Project 4: Illuminate (Algo)

You can find the handout for this project here. Please skim the handout before your Algo Section!

You may look through the questions below before your section, but we will work through each question together, so make sure to attend section and participate to get full credit!

Please read the project handout before going to algo section and working on these questions!

Raytracing Pipeline

As a group, come up with four or more aspects of the fully fledged raytracing pipeline that were omitted in Intersect, but are required for Illuminate. Discuss how you can use your code from Intersect to implement these components.

There is not necessarily a correct answer! We are looking for a qualitative explanation of your approach. Share your ideas with the TA before moving on.

Reflection Equation

TODO
Figure 1: Reflection across a normal.

Given an incoming light direction (from light source to point of intersection) and surface normal (on point of intersection), the equation for the reflected outgoing ray is given by:

Assuming both and are unit vectors, discuss why this equation makes sense.

If you get stuck, try drawing out a diagram on the whiteboard with your group! How might you break down ?

Texture Coordinates

In Illuminate, you will be texture-mapping images onto your implicit shapes. One step of this process is taking a given intersection point, with known UV coordinates, and figuring out which pixel of the image we should use.

However, two different coordinate systems are in play here:

  • Image coordinates have their origin at the top left of a width x height pixel grid. These are used for images like our Brush canvas, our Intersect output, and, most relevantly, images we use as textures.
  • Texture (UV) coordinates have their origin at the bottom left of a unit square. These are used on the surfaces of our objects, as inputs to the equations you will write below.

Make sure you are comfortable with the diagram below, then work through the next two questions, where you will define a mapping from UV coordinates to image coordinates.

TODOTODO
Figure 2: Image coordinates vs texture (UV) coordinates.

A Single Texture

Suppose we have an image of size , which we'd like to use as a texture.

What is the pixel index for a given UV coordinate ? Please use nearest-neighbor texture sampling, and be mindful of your bounds.

Repeated Textures

Suppose that we'd now like to repeat the texture times horizontally and times vertically.

Now, what is the pixel index for a given UV coordinate ? Again, be mindful of the bounds on and , and be prepared to explain your answers as a group.

Shadow Generation

To test if some intersection point is in shadow relative to some light, you must check if there are any objects blocking that light. This can be done by casting a "shadow ray" from towards the light, and checking for intersections between that ray and other objects within the scene.

TODO
Figure 3: Recursive raytracing for shadows.

Suppose point is on object . When casting your shadow ray, do you have to check for intersections between that ray and object ? Why, or why not?

Does your answer change if we are restricted to the primitives we use in this course? Discuss with your group.

Submission

Algo Sections are graded on attendance and participation, so make sure the TAs know you're there!

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