curves, we derive a discrete orthogonality structure on these node sets. Using this discrete orthogonality structure, we can deriv...

We describe a new method for analyzing and extracting human gait motion by combining statistical methods with image processing. The periodic motion of human gait is modeled by trigonometric-polynomial interpolant functions. The gait description is derived by topological analysis guided by medical studies that select areas from which joint angles are derived by regression analysis. Then, the int...