Journal
MATHEMATICS
Volume 9, Issue 21, Pages -Publisher
MDPI
DOI: 10.3390/math9212651
Keywords
C-Bezier basis; geometric continuity; parametric continuity; shape parameters
Categories
Funding
- Fundamental Research Funds for the Central Universities [DUT20LK13]
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By introducing the parametric and geometric continuity constraints of generalized C-Bezier curves and surfaces with shape parameters, it is possible to easily change curves and surfaces while preserving their characteristics and geometrical configuration.
In order to solve the problem of geometric design and architectural design of complex engineering surface, we introduce the parametric and geometric continuity constraints of generalized C-Bezier curves and surfaces with shape parameters. Firstly, based on C-Bezier basis with parameters, we study the constraints of the control points of the curves needed to be satisfied when connecting them. Moreover, we study the continuity conditions between two adjacent C-Bezier surfaces with parameters. By the continuity conditions and different shape parameters, the curve and surface can be changed easily and be more flexible without altering its control points. Therefore, by adjusting the values of shape parameters, the curve and surface still preserve its characteristics and geometrical configuration. Some graphical examples ensure that the proposed method greatly improves the ability to design complex curves and surfaces and easy to implement.
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