Solution

Correct Answerr is : A is correct but R is not correct

Key Points

Based on the principles of computer graphics, here is the step-by-step solution for the question regarding B-Splines and Bezier curves:

1. Analyze Assertion A
Statement: "The control points have only local control over the shape of the B-Splines."

Fact: This is True. One of the primary advantages of a B-Spline over a standard Bezier curve is that moving a single control point only affects a specific, local segment of the curve. It does not alter the shape of the entire curve.

2. Analyze Reason R
Statement: "Bezier curves do have local control."

Fact: This is False. Standard Bezier curves exhibit global control. This means that if you move even a single control point, the mathematical polynomial changes, which mathematically alters the entire curve (even if the visual change is most noticeable near the point you moved).

Conclusion
Since Assertion A is factually correct and Reason R is factually incorrect, the relationship matches the third option.

Correct Answer: Option 3 (A is correct but R is not correct)