# Bezier developable surfaces

## TL;DR

This paper investigates the design of developable surfaces using Bezier patches, identifying the specific classes of polynomial and spline developable surfaces constructible via Aumann's algorithm and polynomial curves.

## Contribution

It characterizes the set of polynomial and spline developable surfaces that can be constructed with Bezier patches and Aumann's algorithm, extending previous methods.

## Key findings

- Developable surfaces with polynomial edges of regression are constructible with Aumann's algorithm.
- Polynomial developable surfaces can be generated using general polynomial curves.
- Results extend to spline surfaces, broadening design possibilities.

## Abstract

In this paper we address the issue of designing developable surfaces with Bezier patches. We show that developable surfaces with a polynomial edge of regression are the set of developable surfaces which can be constructed with Aumann's algorithm. We also obtain the set of polynomial developable surfaces which can be constructed using general polynomial curves. The conclusions can be extended to spline surfaces as well.