//-----------------------------------------------------------------------
    Quaternion Quaternion::Slerp (Real fT, const Quaternion& rkP,
        const Quaternion& rkQ, bool shortestPath)
    {
        Real fCos = rkP.Dot(rkQ);
        Radian fAngle ( Math::ACos(fCos) );

        if ( Math::Abs(fAngle.valueRadians()) < ms_fEpsilon )
            return rkP;

        Real fSin = Math::Sin(fAngle);
        Real fInvSin = 1.0/fSin;
        Real fCoeff0 = Math::Sin((1.0-fT)*fAngle)*fInvSin;
        Real fCoeff1 = Math::Sin(fT*fAngle)*fInvSin;
        // Do we need to invert rotation?
        if (fCos < 0.0f && shortestPath)
        {
            fCoeff0 = -fCoeff0;
            // taking the complement requires renormalisation
            Quaternion t(fCoeff0*rkP + fCoeff1*rkQ);
            t.normalise();
            return t;
        }
        else
        {
            return fCoeff0*rkP + fCoeff1*rkQ;
        }
    }
Ejemplo n.º 2
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// ******************************************************************************** //
// The spherical interpolation for union quaternions
Quaternion OrE::Math::Slerp(const Quaternion& a, const Quaternion& b, const float t)
{
	float fOmega = Arccos( Clamp(a.Dot(b), -1.0f, 1.0f) );
	float f1 = Sin( fOmega * (1.0f-t) );
	float f2 = Sin( fOmega * t );
	return Quaternion( a.r*f1+b.r*f2, a.i*f1+b.i*f2, a.j*f1+b.j*f2, a.k*f1+b.k*f2 );
}
Ejemplo n.º 3
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 //! \verbatim
 //! Real Quaternion.dot( Quaternion other )
 //! \endverbatim
 void Quaternion::jsDot( const FunctionCallbackInfo<v8::Value>& args )
 {
   Quaternion* ptr = unwrap( args.Holder() );
   Quaternion* other = Util::extractQuaternion( 0, args );
   if ( !other )
     return;
   args.GetReturnValue().Set( ptr->Dot( *other ) );
 }
Ejemplo n.º 4
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Quaternion<Real>
Quaternion<Real>::Slerp(Real fT, const Quaternion& rkP, const Quaternion& rkQ)
{
  Real fCos = rkP.Dot(rkQ);
  Real fAngle = Math<Real>::ACos(fCos);

  if (Math<Real>::FAbs(fAngle) < Math<Real>::EPSILON)
    return rkP;

  Real fSin = Math<Real>::Sin(fAngle);
  Real fInvSin = ((Real) 1.0) / fSin;
  Real fCoeff0 = Math<Real>::Sin((((Real) 1.0) - fT) * fAngle) * fInvSin;
  Real fCoeff1 = Math<Real>::Sin(fT* fAngle) * fInvSin;
  return fCoeff0 * rkP + fCoeff1 * rkQ;
}
Ejemplo n.º 5
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    //-----------------------------------------------------------------------
    Quaternion Quaternion::nlerp(Real fT, const Quaternion& rkP,
        const Quaternion& rkQ, bool shortestPath)
    {
		Quaternion result;
        Real fCos = rkP.Dot(rkQ);
		if (fCos < 0.0f && shortestPath)
		{
			result = rkP + fT * ((-rkQ) - rkP);
		}
		else
		{
			result = rkP + fT * (rkQ - rkP);
		}
        result.normalise();
        return result;
    }
Ejemplo n.º 6
0
/*
	为什么下面是-rkQ?
	因为两者角度大于180度时,需要把第二个角度减去360度,表示从反方向变换到rkQ
	令本来rkQ的角度是r, 变过以后就是r-360
	而四元数采取的是cos(r/2), sin(r/2)*xxx
	于是r/2 变成r/2 -180
	而cos(r/2-180) =-cos(r/2), sin(r/2-180) =-sin(r/2)
	所以得到的是-rkQ
*/
Quaternion Quaternion::nlerp(float fT, const Quaternion& rkP,
    const Quaternion& rkQ, bool shortestPath)
{
	Quaternion result;
    float fCos = rkP.Dot(rkQ);
	if (fCos < 0.0f && shortestPath)
	{
		result = rkP + ((-rkQ) - rkP)*fT;
	}
	else
	{
		result = rkP +(rkQ - rkP)*fT;
	}
    result.Normalize();
    return result;
}
Ejemplo n.º 7
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    //-----------------------------------------------------------------------
    Quaternion Quaternion::SlerpExtraSpins (Real fT,
        const Quaternion& rkP, const Quaternion& rkQ, int iExtraSpins)
    {
        Real fCos = rkP.Dot(rkQ);
        Radian fAngle ( Math::ACos(fCos) );

