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

The `tess2prism_flatten.sh` script
converts a tesseroid model to prisms
(using the `--flatten` flag in `tessmodgen`) and
calculates the gravitational potential, gravitational attraction,
and gravity gradient tensor
in Cartesian coordinates:

```
#!/bin/bash
# Generate a prism model from a tesseroid model by
# flattening the tesseroids (1 degree = 111.11 km).
# This way the converted prisms can be used
# with the prism* programs in Cartesian coordinates.
tess2prism --flatten < tess-model.txt > prism-model.txt
# Generate a regular grid in Cartesian coordinates,
# pipe the grid to the computation programs,
# and dump the result on output.txt
tessgrd -r-3e06/3e06/-3e06/3e06 -b50/50 -z250e03 | \
prismpot prism-model.txt | \
prismgx prism-model.txt | \
prismgy prism-model.txt | \
prismgz prism-model.txt | \
prismgxx prism-model.txt | prismgxy prism-model.txt | \
prismgxz prism-model.txt | prismgyy prism-model.txt | \
prismgyz prism-model.txt | prismgzz prism-model.txt > output.txt
```

The tesseroid model file looks like this:

```
# Test tesseroid model file
10 15 10 15 0 -30000 500
-15 -10 -10 10 0 -50000 200
-15 5 -16 -10 0 -30000 -300
```

and the converted prism model looks like this:

```
# Prisms converted from tesseroid model with tess2prism 1.1dev
# local time: Tue May 8 14:55:02 2012
# tesseroids file: stdin
# conversion type: flatten
# format: x1 x2 y1 y2 z1 z2 density
# Test tesseroid model file
1111100 1666650 1111100 1666650 0 30000 487.534658568521
-1111100 1111100 -1666650 -1111100 0 50000 198.175508383774
-1777760 -1111100 -1666650 555550 0 30000 -291.9029748328
```

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).