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math.c

/*
 * Copyright 2007 David Adam
 * Copyright 2008 Jérôme Gardou
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA
 */

#include <stdarg.h>

#define NONAMELESSUNION

#include "windef.h"
#include "winbase.h"
#include "wingdi.h"
#include "d3dx8_private.h"

#include "wine/debug.h"

WINE_DEFAULT_DEBUG_CHANNEL(d3dx);

static const ID3DXMatrixStackVtbl ID3DXMatrixStack_Vtbl;

/*_________________D3DXColor____________________*/

D3DXCOLOR* WINAPI D3DXColorAdjustContrast(D3DXCOLOR *pout, CONST D3DXCOLOR *pc, FLOAT s)
{
    pout->r = 0.5f + s * (pc->r - 0.5f);
    pout->g = 0.5f + s * (pc->g - 0.5f);
    pout->b = 0.5f + s * (pc->b - 0.5f);
    pout->a = pc->a;
    return pout;
}

D3DXCOLOR* WINAPI D3DXColorAdjustSaturation(D3DXCOLOR *pout, CONST D3DXCOLOR *pc, FLOAT s)
{
    FLOAT grey;

    grey = pc->r * 0.2125f + pc->g * 0.7154f + pc->b * 0.0721f;
    pout->r = grey + s * (pc->r - grey);
    pout->g = grey + s * (pc->g - grey);
    pout->b = grey + s * (pc->b - grey);
    pout->a = pc->a;
    return pout;
}

/*_________________Misc__________________________*/

FLOAT WINAPI D3DXFresnelTerm(FLOAT costheta, FLOAT refractionindex)
{
    FLOAT a, d, g, result;

    g = sqrt(refractionindex * refractionindex + costheta * costheta - 1.0f);
    a = g + costheta;
    d = g - costheta;
    result = ( costheta * a - 1.0f ) * ( costheta * a - 1.0f ) / ( ( costheta * d + 1.0f ) * ( costheta * d + 1.0f ) ) + 1.0f;
    result = result * 0.5f * d * d / ( a * a );
    return result;
}

/*_________________D3DXMatrix____________________*/

D3DXMATRIX* WINAPI D3DXMatrixAffineTransformation(D3DXMATRIX *pout, FLOAT scaling, CONST D3DXVECTOR3 *rotationcenter, CONST D3DXQUATERNION *rotation, CONST D3DXVECTOR3 *translation)
{
    D3DXMATRIX m1, m2, m3, m4, m5;

    D3DXMatrixScaling(&m1, scaling, scaling, scaling);
    if ( !rotationcenter )
    {
     D3DXMatrixIdentity(&m2);
     D3DXMatrixIdentity(&m4);
    }
    else
    {
     D3DXMatrixTranslation(&m2, -rotationcenter->x, -rotationcenter->y, -rotationcenter->z);
     D3DXMatrixTranslation(&m4, rotationcenter->x, rotationcenter->y, rotationcenter->z);
    }
    if ( !rotation )
    {
     D3DXMatrixIdentity(&m3);
    }
    else
    {
     D3DXMatrixRotationQuaternion(&m3, rotation);
    }
    if ( !translation )
    {
     D3DXMatrixIdentity(&m5);
    }
    else
    {
     D3DXMatrixTranslation(&m5, translation->x, translation->y, translation->z);
    }
    D3DXMatrixMultiply(&m1, &m1, &m2);
    D3DXMatrixMultiply(&m1, &m1, &m3);
    D3DXMatrixMultiply(&m1, &m1, &m4);
    D3DXMatrixMultiply(pout, &m1, &m5);
    return pout;
}

FLOAT WINAPI D3DXMatrixfDeterminant(CONST D3DXMATRIX *pm)
{
    D3DXVECTOR4 minor, v1, v2, v3;
    FLOAT det;

    v1.x = pm->u.m[0][0]; v1.y = pm->u.m[1][0]; v1.z = pm->u.m[2][0]; v1.w = pm->u.m[3][0];
    v2.x = pm->u.m[0][1]; v2.y = pm->u.m[1][1]; v2.z = pm->u.m[2][1]; v2.w = pm->u.m[3][1];
    v3.x = pm->u.m[0][2]; v3.y = pm->u.m[1][2]; v3.z = pm->u.m[2][2]; v3.w = pm->u.m[3][2];
    D3DXVec4Cross(&minor, &v1, &v2, &v3);
    det =  - (pm->u.m[0][3] * minor.x + pm->u.m[1][3] * minor.y + pm->u.m[2][3] * minor.z + pm->u.m[3][3] * minor.w);
    return det;
}

D3DXMATRIX* WINAPI D3DXMatrixInverse(D3DXMATRIX *pout, FLOAT *pdeterminant, CONST D3DXMATRIX *pm)
{
    int a, i, j;
    D3DXMATRIX out;
    D3DXVECTOR4 v, vec[3];
    FLOAT det;

    det = D3DXMatrixfDeterminant(pm);
    if ( !det ) return NULL;
    if ( pdeterminant ) *pdeterminant = det;
    for (i=0; i<4; i++)
    {
     for (j=0; j<4; j++)
     {
      if (j != i )
      {
       a = j;
       if ( j > i ) a = a-1;
       vec[a].x = pm->u.m[j][0];
       vec[a].y = pm->u.m[j][1];
       vec[a].z = pm->u.m[j][2];
       vec[a].w = pm->u.m[j][3];
      }
     }
    D3DXVec4Cross(&v, &vec[0], &vec[1], &vec[2]);
    out.u.m[0][i] = pow(-1.0f, i) * v.x / det;
    out.u.m[1][i] = pow(-1.0f, i) * v.y / det;
    out.u.m[2][i] = pow(-1.0f, i) * v.z / det;
    out.u.m[3][i] = pow(-1.0f, i) * v.w / det;
   }
   *pout = out;
   return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixLookAtLH(D3DXMATRIX *pout, CONST D3DXVECTOR3 *peye, CONST D3DXVECTOR3 *pat, CONST D3DXVECTOR3 *pup)
{
    D3DXVECTOR3 right, rightn, up, upn, vec, vec2;

    D3DXVec3Subtract(&vec2, pat, peye);
    D3DXVec3Normalize(&vec, &vec2);
    D3DXVec3Cross(&right, pup, &vec);
    D3DXVec3Cross(&up, &vec, &right);
    D3DXVec3Normalize(&rightn, &right);
    D3DXVec3Normalize(&upn, &up);
    pout->u.m[0][0] = rightn.x;
    pout->u.m[1][0] = rightn.y;
    pout->u.m[2][0] = rightn.z;
    pout->u.m[3][0] = -D3DXVec3Dot(&rightn,peye);
    pout->u.m[0][1] = upn.x;
    pout->u.m[1][1] = upn.y;
    pout->u.m[2][1] = upn.z;
    pout->u.m[3][1] = -D3DXVec3Dot(&upn, peye);
    pout->u.m[0][2] = vec.x;
    pout->u.m[1][2] = vec.y;
    pout->u.m[2][2] = vec.z;
    pout->u.m[3][2] = -D3DXVec3Dot(&vec, peye);
    pout->u.m[0][3] = 0.0f;
    pout->u.m[1][3] = 0.0f;
    pout->u.m[2][3] = 0.0f;
    pout->u.m[3][3] = 1.0f;
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixLookAtRH(D3DXMATRIX *pout, CONST D3DXVECTOR3 *peye, CONST D3DXVECTOR3 *pat, CONST D3DXVECTOR3 *pup)
{
    D3DXVECTOR3 right, rightn, up, upn, vec, vec2;

    D3DXVec3Subtract(&vec2, pat, peye);
    D3DXVec3Normalize(&vec, &vec2);
    D3DXVec3Cross(&right, pup, &vec);
    D3DXVec3Cross(&up, &vec, &right);
    D3DXVec3Normalize(&rightn, &right);
    D3DXVec3Normalize(&upn, &up);
    pout->u.m[0][0] = -rightn.x;
    pout->u.m[1][0] = -rightn.y;
    pout->u.m[2][0] = -rightn.z;
    pout->u.m[3][0] = D3DXVec3Dot(&rightn,peye);
    pout->u.m[0][1] = upn.x;
    pout->u.m[1][1] = upn.y;
    pout->u.m[2][1] = upn.z;
    pout->u.m[3][1] = -D3DXVec3Dot(&upn, peye);
    pout->u.m[0][2] = -vec.x;
    pout->u.m[1][2] = -vec.y;
    pout->u.m[2][2] = -vec.z;
    pout->u.m[3][2] = D3DXVec3Dot(&vec, peye);
    pout->u.m[0][3] = 0.0f;
    pout->u.m[1][3] = 0.0f;
    pout->u.m[2][3] = 0.0f;
    pout->u.m[3][3] = 1.0f;
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixMultiply(D3DXMATRIX *pout, CONST D3DXMATRIX *pm1, CONST D3DXMATRIX *pm2)
{
    D3DXMATRIX out;
    int i,j;

