Graphical Transformations

Question 1

How can we rotate a point P (X,Y)
about a point (Q,R)?

Answer 1

Translate P by (-Q,-R) , to place Q at the origin.

Rotate the translated P

Translate the rotated P by (Q,R) to reverse the initial transformation

Question 2

Convert the following into homogenous co-ordinates:

[X,Y,Z]

Answer 2

[ X , Y , Z , 1 ]

Question 3

How can I represent the translation of

[X,Y,Z]

by

[TX,TY,TZ]

as a homogeneous matrix?

Answer 3

[ 1, 0, 0, TX ] [ X ]
[ 0, 1, 0, TY ] [ Y ]
[ 0, 0, 1, TZ ] [ Z ]
[ 0, 0, 0, 1 ] [ 1 ]

Question 4

Is Matrix Multiplication Associative?

Answer 4

Yes

Question 5

Is Matrix Multiplication Commutative?

Answer 5

No

Question 6

If A and B are inverse matrices,

what is their product equivalent to ?

Answer 6

Their product is

The Identity Matrix

Question 7

For normalised vectors, what is the dot product between them equivalent to?

Answer 7

The cosine of the angle between them

Question 8

What does the cross product between two vectors represent?

Answer 8

It gives us the vector which is perpendicular to both input vectors

, forms a right handed system