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Skeleton-Based Parametric 2-D Region Representation: Disk B-Spline Curves
IEEE Computer Graphics and Applications ( IF 1.8 ) Pub Date : 2021-03-31 , DOI: 10.1109/mcg.2021.3069847
Zhongke Wu 1 , Xingce Wang 1 , Shaolong Liu 1 , Quan Chen 2 , Hock Soon Seah 2 , Feng Tian 3
Affiliation  

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.

中文翻译:

基于骨架的参数二维区域表示:磁盘B样条曲线

骨架或中间轴是2D形状的重要属性。磁盘B样条曲线(DBSC)是基于骨架的参数化自由形式2-D区域表示形式,它以B样条形式定义。DBSC不仅描述了适用于描述该区域中异质材料的二维区域,而且还显式地描述了该区域的中心曲线(骨架),该区域适用于动画,模拟和识别。除了可用于B样条曲线的误差估计之外,DBSC还可以用于设计和设置自由形式的二维区域动画。尽管DBSC的应用在增加,但尚未对其理论和基础进行彻底的研究。在本文中,我们讨论了几种基本属性和算法,例如DBSC的de Boor算法。我们首先在由DBSC表示的二维区域(内部和边界)的任意点上导出显式评估和导数公式,然后提供异构对象表示。我们还介绍了DBSC的建模和交互式异构对象设计方法,这些方法巩固了DBSC理论并支持其进一步的应用。
更新日期:2021-05-11
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