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curve.h File Reference

Contains the declaration of the curve class. More...

Compounds
		class	curve
Functions
		void	nearest_point ( const curve &cu, const vector2 &p, const double tol, const unsigned max_iter, double &t, double &d2, unsigned &iter )
			Find the point on a curve that is nearest to a given point. More...

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Detailed Description

Contains the declaration of the curve class.

Author(s):

$Author: ben $

Version:

$Revision: 6.6 $

Date:

$Date: 2002/07/14 17:08:52 $

Definition in file curve.h.

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Function Documentation

void nearest_point (const curve & cu, const vector2 & p, const double tol, const unsigned max_iter, double & t2, double & d22, unsigned & iter)

Find the point on a curve that is nearest to a given point.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Calculates the position on the curve (t on cu) which is closest to the given point (p). Also returns the square of the distance (d2) between the curve and that point. The calculation is done iteratively, so callers must provide iterations limits (tol and max_iter).

Parameters:

cu	the curve
p	the given point
tol	a dimensionless calculation tolerance
max_iter	the maximum number of iterations to perform

Return values:

t	the parameter indicating the position on the curve nearest to p
d2	the square of the distance from p to t
iter	the number of iterations performed

Preconditions:

 assert( 2 <= cu.param.size() );
 assert( 0.0 < tol );
 assert( 0 < max_iter );

Postconditions:

 assert( 0 <= t && t <= 1 );
 assert( iter <= max_iter );
 assert( 0 <= d2 );

Implementation:

This function finds the nearest point on the curve using a minimisation procedure. It uses an auxiliary function, curve_distance2, which gives the square of the distance between the given point (p) and a particular point on the curve, which is indicated by the argument, t, of the function. This argument is the parameter of the curve. The function uses the minimise::bracket() function to create a valid bracket of the minimum. Then it uses the minimise::Brent() function to minimise the function.

Definition at line 219 of file curve.cpp.

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