How do I smoothen a closed, triangulated surface plot?

I have a set of points in R(3) with corresponding (T, x, y, z) values, where T is the measured value at each point (x, y, z). When I create a surface plot of the object, my result looks somewhat choppy (see ClosedSurface.jpg), whereas I would prefer a more rounded and organic shape.
figure(1);
[k, ~] = boundary(Points(:,2),Points(:,3),Points(:,4), 0.7);
trisurfk,(Points(:,2),Points(:,3),Points(:,4),Points(:,1), 'FaceAlpha', 0.5);
Changing the shrink factor in boundary() does not help, and I've been having trouble implementing solutions with scatteredInterpolant, interp3, and mesh. I just need a good way to be able to interporlate additional points so the triangulation of the object is finer. Any help would be appreciated.

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