PVT: Modelling utilities

Module #06.01.01 : Modelling utilities

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DESCRIPTION: This module tests the functions provided by PHIGS
to support modelling transformations.  These functions do not
depend on the state of PHIGS data structures, nor do they affect
them; their behavior interacts only with their input and output
parameters.

SEMANTIC REQUIREMENTS:

SR1.  Modelling transformations are represented as 4x4 (for 3D)
or 3x3 (2D) matrices which pre-multiply points to be transformed.

#F 91-106
#D 7.3.3.1 7.3.3.2 7.3.3.3 7.3.3.4
#S 4.7.2/77/3
#T P01/1 P01/2 P01/3 P01/4 P02/1 P02/2 P02/3 P02/4 P03/1 P03/2 P03/3
#T P03/4 P04/1 P04/2 P05/1 P05/2 P06/1 P06/2 P07/1 P07/2


SR2.  Points are represented as column vectors with homogeneous
coordinates, i.e. the coordinates x,y,z,w represent the three
dimensional point (x/w, y/w, z/w).

#F 91-106
#D 7.3.3.1 7.3.3.2 7.3.3.3 7.3.3.4
#S 4.7.2/77/3
#T P01/1 P01/2 P01/3 P01/4 P02/1 P02/2 P02/3 P02/4 P03/1 P03/2 P03/3
#T P03/4 P04/1 P04/2 P05/1 P05/2 P06/1 P06/2 P07/1 P07/2


SR3.  <Translate 3> generates a 3D homogeneous transformation
matrix to translate a point from (x,y,z) to (x+dx, y+dy, z+dz).

#F 91
#D
#S 4.7.3/79/4
#T P01/1 P01/2


SR4.  <Translate> generates a 2D homogeneous transformation
matrix to translate a point from (x,y) to (x+dx, y+dy).

#F 92
#D
#S 4.7.3/79/4
#T P01/3 P01/4


SR5.  <Scale 3> generates a 3D homogeneous transformation
matrix to scale a point from (x,y,z) to (x*sx, y*sy, z*sz).

#F 93
#D
#S 4.7.3/79/4
#T P02/1 P02/2


SR6.  <Scale> generates a 2D homogeneous transformation
matrix to scale a point from (x,y) to (x*sx, y*sy).

#F 94
#D
#S 4.7.3/79/4
#T P02/3 P02/4


SR7.  <Rotate x> generates a 3D homogeneous transformation matrix
to rotate a point counterclockwise around the X axis by the
specified rotation angle.

#F 95
#D
#S 4.7.3/79/4
#T P03/1


SR8.  <Rotate y> generates a 3D homogeneous transformation matrix
to rotate a point counterclockwise around the Y axis by the
specified rotation angle.

#F 96
#D
#S 4.7.3/79/4
#T P03/2


SR9.  <Rotate z> generates a 3D homogeneous transformation
matrix to rotate a point counterclockwise around the Z axis by
the specified rotation angle.

#F 97
#D
#S 4.7.3/79/4
#T P03/3


SR10.  <Rotate> generates a 2D homogeneous transformation matrix
to rotate a point counterclockwise around the origin by the
specified rotation angle.

#F 98
#D
#S 4.7.3/79/4
#T P03/4


SR11.  <Compose matrix 3> generates a 3D homogeneous
transformation matrix which performs the same transformation as
that resulting from the multiplication of the two specified
matrices.

#F 99
#D
#S 4.7.3/79/4
#T P04/1


SR12.  <Compose matrix> generates a 2D homogeneous transformation
matrix which performs the same transformation as that resulting
from the multiplication of the two specified matrices.

#F 100
#D
#S 4.7.3/79/4
#T P04/2


SR13.  <Transform point 3> returns the 3D point resulting from
applying the specified transformation matrix to the specified
point.

#F 101
#D
#S 4.7.3/79/4
#T P05/1


SR14.  <Transform point> returns the 2D point resulting from
applying the specified transformation matrix to the specified
point.

#F 102
#D
#S 4.7.3/79/4
#T P05/2


SR15.  <Build transformation matrix 3> generates a 3D homogeneous
transformation matrix to perform the specified transformation.
This transformation performs the following operations in order,
relative to the fixed point: scale, rotate x, rotate y, rotate z,
and shift.

#F 103
#D
#S 4.7.3/79/4
#T P06/1


SR16.  <Build transformation matrix> generates a 2D homogeneous
transformation matrix to perform the specified transformation.
This transformation performs the following operations in order,
relative to the fixed point: scale, rotate, and shift.

#F 104
#D
#S 4.7.3/79/4
#T P06/2


SR17.  <Compose transformation matrix 3> generates a 3D
homogeneous transformation matrix to perform the specified
transformation.  This transformation performs the following
operations in order, relative to the fixed point: scale, rotate
x, rotate y, rotate z, and shift, and then apply the specified
matrix.

#F 105
#D
#S 4.7.3/79/4
#T P07/1 #C Note that the specified matrix is applied last, not first.


SR18.  <Compose transformation matrix> generates a 2D homogeneous
transformation matrix  to perform the specified transformation.
This transformation performs the following operations in order,
relative to the fixed point: scale, rotate, and shift, and then
apply the specified matrix.

#F 106
#D
#S 4.7.3/79/4
#T P07/2 #C Note that the specified matrix is applied last, not first.

LOCAL DICTIONARY:


  Functions ---
  091: ptr3    <translate 3>
  092: ptr     <translate>
  093: psc3    <scale 3>
  094: psc     <scale>
  095: prox    <rotate x>
  096: proy    <rotate y>
  097: proz    <rotate z>
  098: pro     <rotate>
  099: pcom3   <compose matrix 3>
  100: pcom    <compose matrix>
  101: ptp3    <transform point 3>
  102: ptp     <transform point>
  103: pbltm3  <build transformation matrix 3>
  104: pbltm   <build transformation matrix>
  105: pcotm3  <compose transformation matrix 3>
  106: pcotm   <compose transformation matrix>
 
  Data Structures ---
  7  ...  structure_state_list
  7.3  ...  list_of_structure_elements
  7.3.3  ...  modelling_transformation_elements
  7.3.3.1  ...  local_transformation_3
  7.3.3.2  ...  local_transformation
  7.3.3.3  ...  global_transformation_3
  7.3.3.4  ...  global_transformation
 
LOCAL SUBROUTINES: These tests use the transformation subroutine
library.  See that library for documentation of the routines.