Given below are two statements: Statement š¼: Bezier curves are curves thatā¦
2020
Given below are two statements:
StatementĀ š¼: Bezier curves are curves that interpolate all of their control points
StatementĀ š¼š¼: A cubic bezier curve has four control points
In the light of the above statements, choose the correct answer from the options given below
Answer: D. Statement š¼ is incorrect but Statement š¼š¼ is true ā Answer: Statement I is incorrect; Statement II is true. Why Statement I is incorrect: A BĆ©zier curve is defined by control points that influence the shape ofā¦
- A.
Both StatementĀ š¼Ā and StatementĀ š¼š¼Ā are true
- B.
Both StatementĀ š¼Ā and StatementĀ š¼š¼Ā are false
- C.
StatementĀ š¼Ā is correct but StatementĀ š¼š¼Ā is false
- D.
StatementĀ š¼Ā is incorrect but StatementĀ š¼š¼Ā is true
Attempted by 138 students.
Show answer & explanation
Correct answer: D
Answer: Statement I is incorrect; Statement II is true.
Why Statement I is incorrect:
A BĆ©zier curve is defined by control points that influence the shape of the curve. The curve generally passes through the first and last control points (endpoints), but intermediate control points do not usually lie on the curve; they pull the curve toward them rather than being interpolated.
Why Statement II is true:
A cubic BĆ©zier curve is specified by four control points, commonly labeled P0, P1, P2, and P3.
Its parametric form (for 0 ā¤ t ā¤ 1) is B(t) = (1 - t)^3 P0 + 3t(1 - t)^2 P1 + 3t^2(1 - t) P2 + t^3 P3, which uses exactly four control points.
Conclusion: Statement I is false because BĆ©zier curves do not interpolate all control points (only endpoints are guaranteed); Statement II is true because a cubic BĆ©zier curve is defined by four control points.