CSC418/2504 : Assignment 2 FAQ

• Question 1:
• Question 2:
• Question 3:
  1. Q: The axes in the picture are wrong!

     A: Sorry about that. The "Z" axis should be "X", "X" should be "Y", and "Y" should be "Z". Here is the correct picture:

     

  2. Q: How do I compute vanishing points????

     A: If you have several parallel lines, they will appear to meet at a point when the perspective projection is applied. We know this, but how do we do it mathematically?

     Think about the equation for a line: (x,y,z) = (Px,Py,Pz) + t(Vx,Vy,Vz). If you project this line using the projection matrix, and keep all the parameters in place, when you let t go to infinity, you should get the vanishing point.

     Another way to look at it is this: A point on the line will have homogeneous coordinates:

     (Px+tVx, Py+tVy, Pz+tVz, 1).

     Since we can multiply homogeneous points by a constant, this is equivalent to the point multiplied by 1/t:

     (Px/t+Vx, Py/t+Vy, Pz/t+Vz, 1/t)

     Now let t go to infinity, and the homogeneous point is

     (Vx,Vy,Vz,0)

     So this should project to the vanishing point. Moral: the "Point at infinity" is a direction vector.

  3. Q: Where is the image plane?

     A: It's 1 (one) unit away from the eye, perpendicular to the eye-reference line, which is the camera's Z axis.

• Question 4:
  1. Q: The XYZ-RGB matrix is giving me negative values!

     A: Sorry. The top-left number is positive, not negative:

           [R]   [ 1.967 -0.548 -0.297] [X]
           [G] = [-0.955  1.938 -0.027] [Y]
           [B]   [ 0.064 -0.130  0.982] [Z]
          

  2. Q: Should we submit the code we wrote for this question?

     A: No. Just write up your values of X,Y,Z, x,y, etc. that you obtained through your calculations.

  3. Q: In lecture, you gave the following formula for calculating X, Y and Z in the CIE colour plot:

     X = k Σ P(λ) X(λ) Δλ

     What is k in that equation?

     A: It can be anything. Make it 1. It gets thrown out by the normalization anyway.

  4. Q: we are asked to plot the colour on the CIE diagram and calculate the dominant wavelength - is it sufficient to estimate the dominant wavelength by visual inspection of the plot?

     A: yes.

• Question 5:
  1. Q: Where is the image plane?

     A: The image plane is located on the front clipping plane, and the image is contained in a rectangle bounded by the left, right, top, and bottom planes. Thus the image is a rectangle whose opposite corners are:

     • (bottom,left,-near)
     • (top,right,-near)

  2. Q: Where is the camera eye point?

     A: In VCS, at the origin, (0,0,0)

  3. Q: How big are the pixels?

     A: On the image rectangle, there are W of them left-right and H of them up-down. You should be able to infer each pixel's VCS coords from this information.

  4. Q: Where exactly is the (0,0) point on the image plane?

     In DEVICE coordinates, on the bottom-left corner of the image rectangle.

  5. Q: Could you provide some test data?

     Sure. Look here.

• Question 6: