function [ point_num2, edge_num2, face_num2, face_order_max2 ] = ...
dual_size_3d ( point_num, edge_num, face_num, face_order_max, ...
point_coord, face_order, face_point )
%*****************************************************************************80
%
%% DUAL_SIZE_3D determines sizes for a dual of a shape in 3D.
%
% Discussion:
%
% We don't actually need FACE_POINT as input here. But since the
% three arrays occur together everywhere else, it seems unnecessarily
% user-confusing to vary the usage here!
%
% Licensing:
%
% This code is distributed under the GNU LGPL license.
%
% Modified:
%
% 22 July 2007
%
% Author:
%
% John Burkardt
%
% Input:
%
% integer POINT_NUM, the number of points.
%
% integer EDGE_NUM, the number of edges.
%
% integer FACE_NUM, the number of faces.
%
% integer FACE_ORDER_MAX, the maximum number of vertices per face.
%
% real POINT_COORD(3,POINT_NUM); POINT_COORD(*,J) is
% the X, Y and Z coordinates of point J.
%
% integer FACE_ORDER(FACE_NUM), the number of vertices per face.
%
% integer FACE_POINT(FACE_ORDER_MAX,FACE_NUM); FACE_POINT(I,J)
% is the index of the I-th point in the J-th face. The
% points are listed in the counter-clockwise direction defined
% by the outward normal at the face.
%
% Output:
%
% integer POINT_NUM2, the number of points in the dual.
%
% integer EDGE_NUM2, the number of edges in the dual.
%
% integer FACE_NUM2, the number of faces in the dual.
%
% integer FACE_ORDER_MAX2, the maximum number of vertices per face
% in the dual.
%
%
% These values are easy to compute:
%
point_num2 = face_num;
edge_num2 = edge_num;
face_num2 = point_num;
%
% To determine FACE_ORDER_MAX2 is not so easy.
% You have to construct the FACE_ORDER array for the dual shape.
% The order of a dual face is the number of edges that the vertex occurs in.
% But then all we have to do is count how many times each item shows up
% in the FACE_POINT array.
%
face_order_max2 = 0;
face_order2(1:face_num2) = 0;
for face = 1 : face_num
for i = 1 : face_order(face)
face2 = face_point(i,face);
face_order2(face2) = face_order2(face2) + 1;
end
end
face_order_max2 = max ( face_order2(1:face_num2) );
return
end