function [sV] = reduceByLayers(xyz, percent, alpha)
% simplify a given structure by capturing and simplifying its surface mesh layer by layer.
% xyz: input point set; percent: reduce rate; alpha: thresold of alphaShape.
% Author: Guang Song
sV = []; % sV: simplified point set
while size(xyz, 1) > 100 % 100: lower bound
  if nargin == 2 
	shp = alphaShape(xyz);
  else 
	shp = alphaShape(xyz, alpha); 
  end
  [facets] = boundaryFacets(shp); % get surface mesh
  % simplify surface mesh using reducepatch
  [F, V] = reducepatch(facets, xyz, percent);
  % collect points from the reduced surface mesh
  sV = [sV; V]; 
  internalNodes = setdiff(1:size(xyz,1), facets(:));
  xyz = xyz(internalNodes,:); % remove surface layer
end