File:Bump2D illustration.png
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[edit]DescriptionBump2D illustration.png | A bump function in 2D |
Date | |
Source | Own work |
Author | Oleg Alexandrov |
PNG development InfoField | This diagram was created with MATLAB. |
Source code InfoField | MATLAB code% 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);
|
Licensing
[edit]Public domainPublic domainfalsefalse |
I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 03:15, 8 August 2007 | 1,604 × 986 (179 KB) | Oleg Alexandrov (talk | contribs) | Trying to fix some odd issues with the bounding box. | |
03:11, 8 August 2007 | 1,590 × 979 (186 KB) | Oleg Alexandrov (talk | contribs) | {{Information |Description=A bump function in 2D |Source=self-made |Date=~~~~~ |Author= Oleg Alexandrov }} {{PD-self}} Category:Partial differential equations | ||
03:11, 8 August 2007 | 1,590 × 979 (186 KB) | Oleg Alexandrov (talk | contribs) | {{Information |Description=A bump function in 2D |Source=self-made |Date=~~~~~ |Author= Oleg Alexandrov }} {{PD-self}} Category:Partial differential equations | ||
03:08, 8 August 2007 | 1,590 × 979 (186 KB) | Oleg Alexandrov (talk | contribs) | {{Information |Description=A bump function in 2D |Source=self-made |Date=~~~~~ |Author= Oleg Alexandrov }} {{PD-self}} Category:Partial differential equations |
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