/*==LICENSE==*

CyanWorlds.com Engine - MMOG client, server and tools
Copyright (C) 2011 Cyan Worlds, Inc.

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*==LICENSE==*/
#include "plAnimEaseTypes.h"
#include "plAnimTimeConvert.h"

///////////////////////////////////////////////////////////////////////////////////////////////

plATCEaseCurve *plATCEaseCurve::CreateEaseCurve(UInt8 type, hsScalar minLength, hsScalar maxLength, hsScalar length, 
												hsScalar startSpeed, hsScalar goalSpeed)
{
	if (type == plAnimEaseTypes::kConstAccel)
		return TRACKED_NEW plConstAccelEaseCurve(minLength, maxLength, length, startSpeed, goalSpeed);
	if (type == plAnimEaseTypes::kSpline)
		return TRACKED_NEW plSplineEaseCurve(minLength, maxLength, length, startSpeed, goalSpeed);

	return nil;
}

void plATCEaseCurve::RecalcToSpeed(hsScalar startSpeed, hsScalar goalSpeed, hsBool preserveRate /* = false */)
{
	hsScalar rate = 1;

	if (fSpeed == goalSpeed && fStartSpeed == startSpeed) // already there, no need to do anything
		return;

	if (preserveRate)
		rate = (fSpeed - fStartSpeed) / fLength;

	fStartSpeed = startSpeed;
	fSpeed = goalSpeed;

	if (preserveRate)
		SetLengthOnRate(rate);
}

void plATCEaseCurve::SetLengthOnRate(hsScalar rate)
{
	fLength = (fSpeed - fStartSpeed) / rate;
	if (fLength < 0)
		fLength = -fLength;
}

hsScalar plATCEaseCurve::GetMinDistance()
{
	if (fMinLength == 0)
		return 0;
	
	hsScalar oldLength = fLength;
	fLength = fMinLength;
	hsScalar result = PositionGivenTime(fMinLength);
	fLength = oldLength;
	return result;
}

hsScalar plATCEaseCurve::GetMaxDistance()
{
	if (fMaxLength == 0)
		return 0;

	hsScalar oldLength = fLength;
	fLength = fMaxLength;
	hsScalar result = PositionGivenTime(fMaxLength);
	fLength = oldLength;
	return result;
}

hsScalar plATCEaseCurve::GetNormDistance()
{
	if (fNormLength == 0)
		return 0;
	
	hsScalar oldLength = fLength;
	fLength = fNormLength;
	hsScalar result = PositionGivenTime(fNormLength);
	fLength = oldLength;
	return result;
}

void plATCEaseCurve::Read(hsStream *s, hsResMgr *mgr)
{
	plCreatable::Read(s, mgr);

	fMinLength = s->ReadSwapScalar();
	fMaxLength = s->ReadSwapScalar();
	fNormLength = fLength = s->ReadSwapScalar();
	fStartSpeed = s->ReadSwapScalar();
	fSpeed = s->ReadSwapScalar();
	fBeginWorldTime = s->ReadSwapDouble();
}

void plATCEaseCurve::Write(hsStream *s, hsResMgr *mgr)
{
	plCreatable::Write(s, mgr);

	s->WriteSwapScalar(fMinLength);
	s->WriteSwapScalar(fMaxLength);
	s->WriteSwapScalar(fNormLength);
	s->WriteSwapScalar(fStartSpeed);
	s->WriteSwapScalar(fSpeed);
	s->WriteSwapDouble(fBeginWorldTime);
}

///////////////////////////////////////////////////////////////////////////////////////////////

plConstAccelEaseCurve::plConstAccelEaseCurve()
{
	fMinLength = fMaxLength = fNormLength = fLength = 1;
	fBeginWorldTime = 0;

	RecalcToSpeed(0, 1);
}

plConstAccelEaseCurve::plConstAccelEaseCurve(hsScalar minLength, hsScalar maxLength, hsScalar length, 
											 hsScalar startSpeed, hsScalar goalSpeed)
{
	fMinLength = minLength;
	fMaxLength = maxLength;
	fNormLength = fLength = length; 
	fBeginWorldTime = 0;

