-+-+-+-+-+-+-+-+ START OF PART 262 -+-+-+-+-+-+-+-+
X** \parambegin
X** \param`7BPpoint *`7D`7Bvec`7D`7B2D vector`7D`7BIN`7D
X** \paramend
X** \blurb`7BThis function generates and returns a unit vector from
X** the supplied 2D vector`20
X** \pardesc`7Bvec`7D.`7D
X*/
X`7B
X  Pfloat modu;
X  Ppoint temp;
X
X  modu = ptk_modv(vec);
X  if (!ptk_equal(modu, 0.0))`20
X  `7B
X    temp = ptk_point(vec->x / modu, vec->y / modu);
X    return temp;
X  `7D`20
X  else`20
X  `7B
X    temp = ptk_point(0.0, 0.0);
X    return temp;
X  `7D
X`7D  /* ptk_unitv */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern Ppoint3 ptk_scalev3(C(Ppoint3 *) vec, C(Pfloat) scale)
XPreANSI(Ppoint3 *vec)
XPreANSI(Pfloat scale)
X/*
X** \parambegin
X** \param`7BPpoint3 *`7D`7Bvec`7D`7B3D vector`7D`7BIN`7D
X** \param`7BPfloat`7D`7Bscale`7D`7Bscale factor`7D`7BIN`7D
X** \paramend
X** \blurb`7BThis function multiplies the 3D vector \pardesc`7Bv`7D
X**  by the  scalar \pardesc`7Bs`7D and
X** returns the result.`7D
X*/
X`7B
X  Ppoint3 temp;
X
X  temp = ptk_point3(vec->x * scale, vec->y * scale, vec->z * scale);
X  return temp;
X`7D  /* ptk_scalev3 */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern Ppoint ptk_scalev(C(Ppoint *) vec, C(Pfloat) scale)
XPreANSI(Ppoint *vec)
XPreANSI(Pfloat scale)
X/*
X** \parambegin
X** \param`7BPpoint *`7D`7Bvec`7D`7B2D vector`7D`7BIN`7D
X** \param`7BPfloat`7D`7Bscale`7D`7Bscale factor`7D`7BIN`7D
X** \paramend
X** \blurb`7BThis function multiplies the 2D vector
X** \pardesc`7Bv`7D by the scalar \pardesc`7Bs`7D and
X** returns the result.`7D
X*/
X`7B
X  Ppoint temp;
X
X  temp = ptk_point(vec->x * scale, vec->y * scale);
X  return temp;
X`7D  /* ptk_scalev */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern Ppoint3 ptk_subv3(C(Ppoint3 *) p1, C(Ppoint3 *) p2)
XPreANSI(Ppoint3 *p1)
XPreANSI(Ppoint3 *p2)
X/*
X** \parambegin
X** \param`7BPpoint3 *`7D`7Bp1`7D`7B3D vector`7D`7BIN`7D
X** \param`7BPpoint3 *`7D`7Bp2`7D`7B3D vector`7D`7BIN`7D
X** \paramend
X** \blurb`7BThis function evaluates the 3D vector \pardesc `7Bv1-v2`7D.`7D
X*/
X`7B
X  Ppoint3 v;
X
X  v = ptk_point3(p1->x - p2->x, p1->y - p2->y, p1->z - p2->z);
X  return v;
X`7D  /* ptk_subv3 */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern Ppoint ptk_subv(C(Ppoint *) p1, C(Ppoint *) p2)
XPreANSI(Ppoint *p1)
XPreANSI(Ppoint *p2)
X/*
X** \parambegin
X** \param`7BPpoint *`7D`7Bp1`7D`7B2D vector`7D`7BIN`7D
X** \param`7BPpoint *`7D`7Bp2`7D`7B2D vector`7D`7BIN`7D
X** \paramend
X** \blurb`7BThis function evaluates the 2D vector \pardesc `7Bv1-v2`7D.`7D
X*/
X`7B
X  Ppoint v;
X
X  v = ptk_point(p1->x - p2->x, p1->y - p2->y);
