-+-+-+-+-+-+-+-+ START OF PART 263 -+-+-+-+-+-+-+-+
Xextern void ptk_shift3(C(Ppoint3 *) shift, C(Pcomptype) operation,`20
X                       C(Pmatrix3) matrix)
XPreANSI(Ppoint3 *shift)
XPreANSI(Pcomptype operation)
XPreANSI(Pmatrix3 matrix)
X/*
X** \parambegin
X** \param`7BPpoint3 *`7D`7Bshift`7D`7Bshift factor`7D`7BIN`7D
X** \param`7BPcomptype`7D`7Boperation`7D`7Bconcatenation operation`7D`7BIN`7D
X** \param`7BPmatrix3`7D`7Bmatrix`7D`7B4x4 matrix`7D`7BOUT`7D
X** \paramend
X** \blurb`7BThis function computes
X**  a matrix to perform the specified 3D shift and concatenates`20
X** this matrix with \pardesc`7Bmatrix`7D on the basis of \pardesc`7Boperatio
Vn`7D.`7D
X*/
X`7B
X  Pmatrix3 temp;
X
X  ptk_unitmatrix3(temp);
X  temp`5B0`5D`5B3`5D = shift->x;
X  temp`5B1`5D`5B3`5D = shift->y;
X  temp`5B2`5D`5B3`5D = shift->z;
X  ptk_concatenatematrix3(operation, temp, matrix, matrix);
X`7D  /* ptk_shift3 */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern void ptk_shift(C(Ppoint *) shift, C(Pcomptype) operation,`20
X                       C(Pmatrix) matrix)
XPreANSI(Ppoint *shift)
XPreANSI(Pcomptype operation)
XPreANSI(Pmatrix matrix)
X/*
X** \parambegin
X** \param`7BPpoint *`7D`7Bshift`7D`7Bshift factor`7D`7BIN`7D
X** \param`7BPcomptype`7D`7Boperation`7D`7Bconcatenation operation`7D`7BIN`7D
X** \param`7BPmatrix`7D`7Bmatrix`7D`7B3x3 matrix`7D`7BOUT`7D
X** \paramend
X** \blurb`7BThis function computes
X** a matrix to perform the specified 2D shift and concatenates`20
X** this matrix with \pardesc`7Bmatrix`7D on the basis of \pardesc`7Boperatio
Vn`7D.`7D
X*/
X`7B
X  Pmatrix temp;
X
X  ptk_unitmatrix(temp);
X  temp`5B0`5D`5B2`5D = shift->x;
X  temp`5B1`5D`5B2`5D = shift->y;
X  ptk_concatenatematrix(operation, temp, matrix, matrix);
X`7D  /* ptk_shift */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern void ptk_scale3(C(Ppoint3 *) scale, C(Pcomptype) operation,`20
X                       C(Pmatrix3) matrix)
XPreANSI(Ppoint3 *scale)
XPreANSI(Pcomptype operation)
XPreANSI(Pmatrix3 matrix)
X/*
X** \parambegin
X** \param`7BPpoint3 *`7D`7Bshift`7D`7Bshift factor`7D`7BIN`7D
X** \param`7BPcomptype`7D`7Boperation`7D`7Bconcatenation operation`7D`7BIN`7D
X** \param`7BPmatrix3`7D`7Bmatrix`7D`7B4x4 matrix`7D`7BOUT`7D
X** \paramend
X** \blurb`7BThis function`20
X** computes a matrix to perform the specified 3D scale and concatenates`20
X** this with \pardesc`7Bmatrix`7D on the basis of \pardesc`7Boperation`7D.`7
VD
X*/
X`7B
X  Pmatrix3 temp;
X
X  ptk_unitmatrix3(temp);
X  temp`5B0`5D`5B0`5D = scale->x; `20
X  temp`5B1`5D`5B1`5D = scale->y;
X  temp`5B2`5D`5B2`5D = scale->z;
X  ptk_concatenatematrix3(operation, temp, matrix, matrix);