        if ( Math::Abs(fAngle.valueRadians()) < msEpsilon )
            return rkP;

        Real fSin = Math::Sin(fAngle);
        Radian fPhase ( Math::PI*iExtraSpins*fT );
        Real fInvSin = 1.0f/fSin;
        Real fCoeff0 = Math::Sin((1.0f-fT)*fAngle - fPhase)*fInvSin;
        Real fCoeff1 = Math::Sin(fT*fAngle + fPhase)*fInvSin;
        return fCoeff0*rkP + fCoeff1*rkQ;
    }
Ejemplo n.º 8
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    //-----------------------------------------------------------------------
    Quaternion Quaternion::SlerpExtraSpins (float fT,
        const Quaternion& rkP, const Quaternion& rkQ, int iExtraSpins)
    {
        float fCos = rkP.Dot(rkQ);
        float fAngle ( acosf(fCos) );

        if ( fabs(fAngle) < ms_fEpsilon )
            return rkP;

        float fSin = sinf(fAngle);
        float fPhase (float(M_PI)*iExtraSpins*fT );
        float fInvSin = 1.0f/fSin;
        float fCoeff0 = sinf((1.0f-fT)*fAngle - fPhase)*fInvSin;
        float fCoeff1 = sinf(fT*fAngle + fPhase)*fInvSin;
        return fCoeff0*rkP + fCoeff1*rkQ;
    }
Ejemplo n.º 9
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Quaternion<Real>
Quaternion<Real>::SlerpExtraSpins(Real fT, const Quaternion& rkP, const Quaternion& rkQ, int iExtraSpins)
{
  Real fCos = rkP.Dot(rkQ);
  Real fAngle = Math<Real>::ACos(fCos);

  if (Math<Real>::FAbs(fAngle) < Math<Real>::EPSILON)
    return rkP;

  Real fSin = Math<Real>::Sin(fAngle);
  Real fPhase = Math<Real>::PI* iExtraSpins* fT;
  Real fInvSin = ((Real) 1.0) / fSin;
  Real fCoeff0 = Math<Real>::Sin((((Real) 1.0) - fT) * fAngle - fPhase) * fInvSin;
  Real fCoeff1 = Math<Real>::Sin(fT* fAngle + fPhase) * fInvSin;
  return fCoeff0 * rkP + fCoeff1 * rkQ;
}
Ejemplo n.º 10
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Quaternion Quaternion::Slerp(const Quaternion &first, const Quaternion &second, float interpolationCoefficient)
{
	float dot = first.Dot(second);

	if(dot > s_quaternionDotTolerance)
		return Lerp(first, second, interpolationCoefficient);

	dot = Clamp(dot, -1.0f, 1.0f);

	float theta = acosf(dot) * interpolationCoefficient;

	Quaternion third(second - first * dot);

	third.NormalizeThis();

	return first * cosf(theta) + third * sinf(theta);
}
Ejemplo n.º 11
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const Ellipsoid3<Real> MergeEllipsoids (const Ellipsoid3<Real>& ellipsoid0,
    const Ellipsoid3<Real>& ellipsoid1)
{
    Ellipsoid3<Real> merge;

    // compute the average of the input centers
    merge.Center = ((Real)0.5)*(ellipsoid0.Center + ellipsoid1.Center);

    // bounding ellipsoid orientation is average of input orientations
    Quaternion<Real> q0(ellipsoid0.Axis), q1(ellipsoid1.Axis);
    if (q0.Dot(q1) < (Real)0)
    {
        q1 = -q1;
    }
    Quaternion<Real> q = q0 + q1;
    q = Math<Real>::InvSqrt(q.Dot(q))*q;
    q.ToRotationMatrix(merge.Axis);

