Given below are two statements Statement I: The maximum number of sides that a…
2021
Given below are two statements Statement
I: The maximum number of sides that a triangle might have when clipped to a rectangular viewport is 6. Statement
II: In 3D graphics, the perspective transformation is nonlinear in z.
In light of the above statements, choose the correct answer from the options given below
Answer: D. Statement I is false but Statement II is true — Correct answer: Statement I is false; Statement II is true. Why Statement I is false: The intersection of two convex polygons with m and n edges can have at…
- A.
Both Statement I and Statement II are true
- B.
Both Statement I and Statement II are false
- C.
Statement I is true but Statement II is false
- D.
Statement I is false but Statement II is true
Attempted by 53 students.
Show answer & explanation
Correct answer: D
Correct answer: Statement I is false; Statement II is true.
Why Statement I is false:
The intersection of two convex polygons with m and n edges can have at most m + n vertices.
For a triangle (3 edges) clipped by a rectangular viewport (4 edges), the maximum number of sides in the clipped polygon is 3 + 4 = 7, so the claim of 6 is incorrect.
Why Statement II is true:
Perspective projection uses homogeneous coordinates and a subsequent division by the depth (z) to convert to Cartesian coordinates.
Because x and y are divided by z (e.g., x' = x/z, y' = y/z), the mapping of Cartesian coordinates is nonlinear in z.
Summary: The first statement is false (maximum 7 sides), and the second statement is true (perspective is nonlinear in z).