CWE-ou-minkata/Sources/Plasma/CoreLib/hsMatrix44.cpp

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*==LICENSE==*/

#include <cmath>
#include "HeadSpin.h"
#pragma hdrstop

#include "hsGeometry3.h"
#include "hsQuat.h"
#include "hsMatrix44.h"
#include "hsStream.h"

#ifdef HS_SIMD_INCLUDE
#  include HS_SIMD_INCLUDE
#endif

static hsMatrix44 myIdent = hsMatrix44().Reset();
const hsMatrix44& hsMatrix44::IdentityMatrix() { return myIdent; }

/*
    For the rotation:
         <EFBFBD>        2     2                                      <EFBFBD>
         <EFBFBD> 1 - (2Y  + 2Z )   2XY + 2ZW         2XZ - 2YW       <EFBFBD>
         <EFBFBD>                                                     <EFBFBD>
         <EFBFBD>                          2     2                    <EFBFBD>
     M = <EFBFBD> 2XY - 2ZW         1 - (2X  + 2Z )   2YZ + 2XW       <EFBFBD>
         <EFBFBD>                                                     <EFBFBD>
         <EFBFBD>                                            2     2  <EFBFBD>
         <EFBFBD> 2XZ + 2YW         2YZ - 2XW         1 - (2X  + 2Y ) <EFBFBD>
         <EFBFBD>                                                     <EFBFBD>

    The translation is far too complex to discuss here. ;^)
*/
hsMatrix44::hsMatrix44(const hsScalarTriple &translate, const hsQuat &rotate)
{
    float xx = rotate.fX * rotate.fX;
    float xy = rotate.fX * rotate.fY;
    float xz = rotate.fX * rotate.fZ;
    float xw = rotate.fX * rotate.fW;

    float yy = rotate.fY * rotate.fY;
    float yz = rotate.fY * rotate.fZ;
    float yw = rotate.fY * rotate.fW;

    float zz = rotate.fZ * rotate.fZ;
    float zw = rotate.fZ * rotate.fW;

    fMap[0][0] = 1 - 2 * ( yy + zz ); fMap[0][1] =     2 * ( xy - zw ); fMap[0][2] =     2 * ( xz + yw ); fMap[0][3] = translate.fX;
    fMap[1][0] =     2 * ( xy + zw ); fMap[1][1] = 1 - 2 * ( xx + zz ); fMap[1][2] =     2 * ( yz - xw ); fMap[1][3] = translate.fY;
    fMap[2][0] =     2 * ( xz - yw ); fMap[2][1] =     2 * ( yz + xw ); fMap[2][2] = 1 - 2 * ( xx + yy ); fMap[2][3] = translate.fZ;
    fMap[3][0] = fMap[3][1] = fMap[3][2] = 0.0f;
    fMap[3][3] = 1.0f;
    NotIdentity();
}

void hsMatrix44::DecompRigid(hsScalarTriple &translate, hsQuat &rotate) const
{
    translate = GetTranslate();
    rotate.QuatFromMatrix44(*this);
}

static hsMatrix44 mat_mult_fpu(const hsMatrix44 &a, const hsMatrix44 &b)
{
    hsMatrix44 c;

    if( a.fFlags & b.fFlags & hsMatrix44::kIsIdent )
    {
        c.Reset();
        return c;
    }

    if( a.fFlags & hsMatrix44::kIsIdent )
        return b;
    if( b.fFlags & hsMatrix44::kIsIdent )
        return a;

    c.fMap[0][0] = (a.fMap[0][0] * b.fMap[0][0]) + (a.fMap[0][1] * b.fMap[1][0]) + (a.fMap[0][2] * b.fMap[2][0]) + (a.fMap[0][3] * b.fMap[3][0]);
    c.fMap[0][1] = (a.fMap[0][0] * b.fMap[0][1]) + (a.fMap[0][1] * b.fMap[1][1]) + (a.fMap[0][2] * b.fMap[2][1]) + (a.fMap[0][3] * b.fMap[3][1]);
    c.fMap[0][2] = (a.fMap[0][0] * b.fMap[0][2]) + (a.fMap[0][1] * b.fMap[1][2]) + (a.fMap[0][2] * b.fMap[2][2]) + (a.fMap[0][3] * b.fMap[3][2]);
    c.fMap[0][3] = (a.fMap[0][0] * b.fMap[0][3]) + (a.fMap[0][1] * b.fMap[1][3]) + (a.fMap[0][2] * b.fMap[2][3]) + (a.fMap[0][3] * b.fMap[3][3]);