    for (i=0; i<4; i++)
    {
     for (j=0; j<4; j++)
     {
      out.u.m[i][j] = pm1->u.m[i][0] * pm2->u.m[0][j] + pm1->u.m[i][1] * pm2->u.m[1][j] + pm1->u.m[i][2] * pm2->u.m[2][j] + pm1->u.m[i][3] * pm2->u.m[3][j];
     }
    }
    *pout = out;
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixMultiplyTranspose(D3DXMATRIX *pout, CONST D3DXMATRIX *pm1, CONST D3DXMATRIX *pm2)
{
    D3DXMatrixMultiply(pout, pm1, pm2);
    D3DXMatrixTranspose(pout, pout);
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixOrthoLH(D3DXMATRIX *pout, FLOAT w, FLOAT h, FLOAT zn, FLOAT zf)
{
    D3DXMatrixIdentity(pout);
    pout->u.m[0][0] = 2.0f / w;
    pout->u.m[1][1] = 2.0f / h;
    pout->u.m[2][2] = 1.0f / (zf - zn);
    pout->u.m[3][2] = zn / (zn - zf);
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixOrthoOffCenterLH(D3DXMATRIX *pout, FLOAT l, FLOAT r, FLOAT b, FLOAT t, FLOAT zn, FLOAT zf)
{
    D3DXMatrixIdentity(pout);
    pout->u.m[0][0] = 2.0f / (r - l);
    pout->u.m[1][1] = 2.0f / (t - b);
    pout->u.m[2][2] = 1.0f / (zf -zn);
    pout->u.m[3][0] = -1.0f -2.0f *l / (r - l);
    pout->u.m[3][1] = 1.0f + 2.0f * t / (b - t);
    pout->u.m[3][2] = zn / (zn -zf);
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixOrthoOffCenterRH(D3DXMATRIX *pout, FLOAT l, FLOAT r, FLOAT b, FLOAT t, FLOAT zn, FLOAT zf)
{
    D3DXMatrixIdentity(pout);
    pout->u.m[0][0] = 2.0f / (r - l);
    pout->u.m[1][1] = 2.0f / (t - b);
    pout->u.m[2][2] = 1.0f / (zn -zf);
    pout->u.m[3][0] = -1.0f -2.0f *l / (r - l);
    pout->u.m[3][1] = 1.0f + 2.0f * t / (b - t);
    pout->u.m[3][2] = zn / (zn -zf);
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixOrthoRH(D3DXMATRIX *pout, FLOAT w, FLOAT h, FLOAT zn, FLOAT zf)
{
    D3DXMatrixIdentity(pout);
    pout->u.m[0][0] = 2.0f / w;
    pout->u.m[1][1] = 2.0f / h;
    pout->u.m[2][2] = 1.0f / (zn - zf);
    pout->u.m[3][2] = zn / (zn - zf);
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixPerspectiveFovLH(D3DXMATRIX *pout, FLOAT fovy, FLOAT aspect, FLOAT zn, FLOAT zf)
{
    D3DXMatrixIdentity(pout);
    pout->u.m[0][0] = 1.0f / (aspect * tan(fovy/2.0f));
    pout->u.m[1][1] = 1.0f / tan(fovy/2.0f);
    pout->u.m[2][2] = zf / (zf - zn);
    pout->u.m[2][3] = 1.0f;
    pout->u.m[3][2] = (zf * zn) / (zn - zf);
    pout->u.m[3][3] = 0.0f;
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixPerspectiveFovRH(D3DXMATRIX *pout, FLOAT fovy, FLOAT aspect, FLOAT zn, FLOAT zf)
{
    D3DXMatrixIdentity(pout);
    pout->u.m[0][0] = 1.0f / (aspect * tan(fovy/2.0f));
    pout->u.m[1][1] = 1.0f / tan(fovy/2.0f);
    pout->u.m[2][2] = zf / (zn - zf);
    pout->u.m[2][3] = -1.0f;
    pout->u.m[3][2] = (zf * zn) / (zn - zf);
    pout->u.m[3][3] = 0.0f;
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixPerspectiveLH(D3DXMATRIX *pout, FLOAT w, FLOAT h, FLOAT zn, FLOAT zf)
{
    D3DXMatrixIdentity(pout);
    pout->u.m[0][0] = 2.0f * zn / w;
    pout->u.m[1][1] = 2.0f * zn / h;
    pout->u.m[2][2] = zf / (zf - zn);
    pout->u.m[3][2] = (zn * zf) / (zn - zf);
    pout->u.m[2][3] = 1.0f;
    pout->u.m[3][3] = 0.0f;
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixPerspectiveOffCenterLH(D3DXMATRIX *pout, FLOAT l, FLOAT r, FLOAT b, FLOAT t, FLOAT zn, FLOAT zf)
{
    D3DXMatrixIdentity(pout);
    pout->u.m[0][0] = 2.0f * zn / (r - l);
    pout->u.m[1][1] = -2.0f * zn / (b - t);
    pout->u.m[2][0] = -1.0f - 2.0f * l / (r - l);
    pout->u.m[2][1] = 1.0f + 2.0f * t / (b - t);
    pout->u.m[2][2] = - zf / (zn - zf);
    pout->u.m[3][2] = (zn * zf) / (zn -zf);
    pout->u.m[2][3] = 1.0f;
    pout->u.m[3][3] = 0.0f;
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixPerspectiveOffCenterRH(D3DXMATRIX *pout, FLOAT l, FLOAT r, FLOAT b, FLOAT t, FLOAT zn, FLOAT zf)
{
    D3DXMatrixIdentity(pout);
    pout->u.m[0][0] = 2.0f * zn / (r - l);
    pout->u.m[1][1] = -2.0f * zn / (b - t);
    pout->u.m[2][0] = 1.0f + 2.0f * l / (r - l);
    pout->u.m[2][1] = -1.0f -2.0f * t / (b - t);
    pout->u.m[2][2] = zf / (zn - zf);
    pout->u.m[3][2] = (zn * zf) / (zn -zf);
    pout->u.m[2][3] = -1.0f;
    pout->u.m[3][3] = 0.0f;
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixPerspectiveRH(D3DXMATRIX *pout, FLOAT w, FLOAT h, FLOAT zn, FLOAT zf)
{
    D3DXMatrixIdentity(pout);
    pout->u.m[0][0] = 2.0f * zn / w;
    pout->u.m[1][1] = 2.0f * zn / h;
    pout->u.m[2][2] = zf / (zn - zf);
    pout->u.m[3][2] = (zn * zf) / (zn - zf);
    pout->u.m[2][3] = -1.0f;
    pout->u.m[3][3] = 0.0f;
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixReflect(D3DXMATRIX *pout, CONST D3DXPLANE *pplane)
{
    D3DXPLANE Nplane;

    D3DXPlaneNormalize(&Nplane, pplane);
    D3DXMatrixIdentity(pout);
    pout->u.m[0][0] = 1.0f - 2.0f * Nplane.a * Nplane.a;
    pout->u.m[0][1] = -2.0f * Nplane.a * Nplane.b;
    pout->u.m[0][2] = -2.0f * Nplane.a * Nplane.c;
    pout->u.m[1][0] = -2.0f * Nplane.a * Nplane.b;
    pout->u.m[1][1] = 1.0f - 2.0f * Nplane.b * Nplane.b;
    pout->u.m[1][2] = -2.0f * Nplane.b * Nplane.c;
    pout->u.m[2][0] = -2.0f * Nplane.c * Nplane.a;
    pout->u.m[2][1] = -2.0f * Nplane.c * Nplane.b;
    pout->u.m[2][2] = 1.0f - 2.0f * Nplane.c * Nplane.c;
    pout->u.m[3][0] = -2.0f * Nplane.d * Nplane.a;
    pout->u.m[3][1] = -2.0f * Nplane.d * Nplane.b;
    pout->u.m[3][2] = -2.0f * Nplane.d * Nplane.c;
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixRotationAxis(D3DXMATRIX *pout, CONST D3DXVECTOR3 *pv, FLOAT angle)
{
    D3DXVECTOR3 v;