X  return v;
X`7D  /* ptk_subv */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern Ppoint3 ptk_addv3(C(Ppoint3 *) p1, C(Ppoint3 *) p2)
XPreANSI(Ppoint3 *p1)
XPreANSI(Ppoint3 *p2)
X/*
X** \parambegin
X** \param`7BPpoint3 *`7D`7Bp1`7D`7B3D vector`7D`7BIN`7D
X** \param`7BPpoint3 *`7D`7Bp2`7D`7B3D vector`7D`7BIN`7D
X** \paramend
X** \blurb`7BThis function adds the two 3D vectors \pardesc`7Bv1`7D and \pard
Vesc`7Bv2`7D,
X** and returns the result.`7D
X*/
X`7B
X  Ppoint3 v;
X
X  v = ptk_point3(p1->x + p2->x, p1->y + p2->y, p1->z + p2->z);
X  return v;
X`7D  /* ptk_addv3 */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern Ppoint ptk_addv(C(Ppoint *) p1, C(Ppoint *) p2)
XPreANSI(Ppoint *p1)
XPreANSI(Ppoint *p2)
X/*
X** \parambegin
X** \param`7BPpoint *`7D`7Bp1`7D`7B2D vector`7D`7BIN`7D
X** \param`7BPpoint *`7D`7Bp2`7D`7B2D vector`7D`7BIN`7D
X** \paramend
X** \blurb`7BThis function adds the two 2D vectors \pardesc`7Bv1`7D
X** and \pardesc`7Bv2`7D, and returns the result.`7D
X*/
X`7B
X  Ppoint v;
X
X  v = ptk_point(p1->x + p2->x, p1->y + p2->y);
X  return v;
X`7D  /* ptk_addv */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern void ptk_unitmatrix(C(Pmatrix) matrix)
XPreANSI(Pmatrix matrix)
X/*
X** \parambegin
X** \param`7BPmatrix`7D`7Bmatrix`7D`7B3x3 matrix`7D`7BIN`7D
X** \paramend
X** \blurb`7BThis procedure creates a unit $3\times 3$ matrix, and stores it
V in`20
X** \pardesc`7Bmatrix`7D.`7D
X*/
X`7B
X  /*  */
X  Pint jj, ii;
X
X  for (ii = 0; ii <= 2; ii++)`20
X  `7B
X    for (jj = 0; jj <= 2; jj++)
X      matrix`5Bii`5D`5Bjj`5D = 0.0;
X    matrix`5Bii`5D`5Bii`5D = 1.0;
X  `7D
X`7D  /* ptk_unitmatrix */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern void ptk_unitmatrix3(C(Pmatrix3) matrix)
XPreANSI(Pmatrix3 matrix)
X/*
X** \parambegin
X** \param`7BPmatrix3`7D`7Bmatrix`7D`7B4x4 matrix`7D`7BIN`7D
X** \paramend
X** \blurb`7BThis procedure creates a unit $4\times 4$ matrix, and stores it
V in`20
X** \pardesc`7Bmatrix`7D.`7D
X*/
X`7B
X  /*  */
X  Pint jj, ii;
X
X  for (ii = 0; ii <= 3; ii++)`20
X  `7B
X    for (jj = 0; jj <= 3; jj++)
X      matrix`5Bii`5D`5Bjj`5D = 0.0;
X    matrix`5Bii`5D`5Bii`5D = 1.0;
X  `7D
X`7D  /* ptk_unitmatrix3 */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern void ptk_transposematrix3(C(Pmatrix3) matrix, C(Pmatrix3) result)
XPreANSI(Pmatrix3 matrix)
XPreANSI(Pmatrix3 result)
X/*
X** \parambegin
X** \param`7BPmatrix3`7D`7Bmatrix`7D`7B4x4 matrix`7D`7BIN`7D
X** \param`7BPmatrix3`7D`7Bresult`7D`7B4x4 matrix`7D`7BOUT`7D
X** \paramend
X** \blurb`7BThis function transposes \pardesc`7Bmatrix`7D, and returns the r
Vesul
X** in \pardesc`7Bresult`7D.
