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I love the connections to the continuum case where these problems show up looking like ways of solving path integrals, Huygens principle, etc. In particular, so
by mathgenius 11y ago
I love the connections to the continuum case where these problems show up looking like ways of solving path integrals, Huygens principle, etc. In particular, some of these jump point rules look alot like diffraction (of a wave) around a boundary.
- mathgenius 11y agoAh, and it seems to be connected to ray marching also, as demonstrated so well by the fractal lab guy: http://sub.blue/fractal-lab http://sub.blue/fractal-lab
- willvarfar 11y agoHow is it connected to ray marching? I'm curious; my own playing with the area: http://williamedwardscoder.tumblr.com/post/26628848007/rod-marching http://williamedwardscoder.tumblr.com/post/26628848007/rod-m... http://williamedwardscoder.tumblr.com/post/28935319219/rod-marching-on-the-gpu http://williamedwardscoder.tumblr.com/post/28935319219/rod-m... Would like to make it faster :)
- mathgenius 11y agoI just think it is interesting to consider all these path finding algorithms, and compare/contrast them. So with ray marching, we already have access to a "distance" function. And it's not one but many targets we are looking for. It does seem to me like JPS tries to do something similar, the cacheing of jump points looks alot like the distance function, and now we are going to cast rays out looking for the target point, and let rays "bend" around corners, etc.
- darkmighty 11y agoIndeed light simply just uses a Dijkstra-like flood [1] fill :) This isotropic propagation is the reason Fermat's principle [2] works. [1] The flood pattern, or Huygens principle, in turns follow from the local (fundamental) and isotropic (for most media) nature of Maxwell's equations for electromagnetic propagation. [2] https://en.wikipedia.org/wiki/Fermat's_principle https://en.wikipedia.org/wiki/Fermat's_principle