Assignment (4)

Graphics Due: Mon. March 15

In the following problems,
consider a homogeneous coordinate system Also, if you need an origin use **p _{0}
**which is at (0,0,0).

1.Translation of a point is
defined as: **p’ = p + d** (See 4.7.1 for more info). Suppose we are given a point as:

Translate this point by –2 on the
*x *direction, 6 on the *y *direction, and –2 on *z *direction. Please show your work.

2. Inverse the translation that
you have done in the previous part to obtain the original point, **p**, from
**p’**.

3. Suppose a vector is defined
using the **p **given in the part (1) and the origin at **p _{0}**

4. Rotate the vector **p _{0}p
**from part 3 by 60 degree around

5. Undo the rotation in part 4, i.e., do the inverse 60
degree rotation on the resulting vector on part 4 to get the original vector, **p _{0}p**
back.

6. Scale the vector in part 2 by
(3, 2, 2), order is *x, y, *and *z.*

* *

* *

7. Rotate **p _{0}p**
by 30 degree to get