3D Probe Calculation

Problem:

What process does Tecplot use for probing in 3D? Also for streamtrace placement contour labeling linear interpolation and polyline extraction in 3D.

Solution:

Tecplot determines the tetrahedron that the point is inside and then does a weighted average of the data set values at the four corners of the tetrahedron to get the values at the point. This method is not the most accurate – especially if your grid is coarse or has long skinny cells. That type of grid also leads to other inaccuracies. To find the right tetrahedron:

1. If possible a group of cells are identified as candidates for containing the particle position. For Streamtrace calculations the candidate cells are known to be in the neighborhood of where the particle was previously found.
2. These candidate cells are examined one at a time. If the cells are bricks (i.e. they are not FE-Tetrahedral) then they are divided up into 6-tetrahedrons. Each is evaluated (steps 3 and 4) until the point is located in one.
3. The volume of the tetrahedron is calculated: VT
4. The volume of the four sub-tetrahedrons formed by connecting the particle position with three of the sides of the tetrahedron at a time. This gives: V1 V2 V3 V4 if ABS(V1+V2+V3+V4 – VT) < epsilon then the particle is said to be inside the tetrahedron and the weight to assign to each corner of the tetrahedron is:

Wn = Vn/VT where Vn is the volume of the sub-tetrahedron opposite the corner assigned to Wn 1 <= n <= 4. 5. If none of the candidate cells contains the point the search is expanded until the point is found.

Tecplot determines the weighting to give each of the four corners of the tetrahedron where the point is located.