====== Calc Interaction Potential Map ====== 

===== Description =====

This functor generates an interaction potential map, which is a gravitational model between null cells and non-null cells whose values represent the gravitational masses. The denominator is a function of distance to the non-null cells raised to an exponent denoting a friction coefficient.

===== Inputs =====

^ Name  ^ Type  ^ Description  ^
| Source  | [[Map Type]]  | Map whose non-null cells correspond to attraction features.  |

===== Optional Inputs =====

^ Name  ^ Type  ^ Description  ^ Default Value  ^
| Mask  | [[Map Type]]  | Map whose null cells mask the calculation of the interaction potential.  | None  |
| Distance Decay Exponent  | [[Real Value Type]]  | Exponent used as a friction coefficient.   | 2.0  |
| Cell Type  | [[Cell Type Type]]  | Data cell type. This type must be compatible with source map values, or an error will be reported during execution.  | Signed 32 Bit Integer  |
| Null Value  | [[Integer Value Type]]  | Null Value.  | -2147483648  |

===== Output =====

^ Name  ^ Type  ^ Description  ^
| Interaction Potential  | [[Map Type]]  | Area of each map category in cells.  |

===== Group =====

[[Functor List#Map Algebra | Map Algebra]]

===== Notes =====

The interaction potential is calculated using float and converted to "Signed 32 Bit Integer". In case cell type is set to "IEEE 754 32 Bit Real", no conversion is done.

The mask map does not mask the feature cells, only the calculation for the null-cells.

For each null cell, the interaction potential is the sum of the mass of each feature cell divided by the distance to it raised  to an exponent of decay.

<m 10>p(i) = sum{j=0}{n}{{value(j)}/{dist(i,j)}^de}</m>

===== Internal Name =====

CalcInteractionPotentialMap