Intersecting a freeform surface with a general swept surface

Joon Kyung Seong; Ku Jin Kim; Myung Soo Kim; Gershon Elber; Ralph R. Martin

doi:10.1016/j.cad.2004.10.006

Intersecting a freeform surface with a general swept surface

Joon Kyung Seong, Ku Jin Kim, Myung Soo Kim, Gershon Elber, Ralph R. Martin

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

We present efficient and robust algorithms for intersecting a rational parametric freeform surface with a general swept surface. A swept surface is given as a one-parameter family of cross-sectional curves. By computing the intersection between a freeform surface and each cross-sectional curve in the family, we can solve the intersection problem. We propose two approaches, which are closely related to each other. The first approach detects certain critical points on the intersection curve, and then connects them in a correct topology. The second approach converts the intersection problem to that of finding the zero-set of polynomial equations in the parameter space. We first present these algorithms for the special case of intersecting a freeform surface with a ruled surface or a ringed surface. We then consider the intersection with a general swept surface, where each cross-sectional curve may be defined as a rational parametric curve or as an implicit algebraic curve.

Original language	English
Pages (from-to)	473-483
Number of pages	11
Journal	CAD Computer Aided Design
Volume	37
Issue number	5 SPEC.ISS.
DOIs	https://doi.org/10.1016/j.cad.2004.10.006
Publication status	Published - 2005 Apr 15
Externally published	Yes

Bibliographical note

Funding Information:
The authors would like to thank the anonymous reviewers for their useful comments. All the algorithms and figures presented in this paper were implemented and generated using the IRIT solid modeling system [4] developed at the Technion, Israel. This research was supported in part by the Israeli Ministry of Science Grant No. 01-01-01509, in part by the Korean Ministry of Science and Technology (MOST) under the Korean-Israeli binational research grant, in part by grants No. R01-2002-000-00512-0 and No. R04-2004-000-10099-0 from the Basic Research Program of the Korea Science and Engineering Foundation (KOSEF), and in part by Kyungpook National University Research Fund 2004.

Keywords

Freeform surfaces
Ringed surfaces
Ruled surfaces
Surface-surface intersection
Swept surfaces

ASJC Scopus subject areas

Computer Science Applications
Computer Graphics and Computer-Aided Design
Industrial and Manufacturing Engineering

Access to Document

10.1016/j.cad.2004.10.006

Cite this

@article{58748b1f6c1e43009504f5bb0ef21f6f,

title = "Intersecting a freeform surface with a general swept surface",

abstract = "We present efficient and robust algorithms for intersecting a rational parametric freeform surface with a general swept surface. A swept surface is given as a one-parameter family of cross-sectional curves. By computing the intersection between a freeform surface and each cross-sectional curve in the family, we can solve the intersection problem. We propose two approaches, which are closely related to each other. The first approach detects certain critical points on the intersection curve, and then connects them in a correct topology. The second approach converts the intersection problem to that of finding the zero-set of polynomial equations in the parameter space. We first present these algorithms for the special case of intersecting a freeform surface with a ruled surface or a ringed surface. We then consider the intersection with a general swept surface, where each cross-sectional curve may be defined as a rational parametric curve or as an implicit algebraic curve.",

keywords = "Freeform surfaces, Ringed surfaces, Ruled surfaces, Surface-surface intersection, Swept surfaces",

author = "Seong, {Joon Kyung} and Kim, {Ku Jin} and Kim, {Myung Soo} and Gershon Elber and Martin, {Ralph R.}",

note = "Funding Information: The authors would like to thank the anonymous reviewers for their useful comments. All the algorithms and figures presented in this paper were implemented and generated using the IRIT solid modeling system [4] developed at the Technion, Israel. This research was supported in part by the Israeli Ministry of Science Grant No. 01-01-01509, in part by the Korean Ministry of Science and Technology (MOST) under the Korean-Israeli binational research grant, in part by grants No. R01-2002-000-00512-0 and No. R04-2004-000-10099-0 from the Basic Research Program of the Korea Science and Engineering Foundation (KOSEF), and in part by Kyungpook National University Research Fund 2004. ",

year = "2005",

month = apr,

day = "15",

doi = "10.1016/j.cad.2004.10.006",

language = "English",

volume = "37",

pages = "473--483",

journal = "CAD Computer Aided Design",

issn = "0010-4485",

publisher = "Elsevier Ltd",

number = "5 SPEC.ISS.",

}

TY - JOUR

T1 - Intersecting a freeform surface with a general swept surface

AU - Seong, Joon Kyung

AU - Kim, Ku Jin

AU - Kim, Myung Soo

AU - Elber, Gershon

AU - Martin, Ralph R.

N1 - Funding Information: The authors would like to thank the anonymous reviewers for their useful comments. All the algorithms and figures presented in this paper were implemented and generated using the IRIT solid modeling system [4] developed at the Technion, Israel. This research was supported in part by the Israeli Ministry of Science Grant No. 01-01-01509, in part by the Korean Ministry of Science and Technology (MOST) under the Korean-Israeli binational research grant, in part by grants No. R01-2002-000-00512-0 and No. R04-2004-000-10099-0 from the Basic Research Program of the Korea Science and Engineering Foundation (KOSEF), and in part by Kyungpook National University Research Fund 2004.

PY - 2005/4/15

Y1 - 2005/4/15

N2 - We present efficient and robust algorithms for intersecting a rational parametric freeform surface with a general swept surface. A swept surface is given as a one-parameter family of cross-sectional curves. By computing the intersection between a freeform surface and each cross-sectional curve in the family, we can solve the intersection problem. We propose two approaches, which are closely related to each other. The first approach detects certain critical points on the intersection curve, and then connects them in a correct topology. The second approach converts the intersection problem to that of finding the zero-set of polynomial equations in the parameter space. We first present these algorithms for the special case of intersecting a freeform surface with a ruled surface or a ringed surface. We then consider the intersection with a general swept surface, where each cross-sectional curve may be defined as a rational parametric curve or as an implicit algebraic curve.

AB - We present efficient and robust algorithms for intersecting a rational parametric freeform surface with a general swept surface. A swept surface is given as a one-parameter family of cross-sectional curves. By computing the intersection between a freeform surface and each cross-sectional curve in the family, we can solve the intersection problem. We propose two approaches, which are closely related to each other. The first approach detects certain critical points on the intersection curve, and then connects them in a correct topology. The second approach converts the intersection problem to that of finding the zero-set of polynomial equations in the parameter space. We first present these algorithms for the special case of intersecting a freeform surface with a ruled surface or a ringed surface. We then consider the intersection with a general swept surface, where each cross-sectional curve may be defined as a rational parametric curve or as an implicit algebraic curve.

KW - Freeform surfaces

KW - Ringed surfaces

KW - Ruled surfaces

KW - Surface-surface intersection

KW - Swept surfaces

UR - http://www.scopus.com/inward/record.url?scp=15744371015&partnerID=8YFLogxK

U2 - 10.1016/j.cad.2004.10.006

DO - 10.1016/j.cad.2004.10.006

M3 - Article

AN - SCOPUS:15744371015

SN - 0010-4485

VL - 37

SP - 473

EP - 483

JO - CAD Computer Aided Design

JF - CAD Computer Aided Design

IS - 5 SPEC.ISS.

ER -

Intersecting a freeform surface with a general swept surface

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this