    D3DXVec3Normalize(&v,pv);
    D3DXMatrixIdentity(pout);
    pout->u.m[0][0] = (1.0f - cos(angle)) * v.x * v.x + cos(angle);
    pout->u.m[1][0] = (1.0f - cos(angle)) * v.x * v.y - sin(angle) * v.z;
    pout->u.m[2][0] = (1.0f - cos(angle)) * v.x * v.z + sin(angle) * v.y;
    pout->u.m[0][1] = (1.0f - cos(angle)) * v.y * v.x + sin(angle) * v.z;
    pout->u.m[1][1] = (1.0f - cos(angle)) * v.y * v.y + cos(angle);
    pout->u.m[2][1] = (1.0f - cos(angle)) * v.y * v.z - sin(angle) * v.x;
    pout->u.m[0][2] = (1.0f - cos(angle)) * v.z * v.x - sin(angle) * v.y;
    pout->u.m[1][2] = (1.0f - cos(angle)) * v.z * v.y + sin(angle) * v.x;
    pout->u.m[2][2] = (1.0f - cos(angle)) * v.z * v.z + cos(angle);
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixRotationQuaternion(D3DXMATRIX *pout, CONST D3DXQUATERNION *pq)
{
    D3DXMatrixIdentity(pout);
    pout->u.m[0][0] = 1.0f - 2.0f * (pq->y * pq->y + pq->z * pq->z);
    pout->u.m[0][1] = 2.0f * (pq->x *pq->y + pq->z * pq->w);
    pout->u.m[0][2] = 2.0f * (pq->x * pq->z - pq->y * pq->w);
    pout->u.m[1][0] = 2.0f * (pq->x * pq->y - pq->z * pq->w);
    pout->u.m[1][1] = 1.0f - 2.0f * (pq->x * pq->x + pq->z * pq->z);
    pout->u.m[1][2] = 2.0f * (pq->y *pq->z + pq->x *pq->w);
    pout->u.m[2][0] = 2.0f * (pq->x * pq->z + pq->y * pq->w);
    pout->u.m[2][1] = 2.0f * (pq->y *pq->z - pq->x *pq->w);
    pout->u.m[2][2] = 1.0f - 2.0f * (pq->x * pq->x + pq->y * pq->y);
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixRotationX(D3DXMATRIX *pout, FLOAT angle)
{
    D3DXMatrixIdentity(pout);
    pout->u.m[1][1] = cos(angle);
    pout->u.m[2][2] = cos(angle);
    pout->u.m[1][2] = sin(angle);
    pout->u.m[2][1] = -sin(angle);
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixRotationY(D3DXMATRIX *pout, FLOAT angle)
{
    D3DXMatrixIdentity(pout);
    pout->u.m[0][0] = cos(angle);
    pout->u.m[2][2] = cos(angle);
    pout->u.m[0][2] = -sin(angle);
    pout->u.m[2][0] = sin(angle);
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixRotationYawPitchRoll(D3DXMATRIX *pout, FLOAT yaw, FLOAT pitch, FLOAT roll)
{
    D3DXMATRIX m;

    D3DXMatrixIdentity(pout);
    D3DXMatrixRotationZ(&m, roll);
    D3DXMatrixMultiply(pout, pout, &m);
    D3DXMatrixRotationX(&m, pitch);
    D3DXMatrixMultiply(pout, pout, &m);
    D3DXMatrixRotationY(&m, yaw);
    D3DXMatrixMultiply(pout, pout, &m);
    return pout;
}
D3DXMATRIX* WINAPI D3DXMatrixRotationZ(D3DXMATRIX *pout, FLOAT angle)
{
    D3DXMatrixIdentity(pout);
    pout->u.m[0][0] = cos(angle);
    pout->u.m[1][1] = cos(angle);
    pout->u.m[0][1] = sin(angle);
    pout->u.m[1][0] = -sin(angle);
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixScaling(D3DXMATRIX *pout, FLOAT sx, FLOAT sy, FLOAT sz)
{
    D3DXMatrixIdentity(pout);
    pout->u.m[0][0] = sx;
    pout->u.m[1][1] = sy;
    pout->u.m[2][2] = sz;
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixShadow(D3DXMATRIX *pout, CONST D3DXVECTOR4 *plight, CONST D3DXPLANE *pplane)
{
    D3DXPLANE Nplane;
    FLOAT dot;

    D3DXPlaneNormalize(&Nplane, pplane);
    dot = D3DXPlaneDot(&Nplane, plight);
    pout->u.m[0][0] = dot - Nplane.a * plight->x;
    pout->u.m[0][1] = -Nplane.a * plight->y;
    pout->u.m[0][2] = -Nplane.a * plight->z;
    pout->u.m[0][3] = -Nplane.a * plight->w;
    pout->u.m[1][0] = -Nplane.b * plight->x;
    pout->u.m[1][1] = dot - Nplane.b * plight->y;
    pout->u.m[1][2] = -Nplane.b * plight->z;
    pout->u.m[1][3] = -Nplane.b * plight->w;
    pout->u.m[2][0] = -Nplane.c * plight->x;
    pout->u.m[2][1] = -Nplane.c * plight->y;
    pout->u.m[2][2] = dot - Nplane.c * plight->z;
    pout->u.m[2][3] = -Nplane.c * plight->w;
    pout->u.m[3][0] = -Nplane.d * plight->x;
    pout->u.m[3][1] = -Nplane.d * plight->y;
    pout->u.m[3][2] = -Nplane.d * plight->z;
    pout->u.m[3][3] = dot - Nplane.d * plight->w;
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixTransformation(D3DXMATRIX *pout, CONST D3DXVECTOR3 *pscalingcenter, CONST D3DXQUATERNION *pscalingrotation, CONST D3DXVECTOR3 *pscaling, CONST D3DXVECTOR3 *protationcenter, CONST D3DXQUATERNION *protation, CONST D3DXVECTOR3 *ptranslation)
{
    D3DXMATRIX m1, m2, m3, m4, m5, m6, m7;
    D3DXQUATERNION prc;
    D3DXVECTOR3 psc, pt;

    if ( !pscalingcenter )
    {
     psc.x = 0.0f;
     psc.y = 0.0f;
     psc.z = 0.0f;
    }
    else
    {
     psc.x = pscalingcenter->x;
     psc.y = pscalingcenter->y;
     psc.z = pscalingcenter->z;
    }
    if ( !protationcenter )
    {
     prc.x = 0.0f;
     prc.y = 0.0f;
     prc.z = 0.0f;
    }
    else
    {
     prc.x = protationcenter->x;
     prc.y = protationcenter->y;
     prc.z = protationcenter->z;
    }
    if ( !ptranslation )
    {
     pt.x = 0.0f;
     pt.y = 0.0f;
     pt.z = 0.0f;
    }
    else
    {
     pt.x = ptranslation->x;
     pt.y = ptranslation->y;
     pt.z = ptranslation->z;
    }
    D3DXMatrixTranslation(&m1, -psc.x, -psc.y, -psc.z);
    if ( !pscalingrotation )
    {
     D3DXMatrixIdentity(&m2);
     D3DXMatrixIdentity(&m4);
    }
    else
    {
     D3DXMatrixRotationQuaternion(&m4, pscalingrotation);
     D3DXMatrixInverse(&m2, NULL, &m4);
    }
    if ( !pscaling )
    {
     D3DXMatrixIdentity(&m3);
    }
    else
    {
    D3DXMatrixScaling(&m3, pscaling->x, pscaling->y, pscaling->z);
    }
    if ( !protation )
    {
     D3DXMatrixIdentity(&m6);
    }
    else
    {
     D3DXMatrixRotationQuaternion(&m6, protation);
    }
    D3DXMatrixTranslation(&m5, psc.x - prc.x,  psc.y - prc.y,  psc.z - prc.z);
    D3DXMatrixTranslation(&m7, prc.x + pt.x, prc.y + pt.y, prc.z + pt.z);
    D3DXMatrixMultiply(&m1, &m1, &m2);
    D3DXMatrixMultiply(&m1, &m1, &m3);
    D3DXMatrixMultiply(&m1, &m1, &m4);
    D3DXMatrixMultiply(&m1, &m1, &m5);
    D3DXMatrixMultiply(&m1, &m1, &m6);
    D3DXMatrixMultiply(pout, &m1, &m7);
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixTranslation(D3DXMATRIX *pout, FLOAT x, FLOAT y, FLOAT z)
{
    D3DXMatrixIdentity(pout);
    pout->u.m[3][0] = x;
    pout->u.m[3][1] = y;
    pout->u.m[3][2] = z;
    return pout;
}

D3DXMATRIX* WINAPI D3DXMatrixTranspose(D3DXMATRIX *pout, CONST D3DXMATRIX *pm)
{
    CONST D3DXMATRIX m = *pm;
    int i,j;

    for (i=0; i<4; i++)
    {
     for (j=0; j<4; j++)
     {
      pout->u.m[i][j] = m.u.m[j][i];
     }
    }
    return pout;
}

/*_________________D3DXMatrixStack____________________*/

static const unsigned int INITIAL_STACK_SIZE = 32;

HRESULT WINAPI D3DXCreateMatrixStack(DWORD flags, LPD3DXMATRIXSTACK* ppstack)
{
    ID3DXMatrixStackImpl* object;

    TRACE("flags %#x, ppstack %p\n", flags, ppstack);

    object = HeapAlloc(GetProcessHeap(), HEAP_ZERO_MEMORY, sizeof(ID3DXMatrixStackImpl));
    if ( object == NULL )
    {
     *ppstack = NULL;
     return E_OUTOFMEMORY;
    }
    object->lpVtbl = &ID3DXMatrixStack_Vtbl;
    object->ref = 1;

    object->stack = HeapAlloc(GetProcessHeap(), 0, INITIAL_STACK_SIZE * sizeof(D3DXMATRIX));
    if (!object->stack)
    {
        HeapFree(GetProcessHeap(), 0, object);
        *ppstack = NULL;
        return E_OUTOFMEMORY;
    }

    object->current = 0;
    object->stack_size = INITIAL_STACK_SIZE;
    D3DXMatrixIdentity(&object->stack[0]);

    TRACE("Created matrix stack %p\n", object);

