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Politecnico di Milano, DEIB July 8th, 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. Exercise 1 A triangle has the following vertices in normalized screen coordinates: A(0.5, 0.5, 0.5), B(0.5, -­‐0.5, 0.5), C(0, -­‐0.5, 2). It is generated by a parallel projection, with the projection ray oriented along vector (0, 0, -­‐1). a) Determine if the face is visible, using the back-­‐face culling algorithm. b) Clip the triangle against the far plane identified by vector (0, 0, -­‐1, 1). c) Find the pixel coordinates of the vertices of the resulting triangle (triangles) on a 801 x 481 screen. Solution: a) n = (C-­‐B) x (B-­‐A) = ((0, -­‐0.5, 2) – (0.5, -­‐0.5, 0.5)) x ((0.5, -­‐0.5, 0.5) – (0.5, 0.5, 0.5)) = = (-­‐0.5, 0, 1.5) x (0, -­‐1, 0) = (1.5, 0, 0.5) n . p = (-­‐1.5, 0, 0.5) . (0, 0, -­‐1) = -­‐0.5 < 0 The face is visible. b) Let…