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research-article

C2 Continuous Blending of Time-Dependent Parametric Surfaces

[+] Author and Article Information
Xiangyu You

Department of Creative Technology, Faculty of Science and Technology Bournemouth University, Talbot Campus Poole, Dorset BH12 5BB United Kingdom xyou@bournemouth.ac.uk

Feng Tian

Bournemouth University Poole House, Fern Barrow Bournemouth, Dorset BH12 5BB United Kingdom ftian@bournemouth.ac.uk

Tang Wen

Bournemouth University Poole House, Fern Barrow Poole, Dorset BH12 5BB United Kingdom wtang@bournemouth.ac.uk

1Corresponding author.

Manuscript received July 25, 2018; final manuscript received February 18, 2019; published online xx xx, xxxx. Assoc. Editor: Anurag Purwar.

ASME doi:10.1115/1.4043042 History: Received July 25, 2018; Accepted February 19, 2019

Abstract

Surface blending is frequently met 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.

Copyright © 2019 by ASME
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