CMPS 373 - Computer Graphics Homework assignment number 2 To be submitted, through the blackboard system, before Sunday May 28, 2017 Bézier 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 Bézier curve defined by a control polygon of n+1 points Pi i = 0,!,n is given through Bernstein polynomials Bin (t) n
n!
(1− t) n−i t i is the ith Bernstein as follows: C(t) = ∑ Bin (t)Pi Where Bin (t) =
i!(n − i)!
i= 0
polynomial of degree n. €
€
Given a value of parameter t, the Bézier curve can be evaluated either using the above parametric equation or using the Decasteljau subdivision algorithm. €
€ The objective of this homework is to 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. Remarks: • Pay attention to the design of a clean, well-organized and efficient program. • Added any function and/or data structure, not mentioned above but needed to enhance your application. • Identical or similar applications will be ignored. Submission of source code uploaded from Internet is not allowed. How to submit: Comment and organize your program in one single .cc file, then upload this file on the blackboard. email attached submissions will not be considered. Deadline: The homework should be submitted before Sunday May 28, 2017. The blackboard system will not allow any submission after this date.

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