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Cette image (de type math) devrait être recréée dans un format vectoriel, en tant que fichier SVG. Cela offrirait plusieurs avantages : voir Commons:Media for cleanup pour plus d'informations. Si une version SVG de cette image est déjà disponible, merci de bien vouloir l'envoyer. Après cela, remplacez ce modèle par {{vector version available|nouveau nom d'image.svg}}.
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Source code:
function discontinuity()
% set up the plotting window
thick_line=2.5; thin_line=2; arrow_size=14; arrow_type=2;
fs=30; circrad=0.06;
% picture 1
a=-1.5; b=3; h=0.02; x0=1;
X1=a:h:x0; X2=x0:h:b; X=[X1 X2];
Y1=X1.^2; Y2=Y1(length(Y1))+(-1)*(X2-X2(1)); Y=[Y1 Y2]; y01=Y1(length(Y1)); y02=Y2(1);
figure(1); clf; hold on; axis equal; axis off;
axes_points(a, b, thin_line, thick_line, arrow_size, arrow_type, x0, y01, y02, circrad, fs, X, Y, X1, Y1, X2, Y2)
saveas(gcf, 'discontinuity_removable.eps', 'psc2')
% picture 2
a=-1.5; b=3; h=0.02; x0=1;
X1=a:h:x0; X2=x0:h:b; X=[X1 X2];
Y1=X1.^2; Y2=2-(X2-x0).^2; Y=[Y1 Y2]; y01=Y1(length(Y1)); y02=Y2(1);
figure(2); clf; hold on; axis equal; axis off;
axes_points(a, b, thin_line, thick_line, arrow_size, arrow_type, x0, y01, y02, circrad, fs, X, Y, X1, Y1, X2, Y2)
saveas(gcf, 'discontinuity_jump.eps', 'psc2')
% picture 3
a=-1.5; b=3; h=0.001; x0=1;
X1=a:h:x0; X2=x0:h:b; X=[X1 X2];
Y1=sin(5./(X1-x0-eps)); Y2=0.1./(X2-x0+50*h); Y=[Y1 Y2]; y01=Y1(length(Y1)); y02=Y2(1);
figure(3); clf; hold on; axis equal; axis off;
axes_points2(a, b, thin_line, thick_line, arrow_size, arrow_type, x0, NaN, NaN, circrad, fs, X, Y, X1, Y1, X2, Y2)
saveas(gcf, 'discontinuity_essential.eps', 'psc2')
disp('Converting to png...')
! convert -density 400 -antialias discontinuity_removable.eps discontinuity_removable.png
! convert -density 400 -antialias discontinuity_jump.eps discontinuity_jump.png
! convert -density 400 -antialias discontinuity_essential.eps discontinuity_essential.png
function axes_points(a, b, thin_line, thick_line, arrow_size, arrow_type, x0, y01, y02, circrad, fs, X, Y, X1, Y1, X2, Y2)
arrow([a 0], [b, 0], thin_line, arrow_size, pi/8,arrow_type, [0, 0, 0]) % xaxis
small=0.2; arrow([0, min(Y)], [0, max(Y)], thin_line, arrow_size, pi/8,arrow_type, [0, 0, 0]); % y axis
plot(X1, Y1, 'linewidth', thick_line); plot(X2, Y2, 'linewidth', thick_line)
ball(x0, 0, circrad, [0 0 1 ]);
ball_empty(x0, y01, thick_line, circrad, [1 0 0 ]); ball_empty(x0, y02, thick_line, circrad, [1 0 0 ]);
H=text(x0, -0.006*fs, 'x_0'); set(H, 'fontsize', fs, 'HorizontalAlignment', 'c', 'VerticalAlignment', 'c')
function axes_points2(a, b, thin_line, thick_line, arrow_size, arrow_type, x0, y01, y02, circrad, fs, X, Y, X1, Y1, X2, Y2)
arrow([a 0], [b, 0], thin_line, arrow_size, pi/8,arrow_type, [0, 0, 0]) % xaxis
small=0.2; arrow([0, min(Y)], [0, max(Y)], thin_line, arrow_size, pi/8,arrow_type, [0, 0, 0]); % y axis
plot(X1, Y1, 'linewidth', thick_line); plot(X2, Y2, 'linewidth', thick_line)
ball(x0, 0, circrad, [0 0 1 ]);
ball_empty(x0, y01, thick_line, circrad, [1 0 0 ]); ball_empty(x0, y02, thick_line, circrad, [1 0 0 ]);
H=text(x0+0.2, -0.006*fs, 'x_0'); set(H, 'fontsize', fs, 'HorizontalAlignment', 'c', 'VerticalAlignment', 'c')
function ball(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 ball_empty(x, y, thick_line, r, color)
Theta=0:0.1:2*pi;
X=r*cos(Theta)+x;
Y=r*sin(Theta)+y;
H=fill(X, Y, [1 1 1]);
%set(H, 'EdgeColor', color);
plot(X, Y, 'color', color, 'linewidth', thick_line);
function arrow(start, stop, thickness, arrowsize, sharpness, arrow_type, color)
% draw a line with an arrow at the end
% start is the x,y point where the line starts
% stop is the x,y point where the line stops
% thickness is an optional parameter giving the thickness of the lines
% arrowsize is an optional argument that will give the size of the arrow
% It is assumed that the axis limits are already set
% 0 < sharpness < pi/4 determines how sharp to make the arrow
% arrow_type draws the arrow in different styles. Values are 0, 1, 2, 3.
