// Calculation Program for the surface area of an egg body, 08 (Tues.) Dec., 2009

// egg equation: (x*x+y*y)**2=a*(x**3)+(a-b)*x*(y**2), The case that a=4 and b=3.2 (or, a=1 and b=0.8) may be the nearest shape to an actual egg.
// The general condition needs b<=a, and in the case of b=0, the curve is led to a circle.

// file name: surface.c

#include< stdio.h>
#include< math.h>

void main(void)
{
	double a,b,x,dx,y,xmax,s,ds,dydx,p;

// Setting of the constants
	for(;;)
	{
		printf("Input of constant a; a= ? ");
		scanf("%lf",&a);
		if(a>0)
		{
			break;
		}
		else
		{
			printf("Please input the value of a after correcting a as a>0.\n");
		}
	}
	for(;;)
	{
		printf("Input of constant b; b= ? ");
		scanf("%lf",&b);
		if(b>=0&&b<=a)
		{
			break;
		}
		else
		{
			printf("Pleease input the value of b after correcting b as 0< b < a or b=0 or b=a.\n");
		}
	}

	printf("\n");

	p=3.1415927;
	xmax=a;// the maximum value of x
	dx=xmax/1000000;

// execution of calculation
	if(b==0)
	{
		s=p*a*a;
	}
	else
	{
		for(x=dx;x<=xmax;x=x+dx)
		{
			y=sqrt(((a-b-2*x)+sqrt(4*b*x+(a-b)*(a-b)))*x/2);// containing the equation of sphere "y=sqrt(a*a/2/2-(x-a/2)*(x-a/2))" in the case of b=O
			dydx=(1/(2.0*sqrt(2.0)))*sqrt((a-b-2.0*x+sqrt(4.0*b*x+(a-b)*(a-b)))/x)+(sqrt(x/2.0))*((b/sqrt(4.0*b*x+(a-b)*(a-b))-1)/sqrt(a-b-2.0*x+sqrt(4.0*b*x+(a-b)*(a-b))));
			ds=2*p*y*sqrt(1+dydx*dydx)*dx;
			s=s+ds;
		}
	}

	printf("The surface area of the egg body; S=%lf\n",s);
	printf("\n");

	printf("end\n");
}// the end of the program