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>Domokos and colleagues devised an algorithm for smoothly converting geometric tiles — either 2D polygons or 3D polyhedra, like the bubbles of a foam — into sof
by JackFr 2y ago
>Domokos and colleagues devised an algorithm for smoothly converting geometric tiles — either 2D polygons or 3D polyhedra, like the bubbles of a foam — into soft cells, and explored the range of possible shapes these rules permit. In 2D, the options are fairly limited: all tiles must have at least two cusp-like corners.
(Emphasis mine)
Am I reading that wrong or are the kitchen tiles in the images impossible based on the statement above
- A_D_E_P_T 2y agoThat shape has three cusp-like corners -- one at each sharp point, with smooth curves (convex/concave) between them. This satisfies the "at least two" condition. The even simpler "lemon" is an even more egregious example, as it satisfies the conditions in two and three dimensions and yet is rather old and well-defined: https://mathworld.wolfram.com/LemonSurface.html https://mathworld.wolfram.com/LemonSurface.html
- mhandley 2y agoI think that tile shape has one cusp-like corner and two ~90-degree corners. Thus it's not a complete transformation of a polygon into a soft cell, and hence the "at least two" rule doesn't apply.
- A_D_E_P_T 2y agoThey aren't 90° corners -- and in any case it would be simple to modify the angle of those corners and keep the shape basically (or nearly) the same. Also the plain 2D lemon/lozenge/lentil satisfies all conditions.