X`7D  /* ptk_scale3 */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern void ptk_scale(C(Ppoint *) scale, C(Pcomptype) operation,`20
X                       C(Pmatrix) matrix)
XPreANSI(Ppoint *scale)
XPreANSI(Pcomptype operation)
XPreANSI(Pmatrix matrix)
X/*
X** \parambegin
X** \param`7BPpoint *`7D`7Bshift`7D`7Bshift factor`7D`7BIN`7D
X** \param`7BPcomptype`7D`7Boperation`7D`7Bconcatenation operation`7D`7BIN`7D
X** \param`7BPmatrix`7D`7Bmatrix`7D`7B3x3 matrix`7D`7BOUT`7D
X** \paramend
X** \blurb`7BThis function computes
X**  a matrix to perform the specified 2D scale and concatenates`20
X** this matrix with \pardesc`7Bmatrix`7D on the basis of \pardesc`7Boperatio
Vn`7D.`7D
X*/
X`7B
X  Pmatrix temp;
X
X  ptk_unitmatrix(temp);
X  temp`5B0`5D`5B0`5D = scale->x; `20
X  temp`5B1`5D`5B1`5D = scale->y;
X  ptk_concatenatematrix(operation, temp, matrix, matrix);
X`7D  /* ptk_scale */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern void ptk_rotatecs3(C(Pfloat) costheta, C(Pfloat) sinetheta,`20
X                          C(ptkeaxistype) axis, C(Pcomptype) operation,`20
X                          C(Pmatrix3) matrix)
XPreANSI(Pfloat costheta)
XPreANSI(Pfloat sinetheta)
XPreANSI(ptkeaxistype axis)
XPreANSI(Pcomptype operation)
XPreANSI(Pmatrix3 matrix)
X/*
X** \parambegin
X** \param`7BPfloat`7D`7Bcostheta`7D`7Bcosine of angle`7D`7BIN`7D
X** \param`7BPfloat`7D`7Bsinetheta`7D`7Bsine of angle`7D`7BIN`7D
X** \param`7Bptkeaxistype`7D`7Baxis`7D`7Bx, y or z axis`7D`7BIN`7D
X** \param`7BPcomptype`7D`7Boperation`7D`7Bconcatenation operation`7D`7BIN`7D
X** \param`7BPmatrix3`7D`7Bmatrix`7D`7B4x4 matrix`7D`7BOUT`7D
X** \paramend
X** \blurb`7BThis function computes
X** a matrix to perform the specified 3D rotation and concatenates`20
X** this matrix with`20
X** \pardesc`7Bmatrix`7D on the basis of \pardesc`7Boperation`7D.
X** This form assumes that the rotation is specified
X** using the $\cos(theta)$ and $\sin(theta)$ terms.
X** Note that no check is made to ensure that the sum of the squares of these
X** terms is 1.`7D
X*/
X`7B
X  Pmatrix3 temp;
X
X  ptk_unitmatrix3(temp);
X  switch (axis)`20
X  `7B
X  case PTKEXAXIS:
X    temp`5B2`5D`5B2`5D = costheta;
X    temp`5B1`5D`5B1`5D = costheta;
X    temp`5B1`5D`5B2`5D = -sinetheta;
X    temp`5B2`5D`5B1`5D = sinetheta;
X    break;
X
X  case PTKEYAXIS:
X    temp`5B0`5D`5B0`5D = costheta;
X    temp`5B2`5D`5B2`5D = costheta;
X    temp`5B0`5D`5B2`5D = sinetheta;
X    temp`5B2`5D`5B0`5D = -sinetheta;
X    break;
X
X  case PTKEZAXIS:
X    temp`5B0`5D`5B0`5D = costheta;
X    temp`5B1`5D`5B1`5D = costheta;
X    temp`5B0`5D`5B1`5D = -sinetheta;
X    temp`5B1`5D`5B0`5D = sinetheta;
X    break;
X  `7D
X  ptk_concatenatematrix3(operation, temp, matrix, matrix);
