MCQ IN COMPUTER SCIENCE & ENGINEERING

Detailed explanation-1: -Explanation: The matrix representation for translation is P’=T*P. Explanation: The matrix representation for scaling is P’=S*P. Explanation: The matrix representation for rotation is P’=R*P.

Detailed explanation-2: -The transformation matrix of the identity transformation in homogeneous coordinates is the 3 × 3 identity matrix I3. The inverse of a transformation L, denoted L−1, maps images of L back to the original points. More precisely, the inverse L−1 satisfies that L−1 ◦ L = L ◦ L−1 = I.

Detailed explanation-3: -In homogeneous co-ordinates, points in the Euclidean plane become rays from the origin in the projective space. Each point in the ray is given by a different value of z. The homogeneous co-ordinates of the line in the Euclidean plane define the plane between the two rays in the projective space.

Detailed explanation-4: -To treat all 3 transformations in a consistent way, we use homogeneous coordinates and matrix representation. 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).

Detailed explanation-5: -Homogenous Coordinates To convert a 2×2 matrix to 3×3 matrix, we have to add an extra dummy coordinate W. In this way, we can represent the point by 3 numbers instead of 2 numbers, which is called Homogenous Coordinate system. In this system, we can represent all the transformation equations in matrix multiplication.