X** Note that \pardesc`7Brestut`7D can be the same variable
X** as \pardesc`7Bmatrix`7D since a copy is made`20
X** first.`7D
X*/
X`7B
X  Pmatrix3 temp;
X  Pint i, j;
X
X  memcpy(temp, matrix, sizeof(Pmatrix3));
X  for (i = 0; i <= 3; i++)`20
X  `7B
X    for (j = 0; j <= 3; j++)
X      result`5Bi`5D`5Bj`5D = temp`5Bj`5D`5Bi`5D;
X  `7D
X`7D  /* ptk_transposematrix3 */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern void ptk_transposematrix(C(Pmatrix) matrix, C(Pmatrix) result)
XPreANSI(Pmatrix matrix)
XPreANSI(Pmatrix result)
X/*
X** \parambegin
X** \param`7BPmatrix`7D`7Bmatrix`7D`7B3x3 matrix`7D`7BIN`7D
X** \param`7BPmatrix`7D`7Bresult`7D`7B3x3 matrix`7D`7BOUT`7D
X** \paramend
X** \blurb`7BThis function transposes \pardesc`7Bmatrix`7D, and returns the r
Vesul
X** in \pardesc`7Bresult`7D.
X** Note that \pardesc`7Brestut`7D can be the same variable
X** as \pardesc`7Bmatrix`7D since a copy is made`20
X** first.`7D
X*/
X`7B
X  Pmatrix temp;
X  Pint i, j;
X
X  memcpy(temp, matrix, sizeof(Pmatrix));
X  for (i = 0; i <= 2; i++)`20
X  `7B
X    for (j = 0; j <= 2; j++)
X      result`5Bi`5D`5Bj`5D = temp`5Bj`5D`5Bi`5D;
X  `7D
X`7D  /* ptk_transposematrix */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern void ptk_multiplymatrix3(C(Pmatrix3) matrix1, C(Pmatrix3) matrix2,`20
X                          C(Pmatrix3) result)
XPreANSI(Pmatrix3 matrix1)
XPreANSI(Pmatrix3 matrix2)
XPreANSI(Pmatrix3 result)
X/*
X** \parambegin
X** \param`7BPmatrix3`7D`7Bmatrix1`7D`7B4x4 matrix`7D`7BIN`7D
X** \param`7BPmatrix3`7D`7Bmatrix2`7D`7B4x4 matrix`7D`7BIN`7D
X** \param`7BPmatrix3`7D`7Bresult`7D`7B4x4 matrix`7D`7BOUT`7D
X** \paramend
X** \blurb`7BThis function makes \pardesc`7Bresult`7D the product of
X** the $4 \times 4$ matrices  \pardesc`7Bmatrix1`7D and
X** \pardesc`7Bmatrix2`7D, with `7B\tt result $\leftarrow$ matrix1 * matrix2`
V7D.
X** Note that \pardesc`7Bresult`7D can also be \pardesc`7Bmatrix1`7D or \pard
Vesc`7Bmatrix2`7D
X** since a copy is made.
X** This function uses Winograd's method, see "Handbook of Algorithms
X** and Data Structures", G.H. Gonnet, Addison Wesley.
