function [ num_int, pint ] = halfspace_normal_triangle_int_3d ( p, normal, t )
%*****************************************************************************80
%
%% halfspace_normal_triangle_int_3d(): intersection ( normal halfspace, triangle ) in 3D.
%
% Discussion:
%
% The normal form of a halfspace in 3D may be described as the set
% of points (X,Y,Z) on or "above" a plane described in normal form:
%
% P is a point on the plane,
% NORMAL is the unit normal vector, pointing "out" of the
% halfspace.
%
% The triangle is specified by listing its three vertices.
%
% 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 P(3,1), a point on the bounding plane
% that defines the halfspace.
%
% real NORMAL(3,1), the components of the normal vector
% to the bounding plane that defines the halfspace. By convention, the
% normal vector points "outwards" from the halfspace.
%
% 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.
%
p = p(:);
normal = normal(:);
dim_num = 3;
%
% Compute the signed distances between the vertices and the plane.
%
d = - normal(1:dim_num,1)' * p(1:dim_num,1);
%
% Compute the signed distances between the vertices and the plane.
%
dist1 = d + normal(1:dim_num,1)' * t(1:dim_num,1);
dist2 = d + normal(1:dim_num,1)' * t(1:dim_num,2);
dist3 = d + normal(1:dim_num,1)' * t(1:dim_num,3);
%
% Now we can find the intersections.
%
[ num_int, pint ] = halfspace_triangle_int_3d ( t, dist1, dist2, dist3 );
return
end