    *ppstack = (LPD3DXMATRIXSTACK)object;
    return D3D_OK;
}

static HRESULT WINAPI ID3DXMatrixStackImpl_QueryInterface(ID3DXMatrixStack *iface, REFIID riid, void **ppobj)
{
    ID3DXMatrixStackImpl *This = (ID3DXMatrixStackImpl *)iface;
    if (IsEqualGUID(riid, &IID_IUnknown) || IsEqualGUID(riid, &IID_ID3DXMatrixStack))
    {
     ID3DXMatrixStack_AddRef(iface);
     *ppobj = This;
     return S_OK;
    }
    *ppobj = NULL;
    ERR("(%p)->(%s,%p),not found\n",This,debugstr_guid(riid),ppobj);
    return E_NOINTERFACE;
}

static ULONG WINAPI ID3DXMatrixStackImpl_AddRef(ID3DXMatrixStack *iface)
{
    ID3DXMatrixStackImpl *This = (ID3DXMatrixStackImpl *)iface;
    ULONG ref = InterlockedIncrement(&This->ref);
    TRACE("(%p) : AddRef from %d\n", This, ref - 1);
    return ref;
}

static ULONG WINAPI ID3DXMatrixStackImpl_Release(ID3DXMatrixStack* iface)
{
    ID3DXMatrixStackImpl *This = (ID3DXMatrixStackImpl *)iface;
    ULONG ref = InterlockedDecrement(&This->ref);
    if (!ref)
    {
        HeapFree(GetProcessHeap(), 0, This->stack);
        HeapFree(GetProcessHeap(), 0, This);
    }
    TRACE("(%p) : ReleaseRef to %d\n", This, ref);
    return ref;
}

static D3DXMATRIX* WINAPI ID3DXMatrixStackImpl_GetTop(ID3DXMatrixStack *iface)
{
    ID3DXMatrixStackImpl *This = (ID3DXMatrixStackImpl *)iface;

    TRACE("iface %p\n", iface);

    return &This->stack[This->current];
}

static HRESULT WINAPI ID3DXMatrixStackImpl_LoadIdentity(ID3DXMatrixStack *iface)
{
    ID3DXMatrixStackImpl *This = (ID3DXMatrixStackImpl *)iface;

    TRACE("iface %p\n", iface);

    D3DXMatrixIdentity(&This->stack[This->current]);

    return D3D_OK;
}

static HRESULT WINAPI ID3DXMatrixStackImpl_LoadMatrix(ID3DXMatrixStack *iface, CONST D3DXMATRIX *pm)
{
    ID3DXMatrixStackImpl *This = (ID3DXMatrixStackImpl *)iface;

    TRACE("iface %p\n", iface);

    if (!pm) return D3DERR_INVALIDCALL;
    This->stack[This->current] = *pm;

    return D3D_OK;
}

static HRESULT WINAPI ID3DXMatrixStackImpl_MultMatrix(ID3DXMatrixStack *iface, CONST D3DXMATRIX *pm)
{
    ID3DXMatrixStackImpl *This = (ID3DXMatrixStackImpl *)iface;

    TRACE("iface %p\n", iface);

    if (!pm) return D3DERR_INVALIDCALL;
    D3DXMatrixMultiply(&This->stack[This->current], &This->stack[This->current], pm);

    return D3D_OK;
}

static HRESULT WINAPI ID3DXMatrixStackImpl_MultMatrixLocal(ID3DXMatrixStack *iface, CONST D3DXMATRIX *pm)
{
    ID3DXMatrixStackImpl *This = (ID3DXMatrixStackImpl *)iface;

    TRACE("iface %p\n", iface);

    if (!pm) return D3DERR_INVALIDCALL;
    D3DXMatrixMultiply(&This->stack[This->current], pm, &This->stack[This->current]);

    return D3D_OK;
}

static HRESULT WINAPI ID3DXMatrixStackImpl_Pop(ID3DXMatrixStack *iface)
{
    ID3DXMatrixStackImpl *This = (ID3DXMatrixStackImpl *)iface;

    TRACE("iface %p\n", iface);

    /* Popping the last element on the stack returns D3D_OK, but does nothing. */
    if (!This->current) return D3D_OK;

    if (This->current <= This->stack_size / 4 && This->stack_size >= INITIAL_STACK_SIZE * 2)
    {
        unsigned int new_size;
        D3DXMATRIX *new_stack;

        new_size = This->stack_size / 2;
        new_stack = HeapReAlloc(GetProcessHeap(), 0, This->stack, new_size * sizeof(D3DXMATRIX));
        if (new_stack)
        {
            This->stack_size = new_size;
            This->stack = new_stack;
        }
    }

    --This->current;

    return D3D_OK;
}

static HRESULT WINAPI ID3DXMatrixStackImpl_Push(ID3DXMatrixStack *iface)
{
    ID3DXMatrixStackImpl *This = (ID3DXMatrixStackImpl *)iface;

    TRACE("iface %p\n", iface);

    if (This->current == This->stack_size - 1)
    {
        unsigned int new_size;
        D3DXMATRIX *new_stack;

        if (This->stack_size > UINT_MAX / 2) return E_OUTOFMEMORY;

        new_size = This->stack_size * 2;
        new_stack = HeapReAlloc(GetProcessHeap(), 0, This->stack, new_size * sizeof(D3DXMATRIX));
        if (!new_stack) return E_OUTOFMEMORY;

        This->stack_size = new_size;
        This->stack = new_stack;
    }

    ++This->current;
    This->stack[This->current] = This->stack[This->current - 1];

    return D3D_OK;
}

static HRESULT WINAPI ID3DXMatrixStackImpl_RotateAxis(ID3DXMatrixStack *iface, CONST D3DXVECTOR3 *pv, FLOAT angle)
{
    D3DXMATRIX temp;
    ID3DXMatrixStackImpl *This = (ID3DXMatrixStackImpl *)iface;

    TRACE("iface %p\n", iface);

    if (!pv) return D3DERR_INVALIDCALL;
    D3DXMatrixRotationAxis(&temp, pv, angle);
    D3DXMatrixMultiply(&This->stack[This->current], &This->stack[This->current], &temp);

    return D3D_OK;
}

static HRESULT WINAPI ID3DXMatrixStackImpl_RotateAxisLocal(ID3DXMatrixStack *iface, CONST D3DXVECTOR3 *pv, FLOAT angle)
{
    D3DXMATRIX temp;
    ID3DXMatrixStackImpl *This = (ID3DXMatrixStackImpl *)iface;

    TRACE("iface %p\n", iface);

    if (!pv) return D3DERR_INVALIDCALL;
    D3DXMatrixRotationAxis(&temp, pv, angle);
    D3DXMatrixMultiply(&This->stack[This->current], &temp, &This->stack[This->current]);

    return D3D_OK;
}

static HRESULT WINAPI ID3DXMatrixStackImpl_RotateYawPitchRoll(ID3DXMatrixStack *iface, FLOAT x, FLOAT y, FLOAT z)
{
    D3DXMATRIX temp;
    ID3DXMatrixStackImpl *This = (ID3DXMatrixStackImpl *)iface;

    TRACE("iface %p\n", iface);

    D3DXMatrixRotationYawPitchRoll(&temp, x, y, z);
    D3DXMatrixMultiply(&This->stack[This->current], &This->stack[This->current], &temp);

    return D3D_OK;
}

static HRESULT WINAPI ID3DXMatrixStackImpl_RotateYawPitchRollLocal(ID3DXMatrixStack *iface, FLOAT x, FLOAT y, FLOAT z)
{
    D3DXMATRIX temp;
    ID3DXMatrixStackImpl *This = (ID3DXMatrixStackImpl *)iface;

    TRACE("iface %p\n", iface);

    D3DXMatrixRotationYawPitchRoll(&temp, x, y, z);
    D3DXMatrixMultiply(&This->stack[This->current], &temp, &This->stack[This->current]);

    return D3D_OK;
}

static HRESULT WINAPI ID3DXMatrixStackImpl_Scale(ID3DXMatrixStack *iface, FLOAT x, FLOAT y, FLOAT z)
{
    D3DXMATRIX temp;
    ID3DXMatrixStackImpl *This = (ID3DXMatrixStackImpl *)iface;

    TRACE("iface %p\n", iface);

    D3DXMatrixScaling(&temp, x, y, z);
    D3DXMatrixMultiply(&This->stack[This->current], &This->stack[This->current], &temp);

    return D3D_OK;
}

static HRESULT WINAPI ID3DXMatrixStackImpl_ScaleLocal(ID3DXMatrixStack *iface, FLOAT x, FLOAT y, FLOAT z)
{
    D3DXMATRIX temp;
    ID3DXMatrixStackImpl *This = (ID3DXMatrixStackImpl *)iface;

    TRACE("iface %p\n", iface);

    D3DXMatrixScaling(&temp, x, y, z);
    D3DXMatrixMultiply(&This->stack[This->current], &temp, &This->stack[This->current]);

    return D3D_OK;
}

static HRESULT WINAPI ID3DXMatrixStackImpl_Translate(ID3DXMatrixStack *iface, FLOAT x, FLOAT y, FLOAT z)
{
    D3DXMATRIX temp;
    ID3DXMatrixStackImpl *This = (ID3DXMatrixStackImpl *)iface;

    TRACE("iface %p\n", iface);

