clear all

% choice of angles
alpha=pi/2,beta=pi/3,gamma=pi-alpha-beta
l=5; % an arbitrary choice for eigenvalue
R=0.2; 
s=log([0.001:0.01:R]); % s in logarithmic coordinates. 

boundfun=inline('sqrt(2)*alpha/R+1./(2*sqrt(alpha))*l*R+l./(sqrt(2*alpha)).*l.*exp(s)')

%generating figure for bounds around the 3 vertices, single eigenvalue
%guess.

y1=boundfun(R,alpha,l,s);y2=boundfun(R,beta,l,s); y3=boundfun(R,gamma,l,s);

figure(1)
plot(s,y1,'r',s,y2,'b',s,y3,'g'),xlabel s, ylabel('bound'), 
legend(['\alpha=', num2str(alpha)], ['\beta=',num2str(beta)],['\gamma=',num2str(gamma)])




%generating figure for bounds around the 3 vertices, for a range of eigenvalue
%guesses.

figure(2)
ll=[0.3:0.5:20]; % a range of eigenvalues to explore
[S,L]=meshgrid(s,ll);

Y1=boundfun(R,alpha,L,S);Y2=boundfun(R,beta,L,S); Y3=boundfun(R,gamma,L,S);




% Produce the two surface plots


h(1)=surf(S,L,Y1,'FaceAlpha','flat',...
'AlphaDataMapping','scaled',...
'AlphaData',gradient(Y1),...
'FaceColor','red');
% Change the alphamap to be opaque at the middle and
% transparent towards the ends:
alphamap('vup')


hold on
h(2) = surf(S,L,Y2,'FaceAlpha','flat',...
'AlphaDataMapping','scaled',...
'AlphaData',gradient(Y2),...
'FaceColor','blue');
% Change the alphamap to be opaque at the middle and
% transparent towards the ends:
alphamap('vup')



h(3)=surf(S,L,Y3,'FaceAlpha','flat',...
'AlphaDataMapping','scaled',...
'AlphaData',gradient(Y2),...
'FaceColor','green');
% Change the alphamap to be opaque at the middle and
% transparent towards the ends:
alphamap('vup')

xlabel s, ylabel('\lambda')



hold off

title(['Bounds for a range of s and \lambda. Red sheet=bound around corner', num2str(alpha),' blue sheet around', num2str(beta)])


view(3)