    // Project the input ellipsoids onto the axes obtained by the average
    // of the orientations and that go through the center obtained by the
    // average of the centers.
    for (int i = 0; i < 3; ++i)
    {
        // Projection axis.
        Line3<Real> line(merge.Center, merge.Axis[i]);

        // Project ellipsoids onto the axis.
        Real min0, max0, min1, max1;
        ProjectEllipsoid(ellipsoid0, line, min0, max0);
        ProjectEllipsoid(ellipsoid1, line, min1, max1);

        // Determine the smallest interval containing the projected
        // intervals.
        Real maxIntr = (max0 >= max1 ? max0 : max1);
        Real minIntr = (min0 <= min1 ? min0 : min1);

        // Update the average center to be the center of the bounding box
        // defined by the projected intervals.
        merge.Center += line.Direction*(((Real)0.5)*(minIntr + maxIntr));

        // Compute the extents of the box based on the new center.
        merge.Extent[i] = ((Real)0.5)*(maxIntr - minIntr);
    }

    return merge;
}
Ejemplo n.º 12
0
	Quaternion Quaternion::Slerp(float pT, Quaternion &pq)
	{
		//We calculate the angle spread between both quaternions
		float AngleCos = pq.Dot(*this);
		float Angle = qACos(AngleCos); //see the function ACos above

		if (Angle < MINFLOAT)
		{
			return Quaternion(*this);
		}
		//We calculate the interpolated angle and deduce the resulting quaternion
		float InvAngleSin = (1.0f / sin(Angle));

		float Coeff0 = sin((1 - pT) * Angle) * InvAngleSin;
		float Coeff1 = sin(pT * Angle) * InvAngleSin;
		return Quaternion((*this * Coeff0) + (pq * Coeff1));
	}
Ejemplo n.º 13
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Quaternion Quaternion::Slerp (Real fT, const Quaternion& rkP,
        const Quaternion& rkQ, bool shortestPath)
{
    Real fCos = rkP.Dot(rkQ);
    Quaternion rkT;

    // Do we need to invert rotation?
    if (fCos < 0.0f && shortestPath)
    {
        fCos = -fCos;
        rkT = -rkQ;
    }
    else
    {
        rkT = rkQ;
    }

    if (Math::Abs(fCos) < 1 - ms_fEpsilon)
    {
        // Standard case (slerp)
        Real fSin = Math::Sqrt(1 - Math::Sqr(fCos));
        Radian fAngle = Math::ATan2(fSin, fCos);
        Real fInvSin = 1.0f / fSin;
        Real fCoeff0 = Math::Sin((1.0f - fT) * fAngle) * fInvSin;
        Real fCoeff1 = Math::Sin(fT * fAngle) * fInvSin;
        return fCoeff0 * rkP + fCoeff1 * rkT;
    }
    else
    {
        // There are two situations:
        // 1. "rkP" and "rkQ" are very close (fCos ~= +1), so we can do a linear
        // interpolation safely.
        // 2. "rkP" and "rkQ" are almost inverse of each other (fCos ~= -1), there
        // are an infinite number of possibilities interpolation. but we haven't
        // have method to fix this case, so just use linear interpolation here.
        Quaternion t = (1.0f - fT) * rkP + fT * rkT;

        // taking the complement requires renormalisation
        t.normalise();
        return t;
    }
}
Ejemplo n.º 14
0
/*
	球形插值: 以恒定的速率描述两四元数之间的曲线
	即得到的效果是角度的线性插值θ=(1-t)*θ1+t*θ2
	结论是: q(t) = q1*sin(1-t)(θ)/sin(θ) +q2*sin(tθ)/sin(θ)
	因为涉及到tan的计算,所以需要对cos的值进行一个范围的判断,防止越界
*/
Quaternion Quaternion::slerp (float fT, const Quaternion& rkP,
	  const Quaternion& rkQ, bool shortestPath)
  {
	  float fCos = rkP.Dot(rkQ);
	  Quaternion rkT;

