A visual interface for creating and mixing a special class of parameterized curves, described by Dongsung Huh and Terrence J. Sejnowski. Under this parameterization, a linear sum of curves yields a visually intuitive mixture, preserving geometric features of the underlying shapes.
The curves are parameterized as:
$logr(\theta) = \epsilon sin(\frac{m}{n} \theta - \phi)$
Where:
- r is the radius of curvature
- θ is the winding angle tangent to the curve
- m and n are co-prime integers, indexing the symmetry of the shape (m), and its periodicity relative to the winding angle (n).
- ε and φ are eccentricity and phase parameters.
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Huh, D. (2015). The vector space of convex curves: How to mix shapes. arXiv preprint arXiv:1506.07515.
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Huh, D., & Sejnowski, T. J. (2015). Spectrum of power laws for curved hand movements. Proceedings of the National Academy of Sciences, 112(29), E3950-E3958.