File:Tangent bundle.svg

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Full resolution(SVG file, nominally 400 × 963 pixels, file size: 23 KB)
Description Illustration of en:Tangent bundle.
Date 04:06, 12 June 2007 (UTC)
Source self-made, with en:Matlab then tweaked with en:Inkscape
Author Oleg Alexandrov
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This chart was created with MATLAB.
Public domain 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.

[edit] Source code (MATLAB)

 
 
% illustration of tangent bundle
function main()
 
   a=0; b=2*pi; N = 100;
   X=linspace(a, b, N);
   Y=sin(X);    % the function to plot
   XT = 0*X+1;
   YT = cos(X); % derivative
 
   Theta = linspace(a, b, N);
   X =   cos(Theta); Y  = sin(Theta);
   XT = -sin(Theta); YT = cos(Theta);
   ll = 2.5; % length of lines perpendicular to the curve
 
   thin_line = 2;
   thick_line = 4;
 
%  will draw lines tangent to the graph of Y=f(X) at
%  points separted by length of 'spacing'
   spacing = 0.04;
   M = floor(spacing*N); 
 
% colors
   red=[0.867 0.06 0.14];
   blue = [0, 129, 205]/256;
   green = [0, 200,  70]/256;
   gray=0.8*[1, 1, 1];
 
   figure(1); clf; hold on; axis equal; axis off;
   figure(2); clf; hold on; axis equal; axis off; view(18, 36);
 
% plot the curve
   figure(1); s=0.95; plot (s*X, s*Y,      'linewidth', thick_line, 'color', blue);
   figure(2); plot3(X, Y, 0*X, 'linewidth', thick_line, 'color', blue);
 
% plot the lines
   for k=1:N
 
      p = (k-1)*M+2;
      if p >= N
         break;
      end
 
      figure(1);
      x0 = X(p); y0=Y(p); mx = XT(p); my = YT(p);
      plot([x0-mx*ll, x0+mx*ll], [y0-my*ll, y0+my*ll], 'color', red, 'linewidth', thin_line)
 
 
      figure(2);
      plot3([X(p), X(p)], [Y(p), Y(p)], [-ll, ll], 'color', red, 'linewidth', thin_line)
 
   end
 
 
   % save to disk as eps and svg
   figure(1); saveas(gcf, 'Tangent_bundle1.eps', 'psc2'); plot2svg('Tangent_bundle1.svg')
   figure(2); saveas(gcf, 'Tangent_bundle2.eps', 'psc2'); plot2svg('Tangent_bundle2.svg')

File history

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Date/TimeThumbnailDimensionsUserComment
current04:08, 12 June 2007Thumbnail for version as of 04:08, 12 June 2007400 × 963 (23 KB)Oleg AlexandrovTweak
04:06, 12 June 2007Thumbnail for version as of 04:06, 12 June 2007512 × 1,259 (23 KB)Oleg Alexandrov{{Information |Description=Illustration of en:Tangent bundle. |Source=self-made, with en:Matlab then tweaked with en:Inkscape |Date=~~~~~ |Author= Oleg Alexandrov }} {{PD-self}} Category:Differential geometry
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