X*/
X`7B
X  Pint ii, jj;
X  Pmatrix3 sum;
X  Pfloat temp;
X  Pfloat d`5B4`5D, e`5B4`5D;
X
X  for (ii = 0; ii <= 3; ii++)`20
X  `7B
X    d`5Bii`5D = (matrix1`5Bii`5D`5B1`5D * matrix1`5Bii`5D`5B0`5D) +`20
X            (matrix1`5Bii`5D`5B3`5D * matrix1`5Bii`5D`5B2`5D);
X    e`5Bii`5D = (matrix2`5B0`5D`5Bii`5D * matrix2`5B1`5D`5Bii`5D) +`20
X            (matrix2`5B2`5D`5Bii`5D * matrix2`5B3`5D`5Bii`5D);
X  `7D
X
X  for (ii = 0; ii <= 3; ii++)`20
X  `7B
X    for (jj = 0; jj <= 3; jj++)`20
X    `7B
X      temp = (matrix1`5Bii`5D`5B1`5D + matrix2`5B0`5D`5Bjj`5D) *`20
X             (matrix1`5Bii`5D`5B0`5D + matrix2`5B1`5D`5Bjj`5D);
X      temp += (matrix1`5Bii`5D`5B3`5D + matrix2`5B2`5D`5Bjj`5D) *`20
X              (matrix1`5Bii`5D`5B2`5D + matrix2`5B3`5D`5Bjj`5D) - d`5Bii`5D
V - e`5Bjj`5D;
X      sum`5Bii`5D`5Bjj`5D = temp;
X    `7D
X  `7D
X  /* copy matrix back in case result is one of the other two */
X  memcpy(result, sum, sizeof(Pmatrix3));
X`7D  /* ptk_multiplymatrix3 */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern void ptk_multiplymatrix(C(Pmatrix) matrix1, C(Pmatrix) matrix2,`20
X                          C(Pmatrix) result)
XPreANSI(Pmatrix matrix1)
XPreANSI(Pmatrix matrix2)
XPreANSI(Pmatrix result)
X/*
X** \parambegin
X** \param`7BPmatrix`7D`7Bmatrix1`7D`7B3x3 matrix`7D`7BIN`7D
X** \param`7BPmatrix`7D`7Bmatrix2`7D`7B3x3 matrix`7D`7BIN`7D
X** \param`7BPmatrix`7D`7Bresult`7D`7B3x3 matrix`7D`7BOUT`7D
X** \paramend
X** \blurb`7BThis function makes \pardesc`7Bresult`7D the product of the
X** $3 \times 3$ matrices \pardesc`7Bmatrix1`7D and
X** \pardesc`7Bmatrix2`7D, with `7B\tt result $\leftarrow$ matrix1 * matrix2`
V7D.
X** Note that \pardesc`7Bresult`7D can also be \pardesc`7Bmatrix1`7D or \pard
Vesc`7Bmatrix2`7D
X** since a copy is made.`7D
X*/
X`7B
X  Pint ii, jj, kk;
X  Pmatrix sum;
X  Pfloat temp;
X  Pfloat d`5B3`5D, e`5B3`5D;
X
X  for (ii = 0; ii <= 2; ii++)
X    for (jj = 0; jj <= 2; jj++)
X      sum`5Bii`5D`5Bjj`5D = 0.0;
X  for (ii = 0; ii <= 2; ii++)
X    for (jj = 0; jj <= 2; jj++)
X      for (kk = 0; kk <= 2; kk++)
X        sum`5Bii`5D`5Bjj`5D += (matrix1`5Bii`5D`5Bkk`5D * matrix2`5Bkk`5D`5B
Vjj`5D);
X
X/*  for (ii = 0; ii <= 2; ii++)`20
X  `7B
X    d`5Bii`5D = (matrix1`5Bii`5D`5B1`5D * matrix1`5Bii`5D`5B0`5D);
X    e`5Bii`5D = (matrix2`5B0`5D`5Bii`5D * matrix2`5B1`5D`5Bii`5D);`20
X  `7D
X  for (ii = 0; ii <= 2; ii++)`20
X  `7B
X    for (jj = 0; jj <= 2; jj++)`20
X    `7B
X      temp = (matrix1`5Bii`5D`5B1`5D + matrix2`5B0`5D`5Bjj`5D) *`20
X             (matrix1`5Bii`5D`5B0`5D + matrix2`5B1`5D`5Bjj`5D);
X      temp += (matrix1`5Bii`5D`5B2`5D * matrix2`5B2`5D`5B2`5D) - d`5Bii`5D -
V e`5Bjj`5D;
X      sum`5Bii`5D`5Bjj`5D = temp;
X    `7D
X  `7D
X*/
X  /* copy matrix back in case result is one of the other two */
X  memcpy(result, sum, sizeof(Pmatrix));
X`7D  /* ptk_multiplymatrix */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern void ptk_concatenatematrix3(C(Pcomptype) operation,`20
X            C(Pmatrix3) matrix1, C(Pmatrix3) matrix2, C(Pmatrix3) result)
XPreANSI(Pcomptype operation)
XPreANSI(Pmatrix3 matrix1)
XPreANSI(Pmatrix3 matrix2)
XPreANSI(Pmatrix3 result)
X/*
X** \parambegin
X** \param`7BPcomptype`7D`7Boperation`7D`7Bconcatenation operation`7D`7BIN`7D
X** \param`7BPmatrix3`7D`7Bmatrix1`7D`7B4x4 matrix`7D`7BIN`7D
X** \param`7BPmatrix3`7D`7Bmatrix2`7D`7B4x4 matrix`7D`7BIN`7D
X** \param`7BPmatrix3`7D`7Bresult`7D`7B4x4 matrix`7D`7BOUT`7D
X** \paramend
X** \blurb`7BThis function concatenates the $4 \times 4$ matrices
X** \pardesc`7Bmatrix1`7D  and \pardesc`7Bmatrix2`7D
X** on the basis of \pardesc`7Boperation`7D.
