families-of-polar-graphs

University Name : FAST-National University of Computer and Emerging Sciences, Karachi, Pakistan

CALCULUS - II Semester Project MT-115

Project Title : Families of Polar Curves

Abstract:

As per given instructions our group has developed a general program to plot various polar curves. The purpose of the program is to provide assistance to the user while dealing with polar curves of different shapes. The user will be able to draw the curves just by providing the required values of variables involved in the equations. Moreover, user can examine the behaviour of curves by changing values of variables.

Content:

The program is capable of drawing the curves listed below:

1. Polar Circles

2. Lemniscates

3. The Conchoid of Nicomedes

4. Ovals of Cassini

5. Dual Rose Curves

6. Oscar’s Butterfly

7. Asun Phong Curves

8. Valentine Curves

9. Rose Curves

10. Cardioids and Limacons

11. Spirals:

    • Archimedean Spiral

    • Hyperbolic Spiral

    • Parabolic Spiral

    • Lituus Spiral

Tools Used:

The program is made in C++ programming language using “Code::Blocks 10.05”. The libraries we have used are as follows: iostream, stdlib.h, stdio.h, conio.h, windows.h, dos.h, math.h, graphics.h The built-in functions we have used are given below: sin ( ) ,cos ( ), tan( ), pow ( ), sqrt( ), line ( ), moveto ( ), putpixel ( ), lineto ( ), abs ( ), ceil ( ), etc.

Discussion:

The main body of the program is consists of nested conditional loops and statements which leads in developing the required curve and then returning back to its initial state in order to get ready for another curve. After coming to the block of required curve the program will ask to enter values of variables involved in the equation of the curve and also providing the values on which the curve can be created in perfect shape. User can enter positive and negative real numbers in order to completely examine the behaviour of the polar curve.

Conclusion:

The significance of the program is that user will be able to draw the given polar curves just by providing a few values without even solving a single algebraic or trigonometric equation and within no time the required curve will be created.

Project Website:

http://www.stewartcalculus.com/data/ESSENTIAL%20CALCULUS%20Early%20Transcendentals%202e/upfiles/projects/ess_wp_0903_stu.pdf

a. https://thedancingrest.com/2014/10/08/polar-graph-art-equations-by-asunphong/

b. http://jwilson.coe.uga.edu/emt668/EMAT6680.2003.fall/Shiver/assignment11/PolarGraphs.htm

c. http://www.maplesoft.com/applications/view.aspx?SID=4087&view=html

Tools Used :

CodeBlocks 10.05 with graphics library

Group Members:

Muhammad Ahsan

Syed Mustufa Qadri