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Exploring q-Bernstein-Bézier surfaces in Minkowski space: Analysis, modeling, and applications
Sadia Bashir1, Daud Ahmad1, Ghada Ali2
1Department of Mathematics, University of the Punjab, Lahore, Pakistan.
Plos One
|May 30, 2024
Summary
This study analyzes q-Bernstein-Bézier surfaces in Minkowski space, detailing their geometric properties like mean and Gaussian curvature. Findings offer insights into shape operator dependency for timelike and spacelike surfaces.
Area of Science:
- Differential Geometry
- Computer-Aided Geometric Design (CAGD)
- Minkowski Space Geometry
Background:
- Bézier surfaces are fundamental in CAGD.
- Generalizations like q-Bernstein-Bézier surfaces offer enhanced modeling capabilities.
- Minkowski space provides a unique geometric framework for analyzing these surfaces.
Purpose of the Study:
- To investigate the geometric properties of q-Bernstein-Bézier surfaces in Minkowski space.
- To analyze the influence of the shape parameter 'q' on surface characteristics.
- To explore the shape operator dependency for different surface types (timelike and spacelike).
Main Methods:
- Analysis of q-Bernstein-Bézier surfaces using boundary control points.
- Computation of mean and Gaussian curvature via fundamental coefficients.
- Investigation of shape operator dependency in Minkowski space.
Main Results:
- Characterization of timelike and spacelike q-Bernstein-Bézier surfaces.
- Formulas for mean and Gaussian curvature derived.
- Demonstration of shape operator dependency based on the parameter 'q'.
Conclusions:
- Q-Bernstein-Bézier surfaces exhibit distinct geometric behaviors in Minkowski space.
- The shape parameter 'q' significantly influences surface curvature and properties.
- The study provides a foundation for advanced surface modeling in specialized geometric spaces.
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