Computer Graphics

Question 1

Let us assume that we have a parametric ray of the form

(a) If the equation of the plane is , then show that the point of intersection of the ray with the plane is:

(Hint: Substitute the x, y and z values of the line into the equation for the plane).

(b) We are in the middle of ray-tracing a simple scene. Our eye is at (0,0,-2) and the screen is situated in the x-y plane, extending from (-1,-1,0) to (1,1,0). We are rendering the pixel that is situated in the middle of the top row at coordinates (0,1,0). There are two planes. The first (plane A) has an equation x+y+z-4=0 and the second (plane B) has an equation x+2y+3z-18=0. Where does the ray intersect with each of these planes? Which one will we be able to see?

(c) If there is a light source at (10,10,10), are we in shadow at the point of intersection?

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