kbspline.h

// Description: Kochanek-Bartels spline
// Documentation: interpolation.txt

#ifndef PASTELMATH_KBSPLINE_H
#define PASTELMATH_KBSPLINE_H

#include "pastel/sys/mytypes.h"
#include "pastel/math/hermite.h"

namespace Pastel
{

    //! Evaluates a Kochanek-Bartels spline.

    /*!
   A Kochanek-Bartels spline can be used to
   interpolate a sequence of points
   p = (p1, p2, ...) excluding the first point.
   The curve can modified by choosing different
   parameters for 'tension', 'bias' and
   'continuity'. Sometimes these curves are
   also called TCB-splines. A segment of
   this curve is a special case of a cubic
   Hermite curve, see cubicHermite().
   */
    template <
        typename PointType,
        typename Real>
        PointType kbSpline(
        const PointType& previousPoint,
        const PointType& startPoint,
        const PointType& endPoint,
        const Real& tension,
        const Real& bias,
        const Real& continuity,
        const Real& time)
    {
        Real mTension(1 - tension);
        Real mBias(1 - bias);
        Real pBias(1 + bias);
        Real mContinuity(1 - continuity);
        Real pContinuity(1 + continuity);

        Real baFactor1 =
            mTension * pBias *
            mContinuity * Real(0.5);
        Real cbFactor1 =
            mTension * mBias *
            pContinuity * Real(0.5);
        Real baFactor2 =
            mTension * pBias *
            pContinuity * Real(0.5);
        Real cbFactor2 =
            mTension * mBias *
            mContinuity * Real(0.5);

        return hermite(
            startPoint,
            (startPoint - previousPoint) * baFactor1 +
            (endPoint - startPoint) * cbFactor1,
            endPoint,
            (startPoint - previousPoint) * baFactor2 +
            (endPoint - startPoint) * cbFactor2,
            time);
    }

}

#endif