Quick Start (C++ & Python)

This section describes the specification of required inputs and output like required units and characteristics of the mesh. These constraints apply for both, the C++ and Python interface. The actual utilization is presented in Examples Python and Examples C++.

Gravity Model Input

The evaluation of the polyhedral gravity model requires the following parameters.

Name
Polyhedral Mesh (either as vertices & faces or as polyhedral source files)
Constant Density \(\rho\)

The polyhedron’s mesh’s units must match with the constant density! For example, if the mesh is in \([m]\), then the constant density should be in \([\frac{kg}{m^3}]\).

Have a look at Supported Polyhedron Source Files for an overview of supported polyhedral mesh files.

Note

The plane unit normals of every face of the polyhedral mesh must point consistently outwards or inwards the polyhedron! This property is automatically enforced by the class Polyhedron in both C++ library and Python interface as long as not explicit set to DISABLE. Setting this to DISABLE, is recommended for advanced users or when you “know your mesh”. For details, refer to the APIs or Mesh Integrity & Explanation.

Gravity Model Output

The calculation outputs the following parameters for every Computation Point P. The units of the respective output depend on the units of the input parameters (mesh and density)!

Hence, if e.g. your mesh is in \(km\), the density must match. Further, the output units will match the input units.

Name	If mesh \([m]\) and density \([\frac{kg}{m^3}]\)	Comment
\(V\)	\(\frac{m^2}{s^2}\) or \(\frac{J}{kg}\)	The potential or also called specific energy
\(V_x\), \(V_y\), \(V_z\)	\(\frac{m}{s^2}\)	The gravitational acceleration in the three cartesian directions
\(V_{xx}\), \(V_{yy}\), \(V_{zz}\), \(V_{xy}\), \(V_{xz}\), \(V_{yz}\)	\(\frac{1}{s^2}\)	The spatial rate of change of the gravitational acceleration

This model’s output obeys to the geodesy and geophysics sign conventions. Hence, the potential \(V\) for a polyhedron with a mass \(m > 0\) is defined as positive.

The accelerations \(V_x\), \(V_y\), \(V_z\) are defined as

\[\textbf{g} = + \nabla V = \left( \frac{\partial V}{\partial x}, \frac{\partial V}{\partial y}, \frac{\partial V}{\partial z} \right)\]

Accordingly, the second derivative tensor is defined as the derivative of \(\textbf{g}\).