GeometricEquations.cpp

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/* Author: Jonathan Gammell*/

// This file's header
#include "ompl/util/GeometricEquations.h"

// For gamma function
#include <cmath>

// For pi definition
#include <boost/math/constants/constants.hpp>

// OMPL exceptions
#include "ompl/util/Exception.h"

double ompl::nBallMeasure(unsigned int N, double r)
{
    return std::pow(std::sqrt(boost::math::constants::pi<double>()) * r, static_cast<double>(N)) /
           std::tgamma(static_cast<double>(N) / 2.0 + 1.0);
}

double ompl::unitNBallMeasure(unsigned int N)
{
    // This is the radius version with r removed (as it is 1) for efficiency
    return std::pow(std::sqrt(boost::math::constants::pi<double>()), static_cast<double>(N)) /
           std::tgamma(static_cast<double>(N) / 2.0 + 1.0);
}

double ompl::prolateHyperspheroidMeasure(unsigned int N, double dFoci, double dTransverse)
{
    // Sanity check input
    if (dTransverse < dFoci)
    {
        throw Exception("Transverse diameter cannot be less than the minimum transverse diameter.");
    }

    // Variable
    // The conjugate diameter:
    double conjugateDiameter;
    // The Lebesgue measure return value
    double lmeas;

    // Calculate the conjugate diameter:
    conjugateDiameter = std::sqrt(dTransverse * dTransverse - dFoci * dFoci);

    // Calculate the volume
    // First multiply together the radii, noting that the first radius is the transverse diameter/2.0, and the other N-1
    // are the conjugate diameter/2.0
    lmeas = dTransverse / 2.0;
    for (unsigned int i = 1u; i < N; ++i)
    {
        lmeas = lmeas * conjugateDiameter / 2.0;
    }

    // Then multiply by the volume of the unit n-ball.
    lmeas = lmeas * unitNBallMeasure(N);

    // Finally return:
    return lmeas;
}