Reference no: EM132217550

Be´zier curves are a class of parametric curves defined using a set of control points, and a parameter t in [0,1]. The analytic parametric equation of a Be´zier curve defined by a control polygon of n+1 points Pi i = 0,!,n is given through Bernstein polynomials Bin (t)

n n!
as follows: C(t)=?Bin(t)Pi WhereBin(t)=i!(n-i)!(1-t)n-iti is the ith Bernstein

i=0 polynomial of degree n.

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Given a value of parameter t, the Be´zier curve can be evaluated either using the above parametric equation or using the Decasteljau subdivision algorithm.

Develop a tool for visualization and editing of Bézier curves of any degree n. A C++ class should be defined to encapsulate the data and all the functions necessary for easy manipulation of Bézier curves.

A particular attention should be paid to the design of your application and to the graphic user interface that allows the activation of the desired functionality. Recommended functionalities:

1. Appropriate data structures to store the curve properties (number of control points, set of control points, etc.)

2. A Menu to allow navigation through the application functionalities and select the function to launch.

3. Mouse control function: allows the definition of the control polygon, the selection and move of one control point into another position to enhance the curve design

4. A function BezPoint() to compute and return the point on the Bézier curve using the parametric equation.

5. A function CasteljauPoint() to compute and return a point on the Bézier curve using the Decasteljau algorithm.

6. A function CasteljauSubdivid() to compute and return the two sub-curves of a Bézier curve using the Decasteljau algorithm.

7. A function drawBez() to visualize a Bézier curve with (or without) its control polygon.

8. A function to edit the curve: use the mouse to select and move one control point into another position, then trace the resulting curve.