function D3DXVec3Normalize(out vOut: TD3DXVector3;
   const v: TD3DXVector3): PD3DXVector3; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec3Normalize}

// Hermite interpolation between position V1, tangent T1 (when s == 0)
// and position V2, tangent T2 (when s == 1).
function D3DXVec3Hermite(out vOut: TD3DXVector3;
   const v1, t1, v2, t2: TD3DXVector3; s: Single): PD3DXVector3; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec3Hermite}

// CatmullRom interpolation between V1 (when s == 0) and V2 (when s == 1)
function D3DXVec3CatmullRom(out vOut: TD3DXVector3;
   const v1, v2, v3: TD3DXVector3; s: Single): PD3DXVector3; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec3CatmullRom}

// Barycentric coordinates.  V1 + f(V2-V1) + g(V3-V1)
function D3DXVec3BaryCentric(out vOut: TD3DXVector3;
   const v1, v2, v3: TD3DXVector3; f, g: Single): PD3DXVector3; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec3BaryCentric}

// Transform (x, y, z, 1) by matrix.
function D3DXVec3Transform(out vOut: TD3DXVector4;
  const v: TD3DXVector3; const m: TD3DXMatrix): PD3DXVector4; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec3Transform}

// Transform (x, y, z, 1) by matrix, project result back into w=1.
function D3DXVec3TransformCoord(out vOut: TD3DXVector3;
  const v: TD3DXVector3; const m: TD3DXMatrix): PD3DXVector3; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec3TransformCoord}

// Transform (x, y, z, 0) by matrix.  If you transforming a normal by a
// non-affine matrix, the matrix you pass to this function should be the
// transpose of the inverse of the matrix you would use to transform a coord.
function D3DXVec3TransformNormal(out vOut: TD3DXVector3;
  const v: TD3DXVector3; const m: TD3DXMatrix): PD3DXVector3; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec3TransformNormal}


// Transform Array (x, y, z, 1) by matrix.
function D3DXVec3TransformArray(pOut: PD3DXVector4; OutStride: LongWord;
  pV: PD3DXVector3; VStride: LongWord; const m: TD3DXMatrix; n: LongWord): PD3DXVector4; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec3TransformArray}

// Transform Array (x, y, z, 1) by matrix, project result back into w=1.
function D3DXVec3TransformCoordArray(pOut: PD3DXVector3; OutStride: LongWord;
  pV: PD3DXVector3; VStride: LongWord; const m: TD3DXMatrix; n: LongWord): PD3DXVector3; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec3TransformCoordArray}

// Transform (x, y, z, 0) by matrix.  If you transforming a normal by a
// non-affine matrix, the matrix you pass to this function should be the
// transpose of the inverse of the matrix you would use to transform a coord.
function D3DXVec3TransformNormalArray(pOut: PD3DXVector3; OutStride: LongWord;
  pV: PD3DXVector3; VStride: LongWord; const m: TD3DXMatrix; n: LongWord): PD3DXVector3; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec3TransformNormalArray}

// Project vector from object space into screen space
function D3DXVec3Project(out vOut: TD3DXVector3;
  const v: TD3DXVector3; const pViewport: TD3DViewport9;
  const pProjection, pView, pWorld: TD3DXMatrix): PD3DXVector3; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec3Project}

// Project vector from screen space into object space
function D3DXVec3Unproject(out vOut: TD3DXVector3;
  const v: TD3DXVector3; const pViewport: TD3DViewport9;
  const pProjection, pView, pWorld: TD3DXMatrix): PD3DXVector3; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec3Unproject}

// Project vector Array from object space into screen space
function D3DXVec3ProjectArray(pOut: PD3DXVector3; OutStride: LongWord;
  pV: PD3DXVector3; VStride: LongWord; const pViewport: TD3DViewport9;
  const pProjection, pView, pWorld: TD3DXMatrix; n: LongWord): PD3DXVector3; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec3ProjectArray}

// Project vector Array from screen space into object space
function D3DXVec3UnprojectArray(pOut: PD3DXVector3; OutStride: LongWord;
  pV: PD3DXVector3; VStride: LongWord; const pViewport: TD3DViewport9;
  const pProjection, pView, pWorld: TD3DXMatrix; n: LongWord): PD3DXVector3; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec3UnprojectArray}


//--------------------------
// 4D Vector
//--------------------------

// inline

function D3DXVec4Length(const v: TD3DXVector4): Single;
{$EXTERNALSYM D3DXVec4Length}

function D3DXVec4LengthSq(const v: TD3DXVector4): Single;
{$EXTERNALSYM D3DXVec4LengthSq}

function D3DXVec4Dot(const v1, v2: TD3DXVector4): Single;
{$EXTERNALSYM D3DXVec4Dot}

function D3DXVec4Add(out vOut: TD3DXVector4; const v1, v2: TD3DXVector4): PD3DXVector4;
{$EXTERNALSYM D3DXVec4Add}

function D3DXVec4Subtract(out vOut: TD3DXVector4; const v1, v2: TD3DXVector4): PD3DXVector4;
{$EXTERNALSYM D3DXVec4Subtract}

