\parallel

Description 

Operator \parallel is a geometrical operator. It is used to define a line parallel to another meeting a particular point. It takes the following parameters:

• the reference line to build its parallel,
• the starting point of the new line,
• the line defining end of the new line.

The following figure () presents an example of this operator. The code to obtain this result can be found in the next section. The bisector of the half square triangle defines the mark (v1) on which a parallel to the diagonal [d, b] should pass.

This operator should only appear within a step block.

Figure: Example of operator \parallel

Usage

  v1 = \line_to_line(b, a, d, [a, d]); % bisector definition
  v2 = \parallel([d, b],v1, [a, b]);   % found other extermity
  \valley_fold(v1, v2);                % make valley fold line

Formal structure

  RETURN_VERTEX = \parallel(EDGE, VERTEX, LIMIT_EDGE);

Parameters

  EDGE
  Description    : Indicates the edge reference to build its
                   parallel line. 
  Type           : Edge, couple of vertex identifiers.
  Allowed values : Any couple of vertex identifiers already.

  VERTEX
  Description    : Indicates the vertex origin of the parallel
                   line. 
  Type           : Symbol, vertex identifier.
  Allowed values : Any vertex identifier previously defined.

  LIMIT_EDGE
  Description    : Indicates the new parallel line limit. 
  Type           : Edge, couple of vertex identifiers.
  Allowed values : Any couple of vertex identifiers already 
                   defined in a previous step.

Return value

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

Conditions

• length of EDGE shouldn't be null.