405Hw1 Calculate the memory bandwidth for a graphics card with a memory speed of

Question

405Hw1

Calculate the memory bandwidth for a graphics card with a memory speed of 8000 MHz, and a 512-bit memory interface. Calculate the plane coefficients (A, B. C and D) of 3 points in a plane defined by P1, P_2 and P_3. P_1 = (60, 76, 12); P_2 = (-30, 38, 78); P_3 = (35, -10, 55); Then determine if the following point P_4 is behind, in front of or on the polygon surface contained within that plane: P_4 = (10, 72, -29); Be sure to show your work. Explain why determining if Point P4 is behind or in front of the polygon surface relevant to computer graphics applications.

Explanation / Answer

1)

memory bandwidth = 512/8 * 8000 * 2 = 64 * 8000 * 2 = 1024 GB/second

So the memory bandwidth is 1024 GB/second

2)

equation of a plane is

ax+by+cz=d

now we need to convert these into vectors

p1-p3 = <25,86,-43>

p2-p3 = <-65, 48, 23>

product of these two will be

86*23 +43*48 = 4042

65*43 - 25*23 = 2220

25*48 + 86*65 = 6970

so

a = 4042 b =2220 c=6970

putting it in equation we get d = 492720

now ax+by+cz -d

for point 10,72,-29 we get

40420 + 2220*72 - 29*6970 -492720 = 40420 + 159840 - 202130 -492720 < 0

so point is behind the surface.

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