    c.fMap[1][0] = (a.fMap[1][0] * b.fMap[0][0]) + (a.fMap[1][1] * b.fMap[1][0]) + (a.fMap[1][2] * b.fMap[2][0]) + (a.fMap[1][3] * b.fMap[3][0]);
    c.fMap[1][1] = (a.fMap[1][0] * b.fMap[0][1]) + (a.fMap[1][1] * b.fMap[1][1]) + (a.fMap[1][2] * b.fMap[2][1]) + (a.fMap[1][3] * b.fMap[3][1]);
    c.fMap[1][2] = (a.fMap[1][0] * b.fMap[0][2]) + (a.fMap[1][1] * b.fMap[1][2]) + (a.fMap[1][2] * b.fMap[2][2]) + (a.fMap[1][3] * b.fMap[3][2]);
    c.fMap[1][3] = (a.fMap[1][0] * b.fMap[0][3]) + (a.fMap[1][1] * b.fMap[1][3]) + (a.fMap[1][2] * b.fMap[2][3]) + (a.fMap[1][3] * b.fMap[3][3]);

    c.fMap[2][0] = (a.fMap[2][0] * b.fMap[0][0]) + (a.fMap[2][1] * b.fMap[1][0]) + (a.fMap[2][2] * b.fMap[2][0]) + (a.fMap[2][3] * b.fMap[3][0]);
    c.fMap[2][1] = (a.fMap[2][0] * b.fMap[0][1]) + (a.fMap[2][1] * b.fMap[1][1]) + (a.fMap[2][2] * b.fMap[2][1]) + (a.fMap[2][3] * b.fMap[3][1]);
    c.fMap[2][2] = (a.fMap[2][0] * b.fMap[0][2]) + (a.fMap[2][1] * b.fMap[1][2]) + (a.fMap[2][2] * b.fMap[2][2]) + (a.fMap[2][3] * b.fMap[3][2]);
    c.fMap[2][3] = (a.fMap[2][0] * b.fMap[0][3]) + (a.fMap[2][1] * b.fMap[1][3]) + (a.fMap[2][2] * b.fMap[2][3]) + (a.fMap[2][3] * b.fMap[3][3]);

    c.fMap[3][0] = (a.fMap[3][0] * b.fMap[0][0]) + (a.fMap[3][1] * b.fMap[1][0]) + (a.fMap[3][2] * b.fMap[2][0]) + (a.fMap[3][3] * b.fMap[3][0]);
    c.fMap[3][1] = (a.fMap[3][0] * b.fMap[0][1]) + (a.fMap[3][1] * b.fMap[1][1]) + (a.fMap[3][2] * b.fMap[2][1]) + (a.fMap[3][3] * b.fMap[3][1]);
    c.fMap[3][2] = (a.fMap[3][0] * b.fMap[0][2]) + (a.fMap[3][1] * b.fMap[1][2]) + (a.fMap[3][2] * b.fMap[2][2]) + (a.fMap[3][3] * b.fMap[3][2]);
    c.fMap[3][3] = (a.fMap[3][0] * b.fMap[0][3]) + (a.fMap[3][1] * b.fMap[1][3]) + (a.fMap[3][2] * b.fMap[2][3]) + (a.fMap[3][3] * b.fMap[3][3]);

    return c;
}

#ifdef HS_SSE3
#   define MULTBEGIN(i) \
        xmm[0]   = _mm_loadu_ps(a.fMap[i]);
#   define MULTCELL(i, j) \
        xmm[1]   = _mm_set_ps(b.fMap[3][j], b.fMap[2][j], b.fMap[1][j], b.fMap[0][j]); \
        xmm[j+2] = _mm_mul_ps(xmm[0], xmm[1]);
#   define MULTFINISH(i) \
        xmm[6] = _mm_hadd_ps(xmm[2], xmm[3]); \
        xmm[7] = _mm_hadd_ps(xmm[4], xmm[5]); \
        xmm[1] = _mm_hadd_ps(xmm[6], xmm[7]); \
        _mm_storeu_ps(c.fMap[i], xmm[1]);
#endif  // HS_SSE3

static hsMatrix44 mat_mult_sse3(const hsMatrix44 &a, const hsMatrix44 &b)
{
    hsMatrix44 c;
#ifdef HS_SSE3
    if( a.fFlags & b.fFlags & hsMatrix44::kIsIdent )
    {
        c.Reset();
        return c;
    }

    if( a.fFlags & hsMatrix44::kIsIdent )
        return b;
    if( b.fFlags & hsMatrix44::kIsIdent )
        return a;

