Interpolation of a spline developable surface between a curve and two rulings

TL;DR

This paper presents a method for interpolating spline developable surfaces between a curve and two rulings, allowing flexible endpoint selection through degree elevation, which advances the design of developable patches.

Contribution

It introduces a novel degree elevation approach enabling flexible boundary endpoint selection in spline developable surface interpolation.

Findings

Enables interpolation with flexible endpoint choices

Uses degree elevation to solve boundary constraints

Applicable to triangular developable patches

Abstract

In this paper we address the problem of interpolating a spline developable patch bounded by a given spline curve and the first and the last rulings of the developable surface. In order to complete the boundary of the patch a second spline curve is to be given. Up to now this interpolation problem could be solved, but without the possibility of choosing both endpoints for the rulings. We circumvent such difficulty here by resorting to degree elevation of the developable surface. This is useful not only to solve this problem, but also other problems dealing with triangular developable patches.