Dynamic disk B‐spline curves,Computer Animation and Virtual Worlds

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Dynamic disk B‐spline curves
Computer Animation and Virtual Worlds ( IF 0.9 ) Pub Date : 2020-07-01 , DOI: 10.1002/cav.1955
Yu Zhang ₁ , Zhongke Wu ₁ , Xingce Wang ₁

Affiliation

A disk B‐spline curve (DBSC) is an extension of a B‐spline curve and is used to represent a two‐dimensional (2D) region. DBSC is a useful 2D geometric representation and is widely applied in the 2D art design area, such as computer calligraphy, 2D computer animation, and nonphotorealistic rendering. To enhance the flexibility of DBSC, in this article, we propose a physics‐based generalization of DBSC–dynamic DBSC (D‐DBSC), which extends the traditional DBSC in the time domain. We give the mathematical expression of D‐DBSC and prove its several mathematical properties. We derive the motion equations of D‐DBSC based on Lagrangian mechanics and investigate the motion equations when it is under linear geometric constraints. Last, a D‐DBSC physical simulation system based on finite difference method is presented.

中文翻译：

动态磁盘 B 样条曲线

圆盘 B 样条曲线 (DBSC) 是 B 样条曲线的扩展，用于表示二维 (2D) 区域。DBSC 是一种有用的 2D 几何表示，广泛应用于 2D 艺术设计领域，例如计算机书法、2D 计算机动画和非真实感渲染。为了增强 DBSC 的灵活性，在本文中，我们提出了 DBSC 的基于物理的泛化-动态 DBSC（D-DBSC），它在时域上扩展了传统的 DBSC。我们给出了 D-DBSC 的数学表达式并证明了它的几个数学性质。我们基于拉格朗日力学推导了 D-DBSC 的运动方程，并研究了它在线性几何约束下的运动方程。最后，提出了一种基于有限差分法的D-DBSC物理仿真系统。

更新日期：2020-07-01

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