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A quadratic trigonometric spline for curve modeling.
Shamaila Samreen1,2, Muhammad Sarfraz3, Malik Zawwar Hussain2
1Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan.
Plos One
|January 11, 2019
Summary
A new Quadratic Trigonometric Spline (QTS) offers C2 smoothness and superior geometric properties compared to traditional cubic polynomial splines (CPS). This computationally efficient curve modeling technique enhances applications in science, engineering, and design.
Area of Science:
- Computer-Aided Design (CAD)
- Geometric Modeling
- Scientific Computing
Background:
- Traditional cubic polynomial splines (CPS) are widely used but have limitations.
- Need for advanced spline methods with improved geometric and computational properties.
Purpose of the Study:
- Introduce a novel curve modeling technique using piecewise quadratic trigonometric functions.
- Establish a Quadratic Trigonometric Spline (QTS) as a viable alternative to CPS.
Main Methods:
- Developed a new spline method based on piecewise quadratic trigonometric functions.
- Ensured C2 continuity for smooth curve generation.
- Utilized four control points for piecewise curve description.
Main Results:
- The Quadratic Trigonometric Spline (QTS) achieves C2 smoothness.
- QTS demonstrates superior geometric properties compared to CPS.
- Error bounds of order 3 are established for QTS.
- Comparative analysis shows QTS is a better alternative to CPS.
- Time analysis confirms QTS is computationally more efficient than CPS.
Conclusions:
- The proposed Quadratic Trigonometric Spline (QTS) offers significant advantages over traditional cubic polynomial splines (CPS).
- QTS is a computationally efficient and geometrically favorable method for curve design and control.
- The technique is applicable across various scientific and engineering disciplines.
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