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| Keywords: Bump2D illustration.png Created with MATLAB A bump function in 2D own 03 08 8 August 2007 UTC Oleg Alexandrov Source code MATLAB <source lang matlab > illustration of a bump function in two dimensions function main the number of data points More points means prettier picture N 300; a function close to what we want but not smooth Z get_step_function N ; a smooth function with small support that will serve as mollifier W get_mollifier N ; get the convolution of the two so a mollified step function S conv2 Z W ; truncate S at the edges and scale it p 0 2; m n size S ; m1 floor p m +1; m2 floor 1-p m -1; n1 floor p n +1; n2 floor 1-p n -1; S S m1 m2 n1 n2 ; S 100 S/max max S ; plot the surface figure 2 ; clf; hold on; axis equal; axis off; surf S ; make the surface beautiful shading interp; colormap autumn; add in a source of light camlight -50 54 ; viewing angle view -40 38 ; save as png print '-dpng' '-r400' 'Bump2D_illustration_uncropped png' ; optionally crop the margins convert -trim Bump2D_illustration_uncropped png Bump2D_illustration png get a function which is 1 on a set and 0 outside of it function Z get_step_function N XX linspace -1 5 4 N ; YY linspace -4 4 N ; X Y meshgrid XX YY ; c 2; k 1 2; shift 10; Z c 2-X 2-Y 2 2 + k c-X 3-shift; Z 1-max sign Z 0 ; function W get_mollifier N now try to get a function with compact support as a mollifier We will cheat by using a gaussian a 4; XX linspace -a a N ; YY linspace -a a N ; X Y meshgrid XX YY ; K 4; W exp -K X 2+Y 2 ; truncate the Gaussian to make it with compact support trunc 1e-2; W max W-trunc 0 ; </source> Partial differential equations Multivariate calculus Files by User Oleg Alexandrov from en wikipedia Surface plots Shading interpolation Images with Matlab source code | ||||