// Minimize each component.  x = min(x1, x2), y = min(y1, y2), ...
function D3DXVec4Minimize(out vOut: TD3DXVector4; const v1, v2: TD3DXVector4): PD3DXVector4;
{$EXTERNALSYM D3DXVec4Minimize}

// Maximize each component.  x = max(x1, x2), y = max(y1, y2), ...
function D3DXVec4Maximize(out vOut: TD3DXVector4; const v1, v2: TD3DXVector4): PD3DXVector4;
{$EXTERNALSYM D3DXVec4Maximize}

function D3DXVec4Scale(out vOut: TD3DXVector4; const v: TD3DXVector4; s: Single): PD3DXVector4;
{$EXTERNALSYM D3DXVec4Scale}

// Linear interpolation. V1 + s(V2-V1)
function D3DXVec4Lerp(out vOut: TD3DXVector4;
  const v1, v2: TD3DXVector4; s: Single): PD3DXVector4;
{$EXTERNALSYM D3DXVec4Lerp}

// non-inline

// Cross-product in 4 dimensions.
function D3DXVec4Cross(out vOut: TD3DXVector4;
  const v1, v2, v3: TD3DXVector4): PD3DXVector4; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec4Cross}

function D3DXVec4Normalize(out vOut: TD3DXVector4;
  const v: TD3DXVector4): PD3DXVector4; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec4Normalize}

// Hermite interpolation between position V1, tangent T1 (when s == 0)
// and position V2, tangent T2 (when s == 1).
function D3DXVec4Hermite(out vOut: TD3DXVector4;
   const v1, t1, v2, t2: TD3DXVector4; s: Single): PD3DXVector4; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec4Hermite}

// CatmullRom interpolation between V1 (when s == 0) and V2 (when s == 1)
function D3DXVec4CatmullRom(out vOut: TD3DXVector4;
   const v0, v1, v2, v3: TD3DXVector4; s: Single): PD3DXVector4; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec4CatmullRom}

// Barycentric coordinates.  V1 + f(V2-V1) + g(V3-V1)
function D3DXVec4BaryCentric(out vOut: TD3DXVector4;
   const v1, v2, v3: TD3DXVector4; f, g: Single): PD3DXVector4; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec4BaryCentric}

// Transform vector by matrix.
function D3DXVec4Transform(out vOut: TD3DXVector4;
  const v: TD3DXVector4; const m: TD3DXMatrix): PD3DXVector4; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec4Transform}

// Transform vector array by matrix.
function D3DXVec4TransformArray(pOut: PD3DXVector4; OutStride: LongWord;
  pV: PD3DXVector4; VStride: LongWord; const m: TD3DXMatrix; n: LongWord): PD3DXVector4; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXVec4TransformArray}


//--------------------------
// 4D Matrix
//--------------------------

// inline

function D3DXMatrixIdentity(out mOut: TD3DXMatrix): PD3DXMatrix;
{$EXTERNALSYM D3DXMatrixIdentity}

function D3DXMatrixIsIdentity(const m: TD3DXMatrix): BOOL;
{$EXTERNALSYM D3DXMatrixIsIdentity}

// non-inline

function D3DXMatrixDeterminant(const m: TD3DXMatrix): Single; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixDeterminant}

function D3DXMatrixTranspose(out pOut: TD3DXMatrix; const pM: TD3DXMatrix): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixTranspose}

// Matrix multiplication.  The result represents the transformation M2
// followed by the transformation M1.  (Out = M1 * M2)
function D3DXMatrixMultiply(out mOut: TD3DXMatrix; const m1, m2: TD3DXMatrix): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixMultiply}

// Matrix multiplication, followed by a transpose. (Out = T(M1 * M2))
function D3DXMatrixMultiplyTranspose(out pOut: TD3DXMatrix; const pM1, pM2: TD3DXMatrix): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixMultiplyTranspose}

// Calculate inverse of matrix.  Inversion my fail, in which case NULL will
// be returned.  The determinant of pM is also returned it pfDeterminant
// is non-NULL.
function D3DXMatrixInverse(out mOut: TD3DXMatrix; pfDeterminant: PSingle;
    const m: TD3DXMatrix): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixInverse}

// Build a matrix which scales by (sx, sy, sz)
function D3DXMatrixScaling(out mOut: TD3DXMatrix; sx, sy, sz: Single): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixScaling}

// Build a matrix which translates by (x, y, z)
function D3DXMatrixTranslation(out mOut: TD3DXMatrix; x, y, z: Single): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixTranslation}

// Build a matrix which rotates around the X axis
function D3DXMatrixRotationX(out mOut: TD3DXMatrix; angle: Single): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixRotationX}

// Build a matrix which rotates around the Y axis
function D3DXMatrixRotationY(out mOut: TD3DXMatrix; angle: Single): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixRotationY}

// Build a matrix which rotates around the Z axis
function D3DXMatrixRotationZ(out mOut: TD3DXMatrix; angle: Single): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixRotationZ}

