Graphics Assignment No: 2 Solution

Assignment Description



Implement Bresenham's circle drawing algorithm and draw a circle using its center coordinates and radius.




Procedure



Installation




Install the following packages from the Ubuntu repository:




freeglut3-dev




mesa-common-dev










sudo apt-get install freeglut3 freeglut3-dev mesa-common-dev







Check your =usr=include=GL folder to verify the installation of the OpenGL headers that you intend to use.




Compiling and Linking




We will have to use the lglut linker option with gcc=g++ to compile a program with glut library.




For example, to compile the program, use the following to get the binary executable code:










g++ bresenham.cpp -lGL -lGLU -lglut -o bresenham




























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Discussion



The primary objective of the assignment is to implement an algorithm capable of determining the individual pixels needed for rasterizing a circle. For this purpose, Bresenham's Circle Drawing algorithm is implemented. The algorithm works by tracing individual pixels in one of the octants of the standard xy-plane and tracing the corresponding equidistant re ections in the other seven remaining octants. For a detailed explanation, please refer the code.




OpenGL Code







#include <stdio.h




#include <GL/glut.h




Global variables for circle s coordinates and radius. int x_center, y_center, radius;



void plot(int x, int y)




{




Draw the points with respect to the center. glBegin(GL_POINTS);



glVertex2i(x_center + x, y_center + y); glEnd();




}




void display()




{




Set the display area colour set using glClearColor(). glClear(GL_COLOR_BUFFER_BIT);



Colour fill.



glColor3ub(255, 255, 255);




Set point sizes. glPointSize(2.0);



Initial parameters for points. int x = 0;



int y = radius; int h = 1 - radius;




Draw the points where the circle crosses the axes. plot(x, y);



plot(x, -y); plot(y, x); plot(-y, x);




Main part of the algorithm.






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while (y x)




{




if (h < 0)




{




h += (2 * x) + 3;




} else




{




h += (2 * (x - y)) + 5; y -= 1;




}




x += 1;




Plot the points in counter-clockwise fashion. plot(x, y);



plot(-x, y); plot(-y, x); plot(-y, -x); plot(-x, -y); plot(x, -y); plot(y, -x); plot(y, x);




}




Begin execution of the above code. glFlush();



}




int main(int argc, char **argv)




{




char c;




printf("Bresenham s Circle Drawing Algorithm\n"); printf("Please Enter The X-Coordinate of the Center: "); scanf("%d%c", &x_center, &c);




printf("Please Enter The Y-Coordinate of the Center: "); scanf("%d%c", &y_center, &c);




printf("Please Enter The Radius of the Circle: "); scanf("%d%c", &radius, &c);




Initialize to the command-line arguments. glutInit(&argc, argv);



Setup the colour depth of the window buffers. glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB | GLUT_DEPTH);



Assign the position, size and name to the window.






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glutInitWindowPosition(100, 100);




glutInitWindowSize(640, 480);




glutCreateWindow("Bresenham s Circle Drawing Algorithm");




Setup a black background. glClearColor(0.0, 0.0, 0.0, 0.0);



Setup viewing projection. glMatrixMode(GL_PROJECTION);



Initialize identity matrix. glLoadIdentity();



Setup a viewport.



gluOrtho2D(0.0, 640.0, 0.0, 480.0);




Pass the display function to generate the display. glutDisplayFunc(display);



Hand over the execution to the glut library. glutMainLoop();



return 0;




}










Python Code







Using turtle graphics library. import turtle



Function to draw a single point.



def draw_point(x_center, y_center, x, y):




turtle.goto(x_center + x, y_center + y)




turtle.dot(5, "white")




# Function to draw the whole circle.




def draw_circle(x_center, y_center, radius):




# Initial arguments.




x_center = int(x_center)




y_center = int(y_center)




x = int(0)




y = int(radius)




h = int(1 - y)




Draw the points where the circle crosses the axes. draw_point(x_center, y_center, x, y); draw_point(x_center, y_center, x, -y); draw_point(x_center, y_center, y, x);









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draw_point(x_center, y_center, -y, x);




Main part of the algorithm. while y x:



if h < 0:




h += (2 * x) + 3; else:




h += (2 * (x - y)) + 5; y -= 1;




x += 1;




Plot the points in counter-clockwise fashion. draw_point(x_center, y_center, x, y); draw_point(x_center, y_center, -x, y); draw_point(x_center, y_center, -y, x); draw_point(x_center, y_center, -y, -x); draw_point(x_center, y_center, -x, -y); draw_point(x_center, y_center, x, -y); draw_point(x_center, y_center, y, -x); draw_point(x_center, y_center, y, x);



Initial input.



print("Bresenham s Circle Drawing Algorithm\n")




x_center = input("Please Enter The X-Coordinate of the Center: ")




y_center = input("Please Enter The Y-Coordinate of the Center: ")




radius = input("Please Enter The Radius of the Circle: ")




Initialization and background colour. turtle.setup() turtle.bgcolor("black")






Set the fill colour to black/



turtle.fillcolor("black")




# Draw the circle.




draw_circle(x_center, y_center, radius)




Exit on click. turtle.exitonclick()

































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Result



OpenGL






































































Python



























































































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References



How to install OpenGL/GLUT libraries



An Introduction to OpenGL Programming



Turtle Graphics - The Python Standard Library



Wikipedia - Midpoint Circle Algorithm










































































































































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