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/*
* triples.h -- ePiX::P class
*
* This file is part of ePiX, a C++ library for creating high-quality
* figures in LaTeX
*
* Version 1.1.10
* Last Change: August 04, 2007
*/
/*
* Copyright (C) 2001, 2002, 2003, 2004, 2005, 2006, 2007
* Andrew D. Hwang <rot 13 nujnat at zngupf dot ubylpebff dot rqh>
* 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.,
* 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
/*
* This file provides:
*
* The P class (ordered triple of <double>s) and operators
*
* - P(), P() (default to origin), E_1, E_2, E_3 (standard basis)
* - Vector space operators
* - Other vector operators, operands (a,b,c), (x,y,z)
* | dot product ax + by + cz
* norm(p) = sqrt(p|p)
* & componentwise product (ax, by, cz)
* * cross product (bz-cy, cx-az, ay-bx)
* J rotate (x1,x2,0)-plane 1/4 turn (-b,a,0)
* % orthogonalization u%v = u - ((u|v)/(v|v))*v
*/
#ifndef EPIX_TRIPLES
#define EPIX_TRIPLES
namespace ePiX {
class P {
public:
P(double arg1=0, double arg2=0, double arg3=0);
double x1() const;
double x2() const;
double x3() const;
bool is_valid() const; // coords not inf or nan
// increment operators
P& operator += (const P&);
P& operator -= (const P&);
P& operator *= (double); // scalar multipication
// cross product
P& operator *= (const P&);
// componentwise product
P& operator &= (const P&);
// orthogonalization: u %= v is the vector of the form u-k*v perp to v
P& operator %= (const P&);
private:
double m_x1, m_x2, m_x3;
}; // end of class P
// standard basis in global namespace
const P E_1(1,0,0);
const P E_2(0,1,0);
const P E_3(0,0,1);
// vector space operations
P operator- (P u); // unary negation
P operator+ (P u, const P& v);
P operator- (P u, const P& v);
// scalar multiplication
P operator* (double c, P v);
// cross product
P operator* (P, const P&);
P J(P); // quarter turn about E_3-axis
// dot product
double operator | (const P&, const P&);
double norm(const P&);
// componentwise product (a,b,c)&(x,y,z)=(ax,by,cz)
P operator& (P, const P&);
// orthogonalization
P operator% (P, const P&);
// (in)equality
bool operator == (const P&, const P&);
bool operator != (const P&, const P&);
} // end of namespace
#endif /* EPIX_TRIPLES */
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