X`7D  /* ptk_rotatecs3 */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern void ptk_rotatecs(C(Pfloat) costheta, C(Pfloat) sinetheta,`20
X                          C(ptkeaxistype) axis, C(Pcomptype) operation,`20
X                          C(Pmatrix) matrix)
XPreANSI(Pfloat costheta)
XPreANSI(Pfloat sinetheta)
XPreANSI(ptkeaxistype axis)
XPreANSI(Pcomptype operation)
XPreANSI(Pmatrix matrix)
X/*
X** \parambegin
X** \param`7BPfloat`7D`7Bcostheta`7D`7Bcosine of angle`7D`7BIN`7D
X** \param`7BPfloat`7D`7Bsinetheta`7D`7Bsine of angle`7D`7BIN`7D
X** \param`7Bptkeaxistype`7D`7Baxis`7D`7Bx, y or z axis`7D`7BIN`7D
X** \param`7BPcomptype`7D`7Boperation`7D`7Bconcatenation operation`7D`7BIN`7D
X** \param`7BPmatrix`7D`7Bmatrix`7D`7B3x3 matrix`7D`7BOUT`7D
X** \paramend
X** \blurb`7BThis function computes
X** a matrix to perform the specified 2D rotation and concatenates`20
X** this matrix with`20
X** \pardesc`7Bmatrix`7D on the basis of \pardesc`7Boperation`7D.
X** This form assumes that the rotation is specified
X** using the $\cos(theta)$ and $\sin(theta)$ terms.
X** Note that no check is made to ensure that the sum of the squares of these
X** terms is 1.`7D
X*/
X`7B
X  Pmatrix temp;
X
X  ptk_unitmatrix(temp);
X  switch (axis)`20
X  `7B
X  case PTKEXAXIS:
X    temp`5B2`5D`5B2`5D = costheta;
X    temp`5B1`5D`5B1`5D = costheta;
X    temp`5B1`5D`5B2`5D = -sinetheta;
X    temp`5B2`5D`5B1`5D = sinetheta;
X    break;
X
X  case PTKEYAXIS:
X    temp`5B0`5D`5B0`5D = costheta;
X    temp`5B2`5D`5B2`5D = costheta;
X    temp`5B0`5D`5B2`5D = sinetheta;
X    temp`5B2`5D`5B0`5D = -sinetheta;
X    break;
X
X  case PTKEZAXIS:
X    temp`5B0`5D`5B0`5D = costheta;
X    temp`5B1`5D`5B1`5D = costheta;
X    temp`5B0`5D`5B1`5D = -sinetheta;
X    temp`5B1`5D`5B0`5D = sinetheta;
X    break;
X  `7D
X  ptk_concatenatematrix(operation, temp, matrix, matrix);
X`7D  /* ptk_rotatecs */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern void ptk_rotate3(C(Pfloat) rotation, C(ptkeaxistype) axis,`20
X                        C(Pcomptype) operation, C(Pmatrix3) matrix)
XPreANSI(Pfloat rotation)
XPreANSI(ptkeaxistype axis)
XPreANSI(Pcomptype operation)`20
XPreANSI(Pmatrix3 matrix)
X/*
X** \parambegin
X** \param`7BPfloat`7D`7Brotation`7D`7Bangle in degrees`7D`7BIN`7D
X** \param`7Bptkeaxistype`7D`7Baxis`7D`7Bx, y or z axis`7D`7BIN`7D
X** \param`7BPcomptype`7D`7Boperation`7D`7Bconcatenation operation`7D`7BIN`7D
X** \param`7BPmatrix3`7D`7Bmatrix`7D`7B4x4 matrix`7D`7BOUT`7D
X** \paramend
X** \blurb`7BThis function computes
X** a matrix to perform the specified 3D rotation and concatenates`20
X** this matrix with`20
X** \pardesc`7Bmatrix`7D on the basis of \pardesc`7Boperation`7D.