	  // Do we need to invert rotation?
	  if (fCos < 0.0f && shortestPath)
	  {
		  fCos = -fCos;
		  rkT = -rkQ;
	  }
	  else
	  {
		  rkT = rkQ;
	  }

	  if (fabs(fCos) < 1 - msEpsilon)
	  {
		  // Standard case (slerp)
		  float fSin = sqrtf(1 - fCos*fCos);
		  float fAngle = atan2f(fSin, fCos);
		  float fInvSin = 1.0f / fSin;
		  float fCoeff0 = sinf((1.0f - fT) * fAngle) * fInvSin;
		  float fCoeff1 = sinf(fT * fAngle) * fInvSin;
		  return  rkP *fCoeff0 + rkT*fCoeff1;
	  }
	  else
	  {
		  // There are two situations:
		  // 1. "rkP" and "rkQ" are very close (fCos ~= +1), so we can do a linear
		  //	interpolation safely.
		  // 2. "rkP" and "rkQ" are almost inverse of each other (fCos ~= -1), there
		  //	are an infinite number of possibilities interpolation. but we haven't
		  //	have method to fix this case, so just use linear interpolation here.
		  Quaternion t =  rkP  * (1.0f - fT)+ rkT * fT ;
		  // taking the complement requires renormalisation
		  t.Normalize();
		  return t;
	  }
  }
Ejemplo n.º 15
0
	//-----------------------------------------------------------------------
	Quaternion Quaternion::Slerp(Real fT, const Quaternion& rkP,
		const Quaternion& rkQ, bool shortestPath)
	{
		Real fCos = rkP.Dot(rkQ);
		Quaternion rkT;

		// 需要翻转旋转?
		if (fCos < 0.0f && shortestPath)
		{
			fCos = -fCos;
			rkT = -rkQ;
		}
		else
		{
			rkT = rkQ;
		}

		if (Math::Abs(fCos) < 1 - msEpsilon)
		{
			// 正常情况 (slerp)
			Real fSin = Math::Sqrt(1 - Math::Sqr(fCos));
			Radian fAngle = Math::ATan2(fSin, fCos);
			Real fInvSin = 1.0f / fSin;
			Real fCoeff0 = Math::Sin((1.0f - fT) * fAngle.valueRadians()) * fInvSin;
			Real fCoeff1 = Math::Sin(fT * fAngle.valueRadians()) * fInvSin;
			return fCoeff0 * rkP + fCoeff1 * rkT;
		}
		else
		{
			// 这有两种情况
			// 1. "rkP" 和 "rkQ" 是非常接近(fCos ~= +1), 所以我们能做安全的做线性插值
			// 2. "rkP" 和 "rkQ" 几乎是每一个 (fCos ~= -1)的反转,这就有无数种插值的可能性。但是我们不可能有修正这个问题的方法,
			// 所有就在这里用线性插值
			Quaternion t = (1.0f - fT) * rkP + fT * rkT;
			// 使这个分量重新标准化
			t.normalise();
			return t;
		}
	}
Ejemplo n.º 16
0
Box3<Real> Wml::MergeBoxes (const Box3<Real>& rkBox0,
    const Box3<Real>& rkBox1)
{
    // construct a box that contains the input boxes
    Box3<Real> kBox;

    // The first guess at the box center.  This value will be updated later
    // after the input box vertices are projected onto axes determined by an
    // average of box axes.
    kBox.Center() = ((Real)0.5)*(rkBox0.Center() + rkBox1.Center());

    // A box's axes, when viewed as the columns of a matrix, form a rotation
    // matrix.  The input box axes are converted to quaternions.  The average
    // quaternion is computed, then normalized to unit length.  The result is
    // the slerp of the two input quaternions with t-value of 1/2.  The result
    // is converted back to a rotation matrix and its columns are selected as
    // the merged box axes.
    Quaternion<Real> kQ0, kQ1;
    kQ0.FromRotationMatrix(rkBox0.Axes());
    kQ1.FromRotationMatrix(rkBox1.Axes());
    if ( kQ0.Dot(kQ1) < 0.0f )
        kQ1 = -kQ1;