    __m128 xmm[8];

    MULTBEGIN(0);
    MULTCELL(0, 0);
    MULTCELL(0, 1);
    MULTCELL(0, 2);
    MULTCELL(0, 3);
    MULTFINISH(0);

    MULTBEGIN(1);
    MULTCELL(1, 0);
    MULTCELL(1, 1);
    MULTCELL(1, 2);
    MULTCELL(1, 3);
    MULTFINISH(1);

    MULTBEGIN(2);
    MULTCELL(2, 0);
    MULTCELL(2, 1);
    MULTCELL(2, 2);
    MULTCELL(2, 3);
    MULTFINISH(2);

    MULTBEGIN(3);
    MULTCELL(3, 0);
    MULTCELL(3, 1);
    MULTCELL(3, 2);
    MULTCELL(3, 3);
    MULTFINISH(3);
#endif  // HS_SSE3
    return c;
}

// CPU-optimized functions requiring dispatch
hsCpuFunctionDispatcher<hsMatrix44::mat_mult_ptr> hsMatrix44::mat_mult {
    &mat_mult_fpu,
    nullptr,            // SSE1
    nullptr,            // SSE2
    &mat_mult_sse3
};

hsPoint3 hsMatrix44::operator*(const hsPoint3& p) const
{
    if (fFlags & hsMatrix44::kIsIdent)
        return p;

    hsPoint3 rVal;
    rVal.fX = (p.fX * fMap[0][0]) + (p.fY * fMap[0][1]) + (p.fZ * fMap[0][2]) + fMap[0][3];
    rVal.fY = (p.fX * fMap[1][0]) + (p.fY * fMap[1][1]) + (p.fZ * fMap[1][2]) + fMap[1][3];
    rVal.fZ = (p.fX * fMap[2][0]) + (p.fY * fMap[2][1]) + (p.fZ * fMap[2][2]) + fMap[2][3];
    return rVal;
}

hsVector3 hsMatrix44::operator*(const hsVector3& p) const
{
    if( fFlags & hsMatrix44::kIsIdent )
        return p;

    hsVector3 rVal;

    rVal.fX = (p.fX * fMap[0][0]) + (p.fY * fMap[0][1]) + (p.fZ * fMap[0][2]);
    rVal.fY = (p.fX * fMap[1][0]) + (p.fY * fMap[1][1]) + (p.fZ * fMap[1][2]);
    rVal.fZ = (p.fX * fMap[2][0]) + (p.fY * fMap[2][1]) + (p.fZ * fMap[2][2]);

    return rVal;
}

bool hsMatrix44::operator==(const hsMatrix44& ss) const
{
    if( ss.fFlags & fFlags & hsMatrix44::kIsIdent )
    {
        return true;
    }

    for(int i = 0; i < 4; i++)
    {
        for(int j = 0; j < 4; j++)
        {
            if (ss.fMap[i][j] != fMap[i][j])
                return false;
        }
    }

    return true;
}

hsMatrix44& hsMatrix44::Scale(const hsVector3* scale)
{
    fMap[0][0] *= scale->fX;
    fMap[0][1] *= scale->fX;
    fMap[0][2] *= scale->fX;
    fMap[0][3] *= scale->fX;

    fMap[1][0] *= scale->fY;
    fMap[1][1] *= scale->fY;
    fMap[1][2] *= scale->fY;
    fMap[1][3] *= scale->fY;

    fMap[2][0] *= scale->fZ;
    fMap[2][1] *= scale->fZ;
    fMap[2][2] *= scale->fZ;
    fMap[2][3] *= scale->fZ;

