Homework 2 Corrections and Clarifications
Problem 2a asks you to specify normals to the front face of the block at points G, B, and A.
This is not hard to do. If you find yourself going nuts because the location of point A is not given exactly, and you are deep in a formula that requires the coordinates of all three points, step back and take another look at the definition of the face.
You do not need to do a lot of cross products to figure this one out.
In problem 4, you are writing a function to provide color shading at a point. The problem says that you can assume that you have values for the age of the wood and the color for each type of ring.
You can also assume that you have access to any other values that you feel you need. For example, the thickness of each ring type could be assumed to be pre-specified constants like DARK_RING_WIDTH and LIGHT_RING_WIDTH. Furthermore, if you wanted to specify a function that calculated ring width based on the other values you have, that would be okay too.This question does not have a single correct answer that produces "absolutely correct wood shading." The idea behind it is to get you thinking about how a 3-D shading algorithm works, and what some of the features are that would make it realistic and useful.
All shading algorithms are hacks, but some hacks are better than others ...
In problem 5b and 5d, the idea is that you should consider a rotation about one axis, and list the constraints on that rotation that would allow mip-mapping (or summed area tables) to always return the correct average texture value for the area that the image pixel maps onto in the texture (the pre-image). Then reset the situation, and consider a rotation about another axis. What constraints are required? Then do the same thing for the third axis.
In 5d, the question is "As in (b), what restrictions do we have on rotations about any one of the axes in order for summed area tables to return the correct average texture values?" Consider this question in light of the explanation above.