Image:Rotation illustration2.svg

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[edit] Source code

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 reduntant 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);

• Rotation (mathematics)
• User:Oleg Alexandrov/Pictures