Rational geometry (cont’d)

Administrator — Tue, 27 Sep 2005 18:44:50 +0000

I made a recent post about rational geometry, or a way to solve geometric problems with no need for trigonometric functions.

My intuition is that this new (apparently the Chinese invented it more than a thousand years ago) way of doing geometry can be very useful for machines.

I ran a very simple experiment. At the end of Chapter 1 from the referenced book, there is a simple geometric problem with the traditional solution and the rational solution.
I have implemented the solution in Java and run some measurements. The rational solution is x4 faster.
Note that the code requires Java 1.5, in order to access the new nanosecond timer.

The output is as follows:
java Geometry 3.313693059275397 computed in 200000ns 3.3136930592753853 computed in 23000ns 3.313693059275397 computed in 1046.7512ns 3.3136930592753853 computed in 250.1114ns

public class Geometry { public static void main(String args[]) { long start, end; int ITER = 5000000;


		/* WARMING UP */
		// traditional way

	start = getTime();

	double alpha = Math.acos( (float)3/4);

	double beta = Math.PI - Math.PI/4 - alpha;

	double d = 5 * Math.sin(alpha) / Math.sin(beta);

	end = getTime();

	System.out.println(d + " computed in " + (end-start) + "ns");
		// rational geometry

	start = getTime();

	double q1 = 1400 - 525*Math.sqrt(7);

	double d1 = Math.sqrt(q1);

	end = getTime();

	System.out.println(d1 + " computed in " + (end-start) + "ns");
		/* WE ARE WARMED UP */
		// traditional way

	start = getTime();

	for(int i=0; i
	    {

		alpha = Math.acos( (float)3/4);

		// System.out.println("alpha: " + alpha);

		beta = Math.PI - Math.PI/4 - alpha;

		// System.out.println("beta: " + beta);

		d = 5 * Math.sin(alpha) / Math.sin(beta);

	    }

	end = getTime();

	System.out.println(d + " computed in " + (end-start)/(float)ITER + "ns");
		// rational geometry

	start = getTime();

	for(int i=0; i
	    {

		q1 = 1400 - 525*Math.sqrt(7);

		d1 = Math.sqrt(q1);

	    }

	end = getTime();

	System.out.println(d1 + " computed in " + (end-start)/(float)ITER+ "ns");
	    }
	    public final static long getTime()

    {

	return System.nanoTime();

    }

}

Virtual plague spreading like wildfire in World of Warcraft

Administrator — Thu, 22 Sep 2005 03:53:11 +0000

Virtual plague spreading like wildfire in World of Warcraft

This is one of the most interesting stories I have read.
It reminds me of a movie called The 13th Floor where a game goes beyond its purpose.

Poker software

Administrator — Sun, 18 Sep 2005 18:06:46 +0000

I have just been iniated to Texas Hold’em Poker.
To improve my game, I am looking for a decent software to run on my handheld.

Here are some possible candidates that I need to evalute:

the other side of the firewall

Rational geometry (cont’d)

Virtual plague spreading like wildfire in World of Warcraft

Poker software