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+
+/*******************************************************************************
+
+ Copyright (c) 2009, Charles McGarvey
+ All rights reserved.
+ 
+ Redistribution   and   use  in  source  and  binary  forms,  with  or  without
+ modification, are permitted provided that the following conditions are met:
+ 
+   * Redistributions  of  source  code  must retain the above copyright notice,
+     this list of conditions and the following disclaimer.
+   * Redistributions  in binary form must reproduce the above copyright notice,
+     this  list of conditions and the following disclaimer in the documentation
+     and/or other materials provided with the distribution.
+ 
+ THIS  SOFTWARE  IS  PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+ AND  ANY  EXPRESS  OR  IMPLIED  WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED.  IN  NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+ FOR  ANY  DIRECT,  INDIRECT,  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ DAMAGES  (INCLUDING,  BUT  NOT  LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+ SERVICES;  LOSS  OF  USE,  DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+ CAUSED  AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+ OR  TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+ OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+*******************************************************************************/
+
+#ifndef _INTERPOLATOR_HH_
+#define _INTERPOLATOR_HH_
+
+
+namespace dc {
+
+
+class interpolator
+{
+	void clamp(scalar& value)
+	{
+		if (value > 1.0)
+		{
+			switch (theMode)
+			{
+				case stop:
+					value = 1.0;
+					stopped = true;
+					break;
+				case repeat:
+					value -= 1.0;
+					break;
+				case oscillate:
+					value = 2.0 - value;
+					scale *= -1.0;
+					break;
+			}
+		}
+		else if (value < 0.0)
+		{
+			switch (theMode)
+			{
+				case stop:
+					value = 0.0;
+					stopped = true;
+					break;
+				case repeat:
+					value += 1.0;
+					break;
+				case oscillate:
+					value = -value;
+					scale *= -1.0;
+					break;
+			}
+		}
+	}
+
+public:
+	typedef enum
+	{
+		stop		= 0,
+		repeat		= 1,
+		oscillate	= 2
+	} mode;
+
+	void init(scalar seconds = 1.0, mode onFinish = stop)
+	{
+		scale = 1.0 / seconds;
+		alpha = 0.0;
+		setMode(onFinish);
+	}
+
+
+	void setMode(mode onFinish)
+	{
+		theMode = onFinish;
+		stopped = false;
+	}
+
+
+	void update(scalar dt)
+	{
+		if (!stopped)
+		{
+			alpha += dt * scale;
+			clamp(alpha);
+			calculate(alpha);
+		}
+	}
+
+	virtual void calculate(scalar alpha) = 0;
+
+private:
+	mode	theMode;
+	scalar	alpha;
+	scalar	scale;
+	bool	stopped;
+};
+
+template <class T>
+class interpolator_base : public interpolator
+{
+public:
+	void init(scalar seconds = 1.0, mode onFinish = stop)
+	{
+		interpolator::init(seconds, onFinish);
+
+		calculate(0.0);	// set value
+		calculate(0.0);	// set previous
+	}
+
+	void calculate(scalar alpha)
+	{
+		previous = value;
+		calculate(value, alpha);
+	}
+
+	virtual void calculate(T& value, scalar alpha) = 0;
+
+	const T& getValue()
+	{
+		return value;
+	}
+
+	const T getState(scalar alpha)
+	{
+		return cml::lerp(previous, value, alpha);
+	}
+
+private:
+	T value;
+	T previous;
+};
+
+
+template <class T, int D>
+class binomial_interpolator : public interpolator_base<T>
+{
+public:
+	binomial_interpolator() {}
+
+	explicit binomial_interpolator(const T coeff[D+1], scalar seconds = 1.0,
+			interpolator::mode onFinish = interpolator::stop)
+	{
+		init(coeff, seconds, onFinish);
+	}
+
+	void init(const T coeff[D+1], scalar seconds = 1.0,
+			interpolator::mode onFinish = interpolator::stop)
+	{
+		scalar fac[D+1];
+
+		fac[0] = 1.0;
+		fac[1] = 1.0;
+
+		// build an array of the computed factorials we will need
+		for (int i = 2; i <= D; i++)
+		{
+			fac[i] = i * fac[i - 1];
+		}
+
+		// combine the coefficients for fast updating
+		for (int i = 0; i <= D; i++)
+		{
+			// n! / (k! * (n - k)!)
+			coefficient[i] = coeff[i] * fac[D] / (fac[i] * fac[D - i]);
+		}
+
+		interpolator_base<T>::init(seconds, onFinish);
+	}
+
+
+	void calculate(T& value, scalar alpha)
+	{
+		scalar beta = 1.0 - alpha;
+
+		value = coefficient[0] * std::pow(beta, D);
+
+		for (int i = 1; i <= D; i++)
+		{
+			value += coefficient[i] * std::pow(beta, D - i) * std::pow(alpha, i);
+		}
+	}
+
+private:
+
+	T coefficient[D+1];
+};
+
+
+template <class T>
+class binomial_interpolator<T,1> : public interpolator_base<T>
+{
+public:
+	binomial_interpolator() {}
+
+	explicit binomial_interpolator(const T coeff[2], scalar seconds = 1.0,
+			interpolator::mode onFinish = interpolator::stop)
+		//interpolator_base<T>(seconds, onFinish)
+	{
+		init(coeff, seconds, onFinish);
+	}
+
+	void init(const T coeff[2], scalar seconds = 1.0,
+			interpolator::mode onFinish = interpolator::stop)
+	{
+		coefficient[0] = coeff[0];
+		coefficient[1] = coeff[1];
+
+		interpolator_base<T>::init(seconds, onFinish);
+	}
+
+
+	void calculate(T& value, scalar alpha)
+	{
+		value = cml::lerp(coefficient[0], coefficient[1], alpha);
+	}
+
+private:
+	T coefficient[2];
+};
+
+
+// Here are some aliases for more common interpolators.  Also see the
+// interpolation functions in cml for other types of interpolation such as
+// slerp and some multi-alpha interpolators.
+
+typedef binomial_interpolator<scalar, 1>	lerps;	// linear
+typedef binomial_interpolator<vector2,1>	lerpv2;
+typedef binomial_interpolator<vector3,1>	lerpv3;
+typedef binomial_interpolator<vector4,1>	lerpv4;
+
+typedef binomial_interpolator<scalar ,2>	qerps;	// quadratic
+typedef binomial_interpolator<vector2,2>	qerpv2;
+typedef binomial_interpolator<vector3,2>	qerpv3;
+typedef binomial_interpolator<vector4,2>	qerpv4;
+
+typedef binomial_interpolator<scalar ,3>	cerps;	// cubic
+typedef binomial_interpolator<vector2,3>	cerpv2;
+typedef binomial_interpolator<vector3,3>	cerpv3;
+typedef binomial_interpolator<vector4,3>	cerpv4;
+
+
+} // namespace dc
+
+#endif // _INTERPOLATOR_HH_
+
+/** vim: set ts=4 sw=4 tw=80: *************************************************/
+