    D3DXMatrixTranslation(&temp, x, y, z);
    D3DXMatrixMultiply(&This->stack[This->current], &This->stack[This->current], &temp);

    return D3D_OK;
}

static HRESULT WINAPI ID3DXMatrixStackImpl_TranslateLocal(ID3DXMatrixStack *iface, FLOAT x, FLOAT y, FLOAT z)
{
    D3DXMATRIX temp;
    ID3DXMatrixStackImpl *This = (ID3DXMatrixStackImpl *)iface;

    TRACE("iface %p\n", iface);

    D3DXMatrixTranslation(&temp, x, y, z);
    D3DXMatrixMultiply(&This->stack[This->current], &temp,&This->stack[This->current]);

    return D3D_OK;
}

static const ID3DXMatrixStackVtbl ID3DXMatrixStack_Vtbl =
{
    ID3DXMatrixStackImpl_QueryInterface,
    ID3DXMatrixStackImpl_AddRef,
    ID3DXMatrixStackImpl_Release,
    ID3DXMatrixStackImpl_Pop,
    ID3DXMatrixStackImpl_Push,
    ID3DXMatrixStackImpl_LoadIdentity,
    ID3DXMatrixStackImpl_LoadMatrix,
    ID3DXMatrixStackImpl_MultMatrix,
    ID3DXMatrixStackImpl_MultMatrixLocal,
    ID3DXMatrixStackImpl_RotateAxis,
    ID3DXMatrixStackImpl_RotateAxisLocal,
    ID3DXMatrixStackImpl_RotateYawPitchRoll,
    ID3DXMatrixStackImpl_RotateYawPitchRollLocal,
    ID3DXMatrixStackImpl_Scale,
    ID3DXMatrixStackImpl_ScaleLocal,
    ID3DXMatrixStackImpl_Translate,
    ID3DXMatrixStackImpl_TranslateLocal,
    ID3DXMatrixStackImpl_GetTop
};

/*_________________D3DXPLANE________________*/

D3DXPLANE* WINAPI D3DXPlaneFromPointNormal(D3DXPLANE *pout, CONST D3DXVECTOR3 *pvpoint, CONST D3DXVECTOR3 *pvnormal)
{
    pout->a = pvnormal->x;
    pout->b = pvnormal->y;
    pout->c = pvnormal->z;
    pout->d = -D3DXVec3Dot(pvpoint, pvnormal);
    return pout;
}

D3DXPLANE* WINAPI D3DXPlaneFromPoints(D3DXPLANE *pout, CONST D3DXVECTOR3 *pv1, CONST D3DXVECTOR3 *pv2, CONST D3DXVECTOR3 *pv3)
{
    D3DXVECTOR3 edge1, edge2, normal, Nnormal;

    edge1.x = 0.0f; edge1.y = 0.0f; edge1.z = 0.0f;
    edge2.x = 0.0f; edge2.y = 0.0f; edge2.z = 0.0f;
    D3DXVec3Subtract(&edge1, pv2, pv1);
    D3DXVec3Subtract(&edge2, pv3, pv1);
    D3DXVec3Cross(&normal, &edge1, &edge2);
    D3DXVec3Normalize(&Nnormal, &normal);
    D3DXPlaneFromPointNormal(pout, pv1, &Nnormal);
    return pout;
}

D3DXVECTOR3* WINAPI D3DXPlaneIntersectLine(D3DXVECTOR3 *pout, CONST D3DXPLANE *pp, CONST D3DXVECTOR3 *pv1, CONST D3DXVECTOR3 *pv2)
{
    D3DXVECTOR3 direction, normal;
    FLOAT dot, temp;

    normal.x = pp->a;
    normal.y = pp->b;
    normal.z = pp->c;
    direction.x = pv2->x - pv1->x;
    direction.y = pv2->y - pv1->y;
    direction.z = pv2->z - pv1->z;
    dot = D3DXVec3Dot(&normal, &direction);
    if ( !dot ) return NULL;
    temp = ( pp->d + D3DXVec3Dot(&normal, pv1) ) / dot;
    pout->x = pv1->x - temp * direction.x;
    pout->y = pv1->y - temp * direction.y;
    pout->z = pv1->z - temp * direction.z;
    return pout;
}

D3DXPLANE* WINAPI D3DXPlaneNormalize(D3DXPLANE *pout, CONST D3DXPLANE *pp)
{
    D3DXPLANE out;
    FLOAT norm;

    norm = sqrt(pp->a * pp->a + pp->b * pp->b + pp->c * pp->c);
    if ( norm )
    {
     out.a = pp->a / norm;
     out.b = pp->b / norm;
     out.c = pp->c / norm;
     out.d = pp->d / norm;
    }
    else
    {
     out.a = 0.0f;
     out.b = 0.0f;
     out.c = 0.0f;
     out.d = 0.0f;
    }
    *pout = out;
    return pout;
}

D3DXPLANE* WINAPI D3DXPlaneTransform(D3DXPLANE *pout, CONST D3DXPLANE *pplane, CONST D3DXMATRIX *pm)
{
    CONST D3DXPLANE plane = *pplane;
    pout->a = pm->u.m[0][0] * plane.a + pm->u.m[1][0] * plane.b + pm->u.m[2][0] * plane.c + pm->u.m[3][0] * plane.d;
    pout->b = pm->u.m[0][1] * plane.a + pm->u.m[1][1] * plane.b + pm->u.m[2][1] * plane.c + pm->u.m[3][1] * plane.d;
    pout->c = pm->u.m[0][2] * plane.a + pm->u.m[1][2] * plane.b + pm->u.m[2][2] * plane.c + pm->u.m[3][2] * plane.d;
    pout->d = pm->u.m[0][3] * plane.a + pm->u.m[1][3] * plane.b + pm->u.m[2][3] * plane.c + pm->u.m[3][3] * plane.d;
    return pout;
}

/*_________________D3DXQUATERNION________________*/

D3DXQUATERNION* WINAPI D3DXQuaternionBaryCentric(D3DXQUATERNION *pout, CONST D3DXQUATERNION *pq1, CONST D3DXQUATERNION *pq2, CONST D3DXQUATERNION *pq3, FLOAT f, FLOAT g)
{
    D3DXQUATERNION temp1, temp2;
    D3DXQuaternionSlerp(pout, D3DXQuaternionSlerp(&temp1, pq1, pq2, f + g), D3DXQuaternionSlerp(&temp2, pq1, pq3, f+g), g / (f + g));
    return pout;
}

D3DXQUATERNION* WINAPI D3DXQuaternionExp(D3DXQUATERNION *pout, CONST D3DXQUATERNION *pq)
{
    FLOAT norm;

    norm = sqrt(pq->x * pq->x + pq->y * pq->y + pq->z * pq->z);
    if (norm )
    {
     pout->x = sin(norm) * pq->x / norm;
     pout->y = sin(norm) * pq->y / norm;
     pout->z = sin(norm) * pq->z / norm;
     pout->w = cos(norm);
    }
    else
    {
     pout->x = 0.0f;
     pout->y = 0.0f;
     pout->z = 0.0f;
     pout->w = 1.0f;
    }
    return pout;
}

D3DXQUATERNION* WINAPI D3DXQuaternionInverse(D3DXQUATERNION *pout, CONST D3DXQUATERNION *pq)
{
    FLOAT norm;

    norm = D3DXQuaternionLengthSq(pq);
    if ( !norm )
    {
     pout->x = 0.0f;
     pout->y = 0.0f;
     pout->z = 0.0f;
     pout->w = 0.0f;
    }
    else
    {
     pout->x = -pq->x / norm;
     pout->y = -pq->y / norm;
     pout->z = -pq->z / norm;
     pout->w = pq->w / norm;
    }
    return pout;
}

D3DXQUATERNION* WINAPI D3DXQuaternionLn(D3DXQUATERNION *pout, CONST D3DXQUATERNION *pq)
{
    FLOAT norm, normvec, theta;

    norm = D3DXQuaternionLengthSq(pq);
    if ( norm > 1.0001f )
    {
     pout->x = pq->x;
     pout->y = pq->y;
     pout->z = pq->z;
     pout->w = 0.0f;
    }
    else if( norm > 0.99999f)
    {
     normvec = sqrt( pq->x * pq->x + pq->y * pq->y + pq->z * pq->z );
     theta = atan2(normvec, pq->w) / normvec;
     pout->x = theta * pq->x;
     pout->y = theta * pq->y;
     pout->z = theta * pq->z;
     pout->w = 0.0f;
    }
    else
    {
     FIXME("The quaternion (%f, %f, %f, %f) has a norm <1. This should not happen. Windows returns a result anyway. This case is not implemented yet.\n", pq->x, pq->y, pq->z, pq->w);
    }
    return pout;
}

D3DXQUATERNION* WINAPI D3DXQuaternionMultiply(D3DXQUATERNION *pout, CONST D3DXQUATERNION *pq1, CONST D3DXQUATERNION *pq2)
{
    D3DXQUATERNION out;
    out.x = pq2->w * pq1->x + pq2->x * pq1->w + pq2->y * pq1->z - pq2->z * pq1->y;
    out.y = pq2->w * pq1->y - pq2->x * pq1->z + pq2->y * pq1->w + pq2->z * pq1->x;
    out.z = pq2->w * pq1->z + pq2->x * pq1->y - pq2->y * pq1->x + pq2->z * pq1->w;
    out.w = pq2->w * pq1->w - pq2->x * pq1->x - pq2->y * pq1->y - pq2->z * pq1->z;
    *pout = out;
    return pout;
}

