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deepmind.google·6d ago
AI Engineering
Lobsters·Aug 10·5 min read
The mathematical beauty of hyperbezier curves
TL;DR
A new family of curves, based on the CesĂ ro equation, offers smoother curvature variation and better performance than cubic BĂ©ziers for 2D vector graphic design.
✦ Why It Matters
Consider experimenting with the CesĂ ro equation curves in your next design project for improved results.
Key Takeaways
- Explore hyperbezier curves for improved design flexibility.
- Utilize the CesĂ ro equation for smoother curvature representation.
- Experiment with parameter mapping for intuitive control.
- Consider hyperbezier curves for high-tension design scenarios.
How It Works
The hyperbezier curve is defined by the CesĂ ro equation, which specifies curvature as a function of arc length. This allows for smooth curvature variation and better handling of high-tension regions compared to cubic BĂ©ziers.
The mapping of control points from cubic BĂ©ziers to hyperbeziers is designed to maintain intuitive control while allowing for adjustments to achieve desired shapes.