Module: Line Integrals ()

Description:

This module performs calculation of integrals or sums on Line Sets. The computation might involve 3d Unstructured Model Field unstructured scalar or vector fields.

The results of the computation are written in a spreadsheet.

Press the Apply button to start the computation.

Connections:

Data [required]
A Line Set.

Field [optional]
A 3d unstructured scalar or vector field for which an integral or a sum will be computed.
This port is only displayed when a field is required for the selected computation (all computations except arc length computation).

Density [optional]
An unstructured scalar field containing density values.
This port is only displayed when density is required for the selected computation (mass-weigthed computations).
The density has to be connected to the same model as the field in the Field port. tries to retrieve such a density field and if one and only one is found, it is suggested by default.

Ports:

Line integral

We denote by the unstructured scalar or vector field. The following quantities can be computed:

• arc length
  
  where are the (N+1) points of the line and d is the distance.
• linear integral
  
  

  where are the (N+1) points of the line and d is the distance.

• arc length-weighted average
  
  where L is the arc length (see above).
• mass-weighted integral
  
  where is the density, are the (N+1) points of the line and d is the distance.
• mass-weighted average
  
  where is the density.
• minimum
• maximum
• sum
  
  where are the (N+1) points of the line.
• mean
  
  where are the (N+1) points of the line.
• standard deviation
  
  where is the mean value of and are the (N+1) points of the line.

If the field is a vector field, the results will be given component per component, except for minimum and maximum which will be equal to the vector's magnitude scalar field minimum and maximum. Field values are probed at line points.

Spreadsheet

The computation results are written in the tables of a spreadsheet. Choose append table to append the current table, or new table to open a new table.

Table

If this box is checked, a new table will be opened everytime the integral type changes. The new tables will be named after the integral names.

Compute

A Line Set data object stores independent line segments of variable length. Choose globally to get one result corresponding to the global Line Set composed of all the lines selected in Lines port.
Choose per line to compute the result on each selected line.

Lines

A Line Set data object stores independent line segments of variable length. Select the line(s) where the computation should be done. The field(s) will be probed at the selected line(s) points in order to compute the chosen integrals.