\line_to_line

Description 

\line_to_line is a geometrical operator which allows to create one new vertex or two by making an edge meets an other. Suppose we want to create such a fold. We have to know what are the points to give to the fold operation. \line_to_line gives us those points. In such operations, we are only looking for points belonging to certain edges of the figure. In fact there are two different syntaxes for this operator:

1. taking four edges and returning a pair of vertices,
2. taking three vertices and one edge and returning one vertex.

Figure: Computing both opposite edge middles and a bisection case (22.5 degrees)

The first syntax is used when there is no defined intersection between both lines. In this case, the computation procedure is to calculate intersections of the median line (between two given edges) and the others. The two first parameters are edges to calculate median line, and both last are edges on which we expect to find intersection with this median line. The returned vertices pair is bounded respectively to each intersection found with both last edges.

The second syntax allows to compute the intersection of the bisector line and a given edge. The bisector line is obtained according to the three vertices parameters.

Edge parameters are given according to edge syntax ([ ]) but it doesn't impose that a line has been defined for those edges. It is just to make the operator more readable and not ambiguous. The only condition is that edge vertices are not equivalent.
This operator should only appear within a step block.

Usage

  [mid_ab, mid_cd] = \line_to_line([a,d], [b,c], [a, b], [c, d]);
  a2 = \line_to_line(d, a, b, [a,b]);

Formal structure

  [RETURN_V_1, RETURN_V_2]=\line_to_line(EDGE_1, EDGE_2, EDGE_3, EDGE_4);  
  RETURN_VERTEX = \line_to_line(VERTEX_1, VERTEX_2, VERTEX_3, EDGE);

Parameters

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

  EDGE_2
  Description    : Indicates the second segment to calculate median line.
  Type           : Edge, vertex identifier pair.
  Allowed values : Any vertex identifier pair previously defined.
  EDGE_3
  Description    : Indicates the first intersection segment.
  Type           : Edge, vertex identifier pair.
  Allowed values : Any vertex identifier pair previously defined.

  EDGE_4
  Description    : Indicates the second intersection segment.
  Type           : Edge, vertex identifier pair.
  Allowed values : Any vertex identifier pair previously defined.

  VERTEX_1
  Description    : Indicates segments common intersection.
  Type           : Symbol, vertex identifier.
  Allowed values : Any vertex identifier previously defined.
  
  VERTEX_2
  Description    : Indicates the end of the first segment.
                   [VERTEX_1, VERTEX_2] is the first segment.
  Type           : Symbol, vertex identifier.
  Allowed values : Any vertex identifier previously defined.

  VERTEX_3
  Description    : Indicates the end of the second segment.
                   [VERTEX_1, VERTEX_3] is the second segment.
  Type           : Symbol, vertex identifier.
  Allowed values : Any vertex identifier previously defined.

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

Return value

  RETURN_V_1
  Description    : New vertex, first intersection of median 
                   line and EDGE_3 parameter.
  Type           : Symbol, vertex identifier
  Allowed values : Any vertex identifier not already defined

  RETURN_V_2
  Description    : New vertex, second intersection of median
                   line and EDGE_4 parameter.
  Type           : Symbol, vertex identifier
  Allowed values : Any vertex identifier not already defined

  RETURN_VERTEX
  Description    : New vertex intersection of bisector line 
                   and EDGE parameter.
  Type           : Symbol, vertex identifier
  Allowed values : Any vertex identifier not already defined