	RecalcToSpeed(startSpeed, goalSpeed);
}

plATCEaseCurve *plConstAccelEaseCurve::Clone() const
{
	plConstAccelEaseCurve *curve = TRACKED_NEW plConstAccelEaseCurve;
	curve->fStartSpeed = fStartSpeed;
	curve->fMinLength = fMinLength;
	curve->fMaxLength = fMaxLength;
	curve->fNormLength = fNormLength;
	curve->fBeginWorldTime = fBeginWorldTime;
	curve->fLength = fLength;
	curve->fSpeed = fSpeed;

	return curve;
}

void plConstAccelEaseCurve::SetLengthOnDistance(hsScalar dist)
{
	fLength = 2 * dist / (fSpeed + fStartSpeed);
}

hsScalar plConstAccelEaseCurve::PositionGivenTime(hsScalar time) const
{
	return (hsScalar)(fStartSpeed * time + (0.5 * (fSpeed - fStartSpeed) / fLength) * time * time);
}

hsScalar plConstAccelEaseCurve::VelocityGivenTime(hsScalar time) const
{
	return fStartSpeed + ((fSpeed - fStartSpeed) / fLength) * time;
}

hsScalar plConstAccelEaseCurve::TimeGivenVelocity(hsScalar velocity) const
{
	return (velocity - fStartSpeed) / ((fSpeed - fStartSpeed) / fLength);
}

///////////////////////////////////////////////////////////////////////////////////////////////

plSplineEaseCurve::plSplineEaseCurve()
{
	fMinLength = fMaxLength = fNormLength = fLength = 1;
	fBeginWorldTime = 0;

	RecalcToSpeed(0, 1);
}

plSplineEaseCurve::plSplineEaseCurve(hsScalar minLength, hsScalar maxLength, hsScalar length, 
									 hsScalar startSpeed, hsScalar goalSpeed)
{
	fMinLength = minLength;
	fMaxLength = maxLength;
	fNormLength = fLength = length; 
	fBeginWorldTime = 0;

	RecalcToSpeed(startSpeed, goalSpeed);
}

plATCEaseCurve *plSplineEaseCurve::Clone() const
{
	plSplineEaseCurve *curve = TRACKED_NEW plSplineEaseCurve;
	curve->fStartSpeed = fStartSpeed;
	curve->fMinLength = fMinLength;
	curve->fMaxLength = fMaxLength;
	curve->fNormLength = fNormLength;
	curve->fBeginWorldTime = fBeginWorldTime;
	curve->fLength = fLength;
	curve->fSpeed = fSpeed;

	int i;
	for (i = 0; i < 4; i++)
		curve->fCoef[i] = fCoef[i];

	return curve;
}

void plSplineEaseCurve::RecalcToSpeed(hsScalar startSpeed, hsScalar goalSpeed, hsBool preserveRate /* = false */)
{
	plATCEaseCurve::RecalcToSpeed(startSpeed, goalSpeed, preserveRate);
	
	// These are greatly simplified because the in/out tangents are always zero
	// Note: "b" is always zero for the ease splines we're currently doing (and will remain that way
	//       so long as the initial acceleration is zero. Can optimize a bit of the eval math to take 
	//       advantage of this.
	hsScalar a, b, c, d;

	a = fStartSpeed;
	b = 0;
	c = -3 * fStartSpeed + 3 * fSpeed;
	d = 2 * fStartSpeed - 2 * fSpeed;

	fCoef[0] = a;
	fCoef[1] = b;
	fCoef[2] = c;
	fCoef[3] = d;
}

void plSplineEaseCurve::SetLengthOnDistance(hsScalar dist)
{
	hsScalar curDist = PositionGivenTime(fLength);

