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draw_ball_pol.m
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function [t_vect,psi_cell] = draw_ball_pol(tvec,psicell,r,opts)
global balls beta NUMPOINTSINTERACTIVE cont_simu
%colors
green = [51/255 150/255 0 ];
red = [204/255 0 51/255];
DRAW_CENTER_MarkerSize = 20;
DRAW_LineSize = 1.5;
DRAW_DashedLineSize = 2;
%Default Parameters
DRAWOPT = false;
PLOTTILT = [4*sqrt(2) 8];
PLOTTILT_NAME = {'\Gamma' ' '};%{'\Gamma' '\Gamma^{\prime}'};
NUMPOINTS = 100000;
DRAWTITLE = true;
DRAW_CIRCLE_TILT = true;
INTERACTIVE = false;
NUMPOINTSINTERACTIVE = 10000;
DRAW_REGIONS = false;
DRAW_REGIONS_TILT = sqrt(2)*4;
DRAW_CENTER_DISKS_OPTS = '.';
DRAW_CENTER_DISKS_COLOR = green;
DISK_RANDOM_COLOR = false;
% Input Parameters
switch nargin
case 4
if (~isstruct(opts))
error('Optional parameter is not of type struct!');
end
names = fieldnames(opts);
for i=1:length(names)
name = names{i};
switch name
case 'numpoints'
NUMPOINTS = opts.numpoints;
case 'numpointsinteractive'
NUMPOINTSINTERACTIVE = opts.numpointsinteractive;
case 'tilt'
DRAWOPT = true;
PLOTTILT = opts.tilt;
case 'drawtitle'
DRAWTITLE = opts.drawtitle;
case 'draw_circle_eachtilt'
DRAW_CIRCLE_TILT = opts.draw_circle_eachtilt;
case 'interactive'
INTERACTIVE = opts.interactive;
case 'draw_regions'
DRAW_REGIONS = opts.draw_regions;
case 'draw_regions_tilt'
DRAW_REGIONS_TILT = opts.draw_regions_tilt;
case 'draw_center_disks_opts'
DRAW_CENTER_DISKS_OPTS = opts.draw_center_disks_opts;
case 'disk_random_color'
DISK_RANDOM_COLOR = opts.disk_random_color;
case 'draw_center_markersize'
DRAW_CENTER_MarkerSize = opts.draw_center_markersize;
case 'draw_linesize'
DRAW_LineSize = opts.draw_linesize;
case 'draw_dashedlinesize'
DRAW_DashedLineSize = opts.draw_dashedlinesize;
end
end
otherwise
if (nargin~=3)
error('Wrong number of input parameters!');
end
end
gamma = exp(r);
beta = ( (gamma^2)+1 )/(2*gamma);
balls = {};
cont_simu = 0;
phivect = linspace(0,2*pi,NUMPOINTS);
hold on;
for i=1:length(tvec)
t=tvec(i);
psivec=psicell{i};
cont_simu = cont_simu + length(psivec);
for j=1:length(psivec)
psi = psivec(j);
[pointinf,pointsup] = edges_one_ball(phivect,t,psi,beta);
if (~INTERACTIVE)
if (DISK_RANDOM_COLOR)
colorvec = .9*rand(1,3);
else
colorvec =red;
end
ballind = length(balls)+1;
tempball.ballcenter = [t psi];
plot(log(t).*cos(psi),log(t).*sin(psi),DRAW_CENTER_DISKS_OPTS,'MarkerSize',DRAW_CENTER_MarkerSize,'Color',DRAW_CENTER_DISKS_COLOR);
tempball.curvsup = plot(log(pointsup).*cos(phivect),log(pointsup).*sin(phivect),'-','LineWidth',DRAW_LineSize,'Color',colorvec);
tempball.curvinf = plot(log(pointinf).*cos(phivect),log(pointinf).*sin(phivect),'-','LineWidth',DRAW_LineSize,'Color',colorvec);
tempball.colorvec = colorvec;
balls{ballind} = tempball;
else
if (DISK_RANDOM_COLOR)
colorvec = .9*rand(1,3);
else
colorvec = red;
end
h = impoint(gca,log(t).*cos(psi),log(t).*sin(psi));
setColor(h,'r');
ballind = length(balls)+1;
tempball.ballcenter = [t psi];
addNewPositionCallback(h,@(h) MyPositionCallback(h,ballind));
tempball.curvsup = plot(log(pointsup).*cos(phivect),log(pointsup).*sin(phivect),'-','Color',colorvec);
tempball.curvinf = plot(log(pointinf).*cos(phivect),log(pointinf).*sin(phivect),'-','Color',colorvec);
tempball.colorvec = colorvec;
balls{ballind} = tempball;
end
end
if (DRAW_CIRCLE_TILT)
plot(log(t)*cos(phivect),log(t)*sin(phivect),':','Color',.3*rand(1,3));
end
end
if (DRAWOPT)
for i=1:length(PLOTTILT)
tilt2plot = PLOTTILT(i);
plot(log(tilt2plot)*cos(phivect),log(tilt2plot)*sin(phivect),'--k','LineWidth',DRAW_DashedLineSize);
%text((log(tilt2plot)+0.01)*cos(pi/4),(log(tilt2plot)+0.01)*sin(pi/4),['\leftarrow Tilt = ' num2str(tilt2plot) ]);
textpointer = text((log(tilt2plot)+0.05)*cos(pi/4),(log(tilt2plot)+0.05)*sin(pi/4),[PLOTTILT_NAME{i}]);
textpointer.FontWeight='bold';
textpointer.FontSize = DRAW_CENTER_MarkerSize;
end
end
if (DRAWTITLE)
