#  Copyright (c) 1997-2015
#  Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Berlin, Germany)
#  http://www.polymake.org
#
#  This program is free software; you can redistribute it and/or modify it
#  under the terms of the GNU General Public License as published by the
#  Free Software Foundation; either version 2, or (at your option) any
#  later version: http://www.gnu.org/licenses/gpl.txt.
#
#  This program is distributed in the hope that it will be useful,
#  but WITHOUT ANY WARRANTY; without even the implied warranty of
#  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#  GNU General Public License for more details.
#-------------------------------------------------------------------------------

object Polytope {

# @category Geometry
# A weighted inner point depending on the outer angle called Steiner point for all faces of dimensions 2 to d.

property STEINER_POINTS : Matrix<Scalar>;

# @category Geometry
# Steiner point of the whole polytope.
property STEINER_POINT : Vector<Scalar>;

# @notest
rule STEINER_POINTS : HASSE_DIAGRAM, GRAPH.ADJACENCY, VERTICES, CONE_DIM {
   $this->STEINER_POINTS=all_steiner_points($this);
}
precondition : BOUNDED;
weight 6.10;

rule STEINER_POINT : GRAPH.ADJACENCY, VERTICES, CONE_DIM {
   $this->STEINER_POINT=steiner_point($this);
}
precondition : BOUNDED;
weight 5.10;

rule STEINER_POINT : STEINER_POINTS {
   $this->STEINER_POINT=$this->STEINER_POINTS->[0];
}
weight 0.10;

}

package Visual::Color;

# Steiner points are drawn in blue
custom $steiner_point="0 0 255";

package application;

# Steiner points are drawn thicker than the vertices
custom $steiner_point_thickness=1;


###################################################################################
#
#  decoration methods adding Steiner points to various drawings
#
package Visual::Polytope;

# Add the [[Polytope::STEINER_POINTS|STEINER_POINTS]] to the 3-d visualization.
# The facets become transparent.
# @options %Visual::PointSet::decorations
# @return Visual::Polytope
# @example Displays the Steiner points of a random threedimensional sphere with 20 vertices. The labels of the vertices are turned off.
# > rand_sphere(3,20)->VISUAL(VertexLabels=>"hidden")->STEINER;

user_method STEINER(%Visual::PointSet::decorations) {
   my ($self, $decor)=@_;
   my $VP=$self->basis_solid;
   $VP->FacetTransparency //= 0.5;
   my $P=$self->Polytope;
   my $SP=new Visual::PointSet( Name => "Steiner points of " . $P->name,
			        Points => dehomogenize(convert_to<Float>($P->STEINER_POINTS)),
				PointColor => $Visual::Color::steiner_point,
				PointThickness => $steiner_point_thickness,
				PointLabels => "hidden",
				$decor,
			      );
   compose($self, $SP);
}


package Visual::SchlegelDiagram;
# Add the [[Visual::SchlegelDiagram::STEINER_POINTS|STEINER_POINTS]] to the Schlegel Diagram
# @options %Visual::PointSet::decorations
# @option Bool center place the projection center to the Steiner point of the polytope
#                     and the view ray through the Steiner point of the facet
# @return Visual::SchlegelDiagram

user_method STEINER(%Visual::PointSet::decorations, { center => undef }) {
   my ($self, $decor, $opts)=@_;
   my $S=$self->SchlegelObject;
   my $P=$S->parent;
   if ($opts->{center}) {
      $S->begin_transaction;
      $S->INNER_POINT=$P->STEINER_POINTS->[0];
      $S->FACET_POINT=$P->STEINER_POINTS->[$S->FACET+1];
      $S->commit;
   }
   # omit the Steiner point of the whole polytope and the one on the projection facet
   my $omit_points=new Set(0, $S->FACET+1);
   my $SP=new Visual::PointSet( Name => "Steiner points of " . $P->name,
				Points => (new Visual::SchlegelTransform($S, $P->STEINER_POINTS->minor(~$omit_points,All))),
				PointColor => $Visual::Color::steiner_point,
				PointThickness => $steiner_point_thickness,
				PointLabels => "hidden",
				$decor
			      );
   compose($self, $SP);
}


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