D3DXQUATERNION* WINAPI D3DXQuaternionNormalize(D3DXQUATERNION *pout, CONST D3DXQUATERNION *pq)
{
    D3DXQUATERNION out;
    FLOAT norm;

    norm = D3DXQuaternionLength(pq);
    if ( !norm )
    {
     out.x = 0.0f;
     out.y = 0.0f;
     out.z = 0.0f;
     out.w = 0.0f;
    }
    else
    {
     out.x = pq->x / norm;
     out.y = pq->y / norm;
     out.z = pq->z / norm;
     out.w = pq->w / norm;
    }
    *pout=out;
    return pout;
}

D3DXQUATERNION* WINAPI D3DXQuaternionRotationAxis(D3DXQUATERNION *pout, CONST D3DXVECTOR3 *pv, FLOAT angle)
{
    D3DXVECTOR3 temp;

    D3DXVec3Normalize(&temp, pv);
    pout->x = sin( angle / 2.0f ) * temp.x;
    pout->y = sin( angle / 2.0f ) * temp.y;
    pout->z = sin( angle / 2.0f ) * temp.z;
    pout->w = cos( angle / 2.0f );
    return pout;
}

D3DXQUATERNION* WINAPI D3DXQuaternionRotationMatrix(D3DXQUATERNION *pout, CONST D3DXMATRIX *pm)
{
    int i, maxi;
    FLOAT maxdiag, S, trace;

    trace = pm->u.m[0][0] + pm->u.m[1][1] + pm->u.m[2][2] + 1.0f;
    if ( trace > 1.0f)
    {
     pout->x = ( pm->u.m[1][2] - pm->u.m[2][1] ) / ( 2.0f * sqrt(trace) );
     pout->y = ( pm->u.m[2][0] - pm->u.m[0][2] ) / ( 2.0f * sqrt(trace) );
     pout->z = ( pm->u.m[0][1] - pm->u.m[1][0] ) / ( 2.0f * sqrt(trace) );
     pout->w = sqrt(trace) / 2.0f;
     return pout;
     }
    maxi = 0;
    maxdiag = pm->u.m[0][0];
    for (i=1; i<3; i++)
    {
     if ( pm->u.m[i][i] > maxdiag )
     {
      maxi = i;
      maxdiag = pm->u.m[i][i];
     }
    }
    switch( maxi )
    {
     case 0:
       S = 2.0f * sqrt(1.0f + pm->u.m[0][0] - pm->u.m[1][1] - pm->u.m[2][2]);
       pout->x = 0.25f * S;
       pout->y = ( pm->u.m[0][1] + pm->u.m[1][0] ) / S;
       pout->z = ( pm->u.m[0][2] + pm->u.m[2][0] ) / S;
       pout->w = ( pm->u.m[1][2] - pm->u.m[2][1] ) / S;
     break;
     case 1:
       S = 2.0f * sqrt(1.0f + pm->u.m[1][1] - pm->u.m[0][0] - pm->u.m[2][2]);
       pout->x = ( pm->u.m[0][1] + pm->u.m[1][0] ) / S;
       pout->y = 0.25f * S;
       pout->z = ( pm->u.m[1][2] + pm->u.m[2][1] ) / S;
       pout->w = ( pm->u.m[2][0] - pm->u.m[0][2] ) / S;
     break;
     case 2:
       S = 2.0f * sqrt(1.0f + pm->u.m[2][2] - pm->u.m[0][0] - pm->u.m[1][1]);
       pout->x = ( pm->u.m[0][2] + pm->u.m[2][0] ) / S;
       pout->y = ( pm->u.m[1][2] + pm->u.m[2][1] ) / S;
       pout->z = 0.25f * S;
       pout->w = ( pm->u.m[0][1] - pm->u.m[1][0] ) / S;
     break;
    }
    return pout;
}

D3DXQUATERNION* WINAPI D3DXQuaternionRotationYawPitchRoll(D3DXQUATERNION *pout, FLOAT yaw, FLOAT pitch, FLOAT roll)
{
    pout->x = sin( yaw / 2.0f) * cos(pitch / 2.0f) * sin(roll / 2.0f) + cos(yaw / 2.0f) * sin(pitch / 2.0f) * cos(roll / 2.0f);
    pout->y = sin( yaw / 2.0f) * cos(pitch / 2.0f) * cos(roll / 2.0f) - cos(yaw / 2.0f) * sin(pitch / 2.0f) * sin(roll / 2.0f);
    pout->z = cos(yaw / 2.0f) * cos(pitch / 2.0f) * sin(roll / 2.0f) - sin( yaw / 2.0f) * sin(pitch / 2.0f) * cos(roll / 2.0f);
    pout->w = cos( yaw / 2.0f) * cos(pitch / 2.0f) * cos(roll / 2.0f) + sin(yaw / 2.0f) * sin(pitch / 2.0f) * sin(roll / 2.0f);
    return pout;
}

D3DXQUATERNION* WINAPI D3DXQuaternionSlerp(D3DXQUATERNION *pout, CONST D3DXQUATERNION *pq1, CONST D3DXQUATERNION *pq2, FLOAT t)
{
    FLOAT dot, epsilon, temp, theta, u;

    epsilon = 1.0f;
    temp = 1.0f - t;
    u = t;
    dot = D3DXQuaternionDot(pq1, pq2);
    if ( dot < 0.0f )
    {
        epsilon = -1.0f;
        dot = -dot;
    }
    if( 1.0f - dot > 0.001f )
    {
        theta = acos(dot);
        temp  = sin(theta * temp) / sin(theta);
        u = sin(theta * u) / sin(theta);
    }
    pout->x = temp * pq1->x + epsilon * u * pq2->x;
    pout->y = temp * pq1->y + epsilon * u * pq2->y;
    pout->z = temp * pq1->z + epsilon * u * pq2->z;
    pout->w = temp * pq1->w + epsilon * u * pq2->w;
    return pout;
}

D3DXQUATERNION* WINAPI D3DXQuaternionSquad(D3DXQUATERNION *pout, CONST D3DXQUATERNION *pq1, CONST D3DXQUATERNION *pq2, CONST D3DXQUATERNION *pq3, CONST D3DXQUATERNION *pq4, FLOAT t)
{
    D3DXQUATERNION temp1, temp2;

    D3DXQuaternionSlerp(pout, D3DXQuaternionSlerp(&temp1, pq1, pq4, t), D3DXQuaternionSlerp(&temp2, pq2, pq3, t), 2.0f * t * (1.0f - t));
    return pout;
}

void WINAPI D3DXQuaternionToAxisAngle(CONST D3DXQUATERNION *pq, D3DXVECTOR3 *paxis, FLOAT *pangle)
{
    FLOAT norm;

    *pangle = 0.0f;
    norm = D3DXQuaternionLength(pq);
    if ( norm )
    {
     paxis->x = pq->x / norm;
     paxis->y = pq->y / norm;
     paxis->z = pq->z / norm;
     if ( fabs( pq->w ) <= 1.0f ) *pangle = 2.0f * acos(pq->w);
    }
    else
    {
     paxis->x = 1.0f;
     paxis->y = 0.0f;
     paxis->z = 0.0f;
    }
}

/*_________________D3DXVec2_____________________*/

D3DXVECTOR2* WINAPI D3DXVec2BaryCentric(D3DXVECTOR2 *pout, CONST D3DXVECTOR2 *pv1, CONST D3DXVECTOR2 *pv2, CONST D3DXVECTOR2 *pv3, FLOAT f, FLOAT g)
{
    pout->x = (1.0f-f-g) * (pv1->x) + f * (pv2->x) + g * (pv3->x);
    pout->y = (1.0f-f-g) * (pv1->y) + f * (pv2->y) + g * (pv3->y);
    return pout;
}

D3DXVECTOR2* WINAPI D3DXVec2CatmullRom(D3DXVECTOR2 *pout, CONST D3DXVECTOR2 *pv0, CONST D3DXVECTOR2 *pv1, CONST D3DXVECTOR2 *pv2, CONST D3DXVECTOR2 *pv3, FLOAT s)
{
    pout->x = 0.5f * (2.0f * pv1->x + (pv2->x - pv0->x) *s + (2.0f *pv0->x - 5.0f * pv1->x + 4.0f * pv2->x - pv3->x) * s * s + (pv3->x -3.0f * pv2->x + 3.0f * pv1->x - pv0->x) * s * s * s);
    pout->y = 0.5f * (2.0f * pv1->y + (pv2->y - pv0->y) *s + (2.0f *pv0->y - 5.0f * pv1->y + 4.0f * pv2->y - pv3->y) * s * s + (pv3->y -3.0f * pv2->y + 3.0f * pv1->y - pv0->y) * s * s * s);
    return pout;
}