    Quaternion<Real> kQ = kQ0 + kQ1;
    Real fInvLength = Math<Real>::InvSqrt(kQ.Dot(kQ));
    kQ = fInvLength*kQ;
    kQ.ToRotationMatrix(kBox.Axes());

    // Project the input box vertices onto the merged-box axes.  Each axis
    // D[i] containing the current center C has a minimum projected value
    // pmin[i] and a maximum projected value pmax[i].  The corresponding end
    // points on the axes are C+pmin[i]*D[i] and C+pmax[i]*D[i].  The point C
    // is not necessarily the midpoint for any of the intervals.  The actual
    // box center will be adjusted from C to a point C' that is the midpoint
    // of each interval,
    //   C' = C + sum_{i=0}^2 0.5*(pmin[i]+pmax[i])*D[i]
    // The box extents are
    //   e[i] = 0.5*(pmax[i]-pmin[i])

    int i, j;
    Real fDot;
    Vector3<Real> akVertex[8], kDiff;
    Vector3<Real> kMin = Vector3<Real>::ZERO;
    Vector3<Real> kMax = Vector3<Real>::ZERO;

    rkBox0.ComputeVertices(akVertex);
    for (i = 0; i < 8; i++)
    {
        kDiff = akVertex[i] - kBox.Center();
        for (j = 0; j < 3; j++)
        {
            fDot = kDiff.Dot(kBox.Axis(j));
            if ( fDot > kMax[j] )
                kMax[j] = fDot;
            else if ( fDot < kMin[j] )
                kMin[j] = fDot;
        }
    }

    rkBox1.ComputeVertices(akVertex);
    for (i = 0; i < 8; i++)
    {
        kDiff = akVertex[i] - kBox.Center();
        for (j = 0; j < 3; j++)
        {
            fDot = kDiff.Dot(kBox.Axis(j));
            if ( fDot > kMax[j] )
                kMax[j] = fDot;
            else if ( fDot < kMin[j] )
                kMin[j] = fDot;
        }
    }

    // [kMin,kMax] is the axis-aligned box in the coordinate system of the
    // merged box axes.  Update the current box center to be the center of
    // the new box.  Compute the extens based on the new center.
    for (j = 0; j < 3; j++)
    {
        kBox.Center() += (((Real)0.5)*(kMax[j]+kMin[j]))*kBox.Axis(j);
        kBox.Extent(j) = ((Real)0.5)*(kMax[j]-kMin[j]);
    }

    return kBox;
}
Ejemplo n.º 17
0
Box3<Real> MergeBoxes (const Box3<Real>& box0, const Box3<Real>& box1)
{
    // Construct a box that contains the input boxes.
    Box3<Real> box;

    // The first guess at the box center.  This value will be updated later
    // after the input box vertices are projected onto axes determined by an
    // average of box axes.
    box.Center = ((Real)0.5)*(box0.Center + box1.Center);

    // A box's axes, when viewed as the columns of a matrix, form a rotation
    // matrix.  The input box axes are converted to quaternions.  The average
    // quaternion is computed, then normalized to unit length.  The result is
    // the slerp of the two input quaternions with t-value of 1/2.  The result
    // is converted back to a rotation matrix and its columns are selected as
    // the merged box axes.
    Quaternion<Real> q0, q1;
    q0.FromRotationMatrix(box0.Axis);
    q1.FromRotationMatrix(box1.Axis);
    if (q0.Dot(q1) < (Real)0)
    {
        q1 = -q1;
    }

    Quaternion<Real> q = q0 + q1;
    Real invLength = Math<Real>::InvSqrt(q.Dot(q));
    q = invLength*q;
    q.ToRotationMatrix(box.Axis);

