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CryAnimation/BSplineKnots.h

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+//////////////////////////////////////////////////////////////////////
+//
+//  CryEngine Source code
+//	
+//	File:BSplineknots.h
+//  Declaration of class BSplineKnots
+//
+//	History:
+//	06/17/2002 :Created by Sergiy Migdalskiy <sergiy@crytek.de>
+//
+//////////////////////////////////////////////////////////////////////
+#pragma once
+
+//////////////////////////////////////////////////////////////
+// class BSplineKnots
+//
+// This class represents the array of knots used to calculate
+// basis functions of the given degree over the range
+// [knot[degree] .. knot [N-degree]] , N being the total number of knots
+// 
+// NOTE:
+//   order == degree+1
+//   There are always N-degree-1 control points
+//   This class incorporates neither control point nor degree info
+//////////////////////////////////////////////////////////////
+
+class BSplineKnots
+{
+public:
+	// the abscissae and ordinates
+	typedef float Time;
+	typedef float Value;
+
+	// standard scaling between Max and BSpline knot times: max time = g_nStdTicksPerSecond * bspline time
+	//enum {g_nStdTicksPerSecond = 160};
+
+	// allocates the array of the given number of knots, does NOT initialize the knots
+	BSplineKnots(int numKnots);
+	~BSplineKnots(void);
+
+	Time& operator [] (int nKnot)
+	{
+		assert (nKnot >= 0 && nKnot < m_numKnots);
+		return m_pKnots[nKnot];
+	}
+
+	Time operator [] (int nKnot) const
+	{
+		assert (nKnot >= 0 && nKnot < m_numKnots);
+		return m_pKnots[nKnot];
+	}
+
+	// searches and returns the interval to which the given time belongs.
+	// each pair of knots defines interval [k1,k2)
+	// -1 is before the 0-th knot, numKnots() is after the last knot
+	int findInterval (Time fTime)const;
+
+	// number of knots
+	int numKnots() const
+	{
+		return m_numKnots;
+	}
+
+	// returns the i-th basis function of degree d, given the time t
+	Value getBasis (int i, int d, Time t) const;
+
+	// returns the i-th basis function of degree d, given the time t and a hint, in which interval to search for it
+	Value getBasis (int i, int d, Time t, int nIntervalT) const;
+
+	// returns the time where the i-th given basis reaches its maximum
+	Time getBasisPeak (int i/*nStartKnot*/, int d/*nDegree*/);
+
+	// returns the i-th basis d-th derivative discontinuity at knot k
+	// (amplitude of the delta function)
+	Value getDelta (int i, int d, int k) const;
+
+	// Returns the P (product) penalty for knot closeness, as defined by Mary J. Lindstrom "Penalized Estimation of Free Knot Splines" 1999,
+	// logarithmic form
+	double getKnotProductPenalty(int nStartKnot, int nEndKnot);
+protected:
+	// returns the value of the basis function of degree d, given the time t
+	// the knots of the basis function start at pKnotBegin, and the first knot before t is pKnotBeforeT
+	Value getBasis (const Time* pKnotBegin, int d, Time t, const Time* pKnotBeforeT)const;
+
+	// number of knots
+	int m_numKnots;
+
+	// the array of knots
+	// no assumption is made about the multiplicity of knots
+	Time *m_pKnots;
+};