% Schematic7.m %
clc; clf;clear all;n=2000;t=linspace(0,2*pi,n);ep6=0.1;ep0=1; 
r=1+ep6*cos(6*t);x=r.*cos(t);y=r.*sin(t);
xx = cos(t)+ep6*cos(6*t).*cos(t)+6*ep6*sin(6*t).*sin(t); 
yy = sin(t)+ep6*cos(6*t).*sin(t)-6*ep6*sin(6*t).*cos(t); hold on
st = 130;  et = 206; plot(xx(st:et),yy(st:et),'k-','linewidth',1)
st = 463;  et = 539; plot(xx(st:et),yy(st:et),'k-','linewidth',1)
st = 796;  et = 872; plot(xx(st:et),yy(st:et),'k-','linewidth',1)
st = 1129;  et = 1206; plot(xx(st:et),yy(st:et),'k-','linewidth',1)
st = 1462;  et = 1539; plot(xx(st:et),yy(st:et),'k-','linewidth',1)
st = 1795;  et = 1872; plot(xx(st:et),yy(st:et),'k-','linewidth',1)
plot(0,0,'ko','Linewidth',2,'markersize',6)
line([-1.15 1.15],[0 0],'color','k','Linewidth',1,'linestyle','-')
line([0 0],[-1.15 1.15],'color','k','Linewidth',1,'linestyle','-')
kk = 148; plot(xx(kk),yy(kk),'ko','Linewidth',1,'markersize',6,...
    'MarkerEdgeColor','k','MarkerFaceColor','k')
line([0 xx(kk)],[0 yy(kk)],'color','k','Linewidth',2,'linestyle',':')
ss=0.22;st1=1;ee1=160; 
plot(ss*cos(t(st1:ee1)),ss*sin(t(st1:ee1)),'k-')
ss=0.24;st1=1;ee1=160; 
plot(ss*cos(t(st1:ee1)),ss*sin(t(st1:ee1)),'k-')
m3 = (yy(kk+1)-yy(kk-1))/(xx(kk+1)-xx(kk-1)); 
tt = linspace(0.55,1.0,1000); yt = m3*(tt-xx(kk)) + yy(kk); 
plot(tt,yt,'k-','linewidth',2); m2=-1/m3;  tn=linspace(0,1.25,1000);
yn = m2*(tn); plot(tn,yn,'k--','linewidth',2)
tmp = 0.4; line([xx(kk) xx(kk) + tmp],[yy(kk) yy(kk)],'color',...
'k','Linewidth',1,'linestyle','-')
tn2 = linspace(xx(kk),1.45*xx(kk),100); yn2=m2*(tn2-xx(kk))+yy(kk);
plot(tn2,yn2,'k--','linewidth',2)
ss=0.34;st1=1;ee1=80;plot(ss*cos(t(st1:ee1)),ss*sin(t(st1:ee1)),'k-')
plot(0.8052,0.4083,'ko','Linewidth',1,'markersize',6,...
    'MarkerEdgeColor','k','MarkerFaceColor','k')
xxx = linspace(-0.1,1.3,100); xp = 0.8125; yp = 0.4046;
yyy = m3*(tt-tn(600)) + yn(600); yyyy=m2*(tn-tt(370))+yyy(370); 
xp2 = 0.7778; yp2 = 0.4712; line([tn(600) tt(370) xp2],...
    [yn(600) yyy(370) yp2],'color','k','linewidth',1)
ss=0.22;st1=1;ee1=160; 
plot(xx(kk) + ss*cos(t(st1:ee1)), yy(kk) + ss*sin(t(st1:ee1)),'k-')
ss=0.24; plot(xx(kk)+ss*cos(t(st1:ee1)),yy(kk)+ss...
*sin(t(st1:ee1)),'k-')
plot(1.154,0.5745,'kv','Linewidth',2,'markersize',6, ...
   'MarkerEdgeColor', 'k', 'MarkerFaceColor','k')
plot(1.243,0.3760,'kv','Linewidth',2,'markersize',6, ...
   'MarkerEdgeColor', 'k','MarkerFaceColor','k')
tsize = 20; 
text('Interpreter','latex','String','$$\phi$$',...
'Position',[1.195 0.288],'FontSize',tsize)            
text('Interpreter','latex', 'String','$$\theta$$',...
'Position',[0.394 0.045],'FontSize',tsize)            
text('Interpreter','latex','String','$$T=(x,y)$$',...
'Position',[0.809 0.094],'FontSize',tsize)
text('Interpreter','latex','String','$$p$$',...
'Position',[0.394 0.342],'FontSize',tsize)
text('Interpreter','latex','String','$$r$$',...
'Position',[0.468 0.161],'FontSize',tsize)
text('Interpreter','latex','String','$$M$$',...
'Position',[0.783 0.537],'FontSize',tsize)
tmr  = 0.89; tmx = 0.75+tmr*cos(t); tmy = -.48+tmr*sin(t); 
plot(tmx(480:590),tmy(480:590),'k-'); 
plot(tmx(650:820),tmy(650:820),'k-');
tmr  = 1.7; tmx = 0.8+tmr*cos(t); tmy = -1.5+tmr*sin(t); 
plot(tmx(570:655),tmy(570:655),'k-'); 
plot(tmx(485:548),tmy(485:548),'k-');
text('Interpreter','latex','String','$$O$$',...
'Position',[-0.109 0.076],'FontSize',tsize-1)
axis image; axis off; print -deps wulff2.eps
set(gcf,'PaperPositionMode','auto')