;### Set visualization backend
prefer 'jreality';

;### polytope visualization
$oct = cross(3);
$oct_trunc = truncation($oct,All);
$oct_trunc->VISUAL;

;### Visualizing the truncation
compose($oct->VISUAL\n\n\n,$oct_trunc->VISUAL);
compose($oct->VISUAL(FacetStyle=>"hidden",VertexStyle=>"hidden"),$oct_trunc->VISUAL);
$oct_trunc->VISUAL->TRIANGULATION;

;### Visualizing lattice points
$oct_trunc->VISUAL->LATTICE;
$T = new Matrix<Rational>([ [1/2, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]);
$oct_scaled = new Polytope<Rational>(VERTICES => ($oct_trunc->VERTICES)*$T);
$oct_scaled->VISUAL->LATTICE;

;### Visualizing in higher dimensions
$cr4 = cross(4);
$cr4_trunc = truncation($cr4,All);
$cr4_trunc->VISUAL_GRAPH;

;### Visualizing with linear objective
print $cr4_trunc->VERTICES_IN_FACETS;
print rows_numbered($cr4_trunc->VERTICES_IN_FACETS);
$lp = new LinearProgram<Rational>(LINEAR_OBJECTIVE=>${$cr4_trunc->FACETS}[16]);
$cr4_trunc->LP = $lp;
$cr4_trunc->VISUAL_GRAPH->VERTEX_COLORS;
$l = $lp->LINEAR_OBJECTIVE;
$cr4_trunc->VISUAL_GRAPH(NodeLabels=> sub { my $i = shift; my $v = ${$cr4_trunc->VERTICES}[$i]; my $val = $l*$v; return $val;} )->VERTEX_COLORS;

;### Changing face colors
cube(3)->VISUAL(FacetColor=>"green");
@color=split(" ","red red red red blue blue blue blue");
cube(3)->VISUAL(VertexColor=>\@color);
$soccerball = load("~/workshop2012/soccerball.poly");
$soccerball->VISUAL(FacetColor => sub { $i = shift; $s = ${$soccerball->VERTICES_IN_FACETS}[$i]; if($s->size == 5) { return "black"; } else { return "white"; } });
rand_sphere(3,100)->VISUAL(FacetColor => sub { return new RGB(rand,rand,rand); }, VertexColor => sub { return new RGB(rand,rand,rand); }, EdgeStyle => "hidden");

;### Schlegel diagrams
$cr4_trunc->SCHLEGEL(ZOOM=>".6");
$oct_trunc->SCHLEGEL(ZOOM=>".5")->CONSTRUCTION;
compose($oct_trunc->SCHLEGEL(ZOOM=>".5",EdgeColor=>"orange")->CONSTRUCTION, $oct_trunc->SCHLEGEL(ZOOM=>".7")->CONSTRUCTION);

;### Tight spans
$ts = load("~/workshop2012/bees.poly");
$ts->VISUAL_BOUNDED_GRAPH->EDGE_COLORS;
$ts->VISUAL_TIGHT_SPAN;

;### Tropical polytopes
application 'tropical';
$ths = new TropicalHypersurface(MONOMIALS=>[[1,1,2,1],[0,1,3,1],[0,3,2,0],[1,2,1,1]],COEFFICIENTS=>[1,3,2,2]);
$ths->VISUAL;

;### Fans
application 'fan';
$nf = normal_fan($oct_trunc);
$nf->VISUAL;
script("visual_normal_fan",$oct_trunc);

;### LaTeX Export

;## PDF 3D import

prefer('sketch');
cube(3)->VISUAL;
cube(4)->SCHLEGEL(ZOOM=>"0.5");
script("visual_normal_fan",$oct_trunc);
$oct_trunc->VISUAL(ViewPoint=>[1,1,1], ViewDirection=>[0,0,0], ViewUp=>[0,0,1]);
sketch($oct_trunc->VISUAL(ViewPoint=>[1,1,1], ViewDirection=>[0,0,0], ViewUp=>[0,0,1]), File=>"~/workshop2012/oct_trunk.sk");