Unformatted text preview: lue at the centre of
the quadrilateral.
i) Average the vertices to ﬁnd a central point [3.5, 3.5, 11.25].
ii) Find the light source direction [ 3.5, 11.25].
pp
iii) Compute n · l = (0 + 3.5 + 22.5)/(nl) = 24/( 5 151.06) = 0.95
3.5, iv) The ﬁnal shading value is
0.95 ⇥ (255, 255, 255) = (242.25, 242.25, 242.25). Marks: The ﬁve parts carry, respectively, 25%, 15%, 20%, 20%, and 20% of the marks. 4 R2 Ray Tracing "
ay tracing
a The scene in the ﬁgure below has a mirror, a white paper box and two lights:
Light&1& White&
paper&
box&
(diﬀuse)& Eye& Light&2&
& 50%&reﬂec8ve&red&
mirror& i) Starting from the eye ray drawn, draw all additional reﬂection, refraction
and shadow rays needed to compute the colour of the eye ray. Label each
ray clearly.
ii) Write down a formula which describes the computation of the colour for
the ray. Label your drawing from a part i) or add annotations to your terms
in your equation so that it is clear what is being computed.
b Brieﬂy explain which illumination effects can be achieved with ray tracing and mirror& i) Starting from the eye ray drawn, draw all additional reﬂection, refraction
and shadow rays needed to compute the colour of the eye ray. Label each
ray clearly. Ray tracing"
Light&1& Shadow&S2&
Eye& Shadow&S1&
Reﬂec8on& White&
paper&
box&
(diﬀuse)& Shadow&S3& Light&2&
& Shadow&S4&
50%&reﬂec8ve&red&
mirror& Marks:
ii) Write down a formula which describes the computation of the colour for
the ray. Label your drawing from a part i) or add annotations to your terms
in your equation so that it is clear what is being computed. 3 i) Starting from the eye ray drawn, draw all additional reﬂection, refraction
and shadow rays needed to compute the colour of the eye ray. Label each
ray clearly. Ray tracing"a formula which describes the computation of the colour for
ii) Write down
the ray. Label your drawing from a part i) or add annotations to your terms
in your equation so that it is clear what is being computed.
b Brieﬂy explain which illumination effects can be achieved with ray tracing and
how these effects are achieved. What is the key difference between ray tracing
and radiosity? c A ray originates at point V and is parallel with direction vector d. A rightangled
triangle is given by three points P1 , P2 and P3 (the right angle is at point P1 ).
Show in detail how you can calculate the intersection between the ray and the
face deﬁned by the triangle. d In a concrete example, a ray starts at V = (7, 7, 0) and has a direction vector
d = (0, 0, 1). The points of the triangle are given as P1 = (6, 6, 10),
P2 = (12, 6, 10), and P3 = (6, 10, 5). Calculate whether the ray intersects the
face deﬁned by the triangle. The four parts carry, respectively, 30%, 20%, 30%, and 20% of the marks. c A ray originates at point V and is parallel with...
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 Spring '14
 Computer Graphics, Phong shading, ray tracing, Daniel Rueckert

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