Given below are two statements: one is labelled as Assertion A and the other…
2026
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The control points have only local control over the shape of the B-Splines.
Reason R: Bezier curves do have local control.
In the light of the above statements, choose the most appropriate answer from the options given below:
Answer: C. A is correct but R is not correct — Concept: The distinguishing property between B-Spline and Bezier curves is the extent of "control" a single control point has over the curve's shape. A curve…
- A.
Both A and R are correct and R is the correct explanation of A
- B.
Both A and R are correct but R is NOT the correct explanation of A
- C.
A is correct but R is not correct
- D.
A is not correct but R is correct
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Correct answer: C
Concept: The distinguishing property between B-Spline and Bezier curves is the extent of "control" a single control point has over the curve's shape. A curve representation has LOCAL control when its basis functions have compact (bounded) support, so moving one control point reshapes only a limited nearby segment. A curve representation has GLOBAL control when its basis functions have full-domain support instead, so moving any one control point reshapes the curve throughout its span.
Application: B-Spline curves are built from piecewise polynomial basis functions defined over local knot intervals, and each basis function has compact support spanning only a few knot spans. So each control point of a B-Spline affects only that bounded segment of the curve, leaving the rest unchanged — this is exactly local control, so Assertion A is TRUE. Bezier curves, in contrast, are built from Bernstein-polynomial basis functions, each of which is strictly positive throughout the interior of the parameter interval (0, 1) and carries full-domain support rather than the piecewise compact support of B-Spline basis functions. Moving any single Bezier control point therefore reshapes the curve throughout its span, not just a local segment — Bezier curves exhibit GLOBAL control, not local control. So Reason R, which claims Bezier curves have local control, is FALSE.
Cross-check: This local-vs-global distinction is the standard textbook motivation for preferring B-Splines over a single Bezier curve in CAD and interactive design: a designer can locally edit one segment of a B-Spline without disturbing the rest of the curve, which is impossible with a single Bezier curve since every control point there influences the whole shape.
"Both A and R are correct and R is the correct explanation of A" would require R (Bezier curves have local control) to be true and to be the mechanism behind A — but R is false, since Bezier curves have global, not local, control.
"Both A and R are correct but R is NOT the correct explanation of A" would require R to be true as an independent fact — but R is false for the same reason, so this combination does not hold either.
"A is not correct but R is correct" reverses both truth values — A is in fact true (B-Splines do have local control) and R is in fact false, so this combination is also wrong.
Since Assertion A is true (B-Splines have local control) and Reason R is false (Bezier curves have global, not local, control), the correct combination is: A is correct but R is not correct.