    NotIdentity();
    return *this;
}

hsVector3 hsMatrix44::RemoveScale()
{
    hsVector3 xCol(fMap[0][0], fMap[0][1], fMap[0][2]);
    float xLen = xCol.Magnitude();
    hsVector3 yCol(fMap[1][0], fMap[1][1], fMap[1][2]);
    float yLen = yCol.Magnitude();
    hsVector3 zCol(fMap[2][0], fMap[2][1], fMap[2][2]);
    float zLen = zCol.Magnitude();

    fMap[0][0] /= xLen;
    fMap[0][1] /= xLen;
    fMap[0][2] /= xLen;
    fMap[1][0] /= yLen;
    fMap[1][1] /= yLen;
    fMap[1][2] /= yLen;
    fMap[2][0] /= zLen;
    fMap[2][1] /= zLen;
    fMap[2][2] /= zLen;

    hsVector3 oldScale(xLen, yLen, zLen);
    return oldScale;
}

hsMatrix44& hsMatrix44::Translate(const hsVector3* pt)
{
    for (int i =0; i < 3; i++)
    {
        fMap[i][3] += (*pt)[i];
    }
    NotIdentity();
    return *this;
}
hsMatrix44& hsMatrix44::SetTranslate(const hsScalarTriple* pt)
{
    for (int i =0; i < 3; i++)
    {
        fMap[i][3] = (*pt)[i];
    }
    NotIdentity();
    return *this;
}
hsMatrix44&     hsMatrix44::MakeRotateMat(int axis, float radians)
{
    Reset();
    SetRotate(axis, radians);
    NotIdentity();
    return *this;
}

hsMatrix44&     hsMatrix44::Rotate(int axis, float radians)
{
    hsMatrix44 rMat;
    rMat.MakeRotateMat(axis, radians);
    *this = rMat * *this;
    return *this;
}

hsMatrix44&     hsMatrix44::SetRotate(int axis, float radians)
{
    float s = sin(radians);
    float c = cos(radians);
    int c1,c2;
    switch (axis)
    {
    case 0:
        c1 = 1;
        c2 = 2;
        break;
    case 1:
        c1 = 0;
        c2 = 2;
        break;
    case 2:
        c1 = 0;
        c2 = 1;
        break;
    }
    fMap[c1][c1] = c;
    fMap[c2][c2] = c;
    fMap[c1][c2] = s;
    fMap[c2][c1] = -s;

    NotIdentity();

    return *this;
}

void hsMatrix44::MakeXRotation(float radians)
{
    Reset();
    float s = sin(radians);
    float c = cos(radians);

    fMap[1][1] = c;
    fMap[2][2] = c;
    fMap[1][2] = s;
    fMap[2][1] = -s;
    NotIdentity();
}

void hsMatrix44::MakeYRotation(float radians)
{
    Reset();
    float s = sin(radians);
    float c = cos(radians);
    fMap[0][0] = c;
    fMap[2][2] = c;
    fMap[0][2] = -s;
    fMap[2][0] = s;
    NotIdentity();
}

void hsMatrix44::MakeZRotation(float radians)
{
    Reset();
    float s = sin(radians);
    float c = cos(radians);
    fMap[0][0] = c;
    fMap[1][1] = c;
    fMap[0][1] = s;
    fMap[1][0] = -s;
    NotIdentity();
}


//
// Not a camera matrix
//
hsMatrix44& hsMatrix44::Make(const hsPoint3* f, const hsPoint3* at, const hsVector3* up)
{
    hsVector3 trans(f->fX, f->fY, f->fZ);
    MakeTranslateMat(&trans);

    hsVector3 back (f,at);  // Z
    back.Normalize();

    hsVector3 leftEar = *up % back; // X, LHS
    leftEar.Normalize();

#if 1
    // Ignore actual up vector
    hsVector3 topHead = leftEar % back; // Y, RHS (should be flipped)
#else
    hsVector3 topHead = *up;
#endif
    topHead.Normalize();

    for(int i = 0; i < 3; i++)
    {
        fMap[i][0] = leftEar[i];
        fMap[i][1] = back[i];
        fMap[i][2] = topHead[i];
    }
    NotIdentity();
    return *this;
}

