Analytic Definition of Curves and Surfaces by Parabolic Blending

TL;DR

This paper introduces a parabolic blending method for interpolating curves and surfaces that ensures slope continuity and offers flexible shape control through a parametric patch approach.

Contribution

It presents a new interpolation technique that guarantees slope continuity and provides shape flexibility for curves and surfaces using a parametric patch system.

Findings

Ensures slope continuity at all junctions.

Provides shape flexibility through parametric patches.

Applicable to complex surface modeling.

Abstract

A procedure for interpolating between specified points of a curve or surface is described. The method guarantees slope continuity at all junctions. A surface panel divided into p x q contiguous patches is completely specified by the coordinates of (p+1) x (q+1) points. Each individual patch, however, depends parametrically on the coordinates of 16 points, allowing shape flexibility and global conformity.