### Abstract

A developable surface can be formed by bending or rolling a planar surface without stretching or tearing; in other words, it can be developed or unrolled isometrically onto a plane. This paper describes two main differential geometry properties of developable surfaces that have industrial applications. First, a method for identifying the inflection line of a developable surface is described. Second, geodesic lines between two points on a developable surface are found as an initial value problem, which is easier to solve than the boundary value problem that is normally required.

Original language | English |
---|---|

Pages (from-to) | 251-267 |

Number of pages | 17 |

Journal | Mathematical Engineering in Industry |

Volume | 7 |

Issue number | 2 |

Publication status | Published - 1999 Dec 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Developable surface
- Flat points
- Geodesies
- Inflection lines

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Mathematical Engineering in Industry*,

*7*(2), 251-267.

**Computation of inflection lines and geodesies on developable surfaces.** / Maekawa, Takashi; Chalfant, J. S.

Research output: Contribution to journal › Article

*Mathematical Engineering in Industry*, vol. 7, no. 2, pp. 251-267.

}

TY - JOUR

T1 - Computation of inflection lines and geodesies on developable surfaces

AU - Maekawa, Takashi

AU - Chalfant, J. S.

PY - 1999/12/1

Y1 - 1999/12/1

N2 - A developable surface can be formed by bending or rolling a planar surface without stretching or tearing; in other words, it can be developed or unrolled isometrically onto a plane. This paper describes two main differential geometry properties of developable surfaces that have industrial applications. First, a method for identifying the inflection line of a developable surface is described. Second, geodesic lines between two points on a developable surface are found as an initial value problem, which is easier to solve than the boundary value problem that is normally required.

AB - A developable surface can be formed by bending or rolling a planar surface without stretching or tearing; in other words, it can be developed or unrolled isometrically onto a plane. This paper describes two main differential geometry properties of developable surfaces that have industrial applications. First, a method for identifying the inflection line of a developable surface is described. Second, geodesic lines between two points on a developable surface are found as an initial value problem, which is easier to solve than the boundary value problem that is normally required.

KW - Developable surface

KW - Flat points

KW - Geodesies

KW - Inflection lines

UR - http://www.scopus.com/inward/record.url?scp=0032677222&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032677222&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032677222

VL - 7

SP - 251

EP - 267

JO - Mathematical Engineering in Industry

JF - Mathematical Engineering in Industry

SN - 0169-121X

IS - 2

ER -