Question

A unit cube as shown in Figure Q1 is undergoing the transformations described in (i) and (ii) respectively. Sketch the resultant object with coordinates of each vertex after each transformation. (a) Z (0,1,1) (1,1,1) (0,0,1) (1,0,1) (0,0,0) (1,1,0) (1,0,0) Figure Q1 Transformation (i) (6 marks) 1. A Uniform scale by a factor of 2 2. Followed by a rotation about the-axis in counter-clockwise direction by 90 degrees 3. Followed by a transformation moving in the direction of < 2, 1, 2>. Transformation (ii) (6 marks) 1. Scale in they- and --direction using scale factors of 2 and 1.5 respectively 2. Followed by shear of the :-components in both x- and y-directions with a factor of 1. 3. Followed by a transformation moving in the direction of< 1,0, 1>. An object point at (x, y, ) is to be projected onto a: adopted with the center of projection at (0, 0, ep). (b) 0 plane. A perspective projection is Sketch a figure to illustrate the relationship between the center of projection, object point (i) and projected point. (5 marks) 0 0 1 0 Derive the perspective projection matrix T (ii) (5 marks) 0 0 0-1/ 0 0 0 1 (iii) Given the homogeneous representation of a point at infinity is (, 0,-1,0) Show that the perspective projection transforms a point at infinity to a finite point in the space. (3 marks) 2

Answer 1

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