Differential geometry of intersection curves of two surfaces

Xiuzi Ye, Takashi Maekawa

Research output: Contribution to journalArticle

44 Citations (Scopus)

Abstract

We present algorithms for computing the differential geometry properties of intersection curves of two surfaces where the combination of two surfaces can be parametric-parametric, implicit-implicit and parametric-implicit. We derive unit tangent vector, curvature vector, binormal vector, curvature, torsion, and algorithms to evaluate the higher-order derivatives for transversal as well as tangential intersections for all three types of intersection problems.

Original languageEnglish
Pages (from-to)767-788
Number of pages22
JournalComputer Aided Geometric Design
Volume16
Issue number8
DOIs
Publication statusPublished - 1999 Jan 1
Externally publishedYes

Fingerprint

Differential Geometry
Intersection
Curve
Binormal vector
Geometry
Curvature
Unit tangent vector
Higher order derivative
Torsional stress
Torsion
Derivatives
Computing
Evaluate

ASJC Scopus subject areas

  • Modelling and Simulation
  • Automotive Engineering
  • Aerospace Engineering
  • Computer Graphics and Computer-Aided Design

Cite this

Differential geometry of intersection curves of two surfaces. / Ye, Xiuzi; Maekawa, Takashi.

In: Computer Aided Geometric Design, Vol. 16, No. 8, 01.01.1999, p. 767-788.

Research output: Contribution to journalArticle

@article{a42f964dd043496e8839a7aa2e9462e8,
title = "Differential geometry of intersection curves of two surfaces",
abstract = "We present algorithms for computing the differential geometry properties of intersection curves of two surfaces where the combination of two surfaces can be parametric-parametric, implicit-implicit and parametric-implicit. We derive unit tangent vector, curvature vector, binormal vector, curvature, torsion, and algorithms to evaluate the higher-order derivatives for transversal as well as tangential intersections for all three types of intersection problems.",
author = "Xiuzi Ye and Takashi Maekawa",
year = "1999",
month = "1",
day = "1",
doi = "10.1016/S0167-8396(99)00018-7",
language = "English",
volume = "16",
pages = "767--788",
journal = "Computer Aided Geometric Design",
issn = "0167-8396",
publisher = "Elsevier",
number = "8",

}

TY - JOUR

T1 - Differential geometry of intersection curves of two surfaces

AU - Ye, Xiuzi

AU - Maekawa, Takashi

PY - 1999/1/1

Y1 - 1999/1/1

N2 - We present algorithms for computing the differential geometry properties of intersection curves of two surfaces where the combination of two surfaces can be parametric-parametric, implicit-implicit and parametric-implicit. We derive unit tangent vector, curvature vector, binormal vector, curvature, torsion, and algorithms to evaluate the higher-order derivatives for transversal as well as tangential intersections for all three types of intersection problems.

AB - We present algorithms for computing the differential geometry properties of intersection curves of two surfaces where the combination of two surfaces can be parametric-parametric, implicit-implicit and parametric-implicit. We derive unit tangent vector, curvature vector, binormal vector, curvature, torsion, and algorithms to evaluate the higher-order derivatives for transversal as well as tangential intersections for all three types of intersection problems.

UR - http://www.scopus.com/inward/record.url?scp=0033189868&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033189868&partnerID=8YFLogxK

U2 - 10.1016/S0167-8396(99)00018-7

DO - 10.1016/S0167-8396(99)00018-7

M3 - Article

VL - 16

SP - 767

EP - 788

JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

SN - 0167-8396

IS - 8

ER -