Description
Remark: You must NOT use GL’s routines for generating B´ezier or B-spline curves! You can use GL for rendering but not for evaluating these curves.
The fourth project requires the implementation of a 2D B´ezier and B-spline curve editor. A 2D B´ezier curve is defined as
c.
For the evaluation of a B´ezier curve, use the de Casteljau algorithm to compute points on the curve. A single 2D parametric B-spline curve is defined as
c.
Remember that you do not need to evaluate the normalized B-spline basis functions. For the evaluation of a B-spline curve, use the de Boor algorithm to generate points on the curve.
When dealing with a B´ezier curve, the user must be able to add, insert, delete, and modify the B´ezier points bi. The same applies to a B-spline curve: The user must be able to add, insert, delete, and modify the de Boor points di. In addition to this, the user must be able to change the order k of a B-spline curve and modify the values of the knots τ0, … , τn+k. Initially, you can define the order to be k = 2 and the knots to be τi = i, i = 0,…,n + k.
The user must be able to specify the number of points used for rendering a B´ezier or B-spline curve by a sequence of line segments (“display resolution”).
The user should be able to change all parameters easily by providing a screen area used for displaying and specifying the coordinates of control points (B´ezier and de Boor points), the order and the knots of a B-spline curve, and the display resolution. The specification of control points should be made as easy as possible. Either the user types in the control information directly, or – when modifying control points – uses a “rubber band” technique to interactively move control points.
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The curve editor must provide a facility to store the parameters defining a B´ezier or B-spline curve. The system must be capable of reading and writing control information for B´ezier and B-spline curves.
It must be possible to manipulate, create, and display a scene containing multiple B´ezier and multiple B-spline curves. Make it possible to select a certain curve and to operate just on the selected one!
Besides having to hand in a program listing, please prepare a “manual sheet” explaining how to use your program.
