1. The matrix representation for rotation in homogeneous coordinates is
a) P’=T+P
b) P’=S*P
c) P’=R*P
d) P’=dx+dy
Explanation: The matrix representation for rotation is P’=R*P.
2. What is the use of homogeneous coordinates and matrix representation?
a) To treat all 3 transformations in a consistent way
b) To scale
c) To rotate
d) To shear the object
Explanation: To treat all 3 transformations in a consistent way, we use homogeneous coordinates and matrix representation.
3. If point are expressed in homogeneous coordinates then the pair of (x, y) is represented as
a) (x’, y’, z’)
b) (x, y, z)
c) (x’, y’, w’)
d) (x’, y’, w)
Explanation: If point are expressed in homogeneous coordinates then we add 3rd coordinate to the point (x, y), that is represented as (x’, y’, w).
4. For 2D transformation the value of third coordinate i.e. w=?
a) 1
b) 0
c) -1
d) Any value
Explanation: For 2D we have (x, y, 1) i.e. w=1.
5. We can combine the multiplicative and translational terms for 2D into a single matrix representation by expanding
a) 2 by 2 matrix into 4*4 matrix
b) 2 by 2 matrix into 3*3
c) 3 by 3 matrix into 2 by 2
d) Only c
Explanation: We can combine the multiplicative and translational terms for 2D into a single matrix representation by expanding 2 by 2 matrix representation into 3 by 3.
6. The general homogeneous coordinate representation can also be written as
a) (h.x, h.y, h.z)
b) (h.x, h.y, h)
c) (x, y, h.z)
d) (x,y,z)
Explanation: The general homogeneous coordinate representation can also be written as (h.x, h.y, h).
7. Two successive translations are___________________
a) Multiplicative
b) Inverse
c) Subtractive
d) Additive
Explanation: Successive translations are additive.
P’= T(tx1, ty1) .[T(tx2, ty2)] P
= {T(tx1, ty1). T(tx2, ty2)}.P
Or T(tx1, ty1). T(tx2, ty2) = T(tx1+tx2 , ty1 + ty2).
8. Two successive translations are not commutative.
a) True
b) False
Explanation: According to commutative property, the order does not matter. Same as in the case of successive translations. Hence we can say that two successive translations are commutative.
9. General pivot point rotation can be expressed as _____________________
a) T(zr,yr).R(θ).T(-zr,-yr) = R(xr,yr,θ)
b) T(xr,yr).R(θ).T(-xr,-yr) = R(xr,yr,θ)
c) T(xr,yr).R(θ).T(-xr,-yr) = R(zr,yr,θ)
d) T(xr,yr).R(θ).T(-xr,-yr) = R(xr,yr,Q)
Explanation: Since the first two parameters are in 2D, hence only ‘x’ and ‘y’ can be variable along with ‘θ’. In other options, there is one more parameter ‘z’.
10. Which of the following is NOT correct? (A, B and C are matrices)
a) A.B = B.A
b) A.B.C = (A.B).C = A.(B.C)
c) C(A+B) = C.A + C.B
d) 1 A = A 1
Explanation: Matrix multiplication does not commute. We cannot switch the order of the factors and expect to end up with the same result. Hence, A.B ≠ B.A.