/*==LICENSE==*

CyanWorlds.com Engine - MMOG client, server and tools
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*==LICENSE==*/

#include "hsQuat.h"

#include "HeadSpin.h"
#include "hsFastMath.h"
#include "hsGeometry3.h"
#include "hsMatrix44.h"
#include "hsStream.h"


//
// Quaternion class.
// For conversion to and from euler angles, see hsEuler.cpp,h.
// 

//
// Construct quat from angle (in radians) and axis of rotation
//
hsQuat::hsQuat(float rad, const hsVector3* axis)
{
    // hsAssert(rad >= -hsConstants::pi<float> && rad <= hsConstants::pi<float>,
    //          "Quat: Angle should be between -PI and PI");

    fW = cos(rad*0.5f);

    float s = sin(rad*0.5f);
    fX = axis->fX*s;
    fY = axis->fY*s;
    fZ = axis->fZ*s;
}

hsQuat hsQuat::Inverse() const
{
    hsQuat q2 = Conjugate();
    float msInv = 1.0f/q2.MagnitudeSquared();
    return (q2 * msInv);
}

hsPoint3 hsQuat::Rotate(const hsScalarTriple* v) const
{
    hsQuat qInv = Inverse();
    hsQuat qVec(v->fX, v->fY, v->fZ, 0);
    hsQuat t = qInv * qVec;
    hsQuat res = (t * (*this));
    //hsAssert(fabs(res.fW)<1e-5, "Error rotating vector");
    return hsPoint3(res.fX, res.fY, res.fZ);
}

void hsQuat::SetAngleAxis(const float rad, const hsVector3 &axis)
{
    fW = cos(rad*0.5f);

    float s = sin(rad*0.5f);
    fX = axis.fX*s;
    fY = axis.fY*s;
    fZ = axis.fZ*s; 
}

//
// Might want to Normalize before calling this
//
void hsQuat::GetAngleAxis(float *rad, hsVector3 *axis) const
{
    hsAssert((fW >= -1) && (fW <= 1), "Invalid acos argument");
    float ac = acos(fW);
    *rad = 2.0f * ac;

    float s = sin(ac);
    if (s != 0.0f)
    {
        float invS = 1.0f/s;
        axis->Set(fX*invS, fY*invS, fZ*invS);
    }
    else
        axis->Set(0,0,0);
}

//
//
//
float hsQuat::MagnitudeSquared()
{
    return (fX*fX + fY*fY + fZ*fZ + fW*fW);
}

//
//
//
float hsQuat::Magnitude()
{
    return sqrt(MagnitudeSquared());
}

//
//
//
void hsQuat::Normalize()
{
    float invMag = 1.0f/Magnitude();
    fX *= invMag;
    fY *= invMag;
    fZ *= invMag;
    fW *= invMag;
}

//
//
//
void hsQuat::NormalizeIfNeeded()
{

    float magSquared = MagnitudeSquared();
    if (magSquared == 1.0f)
        return;

    float invMag = 1.0f/sqrt(magSquared);
    fX *= invMag;
    fY *= invMag;
    fZ *= invMag;
    fW *= invMag;
}

//
// This is for a RHS.
// The quat should be normalized first.
// 
void hsQuat::MakeMatrix(hsMatrix44 *mat) const
{
    // mf horse - this is transpose of both what
    // Gems says and what i'm expecting to come
    // out of it, so i'm flipping it.
    mat->fMap[0][0] = 1.0f - 2.0f*fY*fY - 2.0f*fZ*fZ;
    mat->fMap[0][1] = 2.0f*fX*fY - 2.0f*fW*fZ;
    mat->fMap[0][2] = 2.0f*fX*fZ + 2.0f*fW*fY;
    mat->fMap[0][3] = 0.0f;

    mat->fMap[1][0] = 2.0f*fX*fY + 2.0f*fW*fZ;
    mat->fMap[1][1] = 1.0f - 2.0f*fX*fX - 2.0f*fZ*fZ;
    mat->fMap[1][2] = 2.0f*fY*fZ - 2.0f*fW*fX;
    mat->fMap[1][3] = 0.0f;

    mat->fMap[2][0] = 2.0f*fX*fZ - 2.0f*fW*fY;
    mat->fMap[2][1] = 2.0f*fY*fZ + 2.0f*fW*fX;
    mat->fMap[2][2] = 1.0f - 2.0f*fX*fX - 2.0f*fY*fY;
    mat->fMap[2][3] = 0.0f;

    mat->fMap[3][0] = 0.0f;
    mat->fMap[3][1] = 0.0f;
    mat->fMap[3][2] = 0.0f;
    mat->fMap[3][3] = 1.0f;
 
