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Self-Assessment Solutions

Distance Between Points

1.

b = 18

2.

No

3.

130

4.

graphics/02nil01.gif

5.

(90,105)

6.

(60,85,25)


Parabolas

1.

(4,7)

2.

(1,5)

3.

(–3,2)

4.

(–12,0)

5.

(–1,0)


6.

The answer is shown in Figure 2.17.

Figure 2.17. y = 10(x–1)2 + 3.

graphics/02fig17.gif

7.

The answer is shown in Figure 2.18.

Figure 2.18. x = y2–2.

graphics/02fig18.gif


Circles and Spheres

1.

center = (30,10), radius = 20

2.

center = (–20,90), radius = 10

3.

center = (–50,0), radius = 25


4.

(x–40)2 + (y+25)2 = 900

5.

x2 + y2 = 225

6.

(x+10)2 + (y–40)2 = 1000


7.

center = (10,30,50), radius = 40

8.

center = (0,0,0), radius = 10

9.

center = (50,0,–40), radius = 1


10.

(x–40)2 + (y+25)2 + (z–30)2 = 100

11.

x2 + y2 + z2 = 484

12.

(x–10)2 + y2 + (z+60)2 = 3400


Applications in Collision Detection

1.

Yes

2.

No

3.

Set up a hierarchy of spheres, and check the smaller ones only if the larger spheres have collided.


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