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 p3 and should have tangents r1 r2 at u 1 2 and u 3 4 respectively Given that our standard matrix form for this cubic splines will be p0 p p u 1 u u2 u3 M 3 r1 r2 derive the 4 4 basis matrix M for 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 a b c d 3 You are given a convex planar polygon P with k sides Side i of the polygon lies on the line ai x bi y 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 4 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 5 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 t1 the particle is at position p1 with velocity v1 2 At time t2 the particle is at position p2 with velocity v2 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 Page 2
View Full Document
Unlocking...