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Midterm Practice Questions - Interactive Computer Graphics | CS 418, Exams of Computer Graphics

University of Illinois - Urbana-ChampaignComputer Graphics

Material Type: Exam; Class: Interactive Computer Graphics; Subject: Computer Science; University: University of Illinois - Urbana-Champaign; Term: Spring 2005;

Typology: Exams

Pre 2010

Uploaded on 03/16/2009

koofers-user-qbe
koofers-user-qbe 🇺🇸

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CS 418: Midterm Practice
Review: Monday March 7 at 6:30 in 1404 Siebel
Midterm: Tuesday March 8 at 3:30 in 1404 Siebel
These questions are intended to help you prepare for the midterm exam. Almost all of them are actual
questions from past exams. We will discuss the solutions at the review session on Monday, March 7.
1. We want to define a new spline type with control points p0,p3,r1,r2. The curve should interpolate its
endpoints p0,p3and should have tangents r1,r2at u=1
/
2and u=3
/
4, respectively. Given that our
standard matrix-form for this cubic splines will be
p(u) = 1u u2u3M
p0
p3
r1
r2
derive the 4×4 basis matrix Mfor this class of splines.
2. Suppose that you are given the following shape:
(−1, −1)
(1, 1)
For each of the following figures, describe how to transform the initial shape above into the given result.
You may only use combinations of the following three transformations:
T: translate by [1 1] S: scale by [2 1] R: rotate (counter-clockwise) by 45◦
NOTE: Your answers should consist of products of these 3 fundamental matrices. Make sure to put
them in the correct order.
pf2

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CS 418: Midterm Practice

Review: Monday March 7 at 6:30 in 1404 Siebel

Midterm: Tuesday March 8 at 3:30 in 1404 Siebel

These questions are intended to help you prepare for the midterm exam. Almost all of them are actual questions from past exams. We will discuss the solutions at the review session on Monday, March 7.

  1. We want to define a new spline type with control points p 0 , p 3 , r 1 , r 2. The curve should interpolate its endpoints p 0 , p 3 and should have tangents r 1 , r 2 at u = 1 / 2 and u = 3 / 4 , respectively. Given that our standard matrix-form for this cubic splines will be

p(u) =

[

1 u u^2 u^3

]

M

p 0 p 3 r 1 r 2

derive the 4×4 basis matrix M for this class of splines.

  1. Suppose that you are given the following shape:

(−1, −1)

(1, 1)

For each of the following figures, describe how to transform the initial shape above into the given result. You may only use combinations of the following three transformations:

T : translate by [1 1] S : scale by [2 1] R : rotate (counter-clockwise) by 45◦

NOTE: Your answers should consist of products of these 3 fundamental matrices. Make sure to put them in the correct order.

(a) (b) (c) (d)

  1. You are given a convex planar polygon P with k sides. Side i of the polygon lies on the line aix+biy+di = 0, where [ai bi] is the outward-pointing normal of that edge. Describe precisely how to test whether a point (x, y) lies within this polygon.
  2. Our standard viewing model is parameterized by two points (lookFrom, lookAt) and a vector (vUp). For each of the following, describe what happens on the screen when applying the described transformations to the camera parameters. (a) Translate lookFrom and lookAt by lookAt − lookFrom. (b) Rotate lookFrom and lookAt counter-clockwise about vUp. (c) Translate lookFrom and lookAt by vUp × (lookAt − lookFrom).
  3. Suppose you are asked to implement a system for key-framing the motion of a particle system. Consider a single particle in this system. You are given two key-frames: 1. At time t 1 the particle is at position p 1 with velocity v 1 2. At time t 2 the particle is at position p 2 with velocity v 2

Give an equation for a function p(u) that linearly interpolates between these two key frames for values of u in the range [0, 1].

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