# Bezier Curve in Computer Graphics - its Characteristics

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Computer Graphics and Multimedia Application: Q1.Bezier Curve in computer graphics? Q2.Characteristics of Bezier Curve? (Computer graphics and multimedia application All Notes)

## Q1. Explain the Bezier curves used in the general graphics package?

Ans. Bezier Curve: A Bezier curve section can be fitted to any number of control points. The number of control points to be approximated and their relative position determines the degree of the Bezier polynomial. For general Bezier curves, the blending function specification is the most convenient.

Suppose, we are given n+1 control points positions Pk(Xk, Yk, Zk) with k varying from 0 to n. These co-ordinate points can be blended to produce the following position vector P (u), which described the path of an approximating Bezier polynomial function between Po and Pn.
where C(n,k) are the binomial coefficients,
Bezier curves are commonly found in painting and drawing packages as well as CAD systems. Since they are easy to implement and they are reasonably powerful in curve design. For example,

## Q2. Characteristics of Bezier Curve in Computer Graphics?

Ans. Characteristics of the Bezier Curve are:-
(a) Bezier curve always passes through the first and last control points, i.e. curve has the same end points as the guiding polygon.

(b) The degree of the polynomial defining the curve segment is one less than the number of defining polygon points. Therefore, for four control points, the degree of the polynomial is three, i.e. cubic polynomial.

### Q3. Numerical = A cubic Bezier curve is defined over control points (1,1),(2,3),(4,4) and (6,1). Calculate parametric midpoints of this curve and shows that its gradient dy/dx is 1/7.

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