Lab 3

Sampling

Due: Monday, November 28 2016, 23:59

Individual Effort:
No team participation is really encouraged in the case of the homework or the labs.
Academic Misconduct
Late Submission:
In general late submission is not encouraged/accepted unless there is a very good reason. You are encouraged to submit on time. We are on a tight schedule. Being late for one lab could affect the time left for you to complete subsequent labs. Late Submissions are possible, yet they will be penalized.
  • One day late: 15% penalty
  • Two days late: 30% penalty
  • Three days late: 50% penalty
  • Four or more days late: 100% penalty.
  1. Area light sources are typically defined by attaching an emission function to a shape. For now, we will assume the emission function is constant; that is, the outgoing radiance from the light source is independent of both position on the source and outgoing direction. Sampling an area light source involves choosing random points on the surface. The number of random points on any subset of the surface should be proportional to the surface area of that subset. This is called uniform area sampling.
    1. (5) Describe an algorithm for generating a uniform distribution of points on a unit cylinder (radius 1, height 1). For this problem, ignore the circular disk at the base and top of the cylinder.
    2. (10) Describe an algorithm for generating a uniform distribution of points on a unit cone (radius 1 on the plane z=0, and height 1; the tip of the cone is at z=1). As before, ignore the base of the cone.
    3. (5) Describe an algorithm for uniformly sampling a unit sphere (radius 1, centered at the origin). (Derive the formulas)

  2. (15) Draw and label a sketch of the function obtained by convolving a 2D box functions B(x,y) with a 1D box function in the direction V=(1,-1). (This is a 1D function placed in the 2D plane along the y=-x axis) I.e. the integral should simplify to int( B(X-tV) dt) between 0 and one (X=(x,y)). Make the sketch clear enough to convey all salient aspects of the function.

  3. (20) The triangle function of width 2 and unit area is frequently used as a filter in computer graphics. In 1D, it is defined as: T(x) = 1+x for -1 < x < 0 and T(x) = 1-x for 0 < x < 1. Using the definition of convolution, prove that reconstructing a sampled 1D signal by convolving it with the triangle function T(x) corresponds to linearly interpolating its samples. Asume that the samples are taken one unit apart.

  4. (25) Final Project (have your wiki page updated by Thursday, November 3rd) You should read about the final project and come up with an interesting project for yourself. I am happy to bounce off ideas. Please start a wiki page off of Moodle.

Submission

Please submit your answers in a single PDF file in moodle, in Lab3 section here.
If you have multiple files to upload (e.g. source code or supplementary pictures), please upload all your submission as a single compressed ZIP file.

We expect a good student to have to work approximately 5 hours on this assignment.

Include one paragraph about your estimated effort you put into this lab. How many (focused) hours of work did it take you and roughly where did you spend most of your time.