Assignment 9b: Last week’s classes

This assignment is due on Wednesday, November 19^{th}. It will be graded check/no check. As long as you turn something in, you get a check. Turn things in on Moodle. We probably won’t even look at your answers. We will post solutions later in the week.

Here are some questions to make sure that you were paying attention in class for the past few weeks. These are the kinds of questions we like to ask on exams. You will need to turn in your answers, but we won’t grade them (it’s just a check no check). You can say “blah blah blah” and get the checkmark – but this won’t help you understand the concepts, or get ready for the exam.

If you want to turn in your sketches (for 1A2&3) take a picture of your paper. Or just describe your sketch in a sentence or two.

Note: bonus problems are a little beyond what we’re doing in class. But if you can figure them out, it’s a good way to re-enforce the concepts.

1.

Consider a triangle with its corners at: (0,0) (10,20), (20,0)

1A.1

Apply Chaikin’s corner cutting algorithm (as we discussed in class) to this triangle (1 iteration).

1A.2

Sketch what the curve will look like in the limit (after infinity iterations)

1A.3

Suppose we doubled the third point (so the triangle is actually a degenerate quadrilateral with two points at (20,0). Sketch what the limit curve looks like.

1.A.bonus

Chakin’s algorithm produces quadratic B-Splines (in the limit). For the first segment (the segment formed with points (0,0) (10,20) (20,0), what is the parametric form of this curve segment? (you can look up the blending functions in the book chapter) Check to see that it matches.

1.B.

Apply Catmull-Clark subdivision to this triangle. Don’t worry about moving the points – just figure out the connectivity. After 2 subdivisions,

1.b.1 How many “ordinary” points are there?

1.b.2 How many internal extra-ordinary points are there (points that aren’t ordinary but not edges)

1.b.3 How many edge points are there?

1.b.4 suppose I wanted to figure out the location of where the point that started out at (0,0) goes to. How many non-edge points will I need to consider?

1.b.bonus Actually apply CC subdivision to figure out where the points go.

2.

Consider some of the non-freeform surfaces we discussed in class. Describe a real case (e.g. a real world object) where:

2.A an object is easily modeled as a surface of revolution

2.B an object is easily modeled as a generalized cylinder (that is not a surface of rev)

2.C an object is easily modeled as a generalized sweep that is not a cylinder (it does not have a circular cross section)

3.

Humans evolved to be (generally) tri-chromats. Many species of birds have more types of cones. European starlings are tetra-chromats.

Imagine that their 4 kinds of cones covered the same range of wavelengths as human vision (this turns out not to be true). Describe a “color blindness” test for humans? (e.g. so that humans would fail, and the birds could pass)