#if 0
    mat->fMap[0][0] = fW*fW + fX*fX - fY*fY - fZ*fZ;
    mat->fMap[1][0] = 2.0f*fX*fY - 2.0f*fW*fZ;
    mat->fMap[2][0] = 2.0f*fX*fZ + 2.0f*fW*fY;
    mat->fMap[3][0] = 0.0f;

    mat->fMap[0][1] = 2.0f*fX*fY + 2.0f*fW*fZ;
    mat->fMap[1][1] = fW*fW - fX*fX + fY*fY - fZ*fZ;
    mat->fMap[2][1] = 2.0f*fY*fZ - 2.0f*fW*fX;
    mat->fMap[3][1] = 0.0f;

    mat->fMap[0][2] = 2.0f*fX*fZ - 2.0f*fW*fY;
    mat->fMap[1][2] = 2.0f*fY*fZ + 2.0f*fW*fX;
    mat->fMap[2][2] = fW*fW - fX*fX - fY*fY + fZ*fZ;
    mat->fMap[3][2] = 0.0f;

    mat->fMap[0][3] = 0.0f;
    mat->fMap[1][3] = 0.0f;
    mat->fMap[2][3] = 0.0f;
    mat->fMap[3][3] = fW*fW + fX*fX + fY*fY + fZ*fZ;
#endif

    mat->NotIdentity();
}

// Binary operators
hsQuat hsQuat::operator-(const hsQuat &in) const
{
    return hsQuat(fX-in.fX, fY-in.fY, fZ-in.fZ, fW-in.fW);
}

hsQuat hsQuat::operator+(const hsQuat &in) const
{
    return hsQuat(fX+in.fX, fY+in.fY, fZ+in.fZ, fW+in.fW);
}

//
// Return quaternion product (this * in).  Note: order is important!
// To combine rotations, use the product (qSecond * qFirst),
// which gives the effect of rotating by qFirst then qSecond.
//
hsQuat hsQuat::operator*(const hsQuat &in) const
{
    hsQuat ret;
    ret.fW = (fW*in.fW - fX*in.fX - fY*in.fY - fZ*in.fZ);
    ret.fX = (fY*in.fZ - in.fY*fZ + fW*in.fX + in.fW*fX);
    ret.fY = (fZ*in.fX - in.fZ*fX + fW*in.fY + in.fW*fY);
    ret.fZ = (fX*in.fY - in.fX*fY + fW*in.fZ + in.fW*fZ);
    return ret;
}


// I/O
void hsQuat::Read(hsStream *stream)
{
     fX = stream->ReadLEFloat();
     fY = stream->ReadLEFloat();
     fZ = stream->ReadLEFloat();
     fW = stream->ReadLEFloat();
}

void hsQuat::Write(hsStream *stream)
{
     stream->WriteLEFloat(fX);
     stream->WriteLEFloat(fY);
     stream->WriteLEFloat(fZ);
     stream->WriteLEFloat(fW);
}


#if 0
//
// Interpolate on a sphere.
//
void hsQuat::SetFromSlerp(hsQuat *q1, hsQuat *q2, float t)
{
    hsAssert(t>=0.0 && t<= 1.0, "Quat slerp param must be between 0 an 1");
    float theta = acos(q1->Dot(*q2));

    float st = sin(theta);
    assert(st != 0.0);

    float s1 = sin(1.0-t)*theta / st;

    float s2 = sin(t)*theta / st;

    *this = (*q1) * s1 + (*q2) * s2;
}
#else
/*
 * Spherical linear interpolation of unit quaternions with spins
 */

#define EPSILON 1.0E-6          /* a tiny number */

void hsQuat::SetFromSlerp(const hsQuat &a, const hsQuat &b, float alpha, int spin)
//  double alpha;           /* interpolation parameter (0 to 1) */
//  Quaternion *a, *b;      /* start and end unit quaternions */
//  int spin;           /* number of extra spin rotations */
{
    float beta;          /* complementary interp parameter */
    float theta;         /* angle between A and B */
    float sin_t, cos_t;      /* sine, cosine of theta */
    float phi;           /* theta plus spins */
    int bflip;          /* use negation of B? */

    /* cosine theta = dot product of A and B */
    cos_t = a.Dot(b);

    /* if B is on opposite hemisphere from A, use -B instead */
    if (cos_t < 0.0)
    {
        cos_t = -cos_t;
        bflip = true;
    } 
    else
        bflip = false;

