Area Coordinate Search

Algorithm

Recursive

Name:	Search
Variables Received:	Elementsearch (first received is the element from which the ideal point was generated)
Variables Returned:	Whether or not the ideal point can be found ( Return 1: cannot or Return 0: can )
	Containing element for the ideal point ( Elementfound )
	Weights for the distribution function values of the containing element's nodes ( PHI1, PHI2, and PHI3 )

Pseudocode

Compute the area of Element_search ( Area_search ).

Compute the area of triangle made by the ideal point and Node 2 and Node 3 of Element_search:

Area₁ = (Point_n2-Point_ideal) x (Point_n3-Point_ideal)

Compute the area of triangle made by the ideal point and Node 3 and Node 1 of Element_search:

Area₂ = (Point_n3-Point_ideal) x (Point_n1-Point_ideal)

Compute the area of triangle made by the ideal point and Node 1 and Node 2 of Element_search:

Area₃ = (Point_n1-Point_ideal) x (Point_n2-Point_ideal)

Compute the minimum of these areas:

Area_min = MIN( Area₁, Area₂, Area₃ )

If Area_min is greater than the negative of the minimum distribution function (-PHI_min):

PHI₁ = Area₁/Area_search
PHI₂ = Area₂/Area_search
PHI₃ = Area₃/Area_search
Return 0

If Area₁ is negative:

Set Element_search to the neighboring element across from Point₁.

If this neighbor is not a boundary and hasn't already been searched:

Search the neighbor.

If the containing element is found (i.e. Search Returns 0 ):

Element_found = Element_search
Return 0

Else:

Return 1

Else:

Return 1

If Area₂ is negative:

Set Element_search to the neighboring element across from Point₂.

If this neighbor is not a boundary and hasn't already been searched:

Search the neighbor.

If the containing element is found (i.e. Search Returns 0 ):

Element_found = Element_search
Return 0

Else:

Return 1

Else:

Return 1

If Area₃ is negative:

Set Element_search to the neighboring element across from Point₃.

If this neighbor is not a boundary and hasn't already been searched:

Search the neighbor.

If the containing element is found (i.e. Search Returns 0 ):

Element_found = Element_search
Return 0

Else:

Return 1

Else:

Return 1