### Abstract

We present algorithms for computing the differential geometry properties of lines of curvature of parametric surfaces. We derive a unit tangent vector, curvature vector, binormal vector, torsion, and algorithms to evaluate their higher-order derivatives of lines of curvature of parametric surfaces. Among these quantities, it is shown that the curvature and its first derivative of the lines of curvature lend a hand for the formation of curved plates in shipbuilding. We also visualize the twist of lines of curvature, which enables us to observe how much the osculating plane of the line of curvature turns about the tangent vector.

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

Pages (from-to) | 224-238 |

Number of pages | 15 |

Journal | Graphical Models |

Volume | 76 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2014 Jan 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Curvature
- Line heating
- Lines of curvature
- Plate development
- Torsion

### ASJC Scopus subject areas

- Software
- Modelling and Simulation
- Geometry and Topology
- Computer Graphics and Computer-Aided Design

### Cite this

*Graphical Models*,

*76*(4), 224-238. https://doi.org/10.1016/j.gmod.2014.05.001

**Differential geometry properties of lines of curvature of parametric surfaces and their visualization.** / Joo, Han Kyul; Yazaki, Tatsuya; Takezawa, Masahito; Maekawa, Takashi.

Research output: Contribution to journal › Article

*Graphical Models*, vol. 76, no. 4, pp. 224-238. https://doi.org/10.1016/j.gmod.2014.05.001

}

TY - JOUR

T1 - Differential geometry properties of lines of curvature of parametric surfaces and their visualization

AU - Joo, Han Kyul

AU - Yazaki, Tatsuya

AU - Takezawa, Masahito

AU - Maekawa, Takashi

PY - 2014/1/1

Y1 - 2014/1/1

N2 - We present algorithms for computing the differential geometry properties of lines of curvature of parametric surfaces. We derive a unit tangent vector, curvature vector, binormal vector, torsion, and algorithms to evaluate their higher-order derivatives of lines of curvature of parametric surfaces. Among these quantities, it is shown that the curvature and its first derivative of the lines of curvature lend a hand for the formation of curved plates in shipbuilding. We also visualize the twist of lines of curvature, which enables us to observe how much the osculating plane of the line of curvature turns about the tangent vector.

AB - We present algorithms for computing the differential geometry properties of lines of curvature of parametric surfaces. We derive a unit tangent vector, curvature vector, binormal vector, torsion, and algorithms to evaluate their higher-order derivatives of lines of curvature of parametric surfaces. Among these quantities, it is shown that the curvature and its first derivative of the lines of curvature lend a hand for the formation of curved plates in shipbuilding. We also visualize the twist of lines of curvature, which enables us to observe how much the osculating plane of the line of curvature turns about the tangent vector.

KW - Curvature

KW - Line heating

KW - Lines of curvature

KW - Plate development

KW - Torsion

UR - http://www.scopus.com/inward/record.url?scp=84903557820&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84903557820&partnerID=8YFLogxK

U2 - 10.1016/j.gmod.2014.05.001

DO - 10.1016/j.gmod.2014.05.001

M3 - Article

VL - 76

SP - 224

EP - 238

JO - Graphical Models

JF - Graphical Models

SN - 1524-0703

IS - 4

ER -