DescartesFolium Class Reference
[Example scripts (models)]

Example: Folium of Descartes More...

Public Member Functions
	DescartesFolium (const Options &opt)
	Actual model.
	DescartesFolium (DescartesFolium &p)
	Constructor for cloning p.
virtual Space *	copy (void)
	Copy during cloning.
virtual FloatVar	cost (void) const
	Cost function.
virtual void	print (std::ostream &os) const
	Print solution coordinates.
Protected Attributes
FloatVarArray	f
	The numbers.
double	step
	Minimum distance between two solutions.

Detailed Description

Example: Folium of Descartes

The folium of Descartes is a curve defined by the equation:

$x^3 + y^3 - 3axy = 0$

A technique to solve it, is to write $y=px$ and solve for $x$ and $y$ in terms of $p$ . By setting $a=1$ , it yields to the paramatric equation:

$x^3 + y^3 - 3xy = 0$

$x=\frac{3p}{1+p^3},\quad y=\frac{3p^2}{1+p^3}$

The parameter $p$ is related to the position on the curve and is constrained to get different solutions for $x$ and $y$ . To get reasonable interval starting sizes, $p$ and $y$ are restricted to $[-20;20]$ and $x$ is restricted to $[-1;2]$ .