# Sample Triangle Geometry on Uncertain Regular Grid¶

## Group (Subgroup)¶

Sampling (Resolution)

## Description¶

This Filter "samples" a triangulated surface mesh on a rectilinear grid, but with "uncertainty" in the absolute position of the Cells. The "uncertainty" is meant to simulate the possible positioning error in a sampling probe. The user can specify the number of Cells along the X, Y, and Z directions in addition to the resolution in each direction and origin to define a rectilinear grid. The sampling, with "uncertainty", is then performed by the following steps:

1. Determine the bounding box and Triangle list of each Feature by scanning all Triangles and noting the Features on either side of the Triangle
2. For each Cell in the rectilinear grid, perturb the location of the Cell by generating a three random numbers between [-1, 1] and multiplying them by the three uncertainty values (one for each direction)
3. For each perturbed Cell in the rectilinear grid, determine which bounding box(es) they fall in (Note: the bounding box of multiple Features can overlap)
4. For each bounding box a Cell falls in, check against that Feature's Triangle list to determine if the Cell falls within that n-sided polyhedra. (Note: if the surface mesh is conformal, then each Cell will only belong to one Feature, but if not, the last Feature the Cell is found to fall inside of will own the Cell)
5. Assign the Feature number that the Cell falls within to the Feature Ids array in the new rectilinear grid geometry

Note that the unperturbed grid is where the Feature Ids actually live, but the perturbed locations are where the Cells are sampled from. Essentially, the Feature Ids are stored where the user thinks the sampling took place, not where it actually took place!

## Parameters¶

Name Type Description
X Points (Column) int32_t Number of Cells along X axis
Y Points (Row) int32_t Number of Cells along Y axis
Z Points (Plane) int32_t Number of Cells along Z axis
Resolution float (3x) The resolution values (dx, dy, dz)
Origin float (3x) The origin of the sampling volume
Uncertainty float (3x) Vector of uncertainty values associated with X, Y and Z positions of Cells

Triangle

## Required Objects¶

Type Default Name Type Component Dimensions Description
Face Attribute Array FaceLabels Int (2) Specifies which Features are on either side of each Face.

## Created Objects¶

Kind Default Name Type Component Dimensions Description
Data Container ImageDataContainer N/A N/A Created Data Container name with an Image Geometry
Attribute Matrix CellData Cell N/A Created Cell Attribute Matrix name
Cell Attribute Array FeatureIds int32_t (1) Specifies to which Feature each Cell belongs

## Example Pipelines¶

Please see the description file distributed with this Plugin

## DREAM.3D Mailing Lists¶

If you need more help with a Filter, please consider asking your question on the DREAM.3D Users Google group!