\point_to_point

Description 

Operator \point_to_point is a geometrical operator. It is useful to define points to draw fold (mountain or valley) line. It allows to get vertices of a frequent origami operation; when a corner (or a general point) comes to another point. \point_to_point takes two points:

1. moving vertex,
2. destination vertex

and also two edges:

1. the edge on which the first intersection with fold line is found,
2. the edge on which the second intersection with fold line is found.

Figure: Example of the operator \point_to_point. Note that this operator does not return an edge but a couple of vertices, on this figure, we have explicitly add a valley fold using those points

Usage

  [i1, i2] = \point_to_point(c, ab, [d, a], [b, c]);

Formal structure

  [RETURN_V_1, RETURN_V_2] = \point_to_point(MOVING, DEST, EDGE_1, EDGE_2);

Parameters

  MOVING
  Description    : Moving vertex.
  Type           : Symbol, vertex identifier.
  Allowed values : Any vertex identifier previously defined.
  DEST
  Description    : Destination vertex. 
  Type           : Symbol, vertex identifier.
  Allowed values : Any vertex identifier previously defined.
  EDGE_1
  Description    : Indicates the edge on which second intersection with 
                   fold line can be found.
  Type           : Edge, couple of vertex identifiers.
  Allowed values : Any couple of vertex identifiers already 
                   defined in a previous step.
  EDGE_2
  Description    : Indicates the edge on which second intersection with 
                   fold line can be found. 
  Type           : Edge, couple of vertex identifiers.
  Allowed values : Any couple of vertex identifiers already 
                   defined in a previous step.

Return value

  RETURN_V_1
  Description    : New vertex, first intersection of fold 
                   line and EDGE_1 parameter.
  Type           : Symbol, vertex identifier.
  Allowed values : Any vertex identifier not already defined

  RETURN_V_2
  Description    : New vertex, second intersection of fold
                   line and EDGE_2 parameter.
  Type           : Symbol, vertex identifier.
  Allowed values : Any vertex identifier not already defined

Conditions

• MOVING should not be equivalent to DEST (equivalence notion is explains in ),
• edge formed by MOVING and DEST should not be orthogonal with EDGE_1 nor EDGE_2,
• length of EDGE_1 and EDGE_2 should not be null.