1. Explanation of ˇ°mandible_hole_patched.matˇ±

ˇ°mandible_hole_patched.matˇ± has two objects. Each object consists of several fields.

mand_iso_fixed: isosurface of hole-patched mandible image
	(fields)
	- mand_iso_fixed.vertices: (x,y,z) coordinates of vertices
				(row: vertex, col: (x,y,z))
	- mand_iso_fixed.faces: vertex indices of each triangle
				(row: vertex, col: indices of three vertices of each triangle)

smooth_info: related information (these are generated by 'smooth_info_const.m')
	(fields)
	- smooth_info.degree: degree of each vertex
				(row: vertex, col: degree (scalar))
	- smooth_info.nbr: neighbors (connectivity information) of each vertex
				(row: vertex, col: indices of neighbors)
	- smooth_info.face_around_vertex: face indices of triangles around each vertex
				(row: vertex, col: face indices of triangles)
	- smooth_info.weight: weight of HKS for each vertex
				(row: vertex, col: weights for neighbors)

[Example] construct 'smooth_info' with sigma = 0.1 for HKS

load('mandible_hole_patched.mat');
smooth_info = smooth_info_const(mand_iso_fixed, 0.1);

2. Explanation of function ˇ°area_regularizeˇ± (area regularization)

note: 'triangle_area_3d.m' should be in the path because it is loaded by the function 'area_regularize'.

[Example] 'mand_iso_ar' is area-regularized 'mand_iso_fixed' with alpha = 0.9.

load('mandible_hole_patched.mat');
% 1 iteration
mand_iso_ar = area_regularize(mand_iso_fixed, 0.9, smooth_info.nbr, smooth_info.face_around_vertex);
% if you want to iterate area regularization 100 times;
for i=1:100
	mand_iso_ar = area_regularize(mand_iso_ar, 0.9, smooth_info.nbr, smooth_info.face_around_vertex);
end