A paper and a poem on repulsion
Keenan Crane, a computer science professor at CMU, recently published with his students two delightful SIGGRAPH papers related to repulsion: âRepulsive Curvesâ and âRepulsive Surfaces.â The papers define an energy function on curves and surfaces; this energy function lets you use gradient descent to optimize geometric objects to fill space and avoid self-intersection.
When I first came across these papers, I was reminded of a poem by Kay Ryan called âRepulsive Theory.â It begins,
Little has been made
of the soft, skirting action
of magnets reversed,
while much has been made of attraction.
Go on, read the rest! I love this poem because of how unexpectedly it creates beauty from mathematical and scientific language. There is hidden delight saved just for the technical reader: knowledge of the mysterious expansion of our cosmos, or the computational nature of âconvolutions,â only heightens the poemâs message, widens the readerâs grin. And even putting aside meaning, on a purely aural level, phrases like âpillowy principleâ and âincurved beachesâ and âpearly convolutionsâ and âpooling spaceâ are a joy to read: they scoop up these tricky technical terms and melt them into smooth, soft songâŚ
âŚerr, almost too smooth, almost too soft, donât you think? On a second or third reading, there is something just a little slimy about the poem: the âdoily edgesâ are dangerously close to âoilyâ edges, and the wires do touch soon enough when we get to the âoiled motions of avoidanceâ and the âwhole swirl.â Ryanâs intellectual theory of avoidance is, at a subconscious or âgutâ level greasy, gross, yucky, unsettling â ah, now we get it: repulsive. I think back to the SIGGRAPH papers and laugh: after showing all of their beautiful figures and examples, the authors really do find themselves calling their results ârepulsive.â