Design: 06.01.02/P09

This is an abstract, language-independent design. Grim details may be found in the corresponding source code. You may return to the documentation for the module containing this program design, or to the entire hierarchical table of topics covered by the PVT.
PROGRAM 9: Visual effect of modelling transformation

CHARACTERISTICS: ynny

OPERATOR SCRIPT:

3D MODELLING TRANSFORMATION: All but one of the six boxes should
contain a single line segment with its endpoints circled.
Identify the line whose endpoints are not accurately marked.

2D MODELLING TRANSFORMATION: Same as 3D MODELLING TRANSFORMATION
above.

DESIGN:

Divide screen up into 6 square labelled areas for all tests
idxf = 3D identity matrix

TEST: #SR 1 8 9 15 16 17
      "The modelling coordinates of a 3D polyline should be
       transformed into world coordinates by 3D local and
       global modelling transformation."

lisbox = permutation of 1-6
ngbox  = incorrect box = random from 1 to 6
for ix = 1 to 6
   this = lisbox(ix)
   xf = 4x4 matrix, values chosen randomly from 0.5 to 1.5

   in order to see effect of z-coord:
   if this = 1 or 4 then
      rotxf = matrix to rotate 90 degrees around x-axis
   elseif this = 2 or 5 then
      rotxf = matrix to rotate 90 degrees around y-axis
   else
      rotxf = matrix to rotate 90 degrees around z-axis
   endif

   calculate effect on position of WC: 1,1,1 and 2,2,2
      wc1x,wc1y,wc1z = rotxf X xf X (1,1,1)
      wc2x,wc2y,wc2z = rotxf X xf X (2,2,2)

   calculate boxf so as to scale and shift WCs into box #ix

   composite transformation will be boxf X rotxf X xf
   matrix fixf = boxf X rotxf

   calculate expected position of WC: 1,1,1 and 2,2,2
      wc1x,wc1y,wc1z = fixf X xf X (1,1,1)
      wc2x,wc2y,wc2z = fixf X xf X (2,2,2)

   if ix = ngbox then
      distort result:
      ngxf = rotate 10 degrees on z-axis, around box center
      fixf = ngxf X fixf
   endif

   if this < 3 then
      replace local with fixf
      preconcatenate xf to local
   elseif this < 5 then
      replace local with xf
      postconcatenate fixf to local
   else
      replace local with xf
      replace global with fixf
   endif
   draw 3D polyline from (1,1,1) to (2,2,2)
   replace local with idxf
   replace global with idxf

   draw expected positions as 2D circle polymarker at
      wc1x,wc1y and wc2x,wc2y
next ix

OPQA/3D MODELLING TRANSFORMATION: Which box contains something
  other than a single line segment with circled endpoints?
pass/fail depending on (operator chooses box #ngbox)

*** *** *** *** *** *** *** *** *** *** *** *** *** *** ***

TEST: #SR 4 8 12 15 16 17 18
      "The modelling coordinates of a 3D polyline should be
       transformed into world coordinates by 2D local and
       global modelling transformation."

lisbox = permutation of 1-6
ngbox  = incorrect box = random from 1 to 6
for ix = 1 to 6
   this = lisbox(ix)
   xf2 = 3x3 matrix, values chosen randomly from 0.5 to 1.5

   in order to see effect of z-coord:
   if this = 1 or 4 then
      rotxf = matrix to rotate 90 degrees around x-axis
   elseif this = 2 or 5 then
      rotxf = matrix to rotate 90 degrees around y-axis
   else
      rotxf = matrix to rotate 90 degrees around z-axis
   endif

   calculate effect on position of WC: 1,1,1 and 2,2,2
      wc1x,wc1y,wc1z = rotxf X xf X (1,1,1)
      wc2x,wc2y,wc2z = rotxf X xf X (2,2,2)

   calculate boxf so as to scale and shift WCs into box #ix

   composite transformation will be boxf X rotxf X xf
   matrix fixf = boxf X rotxf

   calculate expected position of WC: 1,1,1 and 2,2,2
      wc1x,wc1y,wc1z = fixf X xf X (1,1,1)
      wc2x,wc2y,wc2z = fixf X xf X (2,2,2)

   if ix = ngbox then
      distort result:
      ngxf = rotate 10 degrees on z-axis, around box center
      fixf = ngxf X fixf
   endif

   if this < 3 then
      replace local with fixf
      preconcatenate xf2 to local
   elseif this < 5 then
      replace local with xf2
      postconcatenate fixf to local
   else
      replace local with xf2
      replace global with fixf
   endif
   draw 3D polyline from (1,1,1) to (2,2,2)
   replace local with idxf
   replace global with idxf

   draw expected positions as 2D circle polymarker at
      wc1x,wc1y and wc2x,wc2y
next ix

OPQA/2D MODELLING TRANSFORMATION: Which box contains something
  other than a single line segment with circled endpoints?
pass/fail depending on (operator chooses box #ngbox)

END PROGRAM 9