Interpolation of surfaces with asymptotic curves in Euclidean 3-space

TL;DR

This paper explores the unique interpolation of surfaces from isoasymptotic curves in 3D space, establishing conditions for Hermite surface interpolation and illustrating with examples.

Contribution

It introduces a new method for surface interpolation based on isoasymptotic curves with proven uniqueness under specific conditions.

Findings

Existence of a unique $ C^0 $-Hermite surface interpolation

Conditions on marching scale functions for interpolation

Examples demonstrating the interpolation method

Abstract

In this paper, we investigate the interpolation of surfaces which are obtained from an isoasymptotic curve in 3D-Euclidean space. We prove that there exist a unique $ C^0 $-Hermite surface interpolation related to an isoasymptotic curve under some special conditions on the marching scale functions. Finally, we present some examples and plot their graphs.