Repulsive curves

Chris Yu, Henrik Schumacher, and Keenan Crane from Carnegie Mellon University are working on repulsive curves, which is a method to efficiently unravel curves so that they don’t overlap:

Curves play a fundamental role across computer graphics, physical simulation, and mathematical visualization, yet most tools for curve design do nothing to prevent crossings or self-intersections. This paper develops efficient algorithms for (self-)repulsion of plane and space curves that are well-suited to problems in computational design. Our starting point is the so-called tangent-point energy, which provides an infinite barrier to self-intersection. In contrast to local collision detection strategies used in, e.g., physical simulation, this energy considers interactions between all pairs of points, and is hence useful for global shape optimization: local minima tend to be aesthetically pleasing, physically valid, and nicely distributed in space.

Be sure to watch the video demo.

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Flatten the coronavirus curve

The coronavirus can possibly infect a lot more people than there are those who can provide medical care. But if we slow the spread, and there are fewer people in need of care at the same time, the difference might be less overbearing. This version of the “flatten the curve” graphic by Alexander Radtke, first made by Rosamund Pearce for The Economist, illustrates the difference in animated form.

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