//
// Not a camera matrix
//
hsMatrix44& hsMatrix44::MakeUpPreserving(const hsPoint3* f, const hsPoint3* at, const hsVector3* up)
{
    hsVector3 trans(f->fX, f->fY, f->fZ);
    MakeTranslateMat(&trans);

    hsVector3 topHead = *up;
    topHead.Normalize();

    hsVector3 back (f,at);  // Z
    back = -back;   // really front

    hsVector3 leftEar = *up % back; // X
    leftEar.Normalize();

    back = (topHead % leftEar);
    back.Normalize();

    for(int i = 0; i < 3; i++)
    {
        fMap[i][0] = leftEar[i];
        fMap[i][1] = back[i];
        fMap[i][2] = topHead[i];
    }
    NotIdentity();
    return *this;
}

//
// Get info from a non-camera matrix. Vectors are normalized.
//
void    hsMatrix44::GetAxis(hsVector3* view, hsVector3 *up, hsVector3* right)
{
    if (view)
        view->Set(-fMap[0][1],-fMap[1][1],-fMap[2][1]); 
    if (right)
        right->Set(-fMap[0][0],-fMap[1][0],-fMap[2][0]);
    if (up)
        up->Set(fMap[0][2], fMap[1][2], fMap[2][2]);
}

const hsVector3 hsMatrix44::GetAxis(int i) const
{
    hsVector3 ret;
    switch(i)
    {
    case kView:
        {
            ret.Set(-fMap[0][1],-fMap[1][1],-fMap[2][1]);
            break;
        }
    case kUp:
        {
            ret.Set(fMap[0][2], fMap[1][2], fMap[2][2]);
            break;
        }
    case kRight:
        {
            ret.Set(-fMap[0][0],-fMap[1][0],-fMap[2][0]);
            break;
        }
    }
    return ret; 
}


//
// Camera matrix
//
hsMatrix44& hsMatrix44::MakeCamera(const hsPoint3* from, const hsPoint3* at,
                                                    const hsVector3* up)
{
    hsVector3 dirZ(at, from);
    hsVector3 trans( -from->fX, -from->fY, -from->fZ );
    hsVector3 dirY, dirX;
    hsMatrix44 rmat;
    
    dirX = (*up) % dirZ; // Stop passing in down!!! // mf_flip_up - mf
    if (dirX.MagnitudeSquared())
        dirX.Normalize();

    if (dirZ.MagnitudeSquared())
        dirZ.Normalize();
    dirY = dirZ % dirX;
    if (dirY.MagnitudeSquared())
        dirY.Normalize();

    this->Reset();
    this->Translate(&trans);
    rmat.Reset();
    for(int i = 0; i < 3; i++)
    {
        rmat.fMap[0][i] = -dirX[i];
        rmat.fMap[1][i] = dirY[i];
        rmat.fMap[2][i] = dirZ[i];
    }
    rmat.NotIdentity();
    *this = rmat * *this;
    return *this;
}

void hsMatrix44::MakeCameraMatrices(const hsPoint3& from, const hsPoint3& at, const hsVector3& up, hsMatrix44& worldToCamera, hsMatrix44& cameraToWorld)
{
    hsVector3 dirZ(&at, &from);

    hsVector3 dirX(dirZ % up);
    dirX.Normalize();

    hsVector3 dirY(dirX % dirZ);
    dirY.Normalize();

    worldToCamera.Reset(false);
    cameraToWorld.Reset(false);
    int i;
    for( i = 0; i < 3; i++ )
    {
        worldToCamera.fMap[0][i] = dirX[i];
        worldToCamera.fMap[1][i] = dirY[i];
        worldToCamera.fMap[2][i] = dirZ[i];

        cameraToWorld.fMap[i][0] = dirX[i];
        cameraToWorld.fMap[i][1] = dirY[i];
        cameraToWorld.fMap[i][2] = dirZ[i];
    }
    hsPoint3 trans = -from;
    worldToCamera.fMap[0][3] = dirX.InnerProduct(trans);
    worldToCamera.fMap[1][3] = dirY.InnerProduct(trans);
    worldToCamera.fMap[2][3] = dirZ.InnerProduct(trans);

    cameraToWorld.fMap[0][3] = from.fX;
    cameraToWorld.fMap[1][3] = from.fY;
    cameraToWorld.fMap[2][3] = from.fZ;
}

void hsMatrix44::MakeEnvMapMatrices(const hsPoint3& pos, hsMatrix44* worldToCameras, hsMatrix44* cameraToWorlds)
{
    MakeCameraMatrices(pos, hsPoint3(pos.fX - 1.f, pos.fY, pos.fZ), hsVector3(0, 0, 1.f), worldToCameras[0], cameraToWorlds[0]);

