Transféré de en.wikipedia à Commons par Maksim.

Moi, propriétaire des droits d’auteur sur cette œuvre, la place dans le domaine public. Ceci s'applique dans le monde entier. Dans certains pays, ceci peut ne pas être possible ; dans ce cas : J’accorde à toute personne le droit d’utiliser cette œuvre dans n’importe quel but, sans aucune condition, sauf celles requises par la loi.

function main() % Subderivative illustration

%  set up the plotting window, and some graphing paramenters
   figure(1); clf; hold on; axis equal; axis off;
   thick_line=2.5; thin_line=2; arrow_size=0.3; arrow_type=1; arrow_angle=20; %(angle in degrees)
   font_size=30; ball_rad=0.04;
   black=[0, 0, 0]; red=[1, 0, 0];

%  define the function; plot the x and y axes and the function
   a=-1.5; b=3; h=0.02; 
   X=[a  0 1 2 3]; Y=[0.3  0.2 0.5 1.5 3];
   arrow([a 0],       [b, 0],      thin_line, arrow_size, arrow_angle, arrow_type, black)  
   arrow([0, min(Y)-1], [0, max(Y)], thin_line, arrow_size, arrow_angle, arrow_type, black); 
   plot(X, Y, 'linewidth', thick_line); 

   % the "tangent" lines
   x0=X(3); y0=Y(3);
   s=0.8; plot(X, s*(X-x0)+y0, 'linewidth', thick_line, 'color', [1, 0, 0])
   s=0.5; plot(X, s*(X-x0)+y0, 'linewidth', thick_line, 'color', [1, 0, 0])

   % auxiliary line
   plot([x0 x0], [0, y0], 'linewidth', thin_line, 'color', [0, 0, 0], 'linestyle', '--')
   
%  graph some suggestive balls
   ball_full (x0, 0, ball_rad, [0 0 0 ]); 
   ball_full (x0, y0, ball_rad, [1 0 0 ]); 

%   text, sir
   H=text(x0, -0.006*font_size,  'x_0');
   set(H, 'fontsize', font_size, 'HorizontalAlignment', 'c', 'VerticalAlignment', 'c')

   axis(1.1*[a b min(Y)-1 max(Y)])
%  save to postscript
   saveas(gcf, 'Subderivative_illustration.eps', 'psc2')
   
function ball_full(x, y, r, color)
   Theta=0:0.1:2*pi;
   X=r*cos(Theta)+x;
   Y=r*sin(Theta)+y;
   H=fill(X, Y, color);
   set(H, 'EdgeColor', 'none');


  function arrow(start, stop, thickness, arrow_size, sharpness, arrow_type, color)

% Function arguments:
% start, stop:  start and end coordinates of arrow, vectors of size 2
% thickness:    thickness of arrow stick
% arrow_size:   the size of the two sides of the angle in this picture ->
% sharpness:    angle between the arrow stick and arrow side, in degrees
% arrow_type:   1 for filled arrow, otherwise the arrow will be just two segments
% color:        arrow color, a vector of length three with values in [0, 1]
   
% convert to complex numbers
   i=sqrt(-1);
   start=start(1)+i*start(2); stop=stop(1)+i*stop(2);
   rotate_angle=exp(i*pi*sharpness/180);

% points making up the arrow tip (besides the "stop" point)
   point1 = stop - (arrow_size*rotate_angle)*(stop-start)/abs(stop-start);
   point2 = stop - (arrow_size/rotate_angle)*(stop-start)/abs(stop-start);

   if arrow_type==1 % filled arrow

      % plot the stick, but not till the end, looks bad
      t=0.5*arrow_size*cos(pi*sharpness/180)/abs(stop-start); stop1=t*start+(1-t)*stop;
      plot(real([start, stop1]), imag([start, stop1]), 'LineWidth', thickness, 'Color', color);

      % fill the arrow
      H=fill(real([stop, point1, point2]), imag([stop, point1, point2]), color);
      set(H, 'EdgeColor', 'none')
      
   else % two-segment arrow
      plot(real([start, stop]), imag([start, stop]),   'LineWidth', thickness, 'Color', color); 
      plot(real([stop, point1]), imag([stop, point1]), 'LineWidth', thickness, 'Color', color);
      plot(real([stop, point2]), imag([stop, point2]), 'LineWidth', thickness, 'Color', color);
   end

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• (del) (cur) 20:04, 18 December 2005 . . en:User:Oleg_Alexandrov Oleg Alexandrov ( en:User_talk:Oleg_Alexandrov Talk) . . 540x463 (21025 bytes)

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