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-/*
- * plot_algorithms.h -- plot function templates, for build use only
- *
- * This file is part of ePiX, a C++ library for creating high-quality
- * figures in LaTeX
- *
- * Andrew D. Hwang <rot 13 nujnat at zngupf dot ubylpebff dot rqh>
- *
- * Version 1.1.9
- * Last Change: August 01, 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 plotting templates, with T a class
- *
- * void plot_map_dom(const T&, const domain&)
- * void plot_map_domlist(const T&, const domain_list&)
- * void plot_function(const T&, double, double, int)
- * void euler_plot(const T&, const P&, double, double, int)
- * P euler_flow(const T&, P start, double, int)
- */
-
-#ifndef EPIX_PLOT_ALGO
-#define EPIX_PLOT_ALGO
-
-#include <cmath>
-#include <list>
-
-#include "constants.h"
-
-#include "triples.h"
-#include "functions.h"
-
-#include "edge_data.h"
-
-#include "paint_style.h"
-
-#include "domain.h"
-#include "path_data.h"
-
-namespace ePiX {
-
- typedef std::list<domain>::const_iterator dolci;
-
- const double INF(EPIX_INFTY);
-
- // Are args endpoints of a plottable edge?
- static bool is_valid(const P& tail, const P& head)
- {
- return tail.is_valid() && head.is_valid();
- }
-
- template<class T> void plot_map_dom(const T& map, const domain& R)
- {
- // only attempt to fill if plotting a curve
- const bool is_curve(R.dim() == 1);
- const bool filling(is_curve && the_paint_style().fill_flag());
-
- // max summation indices
- unsigned int i_max((R.dx1() > 0) ? R.coarse_n1() : 0);
- unsigned int j_max((R.dx2() > 0) ? R.coarse_n2() : 0);
- unsigned int k_max((R.dx3() > 0) ? R.coarse_n3() : 0);
-
- if (R.dx1() > 0) // there's something to draw
- {
- // number of intervals in subdivision
- unsigned int count1(R.fine_n1());
-
- const double st1(R.dx1());
- const double st2(R.step2());
- const double st3(R.step3());
-
- for (unsigned int j=0; j <= j_max; ++j)
- for (unsigned int k=0; k <= k_max; ++k)
- {
- std::list<edge3d> data1;
- const P init(R.corner1() + (j*st2)*E_2 + (k*st3)*E_3);
-
- for (unsigned int i=0; i < count1; ++i)
- {
- P curr(map(init + P(i*st1,0,0)));
- P next(map(init + P((i+1)*st1,0,0)));
- data1.push_back(edge3d(curr, next, is_valid(curr, next)));
- }
-
- // close path if initial and terminal points coincide
- bool closed(is_curve &&
- map(init) == map(init + P(count1*st1,0,0)));
-
- path_data path1(data1, closed && filling, filling);
- path1.draw();
- }
- }
-
- if (R.dx2() > 0)
- {
- unsigned int count2(R.fine_n2());
-
- const double st1(R.step1());
- const double st2(R.dx2());
- const double st3(R.step3());
-
- for (unsigned int i=0; i <= i_max; ++i)
- for (unsigned int k=0; k <= k_max; ++k)
- {
- std::list<edge3d> data2;
- const P init(R.corner1() + (i*st1)*E_1 + (k*st3)*E_3);
-
- for (unsigned int j=0; j < count2; ++j)
- {
- P curr(map(init + P(0,j*st2,0)));
- P next(map(init + P(0,(j+1)*st2,0)));
- data2.push_back(edge3d(curr, next, is_valid(curr, next)));
- }
-
- // close path if initial and terminal points coincide
- bool closed(is_curve &&
- map(init) == map(init + P(0,count2*st2,0)));
-
- path_data path2(data2, closed && filling, filling);
- path2.draw();
- }
- }
-
- if (R.dx3() > 0)
- {
- unsigned int count3(R.fine_n3());
-
- const double st1(R.step1());
- const double st2(R.step2());
- const double st3(R.dx3());
-
- for (unsigned int i=0; i <= i_max; ++i)
- for (unsigned int j=0; j <= j_max; ++j)
- {
- std::list<edge3d> data3;
- const P init(R.corner1() + (i*st1)*E_1 + (j*st2)*E_2);
-
- for (unsigned int k=0; k < count3; ++k)
- {
- P curr(map(init + P(0,0,k*st3)));
- P next(map(init + P(0,0,(k+1)*st3)));
- data3.push_back(edge3d(curr, next, is_valid(curr, next)));
- }
-
- // close path if initial and terminal points coincide
- bool closed(is_curve &&
- map(init) == map(init + P(0,0,count3*st3)));
-
- path_data path3(data3, closed && filling, filling);
- path3.draw();
- }
- }
- }; // end of plot_map_dom
-
- // plot over a list of domains
- template<class T> void plot_map_domlist(const T& map, const domain_list& R)
- {
- for (dolci p=R.m_list.begin(); p != R.m_list.end(); ++p)
- plot_map_dom(map, *p);
- }
-
- // paths
- template<class T>void plot_function(const T& f, double t1, double t2,
- unsigned int n)
- {
- plot_map_dom(f, domain(t1, t2, n));
- }
-
-
- // Solutions of ODE systems
- template<class VF> void euler_plot(const VF& field, P curr,
- double t_min, double t_max,
- unsigned int num_pts)
- {
- std::list<edge3d> data;
-
- const double dt(t_max/(num_pts*EPIX_ITERATIONS));
- const double dseek(t_min/(num_pts*EPIX_ITERATIONS));
-
- if (fabs(t_min/num_pts) > EPIX_EPSILON) // seek beginning of path
- for (unsigned int i=0; i <= num_pts*EPIX_ITERATIONS; ++i)
- curr += dseek*field(curr);
-
- // curr = "start, flowed by t_min"
- P next(curr);
-
- for (unsigned int i=0; i <= num_pts*EPIX_ITERATIONS; ++i)
- {
- next += dt*field(next); // Euler's method
-
- if (i%EPIX_ITERATIONS == 0)
- {
- data.push_back(edge3d(curr, next, is_valid(curr, next)));
- curr = next;
- }
- }
-
- path_data temp(data, false, false);
-
- temp.draw();
- } // end of euler_plot
-
-
- // flow x0 under field for specified time; pass x0 by value
- template<class VF> P euler_flow(const VF& field, P x0,
- double t_max, unsigned int num_pts=0)
- {
- if (num_pts == 0) // use "sensible" default; hardwired constant 4
- num_pts = 4*(1 + (unsigned int)ceil(fabs(t_max)));
-
- const double dt(t_max/(num_pts*EPIX_ITERATIONS));
-
- for (unsigned int i=0; i <= num_pts*EPIX_ITERATIONS; ++i)
- x0 += dt*field(x0);
-
- return x0;
- }
-} // end of namespace
-
-#endif /* EPIX_PLOT_ALGO */