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Noise derivatives

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Can anyone explain to me how to use analytical derivatives in noises for use in 3D terrain? I have made a very capable game engine but I'm unable to make any cool terrains due to not being good at math. I have looked around on the net but it seems terrain generation is just a creative art no one teaches. For starters, how about how to perturb the top portion of a density bubble so that we can increase the chance of unbroken terrain with overhangs, as opposed to disconnected terrain due to too much perturbation? http://www.iquilezles.org/www/articles/morenoise/morenoise.htm gives an introduction on the topic and shows that it can be useful (which I wasnt sure of beforehand)

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