    /* if B is (within precision limits) the same as A,
     * just linear interpolate between A and B.
     * Can't do spins, since we don't know what direction to spin.
     */
    if (1.0 - cos_t < EPSILON) 
    {
        beta = 1.0f - alpha;
    } else 
    {               /* normal case */
//      hsAssert((cos_t >= -1) && (cos_t <= 1), "Invalid acos argument");
        theta   = acos(cos_t);
        phi     = theta + spin * hsConstants::pi<float>;
        sin_t   = sin(theta);
        hsAssert(sin_t != 0.0, "Invalid sin value in quat slerp");
        beta    = sin(theta - alpha*phi) / sin_t;
        alpha   = sin(alpha*phi) / sin_t;
    }

    if (bflip)
        alpha = -alpha;

    /* interpolate */
    fX = beta*a.fX + alpha*b.fX;
    fY = beta*a.fY + alpha*b.fY;
    fZ = beta*a.fZ + alpha*b.fZ;
    fW = beta*a.fW + alpha*b.fW;
}
#endif

//
//
//
void hsQuat::SetFromMatrix(const hsMatrix44* mat)
{
    float wSq = 0.25f*(1 + mat->fMap[0][0] + mat->fMap[1][1] + mat->fMap[2][2]);
    if (wSq > EPSILON)
    {
        fW = sqrt(wSq);
        float iw4 = 1.0f/(4.0f*fW);
        fX = (mat->fMap[2][1] - mat->fMap[1][2]) * iw4;
        fY = (mat->fMap[0][2] - mat->fMap[2][0]) * iw4;
        fZ = (mat->fMap[1][0] - mat->fMap[0][1]) * iw4;
        return;
    }

    fW = 0;
    float xSq = -0.5f*(mat->fMap[1][1] + mat->fMap[2][2]);
    if (xSq > EPSILON)
    {
        fX = sqrt(xSq);
        float ix2 = 1.0f/(2.0f*fX);
        fY = mat->fMap[1][0] * ix2;
        fZ = mat->fMap[2][0] * ix2;
        return;
    }

    fX = 0;
    float ySq = 0.5f * (1 - mat->fMap[2][2]);
    if (ySq > EPSILON)
    {
        fY = sqrt(ySq);
        fZ = mat->fMap[2][1] / (2.0f*fY);
        return;
    }

    fY = 0;
    fZ = 1;
}

// 9/15/03 - Colin
// Changed to not use hsFastMath::InvSqrt, due to errors occuring at some
// specific angles that caused Havok to blow up.
hsQuat hsQuat::QuatFromMatrix44(const hsMatrix44& mat)
{
    /* This algorithm avoids near-zero divides by looking for a large component
     * - first w, then x, y, or z.  When the trace is greater than zero,
     * |w| is greater than 1/2, which is as small as a largest component can be.
     * Otherwise, the largest diagonal entry corresponds to the largest of |x|,
     * |y|, or |z|, one of which must be larger than |w|, and at least 1/2. */
    hsQuat qu;
    float tr, s;

    const int X = 0;
    const int Y = 1;
    const int Z = 2;
    const int W = 3;
    tr = mat.fMap[X][X] + mat.fMap[Y][Y]+ mat.fMap[Z][Z];
    if (tr >= 0.0) {
        s = float(sqrt(tr + 1.f));
        qu.fW = 0.5f * s;
        s = 0.5f / s;
        qu.fX = (mat.fMap[Z][Y] - mat.fMap[Y][Z]) * s;
        qu.fY = (mat.fMap[X][Z] - mat.fMap[Z][X]) * s;
        qu.fZ = (mat.fMap[Y][X] - mat.fMap[X][Y]) * s;
    } else {
        int h = X;
        if (mat.fMap[Y][Y] > mat.fMap[X][X]) 
            h = Y;
        if (mat.fMap[Z][Z] > mat.fMap[h][h]) 
            h = Z;
        switch (h) {
#define caseMacro(i,j,k,I,J,K) \
        case I:\
        s = float(sqrt( (mat.fMap[I][I] - (mat.fMap[J][J]+mat.fMap[K][K])) + 1.f )); \
        qu.i = 0.5f * s; \
        s = 0.5f / s; \
        qu.j = (mat.fMap[I][J] + mat.fMap[J][I]) * s; \
        qu.k = (mat.fMap[K][I] + mat.fMap[I][K]) * s; \
        qu.fW = (mat.fMap[K][J] - mat.fMap[J][K]) * s; \
        break
        caseMacro(fX,fY,fZ,X,Y,Z);
        caseMacro(fY,fZ,fX,Y,Z,X);
        caseMacro(fZ,fX,fY,Z,X,Y);
        }
    }
    return (qu);
}

hsQuat& hsQuat::SetFromMatrix44(const hsMatrix44& mat)
{
    return (*this = QuatFromMatrix44(mat));
}