/*==LICENSE==*

CyanWorlds.com Engine - MMOG client, server and tools
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*==LICENSE==*/
#include <cmath>

#include "plAnimEaseTypes.h"
#include "plAnimTimeConvert.h"

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

plATCEaseCurve *plATCEaseCurve::CreateEaseCurve(uint8_t type, float minLength, float maxLength, float length, 
                                                float startSpeed, float goalSpeed)
{
    if (type == plAnimEaseTypes::kConstAccel)
        return new plConstAccelEaseCurve(minLength, maxLength, length, startSpeed, goalSpeed);
    if (type == plAnimEaseTypes::kSpline)
        return new plSplineEaseCurve(minLength, maxLength, length, startSpeed, goalSpeed);

    return nil;
}

void plATCEaseCurve::RecalcToSpeed(float startSpeed, float goalSpeed, bool preserveRate /* = false */)
{
    float 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(float rate)
{
    fLength = (fSpeed - fStartSpeed) / rate;
    if (fLength < 0)
        fLength = -fLength;
}

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

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

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

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

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

    fMinLength = s->ReadLEScalar();
    fMaxLength = s->ReadLEScalar();
    fNormLength = fLength = s->ReadLEScalar();
    fStartSpeed = s->ReadLEScalar();
    fSpeed = s->ReadLEScalar();
    fBeginWorldTime = s->ReadLEDouble();
}

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

    s->WriteLEScalar(fMinLength);
    s->WriteLEScalar(fMaxLength);
    s->WriteLEScalar(fNormLength);
    s->WriteLEScalar(fStartSpeed);
    s->WriteLEScalar(fSpeed);
    s->WriteLEDouble(fBeginWorldTime);
}

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

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

    RecalcToSpeed(0, 1);
}

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

    RecalcToSpeed(startSpeed, goalSpeed);
}

plATCEaseCurve *plConstAccelEaseCurve::Clone() const
{
    plConstAccelEaseCurve *curve = 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(float dist)
{
    fLength = 2 * dist / (fSpeed + fStartSpeed);
}

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

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

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

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

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

    RecalcToSpeed(0, 1);
}

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

    RecalcToSpeed(startSpeed, goalSpeed);
}

plATCEaseCurve *plSplineEaseCurve::Clone() const
{
    plSplineEaseCurve *curve = 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(float startSpeed, float goalSpeed, bool 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.
    float 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(float dist)
{
    float curDist = PositionGivenTime(fLength);

    fLength = fLength * dist / curDist;
}

float plSplineEaseCurve::PositionGivenTime(float time) const
{
    float 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);
}

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

float plSplineEaseCurve::TimeGivenVelocity(float 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

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

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

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

        root = (float)(-2 * sqrtQ * cos((theta + 4 * pi) / 3) - c / 3); // Middle root, most likely to match
        if (root < 0.f || root > 1.f)
        {
            root = (float)(-2 * sqrtQ * cos((theta + 2 * pi) / 3) - c / 3); // Lower root
            if (root < 0.f || root > 1.f)
            {
                root = (float)(-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 = (float)((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.
        float dStart = velocity - fStartSpeed;
        if (dStart < 0)
            dStart = -dStart;
        float 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->ReadLEScalar();
    fCoef[1] = s->ReadLEScalar();
    fCoef[2] = s->ReadLEScalar();
    fCoef[3] = s->ReadLEScalar();
}

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

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