We introduce a general definition of refinable Hermite interpolants and investigate their general properties. We study also a notion of symmetry of these refinable interpolants. Results and ideas from the extensive theory of general refinement equations are applied to obtain results on refinable Hermite interpolants. The theory developed here is constructive and yields an easy-to-use constructi...

In this paper, the constructions of both open and closed trigonometric Hermite interpolation curves while using derivatives are presented. The combination tension, continuity, bias control is used as a very powerful type interpolation; they applied to curves. Surface construction utilizing studied explored several examples obtained by C1 surface given show usefulness method.

Bernstein{B ezier two{point Hermite G 2 interpolants to plane and space curves can be of degree up to 5, depending on the situation. We give a complete characterization for the cases of degree 3 to 5 and prove that rational representations are only required for degree 3. x1. Introduction and Overview We consider recovery of curves from irregularly sampled data. If the curves are to be represent...

In this paper, we focus on model reduction of large-scale bilinear systems. The main contributions are threefold. First, we introduce a new framework for interpolatory model reduction of bilinear systems. In contrast to the existing methods where interpolation is forced on some of the leading subsystem transfer functions, the new framework shows how to enforce multipoint interpolation of the un...

Purpose: In the newly released ASTM standard specification for Additive Manufacturing File (AMF) format – version 1.1, Hermite curve based interpolation is employed to refine input triangles to generate denser mesh with smoother geometry. This paper studies the problems of constructing smooth geometry based on Hermite interpolation on curves and proposes a solution to overcome these problems. D...