Approximation by ruled surfaces

Horng Yang Chen; Helmut Pottmann

doi:10.1016/S0377-0427(98)00212-X

Approximation by ruled surfaces

Horng Yang Chen, Helmut Pottmann^*

^*Corresponding author for this work

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

50 Scopus citations

Abstract

Given a surface or scattered data points from a surface in 3-space, we show how to approximate the given data by a ruled surface in tensor product B-spline representation. This leads us to a general framework for approximation in line space by local mappings from the Klein quadric to Euclidean 4-space. The presented algorithm for approximation by ruled surfaces possesses applications in architectural design, reverse engineering, wire electric discharge machining and NC milling.

Original language	English (US)
Pages (from-to)	143-156
Number of pages	14
Journal	Journal of Computational and Applied Mathematics
Volume	102
Issue number	1
DOIs	https://doi.org/10.1016/S0377-0427(98)00212-X
State	Published - Feb 15 1999
Externally published	Yes

Keywords

Computer-aided design
Line geometry
NC milling
Reverse engineering
Ruled surface
Surface approximation
Wire EDM

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1016/S0377-0427(98)00212-X

Cite this

@article{74eec4c8b6c84a27acd2ad44ee3ba990,

title = "Approximation by ruled surfaces",

abstract = "Given a surface or scattered data points from a surface in 3-space, we show how to approximate the given data by a ruled surface in tensor product B-spline representation. This leads us to a general framework for approximation in line space by local mappings from the Klein quadric to Euclidean 4-space. The presented algorithm for approximation by ruled surfaces possesses applications in architectural design, reverse engineering, wire electric discharge machining and NC milling.",

keywords = "Computer-aided design, Line geometry, NC milling, Reverse engineering, Ruled surface, Surface approximation, Wire EDM",

author = "Chen, {Horng Yang} and Helmut Pottmann",

year = "1999",

month = feb,

day = "15",

doi = "10.1016/S0377-0427(98)00212-X",

language = "English (US)",

volume = "102",

pages = "143--156",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

publisher = "Elsevier B.V.",

number = "1",

}

TY - JOUR

T1 - Approximation by ruled surfaces

AU - Chen, Horng Yang

AU - Pottmann, Helmut

PY - 1999/2/15

Y1 - 1999/2/15

N2 - Given a surface or scattered data points from a surface in 3-space, we show how to approximate the given data by a ruled surface in tensor product B-spline representation. This leads us to a general framework for approximation in line space by local mappings from the Klein quadric to Euclidean 4-space. The presented algorithm for approximation by ruled surfaces possesses applications in architectural design, reverse engineering, wire electric discharge machining and NC milling.

AB - Given a surface or scattered data points from a surface in 3-space, we show how to approximate the given data by a ruled surface in tensor product B-spline representation. This leads us to a general framework for approximation in line space by local mappings from the Klein quadric to Euclidean 4-space. The presented algorithm for approximation by ruled surfaces possesses applications in architectural design, reverse engineering, wire electric discharge machining and NC milling.

KW - Computer-aided design

KW - Line geometry

KW - NC milling

KW - Reverse engineering

KW - Ruled surface

KW - Surface approximation

KW - Wire EDM

UR - http://www.scopus.com/inward/record.url?scp=0033078849&partnerID=8YFLogxK

U2 - 10.1016/S0377-0427(98)00212-X

DO - 10.1016/S0377-0427(98)00212-X

M3 - Article

AN - SCOPUS:0033078849

SN - 0377-0427

VL - 102

SP - 143

EP - 156

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1

ER -

Approximation by ruled surfaces

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this