function [ num_int, pint ] = halfspace_imp_triangle_int_3d ( a, b, c, d, t )
%*****************************************************************************80
%
%% halfspace_imp_triangle_int_3d(): intersection ( implicit halfspace, triangle ) in 3D.
%
% Discussion:
%
% The implicit form of a half-space in 3D may be described as the set
% of points (X,Y,Z) on or "above" an implicit plane:
%
% 0 <= A * X + B * Y + C * Z + D
%
% 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 MIT license.
%
% Modified:
%
% 08 May 2005
%
% Author:
%
% John Burkardt
%
% Input:
%
% real A, B, C, D, the parameters that define the
% implicit plane, which in turn define the implicit halfspace.
%
% real T(3,3), the vertices of the triangle.
%
% 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.
%
%
% Compute the signed distances between the vertices and the plane.
%
dist1 = a * t(1,1) + b * t(2,1) + c * t(3,1) + d;
dist2 = a * t(1,2) + b * t(2,2) + c * t(3,2) + d;
dist3 = a * t(1,3) + b * t(2,2) + c * t(3,3) + d;
%
% Now we can find the intersections.
%
[ num_int, pint ] = halfspace_triangle_int_3d ( t, dist1, dist2, dist3 );
return
end