% 8/4/93 Jeffery Faneuff
% Copyright (c) 1988-93 by the MathWorks, Inc.
% Modified by Oleg Alexandrov 2/16/03
if nargin <=6
color=[0, 0, 0];
end
if (nargin <=5)
arrow_type=0; % the default arrow, it looks like this: ->
end
if (nargin <=4)
sharpness=pi/4; % the arrow sharpness - default = pi/4
end
if nargin<=3
xl = get(gca,'xlim');
yl = get(gca,'ylim');
xd = xl(2)-xl(1);
yd = yl(2)-yl(1);
arrowsize = (xd + yd) / 2; % this sets the default arrow size
end
if (nargin<=2)
thickness=0.5; % default thickness
end
xdif = stop(1) - start(1);
ydif = stop(2) - start(2);
if (xdif == 0)
if (ydif >0)
theta=pi/2;
else
theta=-pi/2;
end
else
theta = atan(ydif/xdif); % the angle has to point according to the slope
end
if(xdif>=0)
arrowsize = -arrowsize;
end
if (arrow_type == 0) % draw the arrow like two sticks originating from its vertex
xx = [start(1), stop(1),(stop(1)+0.02*arrowsize*cos(theta+sharpness)),NaN,stop(1),...
(stop(1)+0.02*arrowsize*cos(theta-sharpness))];
yy = [start(2), stop(2), (stop(2)+0.02*arrowsize*sin(theta+sharpness)),NaN,stop(2),...
(stop(2)+0.02*arrowsize*sin(theta-sharpness))];
plot(xx,yy, 'LineWidth', thickness, 'color', color)
end
if (arrow_type == 1) % draw the arrow like an empty triangle
xx = [stop(1),(stop(1)+0.02*arrowsize*cos(theta+sharpness)), ...
stop(1)+0.02*arrowsize*cos(theta-sharpness)];
xx=[xx xx(1) xx(2)];
yy = [stop(2),(stop(2)+0.02*arrowsize*sin(theta+sharpness)), ...
stop(2)+0.02*arrowsize*sin(theta-sharpness)];
yy=[yy yy(1) yy(2)];
plot(xx,yy, 'LineWidth', thickness, 'color', color)
% plot the arrow stick
plot([start(1) stop(1)+0.02*arrowsize*cos(theta)*cos(sharpness)], [start(2), stop(2)+ ...
0.02*arrowsize*sin(theta)*cos(sharpness)], 'LineWidth', thickness, 'color', color)
end
if (arrow_type==2) % draw the arrow like a full triangle
xx = [stop(1),(stop(1)+0.02*arrowsize*cos(theta+sharpness)), ...
stop(1)+0.02*arrowsize*cos(theta-sharpness),stop(1)];
yy = [stop(2),(stop(2)+0.02*arrowsize*sin(theta+sharpness)), ...
stop(2)+0.02*arrowsize*sin(theta-sharpness),stop(2)];
H=fill(xx, yy, color);% fill with black
set(H, 'EdgeColor', 'none')
% plot the arrow stick
plot([start(1) stop(1)+0.01*arrowsize*cos(theta)], [start(2), stop(2)+ ...
0.01*arrowsize*sin(theta)], 'LineWidth', thickness, 'color', color)
end
if (arrow_type==3) % draw the arrow like a filled 'curvilinear' triangle
curvature=0.5; % change here to make the curved part more curved (or less curved)
radius=0.02*arrowsize*max(curvature, tan(sharpness));
x1=stop(1)+0.02*arrowsize*cos(theta+sharpness);
y1=stop(2)+0.02*arrowsize*sin(theta+sharpness);
x2=stop(1)+0.02*arrowsize*cos(theta)*cos(sharpness);
y2=stop(2)+0.02*arrowsize*sin(theta)*cos(sharpness);
d1=sqrt((x1-x2)^2+(y1-y2)^2);
d2=sqrt(radius^2-d1^2);
d3=sqrt((stop(1)-x2)^2+(stop(2)-y2)^2);
center(1)=stop(1)+(d2+d3)*cos(theta);
center(2)=stop(2)+(d2+d3)*sin(theta);
alpha=atan(d1/d2);
Alpha=-alpha:0.05:alpha;
xx=center(1)-radius*cos(Alpha+theta);
yy=center(2)-radius*sin(Alpha+theta);
xx=[xx stop(1) xx(1)];
yy=[yy stop(2) yy(1)];
H=fill(xx, yy, color);% fill with black
set(H, 'EdgeColor', 'none')
% plot the arrow stick
plot([start(1) center(1)-radius*cos(theta)], [start(2), center(2)- ...
radius*sin(theta)], 'LineWidth', thickness, 'color', color);
end
Transféré de en.wikipedia à Commons par Maksim.
La page de description originale était
removable.eps.png ici. Tous les noms d'utilisateur qui suivent se rapportent à en.wikipedia.
date/time |
username |
edit summary
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03:11, 14 September 2005 |
en:User:Oleg Alexandrov |
(<span class="autocomment"><a href="/wiki/Image:Discontinuity_removable.eps.png#Licensing" title="Image:Discontinuity removable.eps.png">→</a>Licensing</span>)
|
00:51, 12 September 2005 |
en:User:Oleg Alexandrov |
(Made by me with matlab. )
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Conditions d’utilisation
Public domainPublic domainfalsefalse
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Cette image n'est pas protégée par un copyright et demeure donc dans le domaine publique. Elle est constituée d'informations elles-mêmes dans le domaine publique et ne contient aucune création originale. Pour plus de détails, lire Commons:Threshold of originality § Charts
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