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-/*
- * plots.cc: Plotting functions
- *
- * This file is part of ePiX, a C++ library for creating high-quality
- * figures in LaTeX
- *
- * Version 1.2.0-2
- * Last Change: September 26, 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
- */
-
-#include "constants.h"
-#include "errors.h"
-
-#include "triples.h"
-#include "functions.h"
-
-#include "camera.h"
-#include "map.h"
-#include "domain.h"
-
-#include "path.h"
-
-#include "markers.h"
-#include "curves.h"
-
-#include "deriv.h"
-#include "plot_algorithms.h"
-#include "plots.h"
-
-namespace ePiX {
-
- typedef std::list<domain>::const_iterator dolci;
-
- // f:R -> R^3
- void plot(P f(double), double t_min, double t_max, unsigned int num_pts)
- {
- plot_map_dom(path_map(f), domain(t_min, t_max, num_pts));
- }
-
- // f:R -> R x R x R
- void plot(double f1(double), double f2(double), double f3(double),
- double t_min, double t_max, unsigned int num_pts)
- {
- plot_map_dom(column_1var(f1,f2,f3), domain(t_min, t_max, num_pts));
- }
-
- // f:R -> R
- void plot(double f(double), double t_min, double t_max, unsigned int num_pts)
- {
- plot(id, f, zero, t_min, t_max, num_pts);
- }
-
- void plot(const Deriv& f, double t_min, double t_max, unsigned int num_pts)
- {
- plot_map_dom(f, domain(t_min, t_max, num_pts));
- }
-
- void plot(const Integral& f, double t_min, double t_max,
- unsigned int num_pts)
- {
- plot_map_dom(f, domain(t_min, t_max, num_pts));
- }
-
- // f: R -> R x R
- void plot(double f1(double), double f2(double),
- double t_min, double t_max, unsigned int num_pts)
- {
- plot(f1, f2, zero, t_min, t_max, num_pts);
- }
-
- void polarplot (double f(double), double t_min, double t_max,
- unsigned int num_pts)
- {
- plot_map_dom(column_1var(f, id, zero, cylindrical),
- domain(t_min, t_max, num_pts));
- }
-
- // surfaces
- // f:R^2 -> R x R x R
- void plot(double f1(double u1, double u2),
- double f2(double u1, double u2),
- double f3(double u1, double u2),
- const P& min, const P& max, const mesh& coarse, const mesh& fine)
- {
- plot_map_dom(column_2var(f1,f2,f3), domain(min, max, coarse, fine));
- }
-
- void plot(double f1(double u1, double u2),
- double f2(double u1, double u2),
- double f3(double u1, double u2),
- const domain& R)
- {
- plot_map_dom(column_2var(f1,f2,f3), R);
- }
-
- // f:R^2 -> R
- void plot(double f(double u1, double u2),
- const P& p1, const P& p2, const mesh& coarse, const mesh& fine)
- {
- plot(proj1, proj2, f, p1, p2, coarse, fine);
- }
-
- // f:R^2 -> R^3
- void plot(P f(double u1, double u2), const domain& R)
- {
- plot_map_dom(surface_map(f), R);
- }
-
- void plot(P f(double u1, double u2), const domain_list& R)
- {
- surface_map phi(f);
-
- for (dolci p=R.m_list.begin(); p != R.m_list.end(); ++p)
- plot_map_dom(phi, *p);
- }
-
-
- // f:R^3 -> R^3
- void plot(P f(double, double, double), const domain& R)
- {
- plot_map_dom(space_map(f), R);
- }
-
- void plot(P f(double, double, double), const domain_list& R)
- {
- space_map phi(f);
-
- for (dolci p=R.m_list.begin(); p != R.m_list.end(); ++p)
- plot_map_dom(phi, *p);
- }
-
-
- // Derivatives and integrals
- void plot_deriv(double f(double t), double a, double b,
- unsigned int num_pts)
- {
- plot_function(Deriv(f), a, b, num_pts);
- }
-
- void plot_int(double f(double), double a, double b,
- unsigned int num_pts)
- {
- plot_function(Integral(f, a), a, b, num_pts);
- }
-
- void plot_int(double f(double), double x0, double a, double b,
- unsigned int num_pts)
- {
- plot_function(Integral(f, x0), a, b, num_pts);
- }
-
- // tuples of real-valued plot arguments
- void tan_line(double f1(double t), double f2(double t), double t0)
- {
- Line(P(f1(t0), f2(t0)),
- P(f1(t0), f2(t0)) + P(deriv(f1, t0), deriv(f2, t0)));
- }
-
- void tan_line(double f(double t), double t0)
- {
- Line(P(t0, f(t0)), P(t0, f(t0)) + P(1, deriv(f, t0)));
- }
-
- void envelope(double f1(double t), double f2(double t),
