Raccolta temi 2017

Pagina 1

In this file you will find a collection of the exams given in the year 2015. Most of the topics are covered also this year, but there are some changes. Moreover, not all the solutions are available, and some of the available solutions are not correct. The purpose of this document is to give the idea to the student what to expect during the exam, and to make her/him think about the topic studied during the course. Please use this material wisely, keeping these assumptions in mind! DRAFT y +1/3/58+ y Exercise: 3D transforms The world matrix of an object rotates it 50 around the y axis, and scales it twice along the z axis and a half along the x axis. Question 1 The rotation matrix is: A 0.766 0 0 .643 0 01 0 0 0.643 0 0 .766 0 00 0 1 B 0.643 0 0 .766 0 01 0 0 0.766 0 0 .643 0 00 0 1 C 0.643 0 0.766 0 01 0 0 0.766 0 0 .643 0 00 0 1 D 0.766 0 0.643 0 01 0 0 0.643 0 0 .766 0 00 0 1 SOLUTION: Ry (50 )= 0.643 0 0 .766 0 01 0 0 0.766 0 0 .643 0 00 0 1 Question 2 The scaling matrix is: A 0.5000 01 0 0 00 2 0 00 0 1 B 20 0 0 00 0 0 000 .50 00 0 1 C 20 0 0 01 0 0 000 .50 00 0 1 D 100 2 010 0 0010 .5 000 1 SOLUTION: S(0.5, 1, 2) = 0.5000 01 0 0 00 2 0 00 0 1 Question 3 The world matrix is: A 0.321 0 0 .383 0 01 0 0 1.532 0 1 .286 0 00 0 1 B 0.321 0 1 .532 0 01 0 0 0.383 0 1 .286 0 00 0 1 C 0.321 0 0.383 0 01 0 0 1.532 0 1 .286 0 00 0 1 D 0.321 0 1.532 0 01 0 0 0.383 0 1 .286 0 00 0 1 SOLUTION: MW = Ry (50 ) · S(0.5, 1, 2) = 0.321 0 1 .532 0 01 0 0 0.383 0 1 .286 0 00 0 1 y For your examination, preferably print do cuments compiled from auto-multiple-choice. y DRAFT y +1/4/57+ y Question 4 The complete transform matrix for the normal vectors is: A 0.321 0 1 .532 01 0 0.383 0 1 .286 B 0.321 0 1.532 01 0 0.383 0 1 .286 C 0.321 0 1 .532 0 01 0 0 0.383 0 1 .286 0 00 0 1 D 1.286 0 0…