Given below are different properties of 3D projections from A-D. Identify the…
2020
Given below are different properties of 3D projections from A-D. Identify the correct order on the basis of property true of (i) a perspective projection only, (ii) an orthographic projection only, (iii) both orthographic and projective transformations and (iv) neither orthographic nor projective transformation, respectively.
(A) Straight lines are mapped to straight lines
(B) Distances and angles are (in general) preserved
(C) Far away objects appear the same size as closer ones
(D) Requires homogeneous coordinates in order for it to be encoded into a linear transformation
Choose the correct answer from the options given below:
Answer: C. D,C,A,B — Correct order: D, C, A, B Explanation: Perspective only (D): "Requires homogeneous coordinates in order for it to be encoded into a linear transformation."…
- A.
D,C,B,A
- B.
B,C,D,A
- C.
D,C,A,B
- D.
C,D,B,A
Attempted by 37 students.
Show answer & explanation
Correct answer: C
Correct order: D, C, A, B
Explanation:
Perspective only (D): "Requires homogeneous coordinates in order for it to be encoded into a linear transformation." Perspective projection is a projective transformation and is represented linearly only after introducing homogeneous coordinates.
Orthographic only (C): "Far away objects appear the same size as closer ones." Orthographic (parallel) projection does not scale objects with distance, so objects at different depths can appear the same size.
Both orthographic and projective (A): "Straight lines are mapped to straight lines." Both affine/orthographic and projective mappings send straight lines in 3D to straight lines in the image.
Neither orthographic nor projective (B): "Distances and angles are (in general) preserved." Neither orthographic nor perspective projections generally preserve true Euclidean distances or angles except in special configurations; therefore this property does not hold in general.
Summary: D corresponds to perspective-only, C to orthographic-only, A to both, and B to neither.