C3two-harmonic rational b-spline curves for trajectory synthesis

Q. J. Ge; J. Xia; J. Rastegar

doi:10.1115/DETC99/DAC-8653

C³two-harmonic rational b-spline curves for trajectory synthesis

Q. J. Ge
, J. Xia
, J. Rastegar

Mechanical Engineering

Stony Brook University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

This paper extends the recent work on rational Bezier representation of trigonometric polynomial curves to develop piecewise two-harmonic curves with the third order (or C3) continuity. First, continuity conditions are derived for piecing together two-harmonic rational Bezier curve segments. These conditions are then used to obtain C3 two-harmonic rational B-spline curves that have similarities to C3 quartic B-spline curves. Lowharmonic rational B-spline curves are compatible with the existing NURBS based CAD systems and can be used to synthesize low-harmonic motions of high-speed machinery to avoid vibration and control related problems.

Original language	English
Title of host publication	25th Design Automation Conference
Publisher	American Society of Mechanical Engineers (ASME)
Pages	649-661
Number of pages	13
ISBN (Electronic)	9780791819715
DOIs	https://doi.org/10.1115/DETC99/DAC-8653
State	Published - 1999
Event	ASME 1999 Design Engineering Technical Conferences, DETC 1999 - Las Vegas, United States Duration: Sep 12 1999 → Sep 16 1999

Publication series

Name	Proceedings of the ASME Design Engineering Technical Conference
Volume	1

Conference

Conference	ASME 1999 Design Engineering Technical Conferences, DETC 1999
Country/Territory	United States
City	Las Vegas
Period	09/12/99 → 09/16/99

Access to Document

10.1115/DETC99/DAC-8653

Cite this

@inproceedings{6151876f08c345ffbe675732fb2710ed,

title = "C3two-harmonic rational b-spline curves for trajectory synthesis",

abstract = "This paper extends the recent work on rational Bezier representation of trigonometric polynomial curves to develop piecewise two-harmonic curves with the third order (or C3) continuity. First, continuity conditions are derived for piecing together two-harmonic rational Bezier curve segments. These conditions are then used to obtain C3 two-harmonic rational B-spline curves that have similarities to C3 quartic B-spline curves. Lowharmonic rational B-spline curves are compatible with the existing NURBS based CAD systems and can be used to synthesize low-harmonic motions of high-speed machinery to avoid vibration and control related problems.",

author = "Ge, \{Q. J.\} and J. Xia and J. Rastegar",

note = "Publisher Copyright: Copyright {\textcopyright} 1999 by ASME.; ASME 1999 Design Engineering Technical Conferences, DETC 1999 ; Conference date: 12-09-1999 Through 16-09-1999",

year = "1999",

doi = "10.1115/DETC99/DAC-8653",

language = "English",

series = "Proceedings of the ASME Design Engineering Technical Conference",

publisher = "American Society of Mechanical Engineers (ASME)",

pages = "649--661",

booktitle = "25th Design Automation Conference",

}

Ge, QJ, Xia, J & Rastegar, J 1999, C³two-harmonic rational b-spline curves for trajectory synthesis. in 25th Design Automation Conference. Proceedings of the ASME Design Engineering Technical Conference, vol. 1, American Society of Mechanical Engineers (ASME), pp. 649-661, ASME 1999 Design Engineering Technical Conferences, DETC 1999, Las Vegas, United States, 09/12/99. https://doi.org/10.1115/DETC99/DAC-8653

C³two-harmonic rational b-spline curves for trajectory synthesis. / Ge, Q. J.; Xia, J.; Rastegar, J.
25th Design Automation Conference. American Society of Mechanical Engineers (ASME), 1999. p. 649-661 (Proceedings of the ASME Design Engineering Technical Conference; Vol. 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

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AU - Ge, Q. J.

AU - Xia, J.

AU - Rastegar, J.

PY - 1999

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N2 - This paper extends the recent work on rational Bezier representation of trigonometric polynomial curves to develop piecewise two-harmonic curves with the third order (or C3) continuity. First, continuity conditions are derived for piecing together two-harmonic rational Bezier curve segments. These conditions are then used to obtain C3 two-harmonic rational B-spline curves that have similarities to C3 quartic B-spline curves. Lowharmonic rational B-spline curves are compatible with the existing NURBS based CAD systems and can be used to synthesize low-harmonic motions of high-speed machinery to avoid vibration and control related problems.

AB - This paper extends the recent work on rational Bezier representation of trigonometric polynomial curves to develop piecewise two-harmonic curves with the third order (or C3) continuity. First, continuity conditions are derived for piecing together two-harmonic rational Bezier curve segments. These conditions are then used to obtain C3 two-harmonic rational B-spline curves that have similarities to C3 quartic B-spline curves. Lowharmonic rational B-spline curves are compatible with the existing NURBS based CAD systems and can be used to synthesize low-harmonic motions of high-speed machinery to avoid vibration and control related problems.

UR - https://www.scopus.com/pages/publications/85101100446

U2 - 10.1115/DETC99/DAC-8653

DO - 10.1115/DETC99/DAC-8653

M3 - Conference contribution

AN - SCOPUS:85101100446

T3 - Proceedings of the ASME Design Engineering Technical Conference

SP - 649

EP - 661

BT - 25th Design Automation Conference

PB - American Society of Mechanical Engineers (ASME)

T2 - ASME 1999 Design Engineering Technical Conferences, DETC 1999

Y2 - 12 September 1999 through 16 September 1999

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