    MakeCameraMatrices(pos, hsPoint3(pos.fX + 1.f, pos.fY, pos.fZ), hsVector3(0, 0, 1.f), worldToCameras[1], cameraToWorlds[1]);

    MakeCameraMatrices(pos, hsPoint3(pos.fX, pos.fY + 1.f, pos.fZ), hsVector3(0, 0, 1.f), worldToCameras[2], cameraToWorlds[2]);

    MakeCameraMatrices(pos, hsPoint3(pos.fX, pos.fY - 1.f, pos.fZ), hsVector3(0, 0, 1.f), worldToCameras[3], cameraToWorlds[3]);

    MakeCameraMatrices(pos, hsPoint3(pos.fX, pos.fY, pos.fZ + 1.f), hsVector3(0, -1.f, 0), worldToCameras[4], cameraToWorlds[4]);

    MakeCameraMatrices(pos, hsPoint3(pos.fX, pos.fY, pos.fZ - 1.f), hsVector3(0, 1.f, 0), worldToCameras[5], cameraToWorlds[5]);
}

//
// Vectors are normalized.
//
void    hsMatrix44::GetAxisFromCamera(hsVector3* view, hsVector3 *up, hsVector3* right)
{
    if (view)
        view->Set(fMap[2][0],fMap[2][1],fMap[2][2]);    
    if (right)
        right->Set(fMap[0][0],fMap[0][1],fMap[0][2]);
    if (up)
        up->Set(fMap[1][0], fMap[1][1], fMap[1][2]);
}

//
// Camera matrix
//
hsMatrix44& hsMatrix44::MakeCameraUpPreserving(const hsPoint3* from, const hsPoint3* at,
                                                    const hsVector3* up)
{
    hsVector3 dirZ(at, from);
    hsVector3 trans( -from->fX, -from->fY, -from->fZ );
    hsVector3 dirY( up->fX, up->fY, up->fZ );
    hsVector3 dirX;
    hsMatrix44 rmat;
    
    dirX =   dirY % dirZ;
    dirX.Normalize();

    dirY.Normalize();
    dirZ = dirX % dirY;
    dirZ.Normalize();

    this->Reset();
    this->Translate(&trans);
    rmat.Reset();
    for(int i = 0; i < 3; i++)
    {
        rmat.fMap[0][i] = -dirX[i];
        rmat.fMap[1][i] = dirY[i];
        rmat.fMap[2][i] = dirZ[i];
    }
    rmat.NotIdentity();
    *this = rmat * *this;
    return *this;
}

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

static float GetDeterminant33(const hsMatrix44* mat)
{
    return  ((mat->fMap[0][0] * mat->fMap[1][1]) * mat->fMap[2][2]) +
            ((mat->fMap[0][1] * mat->fMap[1][2]) * mat->fMap[2][0]) +
            ((mat->fMap[0][2] * mat->fMap[1][0]) * mat->fMap[2][1]) -
            ((mat->fMap[0][2] * mat->fMap[1][1]) * mat->fMap[2][0]) -
            ((mat->fMap[0][1] * mat->fMap[1][0]) * mat->fMap[2][2]) -
            ((mat->fMap[0][0] * mat->fMap[1][2]) * mat->fMap[2][1]);
}

hsMatrix44* hsMatrix44::GetTranspose(hsMatrix44* transp) const
{
    for(int i = 0 ; i < 4; i++)
        for(int j=0; j < 4; j++)
            transp->fMap[i][j] = fMap[j][i];
    return transp;
}


static inline float Determinant2(float a, float b,float c, float d)
{
    return (a * d) - (c * b);
}

static inline float Determinant3(float a, float b, float c,
                       float d, float e, float f,
                       float g, float h, float i)
{
    return (a * Determinant2(e, f, h, i))
        -  (b * Determinant2(d, f, g, i))
        +  (c * Determinant2(d, e, g, h));
}

