Approximate algebraic methods for curves and surfaces and their applications

Bert Jüttler; Pavel Chalmovianský; Mohamed Shalaby; Elmar Wurm

doi:10.1145/1090122.1090124

Approximate algebraic methods for curves and surfaces and their applications

Bert Jüttler^*, Pavel Chalmovianský, Mohamed Shalaby, Elmar Wurm

^*Corresponding author for this work

Research output: Contribution to conference › Paper › peer-review

5 Scopus citations

Abstract

We report on approximate techniques for conversion between the implicit and the parametric representation of curves and surfaces, i.e., implicitization and parameterization. It is shown that these techniques are able to handle general free-form surfaces, and they can therefore be used to exploit the duality of implicit and parametric representations. In addition, we discuss several applications of these techniques, such as detection of self-intersections, ray-tracing, footpoint computation and parameterization of scattered data for parametric curve or surface fitting.

Original language	English (US)
Pages	13-18
Number of pages	6
DOIs	https://doi.org/10.1145/1090122.1090124
State	Published - 2005
Externally published	Yes
Event	Spring Conference on Computer Graphics, SCCG 2005 - Budmerice, Slovakia Duration: May 12 2006 → May 14 2006

Other

Other	Spring Conference on Computer Graphics, SCCG 2005
Country/Territory	Slovakia
City	Budmerice
Period	05/12/06 → 05/14/06

Keywords

Approximation
Distance bounds
Footpoint computation
Implicitization
Intersections and self-intersections
Parameterization
Parameterizing scattered data
Ray-tracing

ASJC Scopus subject areas

General Engineering

Access to Document

10.1145/1090122.1090124

Cite this

@conference{282b7a1fee14431b8e4f0c8cfc43fca1,

title = "Approximate algebraic methods for curves and surfaces and their applications",

abstract = "We report on approximate techniques for conversion between the implicit and the parametric representation of curves and surfaces, i.e., implicitization and parameterization. It is shown that these techniques are able to handle general free-form surfaces, and they can therefore be used to exploit the duality of implicit and parametric representations. In addition, we discuss several applications of these techniques, such as detection of self-intersections, ray-tracing, footpoint computation and parameterization of scattered data for parametric curve or surface fitting.",

keywords = "Approximation, Distance bounds, Footpoint computation, Implicitization, Intersections and self-intersections, Parameterization, Parameterizing scattered data, Ray-tracing",

author = "Bert J{\"u}ttler and Pavel Chalmoviansk{\'y} and Mohamed Shalaby and Elmar Wurm",

year = "2005",

doi = "10.1145/1090122.1090124",

language = "English (US)",

pages = "13--18",

note = "Spring Conference on Computer Graphics, SCCG 2005 ; Conference date: 12-05-2006 Through 14-05-2006",

}

TY - CONF

T1 - Approximate algebraic methods for curves and surfaces and their applications

AU - Jüttler, Bert

AU - Chalmovianský, Pavel

AU - Shalaby, Mohamed

AU - Wurm, Elmar

PY - 2005

Y1 - 2005

N2 - We report on approximate techniques for conversion between the implicit and the parametric representation of curves and surfaces, i.e., implicitization and parameterization. It is shown that these techniques are able to handle general free-form surfaces, and they can therefore be used to exploit the duality of implicit and parametric representations. In addition, we discuss several applications of these techniques, such as detection of self-intersections, ray-tracing, footpoint computation and parameterization of scattered data for parametric curve or surface fitting.

AB - We report on approximate techniques for conversion between the implicit and the parametric representation of curves and surfaces, i.e., implicitization and parameterization. It is shown that these techniques are able to handle general free-form surfaces, and they can therefore be used to exploit the duality of implicit and parametric representations. In addition, we discuss several applications of these techniques, such as detection of self-intersections, ray-tracing, footpoint computation and parameterization of scattered data for parametric curve or surface fitting.

KW - Approximation

KW - Distance bounds

KW - Footpoint computation

KW - Implicitization

KW - Intersections and self-intersections

KW - Parameterization

KW - Parameterizing scattered data

KW - Ray-tracing

UR - http://www.scopus.com/inward/record.url?scp=33749007961&partnerID=8YFLogxK

U2 - 10.1145/1090122.1090124

DO - 10.1145/1090122.1090124

M3 - Paper

AN - SCOPUS:33749007961

SP - 13

EP - 18

T2 - Spring Conference on Computer Graphics, SCCG 2005

Y2 - 12 May 2006 through 14 May 2006

ER -

Approximate algebraic methods for curves and surfaces and their applications

Abstract

Other

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this