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Given below are two statements:

Statement I: Bezier curves are curves that interpolate all of their control points.

Statement II: A cubic Bezier curve has four control points.

In the light of the above statements, choose the correct answer from the options given below:





Solution

Solution:
Statement I is false.

Bezier curves do not interpolate all of their control points.

A Bezier curve passes through the first and last control points, but the intermediate control points generally control the shape of the curve.

So, it does not pass through all control points.

Statement II is true.

A cubic Bezier curve has degree $3$.

For a Bezier curve of degree $n$, number of control points is $n+1$.

So, for cubic Bezier curve:

$n+1=3+1=4$

Therefore, a cubic Bezier curve has four control points.


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