Matrix Transformations

Question 1

What are the types of 3D transformations?

Answer 1

3D transformations will be confined to reflections and rotations.

Question 2

What is a reflection in 3D transformations?

Answer 2

A reflection in one of x=0, y=0, or z=0.

Question 3

What is a rotation in 3D transformations?

Answer 3

A rotation about one of the coordinate axes.

Question 4

What is the matrix for a reflection in the plane x=0?

Answer 4

-100
010
001

Question 5

What is the matrix for a reflection in the plane y=0?

Answer 5

100
0-10
001

Question 6

What is the matrix for a reflection in the plane z=0?

Answer 6

100
010
00-1

Question 7

What is the matrix representation of an anticlockwise rotation around the z-axis by angle x?

Answer 7

The matrix is given by:

cos x -sin x 0
sin x cos x 0
0 0 1

Question 8

What is the matrix for an anticlockwise rotation around the x-axis by angle x?

Answer 8

1 0 0
0 cos x -sin x
0 sin x cos x

Question 9

What is the matrix for an anticlockwise rotation around the y-axis by angle x?

Answer 9

cos x 0 sin x
0 1 0
-sin x 0 cos x