D3DXVECTOR2* WINAPI D3DXVec2Hermite(D3DXVECTOR2 *pout, CONST D3DXVECTOR2 *pv1, CONST D3DXVECTOR2 *pt1, CONST D3DXVECTOR2 *pv2, CONST D3DXVECTOR2 *pt2, FLOAT s)
{
    FLOAT h1, h2, h3, h4;

    h1 = 2.0f * s * s * s - 3.0f * s * s + 1.0f;
    h2 = s * s * s - 2.0f * s * s + s;
    h3 = -2.0f * s * s * s + 3.0f * s * s;
    h4 = s * s * s - s * s;

    pout->x = h1 * (pv1->x) + h2 * (pt1->x) + h3 * (pv2->x) + h4 * (pt2->x);
    pout->y = h1 * (pv1->y) + h2 * (pt1->y) + h3 * (pv2->y) + h4 * (pt2->y);
    return pout;
}

D3DXVECTOR2* WINAPI D3DXVec2Normalize(D3DXVECTOR2 *pout, CONST D3DXVECTOR2 *pv)
{
    D3DXVECTOR2 out;
    FLOAT norm;

    norm = D3DXVec2Length(pv);
    if ( !norm )
    {
     out.x = 0.0f;
     out.y = 0.0f;
    }
    else
    {
     out.x = pv->x / norm;
     out.y = pv->y / norm;
    }
    *pout=out;
    return pout;
}

D3DXVECTOR4* WINAPI D3DXVec2Transform(D3DXVECTOR4 *pout, CONST D3DXVECTOR2 *pv, CONST D3DXMATRIX *pm)
{
    pout->x = pm->u.m[0][0] * pv->x + pm->u.m[1][0] * pv->y  + pm->u.m[3][0];
    pout->y = pm->u.m[0][1] * pv->x + pm->u.m[1][1] * pv->y  + pm->u.m[3][1];
    pout->z = pm->u.m[0][2] * pv->x + pm->u.m[1][2] * pv->y  + pm->u.m[3][2];
    pout->w = pm->u.m[0][3] * pv->x + pm->u.m[1][3] * pv->y  + pm->u.m[3][3];
    return pout;
}

D3DXVECTOR2* WINAPI D3DXVec2TransformCoord(D3DXVECTOR2 *pout, CONST D3DXVECTOR2 *pv, CONST D3DXMATRIX *pm)
{
    FLOAT norm;

    norm = pm->u.m[0][3] * pv->x + pm->u.m[1][3] * pv->y + pm->u.m[3][3];
    if ( norm )
    {
     CONST D3DXVECTOR2 v = *pv;
     pout->x = (pm->u.m[0][0] * v.x + pm->u.m[1][0] * v.y + pm->u.m[3][0]) / norm;
     pout->y = (pm->u.m[0][1] * v.x + pm->u.m[1][1] * v.y + pm->u.m[3][1]) / norm;
    }
    else
    {
     pout->x = 0.0f;
     pout->y = 0.0f;
    }
    return pout;
}

D3DXVECTOR2* WINAPI D3DXVec2TransformNormal(D3DXVECTOR2 *pout, CONST D3DXVECTOR2 *pv, CONST D3DXMATRIX *pm)
{
    CONST D3DXVECTOR2 v = *pv;
    pout->x = pm->u.m[0][0] * v.x + pm->u.m[1][0] * v.y;
    pout->y = pm->u.m[0][1] * v.x + pm->u.m[1][1] * v.y;
    return pout;
}

/*_________________D3DXVec3_____________________*/

D3DXVECTOR3* WINAPI D3DXVec3BaryCentric(D3DXVECTOR3 *pout, CONST D3DXVECTOR3 *pv1, CONST D3DXVECTOR3 *pv2, CONST D3DXVECTOR3 *pv3, FLOAT f, FLOAT g)
{
    pout->x = (1.0f-f-g) * (pv1->x) + f * (pv2->x) + g * (pv3->x);
    pout->y = (1.0f-f-g) * (pv1->y) + f * (pv2->y) + g * (pv3->y);
    pout->z = (1.0f-f-g) * (pv1->z) + f * (pv2->z) + g * (pv3->z);
    return pout;
}

D3DXVECTOR3* WINAPI D3DXVec3CatmullRom( D3DXVECTOR3 *pout, CONST D3DXVECTOR3 *pv0, CONST D3DXVECTOR3 *pv1, CONST D3DXVECTOR3 *pv2, CONST D3DXVECTOR3 *pv3, FLOAT s)
{
    pout->x = 0.5f * (2.0f * pv1->x + (pv2->x - pv0->x) *s + (2.0f *pv0->x - 5.0f * pv1->x + 4.0f * pv2->x - pv3->x) * s * s + (pv3->x -3.0f * pv2->x + 3.0f * pv1->x - pv0->x) * s * s * s);
    pout->y = 0.5f * (2.0f * pv1->y + (pv2->y - pv0->y) *s + (2.0f *pv0->y - 5.0f * pv1->y + 4.0f * pv2->y - pv3->y) * s * s + (pv3->y -3.0f * pv2->y + 3.0f * pv1->y - pv0->y) * s * s * s);
    pout->z = 0.5f * (2.0f * pv1->z + (pv2->z - pv0->z) *s + (2.0f *pv0->z - 5.0f * pv1->z + 4.0f * pv2->z - pv3->z) * s * s + (pv3->z -3.0f * pv2->z + 3.0f * pv1->z - pv0->z) * s * s * s);
    return pout;
}

D3DXVECTOR3* WINAPI D3DXVec3Hermite(D3DXVECTOR3 *pout, CONST D3DXVECTOR3 *pv1, CONST D3DXVECTOR3 *pt1, CONST D3DXVECTOR3 *pv2, CONST D3DXVECTOR3 *pt2, FLOAT s)
{
    FLOAT h1, h2, h3, h4;

    h1 = 2.0f * s * s * s - 3.0f * s * s + 1.0f;
    h2 = s * s * s - 2.0f * s * s + s;
    h3 = -2.0f * s * s * s + 3.0f * s * s;
    h4 = s * s * s - s * s;

    pout->x = h1 * (pv1->x) + h2 * (pt1->x) + h3 * (pv2->x) + h4 * (pt2->x);
    pout->y = h1 * (pv1->y) + h2 * (pt1->y) + h3 * (pv2->y) + h4 * (pt2->y);
    pout->z = h1 * (pv1->z) + h2 * (pt1->z) + h3 * (pv2->z) + h4 * (pt2->z);
    return pout;
}

D3DXVECTOR3* WINAPI D3DXVec3Normalize(D3DXVECTOR3 *pout, CONST D3DXVECTOR3 *pv)
{
    D3DXVECTOR3 out;
    FLOAT norm;

    norm = D3DXVec3Length(pv);
    if ( !norm )
    {
     out.x = 0.0f;
     out.y = 0.0f;
     out.z = 0.0f;
    }
    else
    {
     out.x = pv->x / norm;
     out.y = pv->y / norm;
     out.z = pv->z / norm;
    }
    *pout = out;
    return pout;
}

D3DXVECTOR3* WINAPI D3DXVec3Project(D3DXVECTOR3 *pout, CONST D3DXVECTOR3 *pv, CONST D3DVIEWPORT8 *pviewport, CONST D3DXMATRIX *pprojection, CONST D3DXMATRIX *pview, CONST D3DXMATRIX *pworld)
{
    D3DXMATRIX m;
    D3DXVECTOR3 out;

    D3DXMatrixMultiply(&m, pworld, pview);
    D3DXMatrixMultiply(&m, &m, pprojection);
    D3DXVec3TransformCoord(&out, pv, &m);
    out.x = pviewport->X +  ( 1.0f + out.x ) * pviewport->Width / 2.0f;
    out.y = pviewport->Y +  ( 1.0f - out.y ) * pviewport->Height / 2.0f;
    out.z = pviewport->MinZ + out.z * ( pviewport->MaxZ - pviewport->MinZ );
    *pout = out;
    return pout;
}

D3DXVECTOR4* WINAPI D3DXVec3Transform(D3DXVECTOR4 *pout, CONST D3DXVECTOR3 *pv, CONST D3DXMATRIX *pm)
{
    pout->x = pm->u.m[0][0] * pv->x + pm->u.m[1][0] * pv->y + pm->u.m[2][0] * pv->z + pm->u.m[3][0];
    pout->y = pm->u.m[0][1] * pv->x + pm->u.m[1][1] * pv->y + pm->u.m[2][1] * pv->z + pm->u.m[3][1];
    pout->z = pm->u.m[0][2] * pv->x + pm->u.m[1][2] * pv->y + pm->u.m[2][2] * pv->z + pm->u.m[3][2];
    pout->w = pm->u.m[0][3] * pv->x + pm->u.m[1][3] * pv->y + pm->u.m[2][3] * pv->z + pm->u.m[3][3];
    return pout;
}

