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polyhedralgravity 3.2

polyhedral-gravity-model

Table of Contents

References
Documentation & Examples

Input & Output (C++ and Python)
Minimal Python Example
Minimal C++ Example

Installation

With conda
With pip
From source

C++ Library & Executable

Building the C++ Library & Executable
Running the C++ Executable

Testing
Contributing

References
This code is a validated implementation in C++17 of the Polyhedral Gravity Model
by Tsoulis et al.. It was created in a collaborative project between
TU Munich and ESA's Advanced Concepts Team. Please refer to the
project report
for extensive information about the theoretical background, related work,
implementation & design decisions, application, verification,
and runtime measurements of the presented code.
The implementation is based on the
paper Tsoulis, D., 2012. Analytical computation of the full gravity tensor of a homogeneous arbitrarily shaped polyhedral source using line integrals. Geophysics, 77(2), pp.F1-F11.
and its corresponding implementation in FORTRAN.
Supplementary details can be found in the more recent
paper TSOULIS, Dimitrios; GAVRIILIDOU, Georgia. A computational review of the line integral analytical formulation of the polyhedral gravity signal. Geophysical Prospecting, 2021, 69. Jg., Nr. 8-9, S. 1745-1760.
and its corresponding implementation in MATLAB,
which is strongly based on the former implementation in FORTRAN.
Documentation & Examples

[!NOTE]
The GitHub Pages of this project
contain the full extensive documentation of the C++ Library and Python Interface
as well as background on the gravity model and advanced settings not detailed here.

Input & Output (C++ and Python)
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 ρ

The mesh and the constants density's unit must match.
Have a look the documentation to view the supported mesh files.
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, output units will be different accordingly.

Name
Unit (if mesh in [m] and ρ in [kg/m3])
Comment

V
m2s2 or Jkg
The potential or also called specific energy

Vx, Vy, Vz
ms2
The gravitational accerleration in the three cartesian directions

Vxx, Vyy, Vzz, Vxy, Vxz, Vyz
1s2
The spatial rate of change of the gravitational accleration

[!NOTE]
This gravity 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.
Accordingly, the accelerations are defined as g=+∇V.

Minimal Python Example
The following example shows how to use the python interface to compute the gravity
around a cube:
import numpy as np
from polyhedral_gravity import Polyhedron, GravityEvaluable, evaluate, PolyhedronIntegrity, NormalOrientation

# We define the cube as a polyhedron with 8 vertices and 12 triangular faces
# The polyhedron's normals point outwards (see below for checking this)
# The density is set to 1.0
cube_vertices = np.array(
[[-1, -1, -1], [1, -1, -1], [1, 1, -1], [-1, 1, -1],
[-1, -1, 1], [1, -1, 1], [1, 1, 1], [-1, 1, 1]]
)
cube_faces = np.array(
[[1, 3, 2], [0, 3, 1], [0, 1, 5], [0, 5, 4], [0, 7, 3], [0, 4, 7],
[1, 2, 6], [1, 6, 5], [2, 3, 6], [3, 7, 6], [4, 5, 6], [4, 6, 7]]
)
cube_density = 1.0
computation_point = np.array([0, 0, 0])

We first define a constant density Polyhedron from vertices and faces
cube_polyhedron = Polyhedron(
polyhedral_source=(cube_vertices, cube_faces),
density=cube_density,
)

In case you want to hand over the polyhedron via a supported file format,
just replace the polyhedral_source argument with a list of strings,
where each string is the path to a supported file format, e.g. polyhedral_source=["eros.node","eros.face"] or polyhedral_source=["eros.mesh"].
Continuing, the simplest way to compute the gravity is to use the evaluate function:
potential, acceleration, tensor = evaluate(
polyhedron=cube_polyhedron,
computation_points=computation_point,
parallel=True,
)

The more advanced way is to use the GravityEvaluable class. It caches the
internal data structure and properties which can be reused for multiple
evaluations. This is especially useful if you want to compute the gravity
for multiple computation points, but don't know the "future points" in advance.
evaluable = GravityEvaluable(polyhedron=cube_polyhedron) # stores intermediate computation steps
potential, acceleration, tensor = evaluable(
computation_points=computation_point,
parallel=True,
)
# Any future evaluable call after this one will be faster

Note that the computation_point could also be (N, 3)-shaped array to compute multiple points at once.
In this case, the return value of evaluate(..) or an GravityEvaluable will
be a list of triplets comprising potential, acceleration, and tensor.
The gravity model requires that all the polyhedron's plane unit normals consistently
point outwards or inwards the polyhedron. You can specify this via the normal_orientation.
This property is - by default - checked when constructing the Polyhedron! So, don't worry, it
is impossible if not explicitly disabled to create an invalid Polyhedron.
You can disable/ enable this setting via the optional integrity_check flag and can even
automatically repair the ordering via HEAL.
If you are confident that your mesh is defined correctly (e.g. checked once with the integrity check)
you can disable this check (via DISABLE) to avoid the additional runtime overhead of the check.
cube_polyhedron = Polyhedron(
polyhedral_source=(cube_vertices, cube_faces),
density=cube_density,
normal_orientation=NormalOrientation.INWARDS, # OUTWARDS (default) or INWARDS
integrity_check=PolyhedronIntegrity.VERIFY, # VERIFY (default), DISABLE or HEAL
)

[!TIP]
More examples and plots are depicted in the
jupyter notebook.