- double t_min, double t_max, unsigned int num_pts)
- {
- const double step((t_max - t_min)/num_pts);
- double t(t_min);
-
- for (unsigned int i=0; i <= num_pts; ++i, t += step)
- Line(P(f1(t), f2(t)),
- P(f1(t), f2(t)) + P(deriv(f1, t), deriv(f2, t)));
- }
-
- void envelope(double f(double t), double t_min, double t_max,
- unsigned int num_pts)
- {
- const double step((t_max - t_min)/num_pts);
- double t(t_min);
-
- for (unsigned int i=0; i <= num_pts; ++i, t += step)
- Line(P(t, f(t)), P(t, f(t)) + P(1, deriv(f, t)));
- }
-
- // P-valued plot argument
- void tan_line(P f(double t), double t0)
- {
- Line(f(t0), f(t0) + deriv(f, t0));
- }
-
- void envelope(P f(double t), double t_min, double t_max,
- unsigned int num_pts)
- {
- const double step((t_max - t_min)/num_pts);
- double t(t_min);
-
- for (unsigned int i=0; i <= num_pts; ++i, t += step)
- Line(f(t), f(t) + deriv(f, t));
- }
-
- // Tangent field along parametrized path
- void tan_field(double f1(double), double f2(double), double t_min,
- double t_max, unsigned int num_pts)
- {
- const double step((t_max - t_min)/num_pts);
- double t(t_min);
-
- for (unsigned int i=0; i <= num_pts; ++i, t += step)
- arrow(P(f1(t), f2(t)), P(f1(t), f2(t)) +
- step*P(deriv(f1, t), deriv(f2, t)));
- }
-
- // P-valued plot argument
- void tan_field(P f(double), double t_min, double t_max,
- unsigned int num_pts)
- {
- const double step((t_max - t_min)/num_pts);
- double t(t_min);
-
- for (unsigned int i=0; i <= num_pts; ++i, t += step)
- arrow(f(t), f(t) + step*deriv(f, t));
- }
-
- // Slope, dart, and vector fields
-
- // utility functions
- // vector, dart, and slope fields
- void field_element(const P& tail, const P& head, epix_field_type TYPE,
- double head_scale=1.0)
- {
- switch(TYPE) {
-
- case VECTOR:
- arrow(tail, head, head_scale);
- break;
-
- case DART:
- dart(tail, head);
- break;
-
- case SLOPE:
- line(tail, head, 0, 1);
- break;
-
- default:
- ; // do nothing
- } // end of switch(TYPE)
- } // end of field_element
-
-
- void draw_field(P F(double, double, double), P p, P q,
- unsigned int n1, unsigned int n2,
- epix_field_type TYPE, double scale)
- {
- P diagonal(q-p);
- int perp_count(0);
- P jump1, jump2;
-
- if (fabs(diagonal|E_1) < EPIX_EPSILON)
- {
- ++perp_count;
- jump1 = E_2&diagonal;
- jump2 = E_3&diagonal;
-
- }
- if (fabs(diagonal|E_2) < EPIX_EPSILON)
- {
- ++perp_count;
- jump1 = E_3&diagonal;
- jump2 = E_1&diagonal;
- }
- if (fabs(diagonal|E_3) < EPIX_EPSILON)
- {
- ++perp_count;
- jump1 = E_1&diagonal;
- jump2 = E_2&diagonal;
- }
-
- if (perp_count == 0)
- {
- epix_warning("Projecting corners of vector field plot");
- jump1 = E_1&diagonal;
- jump2 = E_2&diagonal;
- p %= E_3; // project corners to (x1, x2)-plane
- q %= E_3;
- }
-
- // grid line spacing
- jump1 *= 1.0/n1;
- jump2 *= 1.0/n2;
-
- const double d1(norm(jump1));
- const double d2(norm(jump2));
-
- for (unsigned int i=0; i <= n1; ++i)
- for (unsigned int j=0; j <= n2; ++j)
- {
- P base(p + (i*jump1 + j*jump2));
- P vect(F(base.x1(), base.x2(), base.x3()));
-
- if (norm(camera(base+vect) - camera(base)) < EPIX_EPSILON)
- marker(base, BBOX);
-
- else if (TYPE == VECTOR)
- field_element(base, base + vect, VECTOR, scale);
-
- else
- {
- // N.B. May not work if page export bolloxes aspect ratio
- double object_len(norm(camera(base+vect)-camera(base)));
- pair dX(pair(d1, d2));
-
- // Hardwired constant 0.4: Segment 80% of shorter grid length
- double minimum((dX.x1() > dX.x2()) ? 0.4*dX.x2() : 0.4*dX.x1());
-
- if ( object_len > EPIX_EPSILON) // not projected to zero
- vect *= minimum/object_len;
-
- // scale affects length of element, not head size
- field_element(base - scale*vect, base + scale*vect, TYPE);
- }
- }
- } // end of draw_field F(x, y, z)
-
-
- void draw_field(P F(double, double), P p, P q,
- unsigned int n1, unsigned int n2,
- epix_field_type TYPE, double scale)
- {
- P diagonal(q-p);
- P jump1(E_1&diagonal);
- P jump2(E_2&diagonal);
