Polyhedron Potential Model in C++

This project defines the gravitational potential of a polyhedron asteroid. It implements the method derived by Werner and Scheeres.

• Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia
• The gravitational potential of a homogeneous polyhedron or don't cut corners

Dependencies

1. CMake > 3.12
2. Eigen > 3.3.5
3. CGAL > 4.12-1
4. Boost > 1.68

Installation

1. Install dependencies on MacOS

   brew install cgal cmake libomp

   or for linux

   bash ./utilities/build_cmake.sh
   bash ./utilities/build_boost.sh
   bash ./utilities/build_cgal.sh
   bash ./utilities/build_eigen.sh

2. Update the submodules

   git submodule update --init --recursive 

3. LibIGL setup (sometimes)

   CMake doesn't search for matlab in libigl

   Might need to edit

   extern/libigl/shared/cmake/libigl.cmake

References

• SCHEERES, DJ, KHUSHALANI, B y WERNER, Robert A. "Estimating asteroid density distributions from shape and gravity information". Planetary and Space Science. 2000

• WERNER, Robert A. "The Gravitational Potential of a Homogeneous Polyhedron or Don't Cut Corners". Celestial Mechanics and Dynamical Astronomy. 1994

• WERNER, Robert A. "Spherical Harmonic Coefficients for the Potential of a Constant-density Polyhedron". Computers & Geosciences. 1997, vol 23

• WERNER, Robert A y SCHEERES, Daniel J. "Exterior Gravitation of a Polyhedron Derived and Compared with Harmonic and Mascon Gravitation Representations of Asteroid 4769 Castalia". Celestial Mechanics and Dynamical Astronomy. 1996, vol 65

TODO

• Remove dependency on libigl
• Bundle CGAL requirements with app (similar to how igl works)
• Remove boost dependency (probably easy)
• Analytical verification of potential https://arxiv.org/pdf/1206.3857.pdf

/ The attracting shape is a cube of dimensions 1 x 1 x 1 m of density rho = 1e6 kg/m^3
    // The analytic potential and acceleration at (1,2,3) (m) in the shape model's barycentric frame is computed
    // Assumes that G = 6.67408e-11 m^3 / (kg * s ^2)

        // Queried point for pgm validation
        arma::vec p4 = {1, 2, 3};

        arma::vec acc_true = {
            -1.273782722739791e-06,
            -2.548008881415967e-06,
            -3.823026510474731e-06
        };
        double pot_true = 0.26726619638669064 * arma::datum::G * density;