if ((length(tvec)==1) && (length(psicell)==1))
title(['d( T_{' num2str(t) '}R_{' num2str(psi) '} , T_sR_{\phi-' num2str(psi) '} ) \leq ' num2str(r)]);
else
textpointer = title([num2str(cont_simu) ' affine simulations']);
%textpointer.FontSize = 14;
end
end
xlabel('log(\tau) cos(\phi)','FontSize',DRAW_CENTER_MarkerSize);
ylabel('log(\tau) sin(\phi)','FontSize',DRAW_CENTER_MarkerSize);
axis equal
if (INTERACTIVE)
set(gcf,'WindowbuttonDownFcn',@doubleclickcallback)
waitfor(gcf);
else
if (DRAW_REGIONS)
discrete_rho = 500;
discrete_phi = 1000;
[s,phi] = meshgrid(linspace(1,DRAW_REGIONS_TILT,discrete_rho),linspace(0,pi,discrete_phi));
M = zeros(size(s));
for i=1:length(balls)
t = balls{i}.ballcenter(1);
psi = balls{i}.ballcenter(2);
G = ( (t ./s + s ./t).*(cos(phi-psi).^2) + ((1 ./(s.*t)) +s.*t).*(sin(phi-psi).^2) )/2;
M((G<beta)) = M((G<beta)) + 1;
end
Z = NaN(size(s));
Z(M==0)=-.1;
h = surf(log(s).*cos(phi),log(s).*sin(phi),Z,'EdgeColor','none','LineStyle','none');
set(h,'FaceColor',[.5 .5 .5]);
h = surf(log(s).*cos(phi+pi),log(s).*sin(phi+pi),Z,'EdgeColor','none','LineStyle','none');
set(h,'FaceColor',[.5 .5 .5]);
Z = NaN(size(s));
Z(M>1)=-.1;
h = surf(log(s).*cos(phi),log(s).*sin(phi),Z,'EdgeColor','none','LineStyle','none');
set(h,'FaceColor',[.871 .922 .98]);
h = surf(log(s).*cos(phi+pi),log(s).*sin(phi+pi),Z,'EdgeColor','none','LineStyle','none');
set(h,'FaceColor',[.871 .922 .98]);
end
end
t_vect = [];
psi_cell = {};
for i=1:length(balls)
t_vect = [t_vect balls{i}.ballcenter(1)];
psi_cell = [psi_cell [balls{i}.ballcenter(2)]];
end
end
function doubleclickcallback(obj,evt)
global balls cont_simu
switch get(obj,'SelectionType')
case 'normal'
case 'open'
CurrentPoint = get(gca,'CurrentPoint');
point = CurrentPoint(1,1:2);
colorvec = .9*rand(1,3);
ballind = length(balls)+1;
tempball.ballcenter = [exp(sqrt(point(1)^2+point(2)^2)),atan(point(2)/point(1))];
tempball.curvsup = plot(point(1),point(2),'.r');
tempball.curvinf = plot(point(1),point(2),'.r');
tempball.colorvec = colorvec;
h = impoint(gca,point(1),point(2));
setColor(h,'r');
balls{ballind} = tempball;
cont_simu = cont_simu + 1;
title([num2str(cont_simu) ' Simulations']);
addNewPositionCallback(h,@(h) MyPositionCallback(h,ballind));
end
end
function MyPositionCallback(h,ballind)
%hfun = get(gcf,'WindowButtonUpFcn');
%set(gcf,'WindowButtonUpFcn',@(src,event) mybuttonup(src,event,hfun,h));
global balls beta NUMPOINTSINTERACTIVE
phivect = linspace(0,2*pi,NUMPOINTSINTERACTIVE);
[pointinf,pointsup] = edges_one_ball(phivect,exp(sqrt(h(1)^2+h(2)^2)),atan(h(2)/h(1)),beta);
tempball = balls{ballind};
tempball.ballcenter = [exp(sqrt(h(1)^2+h(2)^2)),atan(h(2)/h(1))];
delete(tempball.curvsup);
delete(tempball.curvinf);
colorvec = tempball.colorvec;
tempball.curvsup = plot(log(pointsup).*cos(phivect),log(pointsup).*sin(phivect),'-','Color',colorvec);
tempball.curvinf = plot(log(pointinf).*cos(phivect),log(pointinf).*sin(phivect),'-','Color',colorvec);
tempball.colorvec = colorvec;
balls{ballind} = tempball;
%title(sprintf('indexed at %i -> (%1.1f,%1.1f)',ind,h(1),h(2)));
end
% les A tels que d( T_2, A) <= log(sqrt(2))
% draw_ball(2,0,log(sqrt(2)))
function [pointinf,pointsup] = edges_one_ball(phivect,t,psi,beta)
pointsup = [];
pointinf = [];
for phi = phivect
Gphi = cos(psi-phi)^2;
dis = beta^2 - ( Gphi/t + t*(1-Gphi) )*( (1-Gphi)/t + t*Gphi );
switch (logical(true))
case dis>0
tupper = ( beta + sqrt(dis) )/( Gphi/t + (1-Gphi)*t );
tlower = ( beta - sqrt(dis) )/( Gphi/t + (1-Gphi)*t );
if (tupper<1)
pointsup = [pointsup NaN];
pointinf = [pointinf NaN];
else
pointsup = [pointsup tupper];
if (tlower<1)
pointinf = [pointinf 1];
else
pointinf = [pointinf tlower];
end
end
case dis==0
tupper = beta/( Gphi/t + (1-Gphi)*t );
if (tupper<1)
pointsup = [pointsup NaN];
pointinf = [pointinf NaN];
else
pointsup = [pointsup tupper];
pointinf = [pointinf tupper];
end
case dis<0
pointsup = [pointsup NaN];
pointinf = [pointinf NaN];
end
end
end