Program #2 Solution

Purpose




This programming assignment draws a complex fractal figure using recursive calls. A "Turtle" class will be provided to draw a line segment or changes its forward direction (Lab 2). Then you should derive a "Dragon" class, which draws Dragon curves by calling its methods recursively, using "Turtle"




Please refer the http://sierra.nmsu.edu/morandi/coursematerials/JurassicParkFractal.html (http://sierra.nmsu.edu/morandi/coursematerials/JurassicParkFractal.html)




Heighway Dragon Curves




The Heighway dragon (also known as the Harter–Heighway dragon or the Jurassic Park dragon) was first investigated by NASA (http://en.wikipedia.org/wiki/NASA) physicists John Heighway, Bruce Banks, and William Harter. It was described by Martin Gardner (http://en.wikipedia.org/wiki/Martin_Gardner) in




his Scientific American (http://en.wikipedia.org/wiki/Scientific_American) column Mathematical Games in




1967. Many of its properties were first published by Chandler Davis




(http://en.wikipedia.org/wiki/Chandler_Davis) and Donald Knuth (http://en.wikipedia.org/wiki/Donald_Knuth)




It appeared on the section title pages of the Michael Crichton




(http://en.wikipedia.org/wiki/Michael_Crichton) novel Jurassic Park




(http://en.wikipedia.org/wiki/Jurassic_Park_(novel)) . Here are some examples of Dragon curves.





































Construc on of Dragon







For simplicity, let’s focus on 2 levels of dragon curves.




Assuming that Turtle is initially facing right, the following shows the sequence of drawing a level­1 right




Dragon curve:




Turn ­90



Draw a straight line
Turn ­90



Draw a straight line







































Now, here is a level­1 curve left curve;




Draw a straight line



Turn 90



Draw a straight line



Turn 90






























Similar to a level­1 curve, a level­2 curve has two types, left and right. The following sequence draws a level­2 right Dragon curve.




Turn ­90



Draw a level­1 left curve



Turn ­90



Draw a level­1 right curve







































And a level­2 left Dragon curve;




Draw a level­1 left curve



Turn 90



Draw a level­1 right curve



Turn 90


















Note that right­curve and left curve looks exactly same, but the order of drawing is different.




Now, to go from a level­k to a level k+1, you need to convert each of line segments of level­1 curve into a level­k left or right curve.




Statement of Work




Derive the Dragon class from the Turtle using class inheritance. You can You must work on the Dragon class design by yourself. Note that Dragon is inherited from Turtle:







class Dragon : public Turtle




{




...




}







This class must include two public methods, leftCurve and rightCurve, each drawing a level­k left and a level­k right Dragon curve. Thus, those two methods take two arguments, the depth of level and the length of each line segment. Use the following driver program to verify the correctness of your class design.










#include "dragon.h"




#include <iostream




using namespace std;







#include "dragon.h"




#include <iostream




using namespace std;




int main( ) {




right dragon at level 10



Dragon dragon10( 80, 360, 0 ); dragon10.rightCurve( 10, 6 );

right dragon at level 9 Dragon dragon9( 360, 360, 0 ); dragon9.rightCurve( 9, 6 );



right dragon at level 8 Dragon dragon8( 560, 360, 0 ); dragon8.rightCurve( 8, 6 );
right dragon at level 7 Dragon dragon7( 120, 500, 0 ); dragon7.rightCurve( 7, 8 );



right dragon at level 6 Dragon dragon6( 240, 500, 0 ); dragon6.rightCurve( 6, 8 );



right dragon at level 5 Dragon dragon5( 360, 500, 0 ); dragon5.rightCurve( 5, 8 );



right dragon at level 4 Dragon dragon4( 480, 500, 0 ); dragon4.rightCurve( 4, 8 );



right dragon at level 3



Dragon dragon3( 60, 700, 0 ); dragon3.rightCurve( 3, 16 );




right dragon at level 2 Dragon dragon2( 240, 700, 0 );



dragon2.rightCurve( 2, 16 );







right dragon at level 1 Dragon dragon1( 420, 700, 0 ); dragon1.rightCurve( 1, 16 );



}







To view and print out your result in Linux, follow the directions below:







g++ *.cpp




./a.out




ps2pdf output.ps output.pdf













Windows users should view output.ps through Acrobat. Mac OS users can view it through preview.










Once complete, put the <dragon.h, dragon.cpp, Turtle.h, Turtle.cpp, dragonDriver.cpp in the same folder into linux




Compile with the following command:




g++ Turtle.cpp dragon.cpp dragonDriver.cpp

What to Turn in




Clearly state in your code comments any other assumptions you have made. Assumptions about main are placed in the beginning comment block of your program. Assumptions about Turtle and Dragon members are placed in their class definition (.h file). (Of course member functions in the .cpp file are also commented.) What you have to turn in includes:




source codes (do not zip)



(1a) dragon.h,




(1b), dragon.cpp,




(option) DragonDriver.cpp (Your own driver if it is different from the one provided)










your execution output for Dragon in output.pdf (you need to convert it into PDF).









Note that output must be a PDF file but not output.ps file. To get a PDF output on Windows, you must pass output.ps to Acrobat Distiller/Reader, generate the correspoonding graphical view, and then save it in PDF.










Grading Guide and Answers




The following is the grading guide how your homework will be graded. Key answers will be made available after the due date at the Solution page.













Grade Guideline










1. Correctness (26 pts)




Compilation errors(0pt)




Successful compilation without any method implemented (0 pt)




Successful compilation with constructor and at least one recursion method implementation (10 pts)




Dragon output pdf files (4 pts)



Correct dragon implementation (12 pts)






Program Organization (4 pts)



Proper comments (Have to give comments for each method)




Good (2pts) Poor(1 pt) No explanations(0pt)

Coding style (proper indentations, blank lines, variable names, and nonredundant code)