COMPUTER SCIENCE AND ENGINEERING
COMPUTER GRAPHICS
|
Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
|
|
|
P’=S*P
|
|
|
P’=R*P
|
|
|
P’=dx+dy
|
|
|
P’=S*S
|
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.
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: -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: -Homogeneous coordinates provide another very significant advantage: Affine transformations∗ and projections are linear in homogeneous coordinates, which means we can combine them with other operations by matrix multiplication or composition of linear quaternion systems.