Minimal C++ Example
The following example shows how to use the C++ library to compute the gravity.
It works analogously to the Python example above.
// Defining the input like above in the Python example
std::vector<std::array<double, 3>> vertices = ...
std::vector<std::array<size_t, 3>> faces = ...
double density = 1.0;
// The constant density polyhedron is defined by its vertices & faces
// It also supports the hand-over of NormalOrientation and PolyhedronIntegrity as optional arguments
// as above described for the Python Interface
Polyhedron polyhedron{vertices, faces, density};
std::vector<std::array<double, 3>> points = ...
std::array<double, 3> point = points[0];
bool parallel = true;

The C++ library provides also two ways to compute the gravity. Via
the free function evaluate...
const auto[pot, acc, tensor] = GravityModel::evaluate(polyhedron, point, parallel);

... or via the GravityEvaluable class.
// Instantiation of the GravityEvaluable object
GravityEvaluable evaluable{polyhedron};

// From now, we can evaluate the gravity model for any point with
const auto[potential, acceleration, tensor] = evaluable(point, parallel);
// or for multiple points with
const auto results = evaluable(points, parallel);

Similarly to Python, the C++ implementation also provides mesh checking capabilities.

[!TIP]
For reference, have a look at the main method of the C++ executable.

Installation
With conda
The python interface can be easily installed with
conda:
conda install -c conda-forge polyhedral-gravity-model

With pip
As a second option, you can also install the python interface with pip from PyPi.
pip install polyhedral-gravity

Binaries for the most common platforms are available on PyPI including
Windows, Linux and macOS. For macOS and Linux, binaries for
x86_64 and aarch64 are provided.
In case pip uses the source distribution, please make sure that
you have a C++17 capable compiler and CMake installed.
From source
The project uses the following dependencies,
all of them are automatically set-up via CMake:

GoogleTest (1.13.0 or compatible), only required for testing
spdlog (1.13.0 or compatible), required for logging
tetgen (1.6 or compatible), required for I/O
yaml-cpp (0.8.0 or compatible), required for I/O
thrust (2.1.0 or compatible), required for parallelization and utility
xsimd (11.1.0 or compatible), required for vectorization of the atan(..)
pybind11 (2.12.0 or compatible), required for the Python interface, but not the C++ standalone

The module will be build using a C++17 capable compiler,
CMake. Just execute the following command in
the repository root folder:
pip install .

To modify the build options (like parallelization) have a look
at the next paragraph. The options
are modified by setting the environment variables before executing
the pip install . command, e.g.:
export POLYHEDRAL_GRAVITY_PARALLELIZATION="TBB"
pip install .

(Optional: For a faster build you can install all dependencies available
for your system in your local python environment. That way, they
won't be fetched from GitHub.)
C++ Library & Executable
Building the C++ Library & Executable
The program is build by using CMake. So first make sure that you installed
CMake and then follow these steps:
mkdir build
cd build
cmake .. <options>
cmake --build .

The following options are available:

Name (Default)
Options

POLYHEDRAL_GRAVITY_PARALLELIZATION (CPP)
CPP = Serial Execution / OMP or TBB = Parallel Execution with OpenMP or Intel's TBB

LOGGING_LEVEL (2)
0 = TRACE/ 1 = DEBUG/ 2 = INFO / 3 = WARN/ 4 = ERROR/ 5 = CRITICAL/ 6 = OFF

USE_LOCAL_TBB (OFF)
Use a local installation of TBB instead of setting it up via CMake

BUILD_POLYHEDRAL_GRAVITY_DOCS (OFF)
Build this documentation

BUILD_POLYHEDRAL_GRAVITY_TESTS (ON)
Build the Tests

BUILD_POLYHEDRAL_PYTHON_INTERFACE (ON)
Build the Python interface

During testing POLYHEDRAL_GRAVITY_PARALLELIZATION=TBB has been the most performant.
It is further not recommend to change the LOGGING_LEVEL to something else than INFO=2.
The recommended CMake settings using the TBB backend would look like this:
cmake .. -POLYHEDRAL_GRAVITY_PARALLELIZATION="TBB"

Running the C++ Executable
After the build, the gravity model can be run by executing:
./polyhedralGravity <YAML-Configuration-File>

where the YAML-Configuration-File contains the required parameters.
Examples for Configuration Files and Polyhedral Source Files can be
found in this repository in the folder /example-config/.
Input Configuration File
The configuration should look similar to the given example below.
It is required to specify the source-files of the polyhedron's mesh (more info
about the supported file in the documentation), the density
of the polyhedron, and the wished computation points where the
gravity tensor shall be computed.
Further one must specify the name of the .csv output file.
---
gravityModel:
input:
polyhedron: #polyhedron source-file(s)
- "../example-config/data/tsoulis.node" # .node contains the vertices
- "../example-config/data/tsoulis.face" # .face contains the triangular faces
density: 2670.0 # constant density, units must match with the mesh (see section below)
points: # Location of the computation point(s) P
- [ 0, 0, 0 ] # Here it is situated at the origin
check_mesh: true # Fully optional, enables mesh autodetect+repair of
# the polyhedron's vertex ordering (not given: true)
output:
filename: "gravity_result.csv" # The name of the output file

Output
The executable produces a CSV file containing V, Vx, Vy, Vz,
Vxx, Vyy, Vzz, Vxy, Vxz, Vyz for every
computation point P.
Testing
The project uses GoogleTest for testing. In oder to execute those
tests just execute the following command in the build directory:
ctest

For the Python test suite, please execute the following command in the repository root folder:
pytest

Contributing
We are happy to accept contributions to the project in the form of
suggestions, bug reports and pull requests. Please have a look at
the contributing guidelines for more information.