\perpendicular

Description 

Operator \perpendicular is a geometrical operator. It is used to define a perpendicular line to another meeting a particular point. Principle of this operator is to compute a new point such as the line defined by this point and the point given in parameter is orthogonal to the given line. There are two syntaxes whether the new created point belongs to the given reference line.

The following figure () presents an example of this operator. The code to obtain this result can be found in the next section. In this example there are three instances of operator \perpendicular to compute respectively v2, v3 and v4. Both first use the first syntax because points searched belong to the base line. v4 belongs to [d, c] so this line should be given to the operator. It can be noted that in the former case, the use of operator \intersection could get v4 as the intersection of segment [v3, a] and [d, c].

This operator should only appear within a step block.

Figure: Examples of operator \perpendicular

Usage

  v2 = \perpendicular([v1, b], c);
  v3 = \perpendicular([v1, b], a);
  v4 = \perpendicular([v1, b], a, [d, c]);

Formal structure

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

Parameters

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

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

  LIMIT_EDGE
  Description    : Indicates the new orthogonal 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 new orthogonal
                   line and LIMIT_EDGE.
  Type           : Symbol, vertex identifier.
  Allowed values : Any vertex identifier not yet defined.

Conditions

• length of EDGE shouldn't be null.
• EDGE and LIMIT_EDGE shouldn't be perpendicular.