% Example 6: Combine a transformed copy of a star-shaped domain and a
% transformed copy of a circle into a single multi-component chunker, with
% consistent outward-pointing normals.

mip load --install magland/magland/chunkie;

tic;

% recreate the circle (chnkr1)
rad = 2; ctr = [1.0;-0.5];
circfun = @(t) ctr + rad*[cos(t(:).');sin(t(:).')];
chnkr1 = chunkerfunc(circfun);

% recreate the random-mode star (chnkr2)
rng(0)
modes = randn(11,1); modes(1) = 1.1*sum(abs(modes(2:end)));
ctr2 = [1.0;-0.5];
chnkr2 = chunkerfunc(@(t) chnk.curves.bymode(t,modes,ctr2));

% rotate, reflect, and reverse the star
chnkr5 = chnkr2;
theta = pi/4;
chnkr5 = chnkr5.rotate(theta);
chnkr5 = chnkr5.reflect(pi/2);
chnkr5 = chnkr5.reverse();

% affine-transform the circle and reverse its orientation
chnkr6 = chnkr1;
A = 0.5*[2 -1; 1 1];
r1 = [-1;0.5];
chnkr6 = r1 + A*chnkr6;
chnkr6 = chnkr6.reverse();

% recenter the circle inside the star and scale it down so it fits
mins5 = min(chnkr5); maxs5 = max(chnkr5);
mins6 = min(chnkr6); maxs6 = max(chnkr6);
ctr5 = 0.5*(mins5+maxs5);
ctr6 = 0.5*(mins6+maxs6);
ext5 = min(maxs5 - mins5);
ext6 = max(maxs6 - mins6);
scale = 0.3*ext5/ext6;
chnkr6 = chnkr6 + (-ctr6);
chnkr6 = scale*chnkr6;
chnkr6 = chnkr6 + ctr5;

% merge into one multi-component domain
chnkr7 = merge([chnkr5,chnkr6]);

toc;

figure(5); clf
plot(chnkr7,'b-x'); hold on; quiver(chnkr7,'r')
axis equal tight