function [ num_int, pint ] = halfspace_triangle_int_3d ( t, dist1, dist2, dist3 )
%*****************************************************************************80
%
%% HALFSPACE_TRIANGLE_INT_3D: intersection ( halfspace, triangle ) in 3D.
%
% Discussion:
%
% The triangle is specified by listing its three vertices.
%
% The halfspace is not described in the input data. Rather, the
% distances from the triangle vertices to the halfspace are given.
%
% The intersection may be described by the number of vertices of the
% triangle that are included in the halfspace, and by the location of
% points between vertices that separate a side of the triangle into
% an included part and an unincluded part.
%
% 0 vertices, 0 separators (no intersection)
% 1 vertex, 0 separators (point intersection)
% 2 vertices, 0 separators (line intersection)
% 3 vertices, 0 separators (triangle intersection)
%
% 1 vertex, 2 separators, (intersection is a triangle)
% 2 vertices, 2 separators, (intersection is a quadrilateral).
%
% Licensing:
%
% This code is distributed under the GNU LGPL license.
%
% Modified:
%
% 08 May 2005
%
% Author:
%
% John Burkardt
%
% Input:
%
% real T(3,3), the vertices of the triangle.
%
% real DIST1, DIST2, DIST3, the distances from each of
% the three vertices of the triangle to the halfspace. The distance is
% zero if a vertex lies within the halfspace, or on the plane that
% defines the boundary of the halfspace. Otherwise, it is the
% distance from that vertex to the bounding plane.
%
% Output:
%
% integer NUM_INT, the number of intersection points returned,
% which will always be between 0 and 4.
%
% real PINT(3,4), the coordinates of the NUM_INT
% intersection points. The points will lie in sequence on the triangle.
% Some points will be vertices, and some may be separators.
%
dim_num = 3;
%
% Walk around the triangle, looking for vertices that are included,
% and points of separation.
%
num_int = 0;
pint = [];
if ( dist1 <= 0.0 )
num_int = num_int + 1;
pint(1:dim_num,num_int) = t(1:dim_num,1);
end
if ( dist1 * dist2 < 0.0 )
num_int = num_int + 1;
pint(1:dim_num,num_int) = ( dist1 * t(1:dim_num,2) - dist2 * t(1:dim_num,1) ) ...
/ ( dist1 - dist2 );
end
if ( dist2 <= 0.0 )
num_int = num_int + 1;
pint(1:dim_num,num_int) = t(1:dim_num,2);
end
if ( dist2 * dist3 < 0.0 )
num_int = num_int + 1;
pint(1:dim_num,num_int) = ( dist2 * t(1:dim_num,3) - dist3 * t(1:dim_num,2) ) ...
/ ( dist2 - dist3 );
end
if ( dist3 <= 0.0 )
num_int = num_int + 1;
pint(1:dim_num,num_int) = t(1:dim_num,3);
end
if ( dist3 * dist1 < 0.0 )
num_int = num_int + 1;
pint(1:dim_num,num_int) = ( dist3 * t(1:dim_num,1) - dist1 * t(1:dim_num,3) ) ...
/ ( dist3 - dist1 );
end
return
end