X** \pardesc`7Brotation`7D is expressed in degrees.`7D
X*/
X`7B
X  Pfloat costheta;
X  Pfloat sinetheta;
X
X  costheta  = cos((rotation * ptkcdtor));
X  sinetheta = sin((rotation * ptkcdtor));
X  ptk_rotatecs3(costheta, sinetheta, axis, operation, matrix);
X`7D  /* ptk_rotate3 */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern void ptk_rotate(C(Pfloat) rotation, C(ptkeaxistype) axis,`20
X                        C(Pcomptype) operation, C(Pmatrix) matrix)
XPreANSI(Pfloat rotation)
XPreANSI(ptkeaxistype axis)
XPreANSI(Pcomptype operation)`20
XPreANSI(Pmatrix matrix)
X/*
X** \parambegin
X** \param`7BPfloat`7D`7Brotation`7D`7Bangle in degrees`7D`7BIN`7D
X** \param`7Bptkeaxistype`7D`7Baxis`7D`7Bx, y or z axis`7D`7BIN`7D
X** \param`7BPcomptype`7D`7Boperation`7D`7Bconcatenation operation`7D`7BIN`7D
X** \param`7BPmatrix`7D`7Bmatrix`7D`7B3x3 matrix`7D`7BOUT`7D
X** \paramend
X** \blurb`7BThis function computes
X** a matrix to perform the specified 2D rotation and concatenates`20
X** this matrix with`20
X** \pardesc`7Bmatrix`7D on the basis of \pardesc`7Boperation`7D.
X** \pardesc`7Brotation`7D is expressed in degrees.`7D
X*/
X`7B
X  Pfloat costheta;
X  Pfloat sinetheta;
X
X  costheta  = cos((rotation * ptkcdtor));
X  sinetheta = sin((rotation * ptkcdtor));
X  ptk_rotatecs(costheta, sinetheta, axis, operation, matrix);
X`7D  /* ptk_rotate */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern void ptk_shear3(C(ptkeaxistype) shearaxis, C(ptkeaxistype) sheardir,`
V20
X                       C(Pfloat) shearfactor, C(Pcomptype) operation,`20
X                       C(Pmatrix3) matrix)
XPreANSI(ptkeaxistype shearaxis)
XPreANSI(ptkeaxistype sheardir)
XPreANSI(Pfloat shearfactor)
XPreANSI(Pcomptype operation)
XPreANSI(Pmatrix3 matrix)
X/*
X** \parambegin
X** \param`7Bptkeaxistype`7D`7Bshearaxis`7D`7Bx, y or z axis`7D`7BIN`7D
X** \param`7Bptkeaxistype`7D`7Bsheardir`7D`7Bx, y or z direction`7D`7BIN`7D
X** \param`7BPfloat`7D`7Bshearfactor`7D`7Bshear factor`7D`7BIN`7D
X** \param`7BPcomptype`7D`7Boperation`7D`7Bconcatenation operation`7D`7BIN`7D
X** \param`7BPmatrix3`7D`7Bmatrix`7D`7B4x4 matrix`7D`7BOUT`7D
X** \paramend
X** \blurb`7BThis function computes a matrix to perform the specified 3D
X**  shear and concatenates`20
X** this matrix with`20
X** \pardesc`7Bmatrix`7D on the basis of \pardesc`7Boperation`7D.
X** The shear is specified as an amount \pardesc`7Bf`7D about axis \pardesc`7
VBi`7D
X** in direction \pardesc`7Bj`7D.`7D
X*/
X`7B
X  Pmatrix3 temp;
X
X  ptk_unitmatrix3(temp);
X  temp`5B(Pint)shearaxis - 1`5D`5B(Pint)sheardir - 1`5D = shearfactor;
X  ptk_concatenatematrix3(operation, temp, matrix, matrix);
X`7D  /* ptk_shear3 */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern void ptk_shear(C(ptkeaxistype) shearaxis, C(ptkeaxistype) sheardir,`2
V0
X                       C(Pfloat) shearfactor, C(Pcomptype) operation,`20
X                       C(Pmatrix) matrix)
XPreANSI(ptkeaxistype shearaxis)
XPreANSI(ptkeaxistype sheardir)
XPreANSI(Pfloat shearfactor)
XPreANSI(Pcomptype operation)
XPreANSI(Pmatrix matrix)
X/*
X** \parambegin
X** \param`7Bptkeaxistype`7D`7Bshearaxis`7D`7Bx or y axis`7D`7BIN`7D
X** \param`7Bptkeaxistype`7D`7Bsheardir`7D`7Bx or y direction`7D`7BIN`7D
X** \param`7BPfloat`7D`7Bshearfactor`7D`7Bshear factor`7D`7BIN`7D
X** \param`7BPcomptype`7D`7Boperation`7D`7Bconcatenation operation`7D`7BIN`7D
X** \param`7BPmatrix`7D`7Bmatrix`7D`7B3x3 matrix`7D`7BOUT`7D
X** \paramend
X** \blurb`7BThis function computes a matrix to perform the specified 2D
X**  shear and concatenates`20
X** this matrix with`20
X** \pardesc`7Bmatrix`7D on the basis of \pardesc`7Boperation`7D.
