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/*
* map.h -- classes of map for function plotting
*
* Andrew D. Hwang <ahwang -at- holycross -dot- edu>
*
* Version 1.2.5
* Last Change: June 18, 2008
*/
/*
* Copyright (C) 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008
* Andrew D. Hwang <ahwang -at- holycross -dot- edu>
* Department of Mathematics and Computer Science
* College of the Holy Cross
* Worcester, MA, 01610-2395, USA
*/
/*
* ePiX is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* ePiX is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
* License for more details.
*
* You should have received a copy of the GNU General Public License
* along with ePiX; if not, write to the Free Software Foundation, Inc.,
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
/*
* This file provides classes that represent mappings R -> R^3 or R x R -> R^3,
* both P-valued and assembled from double-valued components. Each class
* provides an evaluation operator that takes 1, 2, or 3 doubles and returns
* a P. Stubs for general coordinate systems are included.
*
* - path_map: R -> R^3
* - surface_map: R x R -> R^3
* - space_map: R x R x R -> R^3
*
* - column_1var: assemble R -> R^3 from components
* - column_2var: assemble R x R -> R^3 from components
*
* These classes are intended primarily for internal use, allowing the
* plot algorithms to be templated. In new code, maps should be defined
* as P-valued, rather than assembled from components; the "column" classes
* are provided solely for backward compatibility.
*/
#ifndef EPIX_MAP
#define EPIX_MAP
#include "triples.h"
#include "functions.h"
namespace ePiX {
// identity and coordinate projection functions
template<typename T>T id(T arg) { return arg; }
template<typename T1, typename T2>T1 proj1(T1 arg1, T2 arg2) { return arg1; }
template<typename T1, typename T2>T2 proj2(T1 arg1, T2 arg2) { return arg2; }
// R -> R^3
class path_map {
private:
P (*y)(double);
P (*Y)(P);
public:
path_map(P f(double), P F(P) = id) : y(f), Y(F) { }
P operator() (const P& arg) const
{
return Y(y(arg.x1()));
}
}; // end of class path_map
// R x R -> R^3
class surface_map {
private:
P (*y)(double, double);
P (*Y)(P);
public:
surface_map(P f(double, double), P F(P) = id) : y(f), Y(F) { }
P operator() (const P& arg) const
{
return Y(y(arg.x1(), arg.x2()));
}
}; // end of class surface_map
// R x R x R -> R^3
class space_map {
private:
P (*y)(double, double, double);
P (*Y)(P);
public:
space_map(P f(double, double, double), P F(P) = id) : y(f), Y(F) { }
P operator() (const P& arg) const
{
return Y(y(arg.x1(), arg.x2(), arg.x3()));
}
}; // end of class space_map
// assemble R -> R^3 from components
class column_1var {
private:
double (*y1)(double);
double (*y2)(double);
double (*y3)(double);
P (*Y)(P);
public:
column_1var(double f1(double), double f2(double), double f3(double) = zero,
P F(P) = id) : y1(f1), y2(f2), y3(f3), Y(F) { }
// parameterized path from f:R -> R
column_1var(double f(double), P F(P) = id)
: y1(id), y2(f), y3(zero), Y(F) { }
P operator() (const P& arg) const
{
double t = arg.x1();
return Y(P(y1(t), y2(t), y3(t)));
}
}; // end of class column_1var
// assemble R x R -> R^3 from components
class column_2var {
private:
double (*y1)(double, double);
double (*y2)(double, double);
double (*y3)(double, double);
P (*Y)(P);
public:
column_2var(double f1(double, double),
double f2(double, double),
double f3(double, double),
P F(P) = id) : y1(f1), y2(f2), y3(f3), Y(F) { }
// omitted third component defaults to zero
column_2var(double f1(double, double),
double f2(double, double),
P F(P) = id) : y1(f1), y2(f2), y3(zero), Y(F) { }
// parameterized surface from f:R x R -> R
column_2var(double f(double, double), P F(P) = id)
: y1(proj1), y2(proj2), y3(f), Y(F) { }
P operator() (const P& arg) const
{
double u(arg.x1());
double v(arg.x2());
return Y(P(y1(u, v), y2(u, v), y3(u, v)));
}
}; // end of class column_2var
} // end of namespace
#endif /* EPIX_MAP */
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