MCQ IN COMPUTER SCIENCE & ENGINEERING

Detailed explanation-1: -Clarification: To treat all 3 transformations in a consistent way, we use homogeneous coordinates and matrix representation. Clarification: 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-2: -Homogeneous coordinates are ubiquitous in computer graphics because they allow common vector operations such as translation, rotation, scaling and perspective projection to be represented as a matrix by which the vector is multiplied.

Detailed explanation-3: -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.

Detailed explanation-4: -Homogeneous coordinates are generally used in design and construction applications. Here we perform translations, rotations, scaling to fit the picture into proper position.

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.