X** The shear is specified as an amount \pardesc`7Bf`7D about axis \pardesc`7
VBi`7D
X** in direction \pardesc`7Bj`7D.`7D
X*/
X`7B
X  Pmatrix temp;
X
X  ptk_unitmatrix(temp);
X  temp`5B(Pint)shearaxis - 1`5D`5B(Pint)sheardir - 1`5D = shearfactor;
X  ptk_concatenatematrix(operation, temp, matrix, matrix);
X`7D  /* ptk_shear */
X
X/*--------------------------------------------------------------------------
V*/
X
X/*function:external*/
Xextern void ptk_rotatevv3(C(Ppoint3 *) v1, C(Ppoint3 *) v2,`20
X                          C(Pcomptype) operation,`20
X                          C(Pmatrix3) matrix, C(Pint *)error)
XPreANSI(Ppoint3 *v1)
XPreANSI(Ppoint3 *v2)
XPreANSI(Pcomptype operation)`20
XPreANSI(Pmatrix3 matrix)
XPreANSI(Pint *error)
X/*
X** \parambegin
X** \param`7BPpoint3 *`7D`7Bv1`7D`7B3D vector`7D`7BIN`7D
X** \param`7BPpoint3 *`7D`7Bv2`7D`7B3D vector`7D`7BIN`7D
X** \param`7BPcomptype`7D`7Boperation`7D`7Bconcatenation operation`7D`7BIN`7D
X** \param`7BPmatrix3`7D`7Bmatrix`7D`7B4x4 matrix`7D`7BOUT`7D
X** \param`7BPint *`7D`7Berror`7D`7Berror code`7D`7BOUT`7D
X** \paramend
X** \blurb`7BThis function computes
X**  a matrix to perform the rotation (about the origin) of the 3D vector
X** \pardesc`7Bv1`7D to the 3D vector`20
X** \pardesc`7Bv2`7D, and concatenates this matrix with`20
X** \pardesc`7Bmatrix`7D on the basis of \pardesc`7Boperation`7D (\cite`7Brog
V:mecg`7D,`20
X**  pages 55--59). If the parameters are invalid, \pardesc`7Berror`7D is set
V to`20
X** -1. Otherwise, its value is \pardesc`7Bptkcpcok`7D.`7D
X*/
X`7B
X  Pmatrix3 temp;
X  Ppoint3 dv1, dv2, nvec;
X  Pfloat t1, costheta, sinetheta;
X
X  /* Create a rotation matrix (about origin) to rotate from
X  ** vector dv1 to vector dv2
X  ** Cf ROGERS and ADAMS page 55-59
X  */
X
X  *error = ptkcpcok;   /* Assume OK */
X  dv1 = ptk_unitv3(v1);
X  dv2 = ptk_unitv3(v2);
X
X  /* Get sine theta (cross product) and cos theta (dot product) */
X
X  costheta = dv1.x * dv2.x + dv1.y * dv2.y + dv1.z * dv2.z;
X  nvec = ptk_crossv3(&dv1, &dv2);
X
X  /* How do I choose sign of sinetheta?
X  ** let A, B and K be unit vectors, then
+-+-+-+-+-+-+-+-  END  OF PART 263 +-+-+-+-+-+-+-+-