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C2 Continuous Blending of Time-Dependent Parametric Surfaces.

You, X., Tian, F. and Tang, W., 2019. C2 Continuous Blending of Time-Dependent Parametric Surfaces. Journal of Computing and Information Science in Engineering, 19 (4), 041005.

Full text available as:

DRAFT-JCISE-18-1185-0.pdf - Accepted Version
Available under License Creative Commons Attribution.


DOI: 10.1115/1.4043042


Surface blending is widely applied in mechanical engineering. Creating a smooth transition surface of C2 continuity between time-dependent parametric surfaces that change their positions and shapes with time is an important and unsolved topic in surface blending. In order to address this issue, this paper develops a new approach to unify both time-dependent and time-independent surface blending with C2 continuity. It proposes a new surface blending mathematical model consisting of a vector-valued sixth-order partial differential equation and blending boundary constraints and investigates a simple and efficient approximate analytical solution of the mathematical model. A number of examples are presented to demonstrate the effectiveness and applications. The proposed approach has the advantages of (1) unifying time-independent and time-dependent surface blending, (2) always maintaining C2 continuity at trimlines when parametric surfaces change their positions and shapes with time, (3) providing effective shape control handles to achieve the expected shapes of blending surfaces but still exactly satisfy the given blending boundary constraints, and (4) quickly generating C2 continuous blending surfaces from the approximate analytical solution with easiness, good accuracy, and high efficiency.

Item Type:Article
Uncontrolled Keywords:computer-aided design; surface blending; time-dependent parametric representations; C2 continuity; sixth-order partial differential equations; approximate analytical solutions
Group:Faculty of Media & Communication
ID Code:33641
Deposited By: Symplectic RT2
Deposited On:11 Mar 2020 15:46
Last Modified:14 Mar 2022 14:20


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