ellipsoid.h

// Description: Algorithms for ellipsoids

#ifndef PASTELGEOMETRY_ELLIPSOID_H
#define PASTELGEOMETRY_ELLIPSOID_H

#include "pastel/math/matrix/matrix.h"

namespace Pastel
{

    //! Computes quadratic form coefficients for an ellipse.
    /*!
   An origin-centered ellipsoid Q is be given by:
   Q = {p | f(p) = 1}
   where
   f(p) = p S p^T
   p is in R^(1 x n)
   S is in R^(n x n) and symmetric positive semi-definite

   This function returns a matrix S such that
   the set Q is an image of the unit sphere under
   the given linear transformation.
   */

    template <typename Real>
    Matrix<Real> ellipsoidQuadraticForm(
        const Matrix<Real>& basis);

    //! Returns a minimum volume aligned box bounding the given ellipse.
    template <typename Real>
    AlignedBox<Real> ellipsoidBoundingAlignedBox(
        const Matrix<Real>& quadraticForm);

}

#include "pastel/geometry/shape/ellipsoid.hpp"

#endif