	fLength = fLength * dist / curDist;
}

hsScalar plSplineEaseCurve::PositionGivenTime(hsScalar time) const
{
	hsScalar t1, t2, t3, t4;
	t1 = time / fLength;
	t2 = t1 * t1;
	t3 = t2 * t1;
	t4 = t3 * t1;
	
	return fLength * (fCoef[0] * t1 + fCoef[1] * t2 / 2 + fCoef[2] * t3 / 3 + fCoef[3] * t4 / 4);
}

hsScalar plSplineEaseCurve::VelocityGivenTime(hsScalar time) const
{
	hsScalar t1, t2, t3;
	t1 = time / fLength;
	t2 = t1 * t1;
	t3 = t2 * t1;
	return fCoef[0] + fCoef[1] * t1 + fCoef[2] * t2 + fCoef[3] * t3;
}

hsScalar plSplineEaseCurve::TimeGivenVelocity(hsScalar velocity) const 
{
	// Code based off of Graphics Gems V, pp 11-12 and
	// http://www.worldserver.com/turk/opensource/FindCubicRoots.c.txt

	// Solving the equation: fCoef[0] + fCoef[1] * t + fCoef[2] * t^2 + fCoef[3] * t^3 - velocity = 0

	hsScalar root;
	hsScalar a = (fCoef[0] - velocity) / fCoef[3];
	hsScalar b = fCoef[1] / fCoef[3];
	hsScalar c = fCoef[2] / fCoef[3];

	hsScalar Q = (c * c - 3 * b) / 9;
	hsScalar R = (2 * c * c * c - 9 * c * b + 27 * a) / 54;
	hsScalar Q3 = Q * Q * Q;
	hsScalar D = Q3 - R * R;

	if (D >= 0) 
	{	
		// 3 roots, find the one in the range [0, 1]
		const hsScalar pi = 3.14159;
		double theta = acos(R / sqrt(Q3));
		double sqrtQ = sqrt(Q);

		root = (hsScalar)(-2 * sqrtQ * cos((theta + 4 * pi) / 3) - c / 3); // Middle root, most likely to match
		if (root < 0.f || root > 1.f)
		{
			root = (hsScalar)(-2 * sqrtQ * cos((theta + 2 * pi) / 3) - c / 3); // Lower root
			if (root < 0.f || root > 1.f)
			{
				root = (hsScalar)(-2 * sqrtQ * cos(theta / 3) - c / 3); // Upper root
			}
		}
	}
	else // One root to the equation (I don't expect this to happen for ease splines, but JIC)
	{
		double E = sqrt(-D) + pow(fabs(R), 1.f / 3.f);
		root = (hsScalar)((E + Q / E) - c / 3);
		if (R > 0)
			root = -root;
	}

	if (root < 0.f || root > 1.f)
	{
		hsAssert(false, "No valid root found while solving animation spline");
		// Either a bug, or a rare case of floating-point inaccuracy. Either way, guess
		// the proper root as either the start or end of the curve based on the velocity.
		hsScalar dStart = velocity - fStartSpeed;
		if (dStart < 0)
			dStart = -dStart;
		hsScalar dEnd = velocity - fSpeed;
		if (dEnd < 0)
			dEnd = -dEnd;

		root = (dStart < dEnd ? 0.f : 1.f);
	}

	return root * fLength;
}

void plSplineEaseCurve::Read(hsStream *s, hsResMgr *mgr)
{
	plATCEaseCurve::Read(s, mgr);

	fCoef[0] = s->ReadSwapScalar();
	fCoef[1] = s->ReadSwapScalar();
	fCoef[2] = s->ReadSwapScalar();
	fCoef[3] = s->ReadSwapScalar();
}

void plSplineEaseCurve::Write(hsStream *s, hsResMgr *mgr)
{
	plATCEaseCurve::Write(s, mgr);

	s->WriteSwapScalar(fCoef[0]);
	s->WriteSwapScalar(fCoef[1]);
	s->WriteSwapScalar(fCoef[2]);
	s->WriteSwapScalar(fCoef[3]);
}