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deepmind.google·6d ago
AI Engineering
Lobsters·Jun 20·5 min read
The cube, the epicycles and the human face
TL;DR
A gap existed in representing complex shapes like human faces using mathematical constructs. A cube was created with three faces containing epicycle constructions that describe a human face through sinusoidal functions.
✦ Why It Matters
Engineers can leverage this approach to enhance shape modeling in graphics and AI applications.
Key Takeaways
- Explore mathematical constructs in shape representation.
- Utilize epicycles for complex shape modeling.
- Implement effective sampling strategies for geometry.
- Investigate the relationship between math and natural forms.
Full Summary
Mathematics has long been considered a tool for approximating shapes, but this work explores the idea that it may also be fundamental to their existence. A cube was constructed where each of its three visible faces features epicycles—circular paths that help describe the contours of a human face.
The methodology involved sampling points from the surface of a face, each defined by three coordinates: x, y, and z. The most challenging aspect was determining an effective sampling strategy to capture the face's geometry accurately.
The resulting visualizations show how sinusoidal functions can interact to create complex shapes, suggesting a deeper relationship between mathematics and physical forms. This work has implications for fields like computer graphics and AI, where understanding shape representation is crucial.