====== BigObject SchlegelDiagram<Scalar> ======
//from application [[..:polytope|polytope]]//\\
\\
 A Schlegel diagram of a polytope.

  ? Type Parameters:
  :: ''Scalar'': default ''[[..:common#Rational |Rational]]''
===== Properties =====

==== no category ====
{{anchor:facet:}}
  ?  **''FACET''**
  :: The facet number in the original polytope, giving the projection plane.
    ? Type:
    :''[[..:common#Int |Int]]''


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{{anchor:facet_point:}}
  ?  **''FACET_POINT''**
  :: The intersection point of the projection facet and the view ray.
    ? Type:
    :''[[..:common#Vector |Vector]]<Scalar>''


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{{anchor:inner_point:}}
  ?  **''INNER_POINT''**
  :: A point on the view ray lying inside the polytope.
    ? Type:
    :''[[..:common#Vector |Vector]]<Scalar>''


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{{anchor:rotation:}}
  ?  **''ROTATION''**
  :: Rotation matrix making the projection facet coinciding with (0 0 0 -1) We want a negatively oriented coordinate system since the view point lies on the negative side of the facet.
    ? Type:
    :''[[..:common#Matrix |Matrix]]<[[..:common#Float |Float]],[[..:common#NonSymmetric |NonSymmetric]]>''


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{{anchor:transform:}}
  ?  **''TRANSFORM''**
  :: Matrix of a projective transformation mapping the whole polytope into the ''[[..:polytope:SchlegelDiagram#FACET |FACET]]'' The points belonging to this facet stay fixed.
    ? Type:
    :''[[..:common#Matrix |Matrix]]<Scalar,[[..:common#NonSymmetric |NonSymmetric]]>''


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{{anchor:vertices:}}
  ?  **''VERTICES''**
  :: Coordinates in affine 3-space of the vertices which correspond to a 3-dimensional (Schlegel-) projection of a 4-polytope.
    ? Type:
    :''[[..:common#Matrix |Matrix]]<[[..:common#Float |Float]],[[..:common#NonSymmetric |NonSymmetric]]>''


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{{anchor:viewpoint:}}
  ?  **''VIEWPOINT''**
  :: The center point of the projection, lying outside the polytope.
    ? Type:
    :''[[..:common#Vector |Vector]]<Scalar>''


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{{anchor:zoom:}}
  ?  **''ZOOM''**
  :: Zoom factor.
    ? Type:
    :''Scalar''


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===== Methods =====

==== no category ====
{{anchor:visual:}}
  ?  **''VISUAL()''**
  :: Draw the Schlegel diagram.
    ? Options:
    : 
    :: ''[[..:graph#Visual_Graph_decorations |Visual::Graph::decorations]]'' ''proj_facet'': decorations for the edges of the projection face
    : option list ''[[..:graph#Visual_Graph_decorations |Visual::Graph::decorations]]''
    ? Returns:
    :''[[..:polytope:Visual_SchlegelDiagram |Visual::SchlegelDiagram]]''


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