# Convert a tesseroid model to prisms and calculate in spherical coordinatesΒΆ

The `tess2prism.sh` script
converts a tesseroid model to prisms
(using `tessmodgen`) and
calculates the gravitational potential, gravitational attraction,
and gravity gradient tensor
in spherical coordinates:

```
#!/bin/bash
# Generate a prism model from a tesseroid model.
# Prisms will have the same mass as the tesseroids and
# associated spherical coordinates of the center of
# the top of the tesseroid.
tess2prism < tess-model.txt > prism-model.txt
# Generate a regular grid in spherical coordinates,
# pipe the grid to the computation programs,
# and dump the result on output.txt
# prismpots calculates the potential in spherical
# coordinates, prismgs calculates the full
# gravity vector, and prismggts calculates the full
# gravity gradient tensor.
tessgrd -r-160/0/-80/0 -b100/100 -z250e03 | \
prismpots prism-model.txt | \
prismgs prism-model.txt | \
prismggts prism-model.txt -v > output.txt
```

The tesseroid model file looks like this:

```
# Test tesseroid model file
-77 -75 -41 -39 0 -50000 500
-79 -77 -41 -39 0 -50000 500
-81 -79 -41 -39 0 -50000 500
-83 -81 -41 -39 0 -50000 500
-85 -83 -41 -39 0 -50000 500
```

and the converted prism model looks like this:

```
# Prisms converted from tesseroid model with tess2prism 1.1dev
# local time: Wed May 16 14:34:47 2012
# tesseroids file: stdin
# conversion type: equal mass|spherical coordinates
# format: dx dy dz density lon lat r
# Test tesseroid model file
221766.31696055 169882.854778591 50000 499.977196258595 -76 -40 6378137
221766.31696055 169882.854778591 50000 499.977196258595 -78 -40 6378137
221766.31696055 169882.854778591 50000 499.977196258595 -80 -40 6378137
221766.31696055 169882.854778591 50000 499.977196258595 -82 -40 6378137
221766.31696055 169882.854778591 50000 499.977196258595 -84 -40 6378137
```

Note that the density of prisms is altered. This is so that the tesseroid and corresponding prism have the same mass.

The result should look like the *following*
(“column” means the column of the output file).