Assignment (4)

Graphics Due: Mon. March 15

 

In the following problems, consider a homogeneous coordinate system Also, if you need an origin use p0 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 p0 (0,0,0). Rotate the vector, p0p, by 30 degree around the z axis to get p0p.

 

4. Rotate the vector p0p from part 3 by 60 degree around y axis (Note: rotate the original vector not the rotated one).

 

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, p0p back.

 

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

 

 

7. Rotate p0p by 30 degree to get p0p, then rotate the resulting vector by 15 degree to get p0p. Is the result the same as rotating the original vector by 45 degree?