Amortized Noise

Abstract
Perlin noise is often used to compute a regularly spaced grid of noise values. The amortized noise algorithm takes advantage of this regular call pattern to amortize the computation cost of floatingpoint computations over interpolated points using dynamic programming techniques. The 2D amortized noise algorithm uses a factor of 17/3 = 5.67 fewer floatingpoint multiplications than the 2D Perlin noise algorithm, resulting in a speedup by a factor of approximately 3.64.8 in practice on available desktop and laptop computing hardware. The 3D amortized noise algorithm uses a factor of 40/7 = 5.71 fewer floatingpoint multiplications than the 3D Perlin noise algorithm; however, the increasing overhead for the initialization of tables limits the speedup factor achieved in practice to around 2.25. Improvements to both 2D Perlin noise and 2D amortized noise include making them infinite and nonrepeating by replacing the permutation table with a perfect hash function, and making them smoother by using quintic splines instead of cubic splines. While these improvements slow down 2D Perlin noise down by a factor of approximately 3292, they slow 2D amortized noise by a negligible amount.
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Citation:
Ian Parberry, Amortized Noise, Journal of Computer Graphics Techniques (JCGT), vol. 3, no. 2, 3147, 2014
Available online http://jcgt.org/published/0003/02/02/
Copyright: © 2014 Parberry
Received: 20140202; Recommended: 20140322; Published: 20140605