X** The result is stored in \pardesc`7Bresult`7D.
X** Note that \pardesc`7Bresult`7D can also be \pardesc`7Bmatrix1`7D or \pard
Vesc`7Bmatrix2`7D
X** since a copy is made. When \pardesc`7Boperation`7D is`20
X** \pardesc`7Bpreconcatenate`7D, then \pardesc`7Bresult $\leftarrow$ matrix2
V * matrix1`7D.
X** When \pardesc`7Boperation`7D is \pardesc`7Bpostconcatenate`7D,`20
X** \pardesc`7Bresult $\leftarrow$  matrix1 * matrix2`7D.`7D
X*/
X`7B
X  switch (operation)`20
X  `7B
X  case PPRECONCATENATE: `20
X    ptk_multiplymatrix3(matrix2, matrix1, result);
X    break;
X
X  case PPOSTCONCATENATE: `20
X    ptk_multiplymatrix3(matrix1, matrix2, result);
X    break;
X
X  case PREPLACE: `20
X    memcpy(result, matrix1, sizeof(Pmatrix3));
X    break;
X  `7D
X`7D  /* ptk_concatenatematrix3 */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern void ptk_concatenatematrix(C(Pcomptype) operation,`20
X            C(Pmatrix) matrix1, C(Pmatrix) matrix2, C(Pmatrix) result)
XPreANSI(Pcomptype operation)
XPreANSI(Pmatrix matrix1)
XPreANSI(Pmatrix matrix2)
XPreANSI(Pmatrix result)
X/*
X** \parambegin
X** \param`7BPcomptype`7D`7Boperation`7D`7Bconcatenation operation`7D`7BIN`7D
X** \param`7BPmatrix`7D`7Bmatrix1`7D`7B3x3 matrix`7D`7BIN`7D
X** \param`7BPmatrix`7D`7Bmatrix2`7D`7B3x3 matrix`7D`7BIN`7D
X** \param`7BPmatrix`7D`7Bresult`7D`7B3x3 matrix`7D`7BOUT`7D
X** \paramend
X** \blurb`7BThis function concatenates
X** the $3 \times 3$ matrices \pardesc`7Bmatrix1`7D  and \pardesc`7Bmatrix2`7
VD
X** on the basis of \pardesc`7Boperation`7D.
X** The result is stored in \pardesc`7Bresult`7D.
X** Note that \pardesc`7Bresult`7D can also be \pardesc`7Bmatrix1`7D or \pard
Vesc`7Bmatrix2`7D
X** since a copy is made. When \pardesc`7Boperation`7D is
X** \pardesc`7Bpreconcatenate`7D, then \pardesc`7Bresult $\leftarrow$ matrix2
V * matrix1`7D.
X** When \pardesc`7Boperation`7D is \pardesc`7Bpostconcatenate`7D,`20
X** \pardesc`7Bresult $\leftarrow$ matrix1 * matrix2`7D.`7D
X*/
X`7B
X  switch (operation)`20
X  `7B
X  case PPRECONCATENATE: `20
X    ptk_multiplymatrix(matrix2, matrix1, result);
X    break;
X
X  case PPOSTCONCATENATE: `20
X    ptk_multiplymatrix(matrix1, matrix2, result);
X    break;
X
X  case PREPLACE: `20
X    memcpy(result, matrix1, sizeof(Pmatrix));
X    break;
X  `7D
X`7D  /* ptk_concatenatematrix */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
+-+-+-+-+-+-+-+-  END  OF PART 262 +-+-+-+-+-+-+-+-