% vec_gradient.m — The surface gradient as a vector field.
%
% grad(f) of a surfacefun is a surfacefunv. The gradient is tangent to
% the surface, as the quiver plot shows.

mip load --install flatironinstitute/flatironinstitute/surfacefun

rng(0)
p = 16;
nref = 2;
dom = surfacemesh.blob(p + 1, nref);

f = surfacefun(@(x, y, z) cos(6*x) .* y + exp(z), dom);

figure(1);
quiver(grad(f), 0.05, 6)
title('Surface gradient of f (tangent to the surface)');

% Identity: the divergence of the gradient is the Laplacian.
fprintf('|| div(grad f) - lap(f) || = %.3e\n', norm(div(grad(f)) - lap(f)));