File:Finite element method 1D illustration1.png
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Finite element method 1D illustration1.png
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Transferred from en.wikipedia to Commons by Maksim.
The original description page was here. All following user names refer to en.wikipedia.
Licensing
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. |
Source code
function main () % draw an illustration for finite element method
% prepare the scrreen and define some parameters
clf; hold on; axis equal; axis off;
fontsize=30; thick_line=3; thin_line=2; black=[0, 0, 0]; red=[1, 0, 0]; blue=[0, 0, 1];
arrowsize=0.1; arrow_type=1; arrow_angle=20; % (angle in degrees)
circrad=0.01; % radius of ball showing up in places
a=0; b=1; % interval endpoints
X=a:0.01:b; f=inline('2*x.*(1-x).^1.1'); Y=f(X); % the function
h=0.2; Xh=a:h:b; Yh=f(Xh); % the linear approximation
% x and y axes
arrow([a-0.2 0], [b+0.2, 0], thin_line, arrowsize, arrow_angle, arrow_type, black)
arrow([-0.15 -0.05], [-0.15, 1.5*max(Y)], thin_line, arrowsize, arrow_angle, arrow_type, black)
% plot the graphs
plot(X, Y, 'linewidth', thick_line); % mesh, and the function
plot(Xh, Yh, 'linewidth', thick_line, 'color', red)
%% place some dashed lines
for i=2:(length(Xh)-1)
plot([Xh(i) Xh(i)], [0, Yh(i)], 'linewidth', thin_line, 'linestyle', '--', 'color', 'black');
end
% some balls for beauty
ball(a, 0, circrad, black);
ball(b, 0, circrad, black);
for i=2:(length(Xh)-1)
ball(Xh(i), 0, circrad, black);
end
%% place text
tiny=0.07;
H=text(a+0.07, -tiny, 'x_0=0'); set(H, 'fontsize', fontsize, 'HorizontalAlignment', 'r', 'VerticalAlignment', 'top');
H=text(b-0.07, -tiny, 'x_5=1'); set(H, 'fontsize', fontsize, 'HorizontalAlignment', 'l', 'VerticalAlignment', 'top');
for i=2:(length(Xh)-1)
H=text(Xh(i), -tiny, sprintf('x_%d', i-1));
set(H, 'fontsize', fontsize, 'HorizontalAlignment', 'c', 'VerticalAlignment', 'top');
end
saveas(gcf, 'Finite_element_method_1D_illustration1.eps', 'psc2') % export to eps
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 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
date/time | username | edit summary |
---|---|---|
01:53, 29 December 2005 | en:User:Oleg Alexandrov | (+source code) |
01:30, 29 December 2005 | en:User:Oleg Alexandrov |
Original upload log
Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version.
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- (del) (cur) 01:51, 29 December 2005 . . en:User:Oleg_Alexandrov Oleg Alexandrov ( en:User_talk:Oleg_Alexandrov Talk) . . 1002x651 (43514 bytes)
- (del) (rev) 01:50, 29 December 2005 . . en:User:Oleg_Alexandrov Oleg Alexandrov ( en:User_talk:Oleg_Alexandrov Talk) . . 1002x636 (43741 bytes)
- (del) (rev) 01:49, 29 December 2005 . . en:User:Oleg_Alexandrov Oleg Alexandrov ( en:User_talk:Oleg_Alexandrov Talk) . . 1002x636 (43741 bytes)
- (del) (rev) 01:48, 29 December 2005 . . en:User:Oleg_Alexandrov Oleg Alexandrov ( en:User_talk:Oleg_Alexandrov Talk) . . 1002x636 (43572 bytes)
- (del) (rev) 01:30, 29 December 2005 . . en:User:Oleg_Alexandrov Oleg Alexandrov ( en:User_talk:Oleg_Alexandrov Talk) . . 1002x636 (43572 bytes)
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 01:31, 19 March 2006 | 1,002 × 651 (42 KB) | wikimediacommons>Maksim | La bildo estas kopiita de wikipedia:en. La originala priskribo estas: == Licensing == {{PD-self}} ==Source code== <pre> <nowiki> function main () % draw an illustration for finite element method % prepare the scrreen and define some parameters clf; |
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