What's wrong with abs? (draw a circle)

[Gunnar <gunix@comhem.se>]

This is somewhat related to my posting "draw an ellipse". But now I'm just 
trying to draw a circle.
I plot the function b2(x)   where b2 is a function that returns a y-value that 
makes x^2+y^2=1 (or very close to 1 any way).

It looks kind of alright when using the code below, (it's a bisection method 
to find the correct y-value) and then change the starting value for y1 in the 
code to
a) 1-x  (to get a better starting value for the lower bound). 
      You get a problem in the second quadrant.
b) 1-abs(x)  to fix the problem. Now it will be a total mess.

So, what is wrong?
I have not looked at the generated postscript, can it be that it is using the 
postscript routins for "abs" and other functions, and that causes the 
problem? 

This is both fun and frustrating....


The code:

#include "epix.h"
#include <cmath>
using namespace ePiX;

double b2(double x){
	double y1,y2,ym;
	y1=0;                 /////// THIS LINE!!!
	y2=1;
	while (y2-y1>0.00001){
		ym=(y1+y2)/2;
		if (x*x + ym*ym >1)
			y2=ym;
		else
			y1=ym;
	}
	return ym;
}
main(){
	bounding_box(P(-1,-1),P(1,1));
	unitlength("1in");
	picture(P(1,1));
	begin();
	plot(b2,x_min,x_max,80);
	end();
}


Gunnar.
-- 
The things that interest people most are usually none of their business.