float hsMatrix44::GetDeterminant() const
{
    return (fMap[0][0]*Determinant3(fMap[1][1], fMap[2][1], fMap[3][1],
                                      fMap[1][2], fMap[2][2], fMap[3][2],
                                      fMap[1][3], fMap[2][3], fMap[3][3]) - 
            fMap[1][0]*Determinant3(fMap[0][1], fMap[2][1], fMap[3][1],
                                      fMap[0][2], fMap[2][2], fMap[3][2],
                                      fMap[0][3], fMap[2][3], fMap[3][3]) +
            fMap[2][0]*Determinant3(fMap[0][1], fMap[1][1], fMap[3][1],
                                      fMap[0][2], fMap[1][2], fMap[3][2],
                                      fMap[0][3], fMap[1][3], fMap[3][3]) -
            fMap[3][0]*Determinant3(fMap[0][1], fMap[1][1], fMap[2][1],
                                      fMap[0][2], fMap[1][2], fMap[2][2],
                                      fMap[0][3], fMap[1][3], fMap[2][3]));
}


hsMatrix44 *hsMatrix44::GetAdjoint(hsMatrix44 *adj) const
{
    float   a1, a2, a3, a4, b1, b2, b3, b4;
    float   c1, c2, c3, c4, d1, d2, d3, d4;
/*
 *     calculate the adjoint of a 4x4 matrix
 *
 *      Let  a   denote the minor determinant of matrix A obtained by
 *           ij
 *
 *      deleting the ith row and jth column from A.
 *
 *                    i+j
 *     Let  b   = (-1)    a
 *          ij            ji
 *
 *    The matrix B = (b  ) is the adjoint of A
 *                     ij
 */

    /* assign to individual variable names to aid  */
    /* selecting correct values  */

    a1 = fMap[0][0];
    b1 = fMap[0][1];
    c1 = fMap[0][2];
    d1 = fMap[0][3];

    a2 = fMap[1][0];
    b2 = fMap[1][1];
    c2 = fMap[1][2];
    d2 = fMap[1][3];

    a3 = fMap[2][0];
    b3 = fMap[2][1];
    c3 = fMap[2][2];
    d3 = fMap[2][3];

    a4 = fMap[3][0];
    b4 = fMap[3][1];
    c4 = fMap[3][2];
    d4 = fMap[3][3];

    /*
     * row column labeling reversed since we transpose rows & columns
     */

    adj->fMap[0][0] = Determinant3(b2, b3, b4, c2, c3, c4, d2, d3, d4);
    adj->fMap[1][0] = -Determinant3(a2, a3, a4, c2, c3, c4, d2, d3, d4);
    adj->fMap[2][0] = Determinant3(a2, a3, a4, b2, b3, b4, d2, d3, d4);
    adj->fMap[3][0] = -Determinant3(a2, a3, a4, b2, b3, b4, c2, c3, c4);

    adj->fMap[0][1] = -Determinant3(b1, b3, b4, c1, c3, c4, d1, d3, d4);
    adj->fMap[1][1] = Determinant3(a1, a3, a4, c1, c3, c4, d1, d3, d4);
    adj->fMap[2][1] = -Determinant3(a1, a3, a4, b1, b3, b4, d1, d3, d4);
    adj->fMap[3][1] = Determinant3(a1, a3, a4, b1, b3, b4, c1, c3, c4);

    adj->fMap[0][2] = Determinant3(b1, b2, b4, c1, c2, c4, d1, d2, d4);
    adj->fMap[1][2] = -Determinant3(a1, a2, a4, c1, c2, c4, d1, d2, d4);
    adj->fMap[2][2] = Determinant3(a1, a2, a4, b1, b2, b4, d1, d2, d4);
    adj->fMap[3][2] = -Determinant3(a1, a2, a4, b1, b2, b4, c1, c2, c4);

    adj->fMap[0][3] = -Determinant3(b1, b2, b3, c1, c2, c3, d1, d2, d3);
    adj->fMap[1][3] = Determinant3(a1, a2, a3, c1, c2, c3, d1, d2, d3);
    adj->fMap[2][3] = -Determinant3(a1, a2, a3, b1, b2, b3, d1, d2, d3);
    adj->fMap[3][3] = Determinant3(a1, a2, a3, b1, b2, b3, c1, c2, c3);

