Calculation of volume and centre of mass of an arbitrary polyhedron

Calculation of volume and centre of mass of an arbitrary polyhedron

Hi I am developing a thesis that will calculate the volume and center of
mass of an arbitrary block of rock.
1- The calculation starts with triple volume integrals. The formulas are
transformed to line integrals using the divergence theorem and Green
theorem. This is a proven method and I have developed software that does
the calculations. The input to the software is the coordinates of the
vertices of the faces.
2- From the field, the orientations of the planes that define the block of
rock are measured using dip and dip direction. These are simply angles
that perfectly identify the planes in space. Additionally, the coordinates
of a point in the planes are measured. This information allows us to
obtain the equation of all the planes that define the block. These planes
are, for example, faults, fractures or geologic layers.
3- The combination of the planes in groups of three, without repetition,
gives us the coordinates of all vertices and the faces they belong to.
4- The last piece of the puzzle is to figure out the sequence of the
coordinates in the face in counterclockwise direction. In other words, it
is necessary to create an index of the coordinates so we know in what
order they are on the face. Moreover, it is required to determine what
vertices really belong to the polyhedron.
I think I can use linear programming to define what vertices (defined by 3
intercepting planes) are really part of the polyhedron. I wont't have an
objective function and I don't know how to define the constraints.
Any suggestion? ideas?
Thanks Jair Santos UBC-Canada