Set up a midpoint algorithm taking symmetry considerations i

Set up a midpoint algorithm, taking symmetry considerations into account to scan convert any parabola of the form y = ax^2 - b, with input values for parameters a, b and the range of x.

Solution

PARABOLA - MID POINT (1st ORDER)

#include<iostream.h>
#include<graphics.h>
#include<stdio.h>
#include<conio.h>
void put_pixel(int x, int y)
{
putpixel((x+300),(240-y),15);
putpixel((x+300),(240+y),15);
}
void para(int cx, int cy, double a)
{
setcolor(BLUE);
line(300,0,300,479);
setcolor(RED);
line(0,240,639,240);
double x=0,y=0; /* initial coorodinates */
double d1;
d1 = (2*a) – 1;
put_pixel(x,y);
while(y<= (2*a*1.0))
{
if(d1<0)
{
d1+= 4*a-3-2*y;
x++;
y++;
}
else
{
d1-= 3 + 2*y;
y++;
}
put_pixel(x,y);
}
d1 = (4.0*a*(x+1) – (y+0.5)*(y+0.5) );
while( y < 220 )
{
if(d1<0)
{
d1+= 4*a;
x++;
}
else
{
d1+= 4.0*a – 2 – 2.0*y ;
x++;
y++;
}
put_pixel(x,y);
}
}
void main()
{
clrscr();
double a;
cout<<“Enter a : “;
cin>>a;
int gdriver = DETECT, gmode;
initgraph(&gdriver, &gmode, “c:\\\\tc\\\\bgi”);
para(0,0,a);
getch();
closegraph();
}

PARABOLA - BRESENHAM’S APPROACH

#include<iostream.h>
#include<graphics.h>
#include<stdio.h>
#include<conio.h>
void plotpixel(int x, int y)
{
putpixel((x+300),(240-y),15);
// putpixel((-x+300),(240-y),15);
putpixel((x+300),(240+y),15);
// putpixel((-x+300),(240+y),15);
}
void para(int cx, int cy, double a)
{
setcolor(BLUE);
line(300,0,300,479);
setcolor(RED);
line(0,240,639,240);
double x=0,y=0; /* initial coorodinates */
double d1 = 1 - (2*a);
plotpixel(x,y);
while( y<= (2*a) )
{
if(d1>0)
{
d1+= 3 + 2*y - 4*a;
plotpixel(x,y);
x++;
y++;
}
else
{
d1+= 3 + 2*y;
plotpixel(x,y);
y++;
}
//plotpixel(x,y);
}
d1 = ((y+0.5)*(y+0.5) - 4*a*(x+1));
while( y < 220 )
{
if(d1>0)
{
d1+= (-4*a);x++;}
else
{
d1+= 2 + 2*y - 4*a;
x++;
y++;
}
plotpixel(x,y);
}
}
void main()
{
clrscr();
double a;
cout<<\"Enter a : \";cin>>a;
int gdriver = DETECT, gmode;
initgraph(&gdriver, &gmode, \"c:\\\\tc\\\\bgi\");
para(0,0,a);
getch();
closegraph();
}