Cubic Catmull-Rom curve segment length approximation

	//
	// CatmullRomLength()
	//
	//
	//*******************************************************************************************
	template <typename T>
	T CatmullRomLength(	const CVector2<T>	&p0, 
						const CVector2<T>	&p1, 
						const CVector2<T>	&p2, 
						const CVector2<T>	&p3,
						T					t)
	{
#if 1
		static const T consts[][2] =
		{
			// coeff, root
			{ 0.118463442f, 0.046910077f },
			{ 0.239314335f, 0.230765345f },
			{ 0.284444444f, 0.500000000f },
			{ 0.239314335f, 0.769234655f },
			{ 0.118463442f, 0.953089922f }
		};
#else
		static const T consts[][2] =
		{		
			{ 0.055668567116174 / 2, (-0.978228658146057 + 1) / 2 },
			{ 0.125580369464905 / 2, (-0.887062599768095 + 1) / 2 },
			{ 0.186290210927734 / 2, (-0.730152005574049 + 1) / 2 },
			{ 0.233193764591990 / 2, (-0.519096129110681 + 1) / 2 },
			{ 0.262804544510247 / 2, (-0.269543155952345 + 1) / 2 },
			{ 0.272925086777901 / 2, (0.000000000000000 + 1) / 2 },
			{ 0.262804544510247 / 2, (0.269543155952345 + 1) / 2 },
			{ 0.233193764591990 / 2, (0.519096129110681 + 1) / 2 },
			{ 0.186290210927734 / 2, (0.730152005574049 + 1) / 2 },
			{ 0.125580369464905 / 2, (0.887062599768095 + 1) / 2 },
			{ 0.055668567116174 / 2, (0.978228658146057 + 1) / 2 }
		};
#endif

		typedef CVector2<T> T_Vec;

		const T_Vec	a = 4.5f * (p1 - p2) + 1.5f * (p3 - p0);
		const T_Vec b = 2.0f * p0 - 5.0f * p1 + 4.0f * p2 - p3;
		const T_Vec c = (p2 - p0) * 0.5f;

		T res = T(0);

		for (uint i = 0; i < NX_COUNTOF(consts); i++)
		{
			const T			tp		= t * consts[i][1];
			const T_Vec		deriv	= (a * tp + b) * tp + c;
			const T			speed	= Sqrt(deriv.Dot(deriv));

			res += consts[i][0] * speed;
		}

		return res * t;
	}
	//*******************************************************************************************