    // Project the input box vertices onto the merged-box axes.  Each axis
    // D[i] containing the current center C has a minimum projected value
    // min[i] and a maximum projected value max[i].  The corresponding end
    // points on the axes are C+min[i]*D[i] and C+max[i]*D[i].  The point C
    // is not necessarily the midpoint for any of the intervals.  The actual
    // box center will be adjusted from C to a point C' that is the midpoint
    // of each interval,
    //   C' = C + sum_{i=0}^2 0.5*(min[i]+max[i])*D[i]
    // The box extents are
    //   e[i] = 0.5*(max[i]-min[i])

    int i, j;
    Real dot;
    Vector3<Real> vertex[8], diff;
    Vector3<Real> pmin = Vector3<Real>::ZERO;
    Vector3<Real> pmax = Vector3<Real>::ZERO;

    box0.ComputeVertices(vertex);
    for (i = 0; i < 8; ++i)
    {
        diff = vertex[i] - box.Center;
        for (j = 0; j < 3; ++j)
        {
            dot = diff.Dot(box.Axis[j]);
            if (dot > pmax[j])
            {
                pmax[j] = dot;
            }
            else if (dot < pmin[j])
            {
                pmin[j] = dot;
            }
        }
    }

    box1.ComputeVertices(vertex);
    for (i = 0; i < 8; ++i)
    {
        diff = vertex[i] - box.Center;
        for (j = 0; j < 3; ++j)
        {
            dot = diff.Dot(box.Axis[j]);
            if (dot > pmax[j])
            {
                pmax[j] = dot;
            }
            else if (dot < pmin[j])
            {
                pmin[j] = dot;
            }
        }
    }

    // [min,max] is the axis-aligned box in the coordinate system of the
    // merged box axes.  Update the current box center to be the center of
    // the new box.  Compute the extents based on the new center.
    for (j = 0; j < 3; ++j)
    {
        box.Center += (((Real)0.5)*(pmax[j] + pmin[j]))*box.Axis[j];
        box.Extent[j] = ((Real)0.5)*(pmax[j] - pmin[j]);
    }

    return box;
}
Ejemplo n.º 18
0
void Animation::SetFrameOverlay( F32 frame, AnimKey &state, F32 controlFrame) const
{
  controlFrame;

  U32 i;
#if 0
  Quaternion conq;
  conq.ClearData();
  for (i = 1; i < keys.count; i++)
  {
    AnimKey &lastKey = keys[i - 1];
    AnimKey &thisKey = keys[i];

    if (controlFrame <= thisKey.frame)
    {
      // determine the current fraction to this cycle
      F32 dk = thisKey.frame - lastKey.frame;
      ASSERT( dk > 0);
      F32 dfdk  = (controlFrame - lastKey.frame) / dk;

      if (lastKey.type & animQUATERNION)
      {
        // do a parametric interpolation of the quaternion using dfdk
        conq = (thisKey.quaternion - lastKey.quaternion) * dfdk + lastKey.quaternion;
      }
      break;
    }
  }
#endif
//         0;  4; 0.923880, 0.382683, 0.0, 0.0;;,
//         0;  4; 0.898028, 0.439939, 0.0, 0.0;;,
//         0;  4; 0.868631, 0.495459, 0.0, 0.0;;,
//         0;  4; 0.770513, 0.637424, 0.0, 0.0;;,

  for (i = 1; i < keys.count; i++)
  {
    AnimKey &lastKey = keys[i - 1];
    AnimKey &thisKey = keys[i];

    if (frame <= thisKey.frame)
    {
//      LOG_DIAG( ("%f ; %f ; %f", lastKey.frame, frame, thisKey.frame) );

      ASSERT( lastKey.frame < thisKey.frame);

      // determine the current fraction to this cycle
      F32 dk = thisKey.frame - lastKey.frame;
      ASSERT( dk > 0);
      F32 dfdk  = (frame - lastKey.frame) / dk;

      if (lastKey.type & animQUATERNION)
      {
        // do a parametric interpolation of the quaternion using dfdk
        Quaternion q = (thisKey.quaternion - lastKey.quaternion) * dfdk + lastKey.quaternion;

