hermite.h

// Description: Cubic and quintic Hermite polynomials
// Documentation: interpolation.txt

#ifndef PASTELMATH_HERMITE_H
#define PASTELMATH_HERMITE_H

#include "pastel/sys/mytypes.h"

namespace Pastel
{

    //! Evaluates a cubic Hermite curve.

    /*!
   A cubic Hermite curve f is a cubic polynomial
   that satisfies the following constraints:
   f(0) = startPoint
   f(1) = endPoint
   f'(0) = startVelocity
   f'(1) = endVelocity

   This can be used to interpolate two points
   and their velocity vectors.

   If startVelocity = endVelocity = 0,
   then you should consider the 'smoothStep()' functions
   in 'pastel/math/interpolation/smoothstep.h' instead.
   */

    template <
        typename PointType,
        typename VectorType,
        typename Real>
        PointType cubicHermite(
        const PointType& startPoint,
        const VectorType& startVelocity,
        const PointType& endPoint,
        const VectorType& endVelocity,
        const Real& time);

    //! Evaluates a quintic Hermite curve.

    /*!
   A quintic Hermite curve f is a quintic polynomial
   that satisfies the following constraints:
   f(0) = startPoint
   f(1) = endPoint
   f'(0) = startVelocity
   f'(1) = endVelocity
   f'(0) = startAcceleration
   f'(1) = endAcceleration

   This can be used to interpolate two points,
   their velocity vectors and their acceleration
   vectors.

   If startVelocity = endVelocity = 0 and
   startAcceleration = endAcceleration = 0
   then you should consider the 'smoothStep()' functions
   in 'pastel/math/interpolation/smoothstep.h' instead.
   */

    template <
        typename PointType,
        typename VectorType,
        typename Real>
        PointType quinticHermite(
        const PointType& startPoint,
        const VectorType& startVelocity,
        const VectorType& startAcceleration,
        const PointType& endPoint,
        const VectorType& endVelocity,
        const VectorType& endAcceleration,
        const Real& time);

}

#include "pastel/math/hermite.hpp"

#endif