    adj->NotIdentity();
    return adj;
}

hsMatrix44* hsMatrix44::GetInverse(hsMatrix44* inverse) const
{
    float det = GetDeterminant();
    int i,j;

    if (det == 0.0f)
    {
        inverse->Reset();
        return inverse;
    }

    det = hsInvert(det);
    GetAdjoint(inverse);

    for (i=0; i<4; i++)
        for (j=0; j<4; j++)
            inverse->fMap[i][j] *= det;

    return inverse;
}

hsMatrix44& hsMatrix44::SetScale(const hsVector3* pt)
{
    for (int i =0; i < 3; i++)
    {
        fMap[i][i] = (*pt)[i];
    }
    NotIdentity();
    return *this;
}

hsMatrix44& hsMatrix44::MakeScaleMat(const hsVector3* pt)
{
    Reset();
    SetScale(pt);
    return *this;
}

hsMatrix44 &hsMatrix44::MakeTranslateMat(const hsVector3 *trans)
{
    Reset();
    SetTranslate(trans);
    return *this;
}

hsVector3* hsMatrix44::GetTranslate(hsVector3 *pt) const
{
    for (int i =0; i < 3; i++)
    {
        (*pt)[i] = fMap[i][3];
    }
    return pt;
}

const hsPoint3 hsMatrix44::GetTranslate() const
{
    hsPoint3 pt;
    for (int i =0; i < 3; i++)
    {
        (pt)[i] = fMap[i][3];
    }
    return pt;
}


hsPoint3*  hsMatrix44::MapPoints(long count, hsPoint3 points[]) const
{
    if( !(fFlags & hsMatrix44::kIsIdent) )
    {
        int i;
        for(i = 0; i < count; i++)
        {
            points[i] = *this * points[i];  
        }
    }
    return points;
}

bool hsMatrix44::IsIdentity(void)
{
    bool retVal = true;
    int i, j;
    for( i = 0; i < 4; i++ )
    {
        for( j = 0; j < 4; j++ )
        {
#if 0 // IDENTITY_CRISIS
            if( i == j)
            {
                if (fMap[i][j] != 1.f) 
                {
                    NotIdentity();
                    retVal = false;
                }
            }
            else
            {
                if( fMap[i][j] != 0 )
                {
                    NotIdentity();
                    retVal = false;
                }
            }
#else // IDENTITY_CRISIS
            const float kEPS = 1.e-5f;
            if( i == j)
            {
                if( (fMap[i][j] < 1.f-kEPS) || (fMap[i][j] > 1.f+kEPS) ) 
                {
                    NotIdentity();
                    retVal = false;
                }
                else
                {
                    fMap[i][j] = 1.f;
                }
            }
            else
            {
                if( (fMap[i][j] < -kEPS) || (fMap[i][j] > kEPS) )
                {
                    NotIdentity();
                    retVal = false;
                }
                else
                {
                    fMap[i][j] = 0;
                }
            }
#endif // IDENTITY_CRISIS
        }
    }
    if( retVal )
        fFlags |= kIsIdent;
    return retVal;
}

bool hsMatrix44::GetParity() const
{
    if( fFlags & kIsIdent )
        return false;

    hsVector3* rows[3];
    rows[0] = (hsVector3*)&fMap[0][0];
    rows[1] = (hsVector3*)&fMap[1][0];
    rows[2] = (hsVector3*)&fMap[2][0];

    hsVector3 zeroXone = *rows[0] % *rows[1];
    return zeroXone.InnerProduct(rows[2]) < 0;
}

void hsMatrix44::Read(hsStream *stream)
{
    if (stream->ReadBool())
    {
        int i,j;
        for(i=0; i<4; i++)
            for(j=0; j<4; j++)
                fMap[i][j] = stream->ReadLEFloat();
        IsIdentity();
    }
    else
        Reset();
}

void hsMatrix44::Write(hsStream *stream)
{
    bool ident = IsIdentity();
    stream->WriteBool(!ident);
    if (!ident)
    {
        int i,j;
        for(i=0; i<4; i++)
            for(j=0; j<4; j++)
                stream->WriteLEFloat(fMap[i][j]);         
    }
}