(NOTE: This is in addition to Professor Hausner's A2 FAQ page.)

Questoin1:

• Question: I have a problem with changing coordinates from frame A to frame O.  The axes in frame A are not orthogonal, then how would you align it with frame O.


Answer:

Say, we first translate frame A's origin to where frame O's origin is.
Now, we know which point is (1,0)_{frame_A} for frame A.
What is this point's coordinate in frame O? -- Say, it is (1,-1)_{frame_O}.

OK, what matrix can you use to change (1,0)_{frame_A} to (1,-1)_{frame_O}?

[ 1]         [ ?  ? ]  [1]
[-1]_{frame_O} = [ ?  ? ]  [0]_{frame_A}
 
• Question: I am stuck on question #1d.  I'm having problems transforming coordinate system B onto co-ord system O and from A -->B because the axes on co-ordinate system B are inverted.  I have tried reflection and rotation but doesn't seem to work, can you please provide any hints?


Answer: Let's say we have a coordinate C which looks like
                | y
                |
                |
         x ------ frame C

 
OK, we know (0,1) of frame_C is also (0,1) of frame_O, if frame_C and frame_O's origins coincide.

What is (1,0) of frame_C in frame_O? -- it is (-1,0)_{frame_O}

What matrix can do this transformation?
    [0]      =  [ a? b? ] [0]
    [1]_{frame_O}    [ c? d? ] [1]_{frame_C}

    [-1]          [ a? b? ] [1]
    [0 ]_{frame_O} =  [ c? d? ] [0]frame_C
 

• Question: I am not sure what 2b) is asking?

 

 

Answer:  Take a look at the tutorial question #3 in
"Tutorial: Geometric Transformations 3"
http://www.dgp.toronto.edu/~ah/csc418/fall_2000/tut/tut_gtrans3.html

The TA should cover this tutorial exercise's solution by Wednesday, Oct 18, 2000.
 

• Question: I found the total number of triangles that could be made if a mesh was used but i was wondering how the statement of in real time(60 frames/sec) changes the result?

 

 

Answer: If you are running an animation which displays
60 frames/sec.  From each frame to the next, the object you animate would change.  When the object is modelled using the triangles, for each frame, the triangle's vertex locations would change.  For each frame, you have to re-compute and re-render and re-project the triangles.

• Question:  For question #3, from what I understand, the vector of Peye and Pref should be perpendicular to Vup, am I right?

Answer:  No.  Please see the Lecture Notes on "The Viewing Transformation"
http://www.dgp.toronto.edu/~ah/csc418/fall_2000/notes/viewing.html
Under the heading "Building M_cam", the formula for vectors i, j, k uses P_ref and P_eye.

• Question: Are the pixel coordinates in the same unit as the VCS?

 

 
 
 

Answer:
The pixel coordinate is in the DCS (Device Coordinate System),
which is related to the flat 2D display below.
For example, if your display has resolutin 5x5
(i.e., width=5, height=5), then you shoot 25 rays from your eye,
one for each pixel.
If your display has resolution 10x10 (width=10, height=10),  then
you shoot 100 rays from your eye.




 

• Question: For suggested procedure #4, is the projection onto one of the xy, yx or xz planes the parallel projection?

 

 

Answer: Yes.