\intersection

Description 

Geometrical operator \intersection returns the intersection vertex of two edges given in parameter. This operator has the two equivalent syntaxes taking:

1. four vertex symbols,
2. two edges.

First syntax is a compact form which can be ambiguous or at least not very clear for beginners. The second one using edge notation can be easier to understand. Nevertheless, the intersection is made with lines instead of edges, this way the resulting point may not belong to the given edges.
This operator should only appear within a step block.

Figure: Point o is built as the intersection of both diagonals

Usage

  o = \intersection(a, c, b, d);     % same as below but shorter ...
  o = \intersection([a, c], [b, d]);

Formal structure

  RETURN_VERTEX = \intersection(VERTEX_1, VERTEX_2, VERTEX_3, VERTEX_4);
  RETURN_VERTEX = \intersection(EDGE_1, EDGE_2);

Parameters

 VERTEX_1
  Description    : Indicates the first vertex of the first segment.
  Type           : Symbol, vertex identifier.
  Allowed values : Any vertex identifier previously defined.
  
  VERTEX_2
  Description    : Indicates the second vertex of the first segment.
  Type           : Symbol, vertex identifier.
  Allowed values : Any vertex identifier previously defined.

  VERTEX_3
  Description    : Indicates the first vertex of the second segment.
  Type           : Symbol, vertex identifier.
  Allowed values : Any vertex identifier previously defined.
  
  VERTEX_4
  Description    : Indicates the second vertex of the second segment.
  Type           : Symbol, vertex identifier.
  Allowed values : Any vertex identifier previously defined.

  EDGE_1
  Description    : Indicates the first segment.
  Type           : Edge, vertex identifier pair.
  Allowed values : Any vertex identifier pair previously defined.

  EDGE_2
  Description    : Indicates the second segment.
  Type           : Edge, vertex identifier pair.
  Allowed values : Any vertex identifier pair previously defined.

Return value

  RETURN_VERTEX
  Description    : New vertex intersection of both segments
  Type           : Symbol, vertex identifier
  Allowed values : Any vertex identifier not already defined

Conditions

• Vertex defined by VERTEX_1 should not be equivalent to the one describe by VERTEX_2.
• Vertex defined by VERTEX_3 should not be equivalent to the one describe by VERTEX_4.
• Edges should not be parallel.