In the context of 3𝐷 Computer graphics, which of the following statements…

Correct answer: (A) and (B) only.

Explanation:

• Parallel lines under perspective: Under perspective projection, sets of parallel lines in 3D generally do not remain parallel in the image because they converge toward vanishing points. An exception is when those lines are parallel to the viewplane; in that case they remain parallel in the image.

• Perspective divide (division by depth): The pipeline applies a projection matrix to a vertex (in homogeneous coordinates) and then performs a perspective divide by the homogeneous w (which corresponds to the view-space depth). In common form this is described as dividing x and y by the vertex's z (or by a quantity proportional to z) to obtain the screen coordinates, so the statement that applying perspective involves dividing by the depth coordinate is correct.

• Linearity of perspective: The mapping from 3D Cartesian coordinates to 2D image coordinates is not a linear transformation because of the division by depth (a nonlinear operation). It can be represented as a linear operation in 4D homogeneous coordinates (matrix multiplication) before the perspective divide, but after converting back to Cartesian coordinates the division makes the final mapping nonlinear.

Summary:

• The statement about parallel lines changing under perspective is true.

• The statement about dividing by the depth coordinate during perspective projection is true (the perspective divide).

• The claim that perspective transformation is a linear transformation is false when interpreted in Cartesian coordinates; linearity holds only before the perspective divide in homogeneous coordinates.