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Politecnico di Milano, DEIB September 9th, 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 view matrix position the camera at coordinates (-­‐10, 0, 0) looking to the origin of the axis, and oriented with the vertical axis parallel to the global y. The scene is composed by two points A(10,5,5) and B(20,5,5). The near and far plane are respectively at n=-­‐15 and f=-­‐115 from the center of the camera, and the aspect ratio is 4:3. The half width of the projection at the near plane is 20. a) Compute the view matrix b) Consider a parallel projection. Compute the projection matrix and the normalized screen coordinates of the two points. c) The two points are projected on a 401x301 screen. If the Z-­‐buffer holds a constant value of 0.1 for all its pixels, which point will be visible? Solution: a) vz = (-­‐1, 0,…