[SOLVED] CS3388 Assignment 3 Bezier curve, B- spline and Beta-spline curves

CS3388 Assignment 3, 2016

Posted: 8th November 2016 Due: 23rd November 2016, 11:55 PM

Description

This assignment is about implementing a curve editor using OpenGL. You are provided with C++ source code which uses OpenGL to draw points on the screen by mouse click. You have to write the code to draw Bezier curve, B- spline and Beta-spline curves using these points. The assignment is worth 10% of the final mark.

Unzip the files, compile and run. At this point you will see a drawing screen where you can click mouse and draw points. This is a simple user interface for manipulating curves. You should be able to create and move the control points by clicking and dragging with the mouse. This functionality is provided by the PointCanvas class. Right-clicking brings up a menu comprising of dierent types of curves that you have to implement: basic B ezier curve, cubic B-spline curve, Beta-spline curve, closed Beta-spline curve and cubic B-spline with phantom endpoints. Finally, last 2 menu items are for clearing the screen and exiting from the program, which are already implemented. You will need to write code at the specified places in curves.cpp (and curves.h if you add any new function).

Following are the details of the tasks for the assignment:

B ezier curve evaluation: Implement simple evaluation and rendering

of B ezier curve. You are provided with an incomplete curveOperations

class in curves.cpp. Implement curveOperations::evaluateBezier to return

the point along the B ezier curve at the given t-value. A function curve-

Operations::binomialCoe cient() is provided to compute m = m! . i i!(m i)!

Next, implement curveOperations::drawBezier. Draw the curve by eval- uating it at uniformly-spaced t-values, and then drawing lines between those points. We have provided a function curveOperations::drawLine() to do the line-drawing for you. It is up to you to choose how many dif- ferent points to evaluate in order to produce a reasonable-looking curve ( t = 0.01 produces pretty good result).

Draw cubic B-spline curve: Implement curveOperations::drawCubicBspline to draw a cubic B-spline curve from the clicked control points. Follow the course notes to get the details of cubic B-spline. There are dierent nota- tions that are used, feel free to use any idea. However, the notation used

in slide 43, 44 are pretty straightforward: 1

nXu+2 i=nu 2

Use the range of (nu 2) from floor(nu 2) to ceil(nu+2). This notation will help you to implement rest of the parts of the assignment without any ambiguities from the course notes. Use curveOperations::drawLine() to draw the curve after generating the points.

Draw Beta-spline curve: Implement curveOperations::drawBetaspline to draw a Beta-spline curve from the clicked control points. Follow the course notes, or this tutorial for detailed theories of Beta-spline. Use skew (s) = 1.0 and tension (t) = 10.0.

Draw closed Beta-spline curve: Implement the function curveOpera- tions::drawBetasplineClosedCurve. This is almost the same as the previous one, the only dierence is that, you have to consider the endpoints in such a way that it draws a closed Beta-spline curve.

Draw cubic B-spline curve with phantom endpoints: Implement curveOperations::drawCubicBsplinePhantom. In cubic B-spline, the curve does not pass through the start and end points. Thats why we add two phantom nodes to force the curve to pass through the endpoints. These are denoted by P 1 and Pn+1 in the course notes. Consider these two phantom points and draw the cubic B-spline. Now it should pass through the endpoints.

Write a short report: Experiment with dierent values of skew and tension parameters of Beta-spline and write a report (less than one page) on your observations on the comparison of the curve behaviour on these parameters, and also compare with cubic B-spline curve.

You should not need to modify any files except for curves.cpp. However, feel free if you want to add any function to curveOperations class (say a sep- arate method for blending function), and obviously you will need to modify curves.h. DO NOT change the names of the provided files. You are welcome to modify anything you like, but you must preserve all the functionalities of the assignment.

What to submit?

Submit the program file(s) you have implemented/modified and the report either in a text or PDF file. Put all the file(s) into a zip and submit via OWL (no files will be accepted by email). Please dont submit any unnecessary files (such as the whole project).

2

P(u) =

PiB(nu i)

Late penalty

The late policy is a penalty of 5% per day up to 3 days of lateness. Saturday and Sunday count as one penalty day.

Plagiarism

Copying the code is a serious academic oence, which will be treated as per university norms. Remind that changing variable names and white spaces do not make your code unique, its very easy to detect these cases using softwares.

General marking scheme

The marks will be distributed as follows: Working program: 70%

(will be divided into dierent parts of the assignment) Documentation: 10%

• Main comment block identifying the student (name, student number, email address): 4%
• Defining input and output parameters for a function: 3%
• Purpose of functions/blocks of code: 3%

  Program style: 10%

  Meaningful variable names: 3%
  Constants instead magic numbers: 2%
  Readability (complete sentences, indentation, white spaces, etc): 2% Code flows nicely: 3%

  Program structure: 10%

  Modular code: 4%
  Uses appropriate data structure: 3%
  Loops when needed/no loops when not needed: 3%

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