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Fair curve designing by Said-Ball curve
1Department of Mathematics, Lahore College for Women University, Lahore, Pakistan.
Plos One
|July 7, 2025
Summary
A new method for designing fair curves using rational cubic Said-Ball curves offers control over length and curvature variation. This approach optimizes curve aesthetics through energy functionals, yielding visually appealing and efficient designs.
Area of Science:
- Computer-Aided Design
- Geometric Modeling
- Computational Geometry
Background:
- Fair curves are essential in design for aesthetic appeal and functional efficiency.
- Existing methods may lack sufficient control over curve properties like curvature variation.
- Rational cubic Said-Ball curves offer a flexible framework for curve design.
Purpose of the Study:
- To introduce a novel method for designing visually fair curves.
- To achieve control over curve length and curvature variation.
- To leverage rational cubic Said-Ball curves for enhanced design capabilities.
Main Methods:
- Utilizing tangential continuous rational cubic Said-Ball curves (RCSBC).
- Employing continuity conditions to fix control points.
- Constructing optimization problems with stretch and curvature variation energy functionals to determine optimal free parameters (weights).
Main Results:
- A method for generating families of fair curves by adjusting free parameters.
- Demonstrated effectiveness through numerical examples.
- Successful application of the technique in two distinct design scenarios.
Conclusions:
- The proposed method effectively generates fair curves with controlled properties.
- The technique offers a flexible approach to curve design with adjustable parameters.
- The method has practical applications in design and modeling.
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