// Build a matrix which rotates around an arbitrary axis
function D3DXMatrixRotationAxis(out mOut: TD3DXMatrix; const v: TD3DXVector3;
  angle: Single): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixRotationAxis}

// Build a matrix from a quaternion
function D3DXMatrixRotationQuaternion(out mOut: TD3DXMatrix; const Q: TD3DXQuaternion): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixRotationQuaternion}

// Yaw around the Y axis, a pitch around the X axis,
// and a roll around the Z axis.
function D3DXMatrixRotationYawPitchRoll(out mOut: TD3DXMatrix; yaw, pitch, roll: Single): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixRotationYawPitchRoll}


// Build transformation matrix.  NULL arguments are treated as identity.
// Mout = Msc-1 * Msr-1 * Ms * Msr * Msc * Mrc-1 * Mr * Mrc * Mt
function D3DXMatrixTransformation(out mOut: TD3DXMatrix;
   pScalingCenter: PD3DXVector3;
   pScalingRotation: PD3DXQuaternion; pScaling, pRotationCenter: PD3DXVector3;
   pRotation: PD3DXQuaternion; pTranslation: PD3DXVector3): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixTransformation}

// Build affine transformation matrix.  NULL arguments are treated as identity.
// Mout = Ms * Mrc-1 * Mr * Mrc * Mt
function D3DXMatrixAffineTransformation(out mOut: TD3DXMatrix;
   Scaling: Single; pRotationCenter: PD3DXVector3;
   pRotation: PD3DXQuaternion; pTranslation: PD3DXVector3): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixAffineTransformation}

// Build a lookat matrix. (right-handed)
function D3DXMatrixLookAtRH(out mOut: TD3DXMatrix; const Eye, At, Up: TD3DXVector3): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixLookAtRH}

// Build a lookat matrix. (left-handed)
function D3DXMatrixLookAtLH(out mOut: TD3DXMatrix; const Eye, At, Up: TD3DXVector3): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixLookAtLH}

// Build a perspective projection matrix. (right-handed)
function D3DXMatrixPerspectiveRH(out mOut: TD3DXMatrix; w, h, zn, zf: Single): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixPerspectiveRH}

// Build a perspective projection matrix. (left-handed)
function D3DXMatrixPerspectiveLH(out mOut: TD3DXMatrix; w, h, zn, zf: Single): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixPerspectiveLH}

// Build a perspective projection matrix. (right-handed)
function D3DXMatrixPerspectiveFovRH(out mOut: TD3DXMatrix; flovy, aspect, zn, zf: Single): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixPerspectiveFovRH}

// Build a perspective projection matrix. (left-handed)
function D3DXMatrixPerspectiveFovLH(out mOut: TD3DXMatrix; flovy, aspect, zn, zf: Single): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixPerspectiveFovLH}

// Build a perspective projection matrix. (right-handed)
function D3DXMatrixPerspectiveOffCenterRH(out mOut: TD3DXMatrix;
   l, r, b, t, zn, zf: Single): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixPerspectiveOffCenterRH}

// Build a perspective projection matrix. (left-handed)
function D3DXMatrixPerspectiveOffCenterLH(out mOut: TD3DXMatrix;
   l, r, b, t, zn, zf: Single): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixPerspectiveOffCenterLH}

// Build an ortho projection matrix. (right-handed)
function D3DXMatrixOrthoRH(out mOut: TD3DXMatrix; w, h, zn, zf: Single): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixOrthoRH}

// Build an ortho projection matrix. (left-handed)
function D3DXMatrixOrthoLH(out mOut: TD3DXMatrix; w, h, zn, zf: Single): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixOrthoLH}

// Build an ortho projection matrix. (right-handed)
function D3DXMatrixOrthoOffCenterRH(out mOut: TD3DXMatrix;
  l, r, b, t, zn, zf: Single): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixOrthoOffCenterRH}

// Build an ortho projection matrix. (left-handed)
function D3DXMatrixOrthoOffCenterLH(out mOut: TD3DXMatrix;
  l, r, b, t, zn, zf: Single): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixOrthoOffCenterLH}

// Build a matrix which flattens geometry into a plane, as if casting
// a shadow from a light.
function D3DXMatrixShadow(out mOut: TD3DXMatrix;
  const Light: TD3DXVector4; const Plane: TD3DXPlane): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixShadow}

// Build a matrix which reflects the coordinate system about a plane
function D3DXMatrixReflect(out mOut: TD3DXMatrix;
   const Plane: TD3DXPlane): PD3DXMatrix; stdcall; external d3dx9mathDLL;
{$EXTERNALSYM D3DXMatrixReflect}


//--------------------------
// Quaternion
//--------------------------

// inline

function D3DXQuaternionLength(const q: TD3DXQuaternion): Single;
{$EXTERNALSYM D3DXQuaternionLength}

// Length squared, or "norm"
function D3DXQuaternionLengthSq(const q: TD3DXQuaternion): Single;
{$EXTERNALSYM D3DXQuaternionLengthSq}

function D3DXQuaternionDot(const q1, q2: TD3DXQuaternion): Single;
{$EXTERNALSYM D3DXQuaternionDot}