Consider a window bounded by the lines : x = 0; y= 0; x = 5 and y = 3. The…
2014
Consider a window bounded by the lines : x = 0; y= 0; x = 5 and y = 3. The line segment joining (–1, 0) and (4, 5), if clipped against this window will connect the points
Answer: A. (0, 1) and (2, 3) — Answer: The clipped segment connects (0, 1) and (2, 3). Parameterize the line segment from (−1, 0) to (4, 5): P(t) = (−1 + 5t, 5t) with 0 ≤ t ≤ 1. Intersect…
- A.
(0, 1) and (2, 3)
- B.
(0, 1) and (3, 3)
- C.
(0, 1) and (4, 3)
- D.
(0, 1) and (3, 2)
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Correct answer: A
Answer: The clipped segment connects (0, 1) and (2, 3).
Parameterize the line segment from (−1, 0) to (4, 5): P(t) = (−1 + 5t, 5t) with 0 ≤ t ≤ 1.
Intersect with left boundary x = 0: −1 + 5t = 0 ⇒ t = 0.2 ⇒ point is (0, 1).
Intersect with top boundary y = 3: 5t = 3 ⇒ t = 0.6 ⇒ point is (2, 3).
Both intersection points lie within the window (0 ≤ x ≤ 5, 0 ≤ y ≤ 3), so the visible (clipped) segment runs from (0, 1) to (2, 3).