Approximation with active B-spline curves and surfaces

Helmut Pottmann; Stefan Leopoldseder; Michael Hofer

doi:10.1109/PCCGA.2002.1167835

Approximation with active B-spline curves and surfaces

Helmut Pottmann, Stefan Leopoldseder, Michael Hofer

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

103 Scopus citations

Abstract

An active contour model for parametric curve and surface approximation is presented. The active curve or surface adapts to the model shape to be approximated in an optimization algorithm. The quasi-Newton optimization procedure in each iteration step minimizes a quadratic function which is built up with the help of local quadratic approximants of the squared distance function of the model shape and an internal energy which has a smoothing and regularization effect. The approach completely avoids the parametrization problem. We also show how to use a similar strategy for the solution of variational problems for curves on surfaces. Examples are the geodesic path connecting two points on a surface and interpolating or approximating spline curves on surfaces. Finally we indicate how the latter topic leads to the variational design of smooth motions which interpolate or approximate given positions.

Original language	English (US)
Title of host publication	Proceedings - 10th Pacific Conference on Computer Graphics and Applications, PG 2002
Editors	Shi-Min Hu, Heung-Yeung Shum, Sabine Coquillart
Publisher	IEEE Computer Society
Pages	8-25
Number of pages	18
ISBN (Electronic)	0769517846
DOIs	https://doi.org/10.1109/PCCGA.2002.1167835
State	Published - 2002
Externally published	Yes
Event	10th Pacific Conference on Computer Graphics and Applications, PG 2002 - Beijing, China Duration: Oct 9 2002 → Oct 11 2002

Publication series

Name	Proceedings - Pacific Conference on Computer Graphics and Applications
Volume	2002-January
ISSN (Print)	1550-4085

Other

Other	10th Pacific Conference on Computer Graphics and Applications, PG 2002
Country/Territory	China
City	Beijing
Period	10/9/02 → 10/11/02

Bibliographical note

Publisher Copyright:
© 2002 IEEE.

Keywords

Active contours
Application software
Character generation
Computer vision
Geometry
Least squares approximation
Parameter estimation
Polynomials
Smoothing methods
Spline

ASJC Scopus subject areas

Software
Computer Graphics and Computer-Aided Design
Modeling and Simulation

Access to Document

10.1109/PCCGA.2002.1167835

Cite this

Pottmann, H., Leopoldseder, S., & Hofer, M. (2002). Approximation with active B-spline curves and surfaces. In S.-M. Hu, H.-Y. Shum, & S. Coquillart (Eds.), Proceedings - 10th Pacific Conference on Computer Graphics and Applications, PG 2002 (pp. 8-25). Article 1167835 (Proceedings - Pacific Conference on Computer Graphics and Applications; Vol. 2002-January). IEEE Computer Society. https://doi.org/10.1109/PCCGA.2002.1167835

Pottmann, Helmut ; Leopoldseder, Stefan ; Hofer, Michael. / Approximation with active B-spline curves and surfaces. Proceedings - 10th Pacific Conference on Computer Graphics and Applications, PG 2002. editor / Shi-Min Hu ; Heung-Yeung Shum ; Sabine Coquillart. IEEE Computer Society, 2002. pp. 8-25 (Proceedings - Pacific Conference on Computer Graphics and Applications).

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abstract = "An active contour model for parametric curve and surface approximation is presented. The active curve or surface adapts to the model shape to be approximated in an optimization algorithm. The quasi-Newton optimization procedure in each iteration step minimizes a quadratic function which is built up with the help of local quadratic approximants of the squared distance function of the model shape and an internal energy which has a smoothing and regularization effect. The approach completely avoids the parametrization problem. We also show how to use a similar strategy for the solution of variational problems for curves on surfaces. Examples are the geodesic path connecting two points on a surface and interpolating or approximating spline curves on surfaces. Finally we indicate how the latter topic leads to the variational design of smooth motions which interpolate or approximate given positions.",

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Pottmann, H, Leopoldseder, S & Hofer, M 2002, Approximation with active B-spline curves and surfaces. in S-M Hu, H-Y Shum & S Coquillart (eds), Proceedings - 10th Pacific Conference on Computer Graphics and Applications, PG 2002., 1167835, Proceedings - Pacific Conference on Computer Graphics and Applications, vol. 2002-January, IEEE Computer Society, pp. 8-25, 10th Pacific Conference on Computer Graphics and Applications, PG 2002, Beijing, China, 10/9/02. https://doi.org/10.1109/PCCGA.2002.1167835

Approximation with active B-spline curves and surfaces. / Pottmann, Helmut; Leopoldseder, Stefan; Hofer, Michael.
Proceedings - 10th Pacific Conference on Computer Graphics and Applications, PG 2002. ed. / Shi-Min Hu; Heung-Yeung Shum; Sabine Coquillart. IEEE Computer Society, 2002. p. 8-25 1167835 (Proceedings - Pacific Conference on Computer Graphics and Applications; Vol. 2002-January).

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

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Pottmann H, Leopoldseder S, Hofer M. Approximation with active B-spline curves and surfaces. In Hu SM, Shum HY, Coquillart S, editors, Proceedings - 10th Pacific Conference on Computer Graphics and Applications, PG 2002. IEEE Computer Society. 2002. p. 8-25. 1167835. (Proceedings - Pacific Conference on Computer Graphics and Applications). doi: 10.1109/PCCGA.2002.1167835

Approximation with active B-spline curves and surfaces

Abstract

Publication series

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Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this