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Politecnico di Milano, DEIB July 28th, 2014 Course 090958 Computer graphics M. Gribaudo First Name - Nome: ................................................... Family Name - Cognome: ............................................. ID - Matricola: ................................... IMPORTANT: • An answer in order to be considered valid must show all computations involved in obtaining the results. This will make it easier to find the mistakes (if any) and will help the grader to assign partial credit. Una risposta per essere considerata valida deve riportare TUTTI i passaggi algebrici necessari per il calcolo delle soluzioni. • Pencils are allowed. È possibile usare la matita. • No cell phones can be used! No electronic devices, except pocket calculators are allowed. I telefoni cellulari non possono essere usati per nessun motivo. Non è consentito l’uso di alcun dispositivo elettronico, eccetto le calcolatrici tascabili. • It is possible to answer in Italian. È possibile (e consigliabile per i madre-lingua) rispondere in italiano. 1 2 3 Tot Exercise 1 A world matrix is composed by setting the center of the object at P(-­‐1, 0, 3), rotating it with a yaw of 30o and a roll of 90o, and by performing a non-­‐uniform scaling along the z-­‐axis of a factor of ½. a) Compute the world matrix to transform the vertices of the object in world space. b) Do the rotations cause a gimbal lock? c) Compute the transform matrix for the normal vectors of the object d) Transform the following vertices of the object: A(0, 0, 0) nA(0, 1, 0) B(1, 1, -­‐1) nB(0.6, 0.8, 0) Solution: a) Mw = T(-­‐1, 0, 3) . Ry(30o) . Rz(90 o) . S(1, 1, ½) 𝑀!=100−1010000130001 0.86600.500100−0.500.86600001 0−100100000100001 10000100000.500001 𝑀!=100−1010000130001 0.86600.500100−0.500.86600001 0−1001000000.500001…