% mesh_sphere.m — The built-in "cubed sphere".
%
% surfacemesh.sphere inflates a cube mesh onto the sphere. The first
% argument is the number of nodes per dimension (order p plus one); the
% second is the number of refinement levels.

mip load --install flatironinstitute/flatironinstitute/surfacefun

p = 16;
nref = 2;
dom = surfacemesh.sphere(p + 1, nref);

figure(1);
plot(dom), camlight
title('Cubed sphere');

% A few queries about the mesh:
fprintf('patches:           %d\n', length(dom));
fprintf('order per patch:   %d\n', order(dom));
fprintf('degrees of freedom:%d\n', numel(dom));
fprintf('surface area err:  %.2e   (vs 4*pi)\n', surfacearea(dom) - 4*pi);
fprintf('enclosed vol err:  %.2e   (vs 4/3*pi)\n', volume(dom) - 4/3*pi);
fprintf('bounding box:      [%g %g %g %g %g %g]\n', boundingbox(dom));