crspline.h

// Description: Catmull-Rom spline
// Documentation: interpolation.txt

#ifndef PASTELMATH_CRSPLINE_H
#define PASTELMATH_CRSPLINE_H

#include "pastel/sys/mytypes.h"

#include "pastel/math/hermite.h"

namespace Pastel
{

    //! Evaluates a Catmull-Rom spline.
    /*!
   Given a sequence of points p = (p1, p2, ...),
   a Catmull-Rom spline interpolates
   all of the points, excluding the end points,
   while obtaining C1 joins
   between segments. The segment between
   'startPoint' and 'endPoint' is given
   by the parameter interval [0, 1].
   To interpolate a sequence p, first use
   the point set (p1, p2, p3, p4) with
   time interval [0, 1], then take another
   point set (p2, p3, p4, p5) with time
   interval [0, 1]. Repeat for all points.
   A Catmull-Rom spline is a special case of
   the Kochanek-Bartels spline, see the
   kbSpline() function. Even more generally,
   one such segment is a special case of a
   cubic Hermite curve, see cubicHermite() function.
   */
    template <typename PointType,
        typename Real>
        PointType crSpline(
        const PointType& previousPoint,
        const PointType& startPoint,
        const PointType& endPoint,
        const PointType& nextPoint,
        const Real& time)
    {
        return cubicHermite(
            startPoint,
            (endPoint - previousPoint) * 0.5,
            endPoint,
            (nextPoint - startPoint) * 0.5,
            time);
    }

}

#endif