File:Rotation illustration.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.
Summary edit
Made by myself with matlab.
Licensing edit
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. |
This diagram was created with MATLAB.
Matlab source code edit
function main()
% prepare the screen
figure(1); clf; hold on; axis equal; axis off;
linewidth=2;
x=[0, 0.7, 0.5 1, 0]+2; y=[0, 0, 0.5, 1 0.8];
do_plot(x, y, linewidth);
theta=pi/3; A=[cos(theta) -sin(theta); sin(theta) cos(theta)];
for i=1:length(x)
v= A*[x(i); y(i)]; x(i)=v(1); y(i)=v(2);
end
do_plot(x, y, linewidth);
red=[1 0 0]; ball_radius=0.025;
x=2.1; y=0.5; plot([0 x], [0, y], 'color', red, 'linewidth', linewidth);
ball(x, y, ball_radius, red);
v= A*[x; y]; x=v(1); y=v(2); plot([0 x], [0, y], 'color', red, 'linewidth', linewidth);
ball(x, y, ball_radius, red);
ball(0, 0, ball_radius, red);
x=1.1*1.9681; y=1.1*0.9548; r=sqrt(x^2+y^2); thetas=atan2(y, x);
thetae=pi/6.2+thetas;
Theta=thetas:0.01:thetae; X=r*cos(Theta); Y=r*sin(Theta); plot(X, Y, 'linewidth', linewidth)
n=length(Theta);
arrow([X(n-1), Y(n-1)], [2*X(n)-X(n-1), 2*Y(n)-Y(n-1)], linewidth, 10, pi/6, 2, [0, 0, 1])
saveas(gcf, 'rotation_illustration.eps', 'psc2')
function do_plot(x, y, linewidth)
n=length(x);
P=5; Q=n+2*P+1; % P will denote the amount of overlap
% Make the 'periodic' sequence xp=[x(1) x(2) x(3) ... x(n) x(1) x(2) x(3) ... ]
% of length Q. Same for yp.
for i=1:Q
j=rem(i, n)+1; % rem() is the remainder of division of i by n
xp(i)=x(j);
yp(i)=y(j);
end
% do the spline interpolation
t=1:length(xp);
N=100; % how fine to make the interpolation
tt=1:(1/N):length(xp);
xx=spline(t, xp, tt);
yy=spline(t, yp, tt);
% discard the redundant pieces
start=N*(P-1)+1;
stop=N*(n+P-1)+1;
xx=xx(start:stop);
yy=yy(start:stop);
lightblue=[176,196,222]/256;
H=fill(xx, yy, lightblue);
set(H, 'linewidth', 0.001, 'edgecolor', lightblue);
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)];
% 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)
H=fill(xx, yy, color);% fill with black
set(H, 'EdgeColor', 'none')
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)];
% plot the arrow stick
plot([start(1) center(1)-radius*cos(theta)], [start(2), center(2)- ...
radius*sin(theta)], 'LineWidth', thickness, 'color', color);
H=fill(xx, yy, color);% fill with black
set(H, 'EdgeColor', 'none')
end
date/time | username | edit summary |
---|---|---|
00:36, 22 November 2005 | en:User:Oleg Alexandrov | (+source code) |
14:06, 3 November 2005 | en:User:Oleg Alexandrov | (Made by myself with matlab.) |
Original upload log edit
Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version.
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- (del) (cur) 23:24, 3 November 2005 . . en:User:Oleg_Alexandrov Oleg Alexandrov ( en:User_talk:Oleg_Alexandrov Talk) . . 936x989 (19116 bytes) (Made by myself with matlab. )
- (del) (rev) 14:06, 3 November 2005 . . en:User:Oleg_Alexandrov Oleg Alexandrov ( en:User_talk:Oleg_Alexandrov Talk) . . 562x593 (20124 bytes) (Made by myself with matlab. )
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 03:31, 6 June 2007 | 936 × 989 (19 KB) | Oleg Alexandrov (talk | contribs) | {{Information |Description=Made by myself with matlab. |Source=Originally from [http://en.wikipedia.org en.wikipedia]; description page is/was [http://en.wikipedia.org/w/index.php?title=Image%3ARotation_illustration.png here]. |Date=2005-11-03 (first ver | |
10:06, 29 January 2006 | 936 × 989 (19 KB) | Maksim (talk | contribs) | La bildo estas kopiita de wikipedia:en. La originala priskribo estas: == Summary == Made by myself with matlab. == Licensing == {{PD-self}} ==Source code (very messy)== <pre> <nowiki> function main() % prepare the screen figure(1); clf; hold on; axis |
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