    #if 1
        if (q.Dot( q) <= 0)
        {
          LOG_WARN( ("Quat::Set q.Dot(q) <= 0: %f %f %f %f", q.s, q.v.x, q.v.y, q.v.z) );
          LOG_WARN( ("lastKey.quat: %f %f %f %f", lastKey.quaternion.s, lastKey.quaternion.v.x, lastKey.quaternion.v.y, lastKey.quaternion.v.z) );
          LOG_WARN( ("thisKey.quat: %f %f %f %f", thisKey.quaternion.s, thisKey.quaternion.v.x, thisKey.quaternion.v.y, thisKey.quaternion.v.z) );
          LOG_WARN( ("dfdk: %f; lastKey.frame %f; thisKey.frame; frame", dfdk, lastKey.frame, thisKey.frame, frame) );

          statQuatError = TRUE;
        }
    #else
        ASSERT( q.Dot( q) > 0);
    #endif

        // blend in the quat
        //
//        q -= conq;
//        q = state.quaternion * q;
//        q.Set( PI * 0.11f, Matrix::I.right);
//        q = state.quaternion * q;
        state.Set( q );
      }
      break;
    }
  }
}
Ejemplo n.º 19
0
void Animation::Set( F32 frame, const AnimKey &lastKey, const AnimKey &thisKey, AnimKey &state)
{
  // determine the current fraction to this cycle
  F32 dk = thisKey.frame - lastKey.frame;
  ASSERT( dk > 0);
  F32 dfdk  = (frame - lastKey.frame) / dk;

//  state.type = 0;

  if (lastKey.type & animSCALE)
  {
    // do a parametric interpolation of the quaternion using dfdk
    Quaternion q = (thisKey.quaternion - lastKey.quaternion) * dfdk + lastKey.quaternion;
    
    // do a parametric interpolation of the quaternion using dfdk
    if (q.Dot( q) <= 0)
    {
      LOG_WARN( ("Quat::Set q.Dot(q) <= 0: %f %f %f %f", q.s, q.v.x, q.v.y, q.v.z) );
      LOG_WARN( ("lastKey.quat: %f %f %f %f", lastKey.quaternion.s, lastKey.quaternion.v.x, lastKey.quaternion.v.y, lastKey.quaternion.v.z) );
      LOG_WARN( ("thisKey.quat: %f %f %f %f", thisKey.quaternion.s, thisKey.quaternion.v.x, thisKey.quaternion.v.y, thisKey.quaternion.v.z) );
      LOG_WARN( ("dfdk: %f; lastKey.frame %f; thisKey.frame %f; frame %f", dfdk, lastKey.frame, thisKey.frame, frame) );

      statQuatError = TRUE;

      state.Set(thisKey.quaternion);
    }
    else
    {
      // set the matrix
      state.Set( q);
    }
    // do a parametric interpolation of the scale using dfdk
    Vector v = (thisKey.scale - lastKey.scale) * dfdk + lastKey.scale;
    // set the matrix
    state.SetScale( v);

//    state.type |= animSCALE;
  }
  else if (lastKey.type & animQUATERNION)
  {
    Quaternion q = (thisKey.quaternion - lastKey.quaternion) * dfdk + lastKey.quaternion;

    // do a parametric interpolation of the quaternion using dfdk
    if (q.Dot( q) <= 0)
    {
      LOG_WARN( ("Quat::Set q.Dot(q) <= 0: %f %f %f %f", q.s, q.v.x, q.v.y, q.v.z) );
      LOG_WARN( ("lastKey.quat: %f %f %f %f", lastKey.quaternion.s, lastKey.quaternion.v.x, lastKey.quaternion.v.y, lastKey.quaternion.v.z) );
      LOG_WARN( ("thisKey.quat: %f %f %f %f", thisKey.quaternion.s, thisKey.quaternion.v.x, thisKey.quaternion.v.y, thisKey.quaternion.v.z) );
      LOG_WARN( ("dfdk: %f; lastKey.frame %f; thisKey.frame %f; frame %f", dfdk, lastKey.frame, thisKey.frame, frame) );

      statQuatError = TRUE;

      state.Set(thisKey.quaternion);
    }
    else
    {
      // set the matrix
      state.Set( q);
    }
//    state.type |= animQUATERNION;
  }

  if (lastKey.type & animPOSITION)
  {
    // do a parametric interpolation of the pos using dfdk
    Vector v = (thisKey.position - lastKey.position) * dfdk + lastKey.position;
    // set the matrix
    state.Set( v);

//    state.type |= animPOSITION;
  }
}