D3DXVECTOR3* WINAPI D3DXVec3TransformCoord(D3DXVECTOR3 *pout, CONST D3DXVECTOR3 *pv, CONST D3DXMATRIX *pm)
{
    D3DXVECTOR3 out;
    FLOAT norm;

    norm = pm->u.m[0][3] * pv->x + pm->u.m[1][3] * pv->y + pm->u.m[2][3] *pv->z + pm->u.m[3][3];

    if ( norm )
    {
     CONST D3DXVECTOR3 v = *pv;
     out.x = (pm->u.m[0][0] * v.x + pm->u.m[1][0] * v.y + pm->u.m[2][0] * v.z + pm->u.m[3][0]) / norm;
     out.y = (pm->u.m[0][1] * v.x + pm->u.m[1][1] * v.y + pm->u.m[2][1] * v.z + pm->u.m[3][1]) / norm;
     out.z = (pm->u.m[0][2] * v.x + pm->u.m[1][2] * v.y + pm->u.m[2][2] * v.z + pm->u.m[3][2]) / norm;
    }
    else
    {
     out.x = 0.0f;
     out.y = 0.0f;
     out.z = 0.0f;
    }
    *pout = out;
    return pout;
}

D3DXVECTOR3* WINAPI D3DXVec3TransformNormal(D3DXVECTOR3 *pout, CONST D3DXVECTOR3 *pv, CONST D3DXMATRIX *pm)
{
    CONST D3DXVECTOR3 v = *pv;
    pout->x = pm->u.m[0][0] * v.x + pm->u.m[1][0] * v.y + pm->u.m[2][0] * v.z;
    pout->y = pm->u.m[0][1] * v.x + pm->u.m[1][1] * v.y + pm->u.m[2][1] * v.z;
    pout->z = pm->u.m[0][2] * v.x + pm->u.m[1][2] * v.y + pm->u.m[2][2] * v.z;
    return pout;

}

D3DXVECTOR3* WINAPI D3DXVec3Unproject(D3DXVECTOR3 *pout, CONST D3DXVECTOR3 *pv, CONST D3DVIEWPORT8 *pviewport, CONST D3DXMATRIX *pprojection, CONST D3DXMATRIX *pview, CONST D3DXMATRIX *pworld)
{
    D3DXMATRIX m;
    D3DXVECTOR3 out;

    D3DXMatrixMultiply(&m, pworld, pview);
    D3DXMatrixMultiply(&m, &m, pprojection);
    D3DXMatrixInverse(&m, NULL, &m);
    out.x = 2.0f * ( pv->x - pviewport->X ) / pviewport->Width - 1.0f;
    out.y = 1.0f - 2.0f * ( pv->y - pviewport->Y ) / pviewport->Height;
    out.z = ( pv->z - pviewport->MinZ) / ( pviewport->MaxZ - pviewport->MinZ );
    D3DXVec3TransformCoord(&out, &out, &m);
    *pout = out;
    return pout;
}

/*_________________D3DXVec4_____________________*/

D3DXVECTOR4* WINAPI D3DXVec4BaryCentric(D3DXVECTOR4 *pout, CONST D3DXVECTOR4 *pv1, CONST D3DXVECTOR4 *pv2, CONST D3DXVECTOR4 *pv3, FLOAT f, FLOAT g)
{
    pout->x = (1.0f-f-g) * (pv1->x) + f * (pv2->x) + g * (pv3->x);
    pout->y = (1.0f-f-g) * (pv1->y) + f * (pv2->y) + g * (pv3->y);
    pout->z = (1.0f-f-g) * (pv1->z) + f * (pv2->z) + g * (pv3->z);
    pout->w = (1.0f-f-g) * (pv1->w) + f * (pv2->w) + g * (pv3->w);
    return pout;
}

D3DXVECTOR4* WINAPI D3DXVec4CatmullRom(D3DXVECTOR4 *pout, CONST D3DXVECTOR4 *pv0, CONST D3DXVECTOR4 *pv1, CONST D3DXVECTOR4 *pv2, CONST D3DXVECTOR4 *pv3, FLOAT s)
{
    pout->x = 0.5f * (2.0f * pv1->x + (pv2->x - pv0->x) *s + (2.0f *pv0->x - 5.0f * pv1->x + 4.0f * pv2->x - pv3->x) * s * s + (pv3->x -3.0f * pv2->x + 3.0f * pv1->x - pv0->x) * s * s * s);
    pout->y = 0.5f * (2.0f * pv1->y + (pv2->y - pv0->y) *s + (2.0f *pv0->y - 5.0f * pv1->y + 4.0f * pv2->y - pv3->y) * s * s + (pv3->y -3.0f * pv2->y + 3.0f * pv1->y - pv0->y) * s * s * s);
    pout->z = 0.5f * (2.0f * pv1->z + (pv2->z - pv0->z) *s + (2.0f *pv0->z - 5.0f * pv1->z + 4.0f * pv2->z - pv3->z) * s * s + (pv3->z -3.0f * pv2->z + 3.0f * pv1->z - pv0->z) * s * s * s);
    pout->w = 0.5f * (2.0f * pv1->w + (pv2->w - pv0->w) *s + (2.0f *pv0->w - 5.0f * pv1->w + 4.0f * pv2->w - pv3->w) * s * s + (pv3->w -3.0f * pv2->w + 3.0f * pv1->w - pv0->w) * s * s * s);
    return pout;
}

D3DXVECTOR4* WINAPI D3DXVec4Cross(D3DXVECTOR4 *pout, CONST D3DXVECTOR4 *pv1, CONST D3DXVECTOR4 *pv2, CONST D3DXVECTOR4 *pv3)
{
    D3DXVECTOR4 out;
    out.x = pv1->y * (pv2->z * pv3->w - pv3->z * pv2->w) - pv1->z * (pv2->y * pv3->w - pv3->y * pv2->w) + pv1->w * (pv2->y * pv3->z - pv2->z *pv3->y);
    out.y = -(pv1->x * (pv2->z * pv3->w - pv3->z * pv2->w) - pv1->z * (pv2->x * pv3->w - pv3->x * pv2->w) + pv1->w * (pv2->x * pv3->z - pv3->x * pv2->z));
    out.z = pv1->x * (pv2->y * pv3->w - pv3->y * pv2->w) - pv1->y * (pv2->x *pv3->w - pv3->x * pv2->w) + pv1->w * (pv2->x * pv3->y - pv3->x * pv2->y);
    out.w = -(pv1->x * (pv2->y * pv3->z - pv3->y * pv2->z) - pv1->y * (pv2->x * pv3->z - pv3->x *pv2->z) + pv1->z * (pv2->x * pv3->y - pv3->x * pv2->y));
    *pout = out;
    return pout;
}

D3DXVECTOR4* WINAPI D3DXVec4Hermite(D3DXVECTOR4 *pout, CONST D3DXVECTOR4 *pv1, CONST D3DXVECTOR4 *pt1, CONST D3DXVECTOR4 *pv2, CONST D3DXVECTOR4 *pt2, FLOAT s)
{
    FLOAT h1, h2, h3, h4;

    h1 = 2.0f * s * s * s - 3.0f * s * s + 1.0f;
    h2 = s * s * s - 2.0f * s * s + s;
    h3 = -2.0f * s * s * s + 3.0f * s * s;
    h4 = s * s * s - s * s;

    pout->x = h1 * (pv1->x) + h2 * (pt1->x) + h3 * (pv2->x) + h4 * (pt2->x);
    pout->y = h1 * (pv1->y) + h2 * (pt1->y) + h3 * (pv2->y) + h4 * (pt2->y);
    pout->z = h1 * (pv1->z) + h2 * (pt1->z) + h3 * (pv2->z) + h4 * (pt2->z);
    pout->w = h1 * (pv1->w) + h2 * (pt1->w) + h3 * (pv2->w) + h4 * (pt2->w);
    return pout;
}

D3DXVECTOR4* WINAPI D3DXVec4Normalize(D3DXVECTOR4 *pout, CONST D3DXVECTOR4 *pv)
{
    D3DXVECTOR4 out;
    FLOAT norm;

    norm = D3DXVec4Length(pv);
    if ( !norm )
    {
     out.x = 0.0f;
     out.y = 0.0f;
     out.z = 0.0f;
     out.w = 0.0f;
    }
    else
    {
     out.x = pv->x / norm;
     out.y = pv->y / norm;
     out.z = pv->z / norm;
     out.w = pv->w / norm;
    }
    *pout = out;
    return pout;
}

D3DXVECTOR4* WINAPI D3DXVec4Transform(D3DXVECTOR4 *pout, CONST D3DXVECTOR4 *pv, CONST D3DXMATRIX *pm)
{
    D3DXVECTOR4 out;
    out.x = pm->u.m[0][0] * pv->x + pm->u.m[1][0] * pv->y + pm->u.m[2][0] * pv->z + pm->u.m[3][0] * pv->w;
    out.y = pm->u.m[0][1] * pv->x + pm->u.m[1][1] * pv->y + pm->u.m[2][1] * pv->z + pm->u.m[3][1] * pv->w;
    out.z = pm->u.m[0][2] * pv->x + pm->u.m[1][2] * pv->y + pm->u.m[2][2] * pv->z + pm->u.m[3][2] * pv->w;
    out.w = pm->u.m[0][3] * pv->x + pm->u.m[1][3] * pv->y + pm->u.m[2][3] * pv->z + pm->u.m[3][3] * pv->w;
    *pout = out;
    return pout;
}

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