Skeleton-Based Parametric 2-D Region Representation: Disk B-Spline Curves

Authors: Wu, Z., Wang, X., Liu, S., Chen, Q., Seah, H.S. and Tian, F.

Journal: IEEE Computer Graphics and Applications

Volume: 41

Issue: 3

Pages: 59-70

eISSN: 1558-1756

ISSN: 0272-1716

DOI: 10.1109/MCG.2021.3069847

Abstract:

The skeleton, or medial axis, is an important attribute of 2-D shapes. The disk B-spline curve (DBSC) is a skeleton-based parametric freeform 2-D region representation, which is defined in the B-spline form. The DBSC describes not only a 2-D region, which is suitable for describing heterogeneous materials in the region, but also the center curve (skeleton) of the region explicitly, which is suitable for animation, simulation, and recognition. In addition to being useful for error estimation of the B-spline curve, the DBSC can be used in designing and animating freeform 2-D regions. Despite increasing DBSC applications, its theory and fundamentals have not been thoroughly investigated. In this article, we discuss several fundamental properties and algorithms, such as the de Boor algorithm for DBSCs. We first derive the explicit evaluation and derivatives formulas at arbitrary points of a 2-D region (interior and boundary) represented by a DBSC and then provide heterogeneous object representation. We also introduce modeling and interactive heterogeneous object design methods for a DBSC, which consolidates DBSC theory and supports its further applications.

http://eprints.bournemouth.ac.uk/35414/

Source: Scopus

Skeleton-Based Parametric 2-D Region Representation: Disk B-Spline Curves.

Authors: Wu, Z., Wang, X., Liu, S., Chen, Q., Seah, H.S. and Tian, F.

Journal: IEEE Comput Graph Appl

Volume: 41

Issue: 3

Pages: 59-70

eISSN: 1558-1756

DOI: 10.1109/MCG.2021.3069847

Abstract:

The skeleton, or medial axis, is an important attribute of 2-D shapes. The disk B-spline curve (DBSC) is a skeleton-based parametric freeform 2-D region representation, which is defined in the B-spline form. The DBSC describes not only a 2-D region, which is suitable for describing heterogeneous materials in the region, but also the center curve (skeleton) of the region explicitly, which is suitable for animation, simulation, and recognition. In addition to being useful for error estimation of the B-spline curve, the DBSC can be used in designing and animating freeform 2-D regions. Despite increasing DBSC applications, its theory and fundamentals have not been thoroughly investigated. In this article, we discuss several fundamental properties and algorithms, such as the de Boor algorithm for DBSCs. We first derive the explicit evaluation and derivatives formulas at arbitrary points of a 2-D region (interior and boundary) represented by a DBSC and then provide heterogeneous object representation. We also introduce modeling and interactive heterogeneous object design methods for a DBSC, which consolidates DBSC theory and supports its further applications.

http://eprints.bournemouth.ac.uk/35414/

Source: PubMed

Skeleton-Based Parametric 2-D Region Representation: Disk B-Spline Curves

Authors: Wu, Z., Wang, X., Liu, S., Chen, Q., Seah, H.S. and Tian, F.

Journal: IEEE COMPUTER GRAPHICS AND APPLICATIONS

Volume: 41

Issue: 3

Pages: 59-69

eISSN: 1558-1756

ISSN: 0272-1716

DOI: 10.1109/MCG.2021.3069847

http://eprints.bournemouth.ac.uk/35414/

Source: Web of Science (Lite)

Skeleton-Based Parametric 2-D Region Representation: Disk B-Spline Curves.

Authors: Wu, Z., Wang, X., Liu, S., Chen, Q., Seah, H.S. and Tian, F.

Journal: IEEE computer graphics and applications

Volume: 41

Issue: 3

Pages: 59-70

eISSN: 1558-1756

ISSN: 0272-1716

DOI: 10.1109/mcg.2021.3069847

Abstract:

The skeleton, or medial axis, is an important attribute of 2-D shapes. The disk B-spline curve (DBSC) is a skeleton-based parametric freeform 2-D region representation, which is defined in the B-spline form. The DBSC describes not only a 2-D region, which is suitable for describing heterogeneous materials in the region, but also the center curve (skeleton) of the region explicitly, which is suitable for animation, simulation, and recognition. In addition to being useful for error estimation of the B-spline curve, the DBSC can be used in designing and animating freeform 2-D regions. Despite increasing DBSC applications, its theory and fundamentals have not been thoroughly investigated. In this article, we discuss several fundamental properties and algorithms, such as the de Boor algorithm for DBSCs. We first derive the explicit evaluation and derivatives formulas at arbitrary points of a 2-D region (interior and boundary) represented by a DBSC and then provide heterogeneous object representation. We also introduce modeling and interactive heterogeneous object design methods for a DBSC, which consolidates DBSC theory and supports its further applications.

http://eprints.bournemouth.ac.uk/35414/

Source: Europe PubMed Central