File:Rotation illustration2.svg

Original file(SVG file, nominally 1,005 × 897 pixels, file size: 12 KB)

Summary

Description Illustration of Rotation (mathematics)
Date
Source self-made, with MATLAB, then tweaked with Inkscape
Author Oleg Alexandrov
SVG development
InfoField
 
The source code of this SVG is invalid due to 5 errors.
 
This W3C-invalid trigonometry was created with an unknown SVG tool.

Licensing

Public domain 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);

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

9 June 2007

image/svg+xml

File history

Click on a date/time to view the file as it appeared at that time.

(newest | oldest) View (newer 10 | ) (10 | 20 | 50 | 100 | 250 | 500)
Date/TimeThumbnailDimensionsUserComment
current09:57, 8 December 2019Thumbnail for version as of 09:57, 8 December 20191,005 × 897 (12 KB)Andrew Pertsevfont «O»
09:52, 8 December 2019Thumbnail for version as of 09:52, 8 December 20191,005 × 897 (12 KB)Andrew Pertsevcolor
09:45, 8 December 2019Thumbnail for version as of 09:45, 8 December 20191,005 × 897 (12 KB)Andrew Pertsevclean, add param, file size
10:16, 6 December 2019Thumbnail for version as of 10:16, 6 December 20191,005 × 897 (19 KB)Andrew Pertsevcrop corr
10:14, 6 December 2019Thumbnail for version as of 10:14, 6 December 2019980 × 859 (19 KB)Andrew Pertsevcrop
10:08, 6 December 2019Thumbnail for version as of 10:08, 6 December 2019930 × 859 (19 KB)Andrew Pertsevdownload error correction
09:52, 6 December 2019Thumbnail for version as of 09:52, 6 December 2019930 × 847 (20 KB)Andrew Pertsevsvg optimization file size, arrow corrrction
03:36, 11 June 2007Thumbnail for version as of 03:36, 11 June 2007875 × 758 (47 KB)Oleg Alexandrovtweak
05:24, 10 June 2007Thumbnail for version as of 05:24, 10 June 2007875 × 758 (47 KB)Oleg AlexandrovTweak.
05:55, 9 June 2007Thumbnail for version as of 05:55, 9 June 2007875 × 874 (40 KB)Oleg Alexandrovtweak
(newest | oldest) View (newer 10 | ) (10 | 20 | 50 | 100 | 250 | 500)
The following pages on the English Wikipedia use this file (pages on other projects are not listed):

Global file usage

The following other wikis use this file:

Metadata