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); 
