File:Rotation_illustration2.svg
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Summary
DescriptionRotation illustration2.svg | Illustration of Rotation (mathematics) |
Date | |
Source | self-made, with MATLAB, then tweaked with Inkscape |
Author | Oleg Alexandrov |
SVG development InfoField |
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 (MATLAB)
function main()
% prepare the screen
figure(1); clf; hold on; axis equal; axis off;
linewidth=2; fs= 30;
N = 11;
a = -2; b = N+a-1;
blue = [0, 0, 1];
red = [1, 0, 0];
gray=[0.7, 0.7, 1.0];
white = 0.99*[1, 1, 1];
lightblue=[176, 196,222]/256;
green = [0, 200, 70]/256;
color1 = gray;
color2 = green;
XX = linspace(a, b, N); YY = XX;
[X, Y] = meshgrid(XX, YY);
factor = 4; shift = 3.6;
x=factor*[0, 0.7, 0.5 1, 0]+shift; y=factor*[0, 0, 0.5, 1 0.8];
do_plot(x, y, X, Y, linewidth, color1);
theta=1.4*pi/4; A=[cos(theta) -sin(theta); sin(theta) cos(theta)];
for i=1:N
for j=1:N
v= A*[X(i, j); Y(i, j)]; X(i, j)=v(1); Y(i, j)=v(2);
end
end
for i=1:length(x)
v= A*[x(i); y(i)]; x(i)=v(1); y(i)=v(2);
end
do_plot(x, y, X, Y, linewidth, color2);
% plot the point around which the rotation takes place
ball_radius = 0.15;
ball(0, 0, ball_radius, red);
text(0, -0.5, '{\it O}', 'color', red, 'fontsize', fs)
% plot the arrow suggesting the rotation
factor = 4;
x=factor*1.7; y=factor*2.1; r=sqrt(x^2+y^2); thetas=atan2(y, x);
thetae=0.7*theta+thetas;
Theta=thetas:0.01:thetae; X=r*cos(Theta); Y=r*sin(Theta);
plot(X, Y, 'linewidth', linewidth, 'color', red)
n=length(Theta);
arrow([X(n-2), Y(n-2)], [2*X(n)-X(n-1), 2*Y(n)-Y(n-1)], linewidth, 1, 30, linewidth, red)
% plot two invisible points, to bypass a saving bug
plot(a, 1.5*b, 'color', white);
plot(a, -0.5*b, 'color', white);
% save to eps and to svg
%saveas(gcf, 'rotation_illustration2.eps', 'psc2')
plot2svg('rotation_illustration2.svg')
function do_plot(x, y, X, Y, linewidth, color)
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);
H=fill(xx, yy, color);
set(H, 'linewidth', 1, 'edgecolor', color);
[M, N]= size(X);
for i=1:N
plot([X(1, i), X(N, i)], [Y(1, i), Y(N, i)], 'linewidth', linewidth, 'color', color)
plot([X(i, 1), X(i, N)], [Y(i, 1), Y(i, N)], 'linewidth', linewidth, 'color', color)
end
% plot some balls, avoid artifacts at the corners
small_rad=0.045;
ball(X(1, 1), Y(1, 1), small_rad, color)
ball(X(1, N), Y(1, N), small_rad, color)
ball(X(N, 1), Y(N, 1), small_rad, color)
ball(X(N, N), Y(N, N), small_rad, color)
function arrow(start, stop, th, arrow_size, sharpness, arrow_type, color)
% Function arguments:
% start, stop: start and end coordinates of arrow, vectors of size 2
% th: 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', th, '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', th, 'Color', color);
plot(real([point1, stop, point2]), imag([point1, stop, point2]), 'LineWidth', th, 'Color', color);
end
function ball(x, y, radius, color) % draw a ball of given uniform color
Theta=0:0.1:2*pi;
X=radius*cos(Theta)+x;
Y=radius*sin(Theta)+y;
H=fill(X, Y, color);
set(H, 'EdgeColor', color);
Items portrayed in this file
depicts
some value
9 June 2007
image/svg+xml
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 09:57, 8 December 2019 | 1,005 × 897 (12 KB) | Andrew Pertsev | font «O» | |
09:52, 8 December 2019 | 1,005 × 897 (12 KB) | Andrew Pertsev | color | ||
09:45, 8 December 2019 | 1,005 × 897 (12 KB) | Andrew Pertsev | clean, add param, file size | ||
10:16, 6 December 2019 | 1,005 × 897 (19 KB) | Andrew Pertsev | crop corr | ||
10:14, 6 December 2019 | 980 × 859 (19 KB) | Andrew Pertsev | crop | ||
10:08, 6 December 2019 | 930 × 859 (19 KB) | Andrew Pertsev | download error correction | ||
09:52, 6 December 2019 | 930 × 847 (20 KB) | Andrew Pertsev | svg optimization file size, arrow corrrction | ||
03:36, 11 June 2007 | 875 × 758 (47 KB) | Oleg Alexandrov | tweak | ||
05:24, 10 June 2007 | 875 × 758 (47 KB) | Oleg Alexandrov | Tweak. | ||
05:55, 9 June 2007 | 875 × 874 (40 KB) | Oleg Alexandrov | tweak |
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Width | 804.2pt |
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Height | 717.3pt |
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