File:Tubular neighborhood.png
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DescriptionTubular neighborhood.png | Illustration of en:Tubular neighborhood |
Source | Made with en:Matlab |
Author | Oleg Alexandrov 03:01, 1 June 2007 (UTC) |
Permission (Reusing this file) |
Public domain |
This diagram was created with MATLAB.
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. |
% illustration of tubular neighborhood
function main()
f=inline('sin(x)', 'x'); % will construct a tubular neighborhood of this curve
a=0; b=2*pi; N = 100; X = linspace(a, b, N); % consider N points in the interval [a, b]
Y = f(X); % the curve
ll = 3; % length of lines perpendicular to the curve
lls = 0.3; % smaller subsegments
thin_line = 2;
thick_line = 4;
% will draw lines perpendicular to the graph of Y=f(X) at
% points separted by length of 'spacing'
spacing = 0.033;
M = floor(spacing*N);
% colors
red=[0.867 0.06 0.14];
blue = [0, 129, 205]/256;
green = [0, 200, 70]/256;
figure(1); clf; hold on; axis equal; axis off;
% plot the lines
for k=1:N
p = (k-1)*M+2;
if p >= N
break;
end
% the normal to the curve at (X(p), Y(p))
Normal = [-(Y(p+1)-Y(p-1)), X(p+1)-X(p-1)]; Normal = Normal/norm(Normal);
plot([X(p)-ll*Normal(1), X(p)+ll*Normal(1)], [Y(p)-ll*Normal(2),...
Y(p)+ll*Normal(2)], 'color', green, 'linewidth', thin_line)
plot([X(p)-lls*Normal(1), X(p)+lls*Normal(1)], [Y(p)-lls*Normal(2),...
Y(p)+lls*Normal(2)], 'color', red, 'linewidth', 0.7*thick_line)
end
% plot the curve
plot(X, Y, 'linewidth', thick_line);
saveas(gcf, 'Tubular_neighborhood.eps', 'psc2')
This math image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with
{{vector version available|new image name}} .
It is recommended to name the SVG file “Tubular neighborhood.svg”—then the template Vector version available (or Vva) does not need the new image name parameter. |
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 05:01, 2 June 2007 | 2,506 × 1,967 (374 KB) | Oleg Alexandrov (talk | contribs) | tweak | |
03:46, 1 June 2007 | 2,506 × 1,967 (367 KB) | Oleg Alexandrov (talk | contribs) | Tweak. | ||
03:10, 1 June 2007 | 626 × 492 (64 KB) | Oleg Alexandrov (talk | contribs) | {{Information |Description=Illustration of en:Tubular neighborhood |Source=Made with en:Matlab |Date= |Author= ~~~~ |Permission=Public domain |other_versions= }} {{PD-self}} | ||
03:09, 1 June 2007 | 626 × 492 (64 KB) | Oleg Alexandrov (talk | contribs) | {{Information |Description=Illustration of en:Tubular neighborhood |Source=Made with en:Matlab |Date= |Author= ~~~~ |Permission=Public domain |other_versions= }} {{PD-self}} | ||
03:08, 1 June 2007 | 626 × 492 (82 KB) | Oleg Alexandrov (talk | contribs) | {{Information |Description=Illustration of en:Tubular neighborhood |Source=Made with en:Matlab |Date= |Author= ~~~~ |Permission=Public domain |other_versions= }} {{PD-self}} | ||
03:01, 1 June 2007 | 626 × 492 (82 KB) | Oleg Alexandrov (talk | contribs) | {{Information |Description=Illustration of en:Tubular neighborhood |Source=Made with en:Matlab |Date= |Author= ~~~~ |Permission=Public domain |other_versions= }} {{PD-self}} |
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