Which of the following statement(s) is/are correct with reference to curve…
2016
Which of the following statement(s) is/are correct with reference to curve generation ?
I. Hermite curves are generated using the concepts of interpolation.
II. Bezier curves are generated using the concepts of approximation.
III. The Bezier curve lies entirely within the convex hull of its control points.
IV. The degree of Bezier curve does not depend on the number of control points.
- A.
I, II and IV only
- B.
II and III only
- C.
I and II only
- D.
I, II and III only
Attempted by 97 students.
Show answer & explanation
Correct answer: D
Answer: Statements I, II and III are correct; statement IV is incorrect.
Explanation:
Statement I — Hermite curves are generated using interpolation: Hermite curves are defined to pass through given end points with specified tangent (derivative) vectors.
Statement II — Bézier curves are generated using approximation: a Bézier curve generally does not pass through its intermediate control points and instead approximates the control polygon (it interpolates only the first and last control points).
Statement III — Convex hull property: a Bézier curve always lies entirely within the convex hull of its control points, preventing unexpected excursions outside the region defined by those points.
Statement IV — Incorrect: the degree of a Bézier curve depends on the number of control points. Specifically, with n+1 control points the curve degree is n.
Therefore the correct set is: I, II and III only.