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b/Surf: Interactive Bézier Splines on Surface Meshes
Summary
This study introduces a robust framework for drawing and editing Bézier curves on 3D surfaces using manifold averages. The new subdivision-based approach ensures stable interactive design on complex meshes.
Area of Science:
- Computer Graphics
- Geometric Modeling
Background:
- Bézier curves are fundamental in computer graphics but extending them to 3D surfaces is challenging.
- Existing methods for manifold Bézier curves often suffer from discontinuities and fragility.
Purpose of the Study:
- To develop a practical and robust framework for interactive Bézier spline manipulation on manifold surfaces.
- To enable direct porting of 2D Bézier editing tools to 3D meshes.
Main Methods:
- Implemented manifold extensions of recursive de Casteljau bisection and Lane-Riesenfeld subdivision schemes.
- Developed algorithms for curve tracing, point evaluation, and point insertion on meshes.
- Utilized repeated manifold averages for robust curve representation.
Main Results:
- The subdivision-based approach proved robust and efficient, avoiding discontinuities common in direct extensions.
- Achieved superior performance and correct results compared to state-of-the-art methods in bulk experiments.
- Successfully ported 2D interactive editing functionalities and SVG drawing mapping to 3D meshes.
Conclusions:
- Subdivision-based methods offer a robust and efficient solution for manifold Bézier curves.
- The framework facilitates intuitive interactive design and editing of complex curves on 3D surfaces.
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