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Dynamic disk B‐spline curves
Author(s) -
Zhang Yu,
Wu Zhongke,
Wang Xingce
Publication year - 2020
Publication title -
computer animation and virtual worlds
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.225
H-Index - 49
eISSN - 1546-427X
pISSN - 1546-4261
DOI - 10.1002/cav.1955
Subject(s) - computer science , animation , rendering (computer graphics) , spline (mechanical) , geometric modeling , computer graphics (images) , mathematics , geometry , structural engineering , engineering
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.