CS 970: Spring 2006 Assignment 1 FAQ

1. Q: When is the assignment due?

   A: Let's aim for Monday, Feb. 6th, in class.

2. Q: What file format am I supposed to use?

   A: Feel free to use your own, or to modify the existing file format as presented in the assignment page.

3. Q: I'm confused about canonical vs. transformed objects. What geometric information should I store in my scene data structure?

   A: It depends on the type of object:

   • Spheres: just store a sphere object, which is centered at the origin, and has radius 1. Also, store its transformation matrix, and the INVERSE of that matrix (see below).
   • Triangles: just store the triangle's vertices, and the identity matrix. You could store a canonical triangle (eg, vertices at [0 0 0], [1 0 0] and [0 1 0]), and compute the transformation matrix that maps those standard vertices to the desired vertices, but you don't have to go to the trouble.

4. Q: If I'm storing a canonical sphere, why does the current file format specify center and radius?

   A: I suggest that you either modify the file format to omit the center and radius info, or to ignore that info. The transformation matrix will do the work of placing and sizing the sphere for you.

5. Q: Why should I store an inverse matrix too?

   A: Well, it costs a lot of CPU time to invert a matrix, so it's best to invert the matrix ONCE when the scene is built, not every time you intersect a ray and an object.

6. Q: What about reflection and transmission coeffients?

   A: When light hits a surface, some is absorbed, some transmitted into it, and some reflected away. Thus there are three coefficients. Each is a number from 0.0 to 1.0, representing a fraction of light, and these three coefficients add up to 1.0. Hence, both absorption and reflection coeffs are from 0 to 1, and absorption + reflection is less than 1.0.

   This ignores color, of course. In practice, there will be three absorption and three reflection coeffs (red, green and blue) per surface (per object).

7. Q: How do I keep track of the indexes of refraction?

   A: Each object will represent the boundary of a solid region. This includes triangles, so your images may not look plausible if the triangles don't join up to enclose a solid region.

   The indexes of refraction n_i and n_t (the incident and transmitted indexes of refraction) should probably be attributes of rays (see the next answer). The index of refraction of air or vaccuum is essentially 1.0, while the index of refraction of common transparent objects is from 1.3 to 2. For each refraction, you need to know if you are entering or leaving the solid region, in order to assign the correct values to n_i and n_t. A simple way is to look at c = N dot L in the pseudocode. If it's positive, you're entering, and if negative, you're leaving (why?).

   One caveat: don't forget to advance the starting point of your reflected and transmitted rays a little bit, to make sure the ray starts clearly in the correct side of the surface (see the pseudocode). Otherwise, numerical error will likely cause rays to intersect the very object they are leaving from! This results in grainy "acne" on the surface.

8. Q: Why should rays carry indexes of refraction?

   A: Initially, only substances (surfaces) have indexes of refraction, which are stored when the scene is initialized (read from a data file). When tracing happens, rays acquire the index of refraction of whatever region they are traveling through. Here is a tabular summary:

   Event	How to detect event	Incoming ray n	Reflected ray n	Transmitted ray n
   Entering Object	N dot L < 0	ni = 1 (vaccuum)	n = 1 (vaccuum)	nt = material's n
   Leaving Object	N dot L > 0	ni = material's n	n = material's n	nt = 1 (vaccuum)

9. Q: How should I specify my transformation matrices?

   A: I think it's simplest not to store 16 numbers in your input file, because it will be hard for you to remember what they mean. It's better to keep a current matrix (which gets reset to the identity matrix when necessary), and apply successive simple transformation matrices to it. Thus your data file could specify a translated, rotated and scaled sphere sort of like this:

   • T 1 2.5 3
   • R 45 0 1 0
   • S 1 2 2
   • Sphere
   and your parsing code could multiply each such matrix into the current matrix

10. Q: How do I specify my bounding spheres?

    A: I think it's easiest to build them as you read the objects. For a sphere, use the unmatrix code I gave you to extract the transformation matrices, and deduce the bounding sphere from that. For triangles, find the average of the vertices' coords to get the sphere center, and then get the radius (this is not the tightest sphere possible, but will provide some acceleration).