- p %= E_3; // project corners to (x1, x2)-plane
- q %= E_3;
-
- // grid line spacing
- jump1 *= 1.0/n1;
- jump2 *= 1.0/n2;
-
- const double d1(norm(jump1));
- const double d2(norm(jump2));
-
- for (unsigned int i=0; i <= n1; ++i)
- for (unsigned int j=0; j <= n2; ++j)
- {
- P base(p + (i*jump1 + j*jump2));
- P vect(F(base.x1(), base.x2()));
-
- if (norm(camera(base+vect) - camera(base)) < EPIX_EPSILON)
- marker(base, BBOX);
-
- // scale affects head size
- else if (TYPE == VECTOR)
- field_element(base, base + vect, VECTOR, scale);
-
- else
- {
- // see caution above
- double object_len(norm(camera(base+vect)-camera(base)));
- pair dX(pair(d1, d2));
- // Hardwired constant 0.4: Segment 80% of shorter grid length
- double minimum((dX.x1() > dX.x2()) ? 0.4*dX.x2() : 0.4*dX.x1());
- if ( object_len > EPIX_EPSILON) // not projected to zero
- vect *= minimum/object_len;
-
- // scale affects length of element, not head size
- field_element(base - scale*vect, base + scale*vect, TYPE);
- }
- }
- } // end of draw_field F(x, y)
-
-
- // planar fields
- void slope_field(P F(double, double), const P& p, const P& q,
- unsigned int n1, unsigned int n2, double scale)
- {
- draw_field(F, p, q, n1, n2, SLOPE, scale);
- }
-
- void dart_field(P F(double, double), const P& p, const P& q,
- unsigned int n1, unsigned int n2, double scale)
- {
- draw_field(F, p, q, n1, n2, DART, scale);
- }
-
- void vector_field(P F(double, double), const P& p, const P& q,
- unsigned int n1, unsigned int n2, double scale)
- {
- draw_field(F, p, q, n1, n2, VECTOR, scale);
- }
-
- void slope_field(P F(double, double), const domain& R, double scale)
- {
- draw_field(F, R.corner1(), R.corner2(),
- R.coarse_n1(), R.coarse_n2(),
- SLOPE, scale);
- }
-
- void dart_field(P F(double, double), const domain& R, double scale)
- {
- draw_field(F, R.corner1(), R.corner2(),
- R.coarse_n1(), R.coarse_n2(),
- DART, scale);
- }
-
- void vector_field(P F(double, double), const domain& R, double scale)
- {
- draw_field(F, R.corner1(), R.corner2(),
- R.coarse_n1(), R.coarse_n2(),
- VECTOR, scale);
- }
-
- // spatial fields
- void slope_field(P F(double, double, double), const P& p, const P& q,
- unsigned int n1, unsigned int n2, double scale)
- {
- draw_field(F, p, q, n1, n2, SLOPE, scale);
- }
-
- void dart_field(P F(double, double, double), const P& p, const P& q,
- unsigned int n1, unsigned int n2, double scale)
- {
- draw_field(F, p, q, n1, n2, DART, scale);
- }
-
- void vector_field(P F(double, double, double), const P& p, const P& q,
- unsigned int n1, unsigned int n2, double scale)
- {
- draw_field(F, p, q, n1, n2, VECTOR, scale);
- }
-
- // spatial fields over a domain
- void slope_field(P F(double, double, double), const domain& R,
- double scale)
- {
- P p(R.corner1()), q(R.corner2());
- double height(q.x3() - p.x3());
- q -= height*E_3; // p.x3() == q.x3()
-
- // horizontal/vertical subdivisions
- unsigned int i_max(R.coarse_n1()), j_max(R.coarse_n2());
- unsigned int k_max((R.dx3() > 0) ? R.coarse_n3() : 0);
- for (unsigned int k = 0; k <= k_max; ++k)
- draw_field(F, p + (k*R.step3())*E_3, q + (k*R.step3())*E_3,
- i_max, j_max, SLOPE, scale);
- }
-
- void dart_field(P F(double, double, double), const domain& R,
- double scale)
- {
- P p(R.corner1()), q(R.corner2());
- double height(q.x3() - p.x3());
- q -= height*E_3; // p.x3() == q.x3()
-
- unsigned int i_max(R.coarse_n1()), j_max(R.coarse_n2());
- unsigned int k_max((R.dx3() > 0) ? R.coarse_n3() : 0);
-
- for (unsigned int k = 0; k <= k_max; ++k)
- draw_field(F, p + (k*R.step3())*E_3, q + (k*R.step3())*E_3,
- i_max, j_max, DART, scale);
- }
-
- void vector_field(P F(double, double, double), const domain& R,
- double scale)
- {
- P p(R.corner1()), q(R.corner2());
- double height(q.x3() - p.x3());
- q -= height*E_3; // p.x3() == q.x3()
-
- unsigned int i_max(R.coarse_n1()), j_max(R.coarse_n2());
- unsigned int k_max((R.dx3() > 0) ? R.coarse_n3() : 0);
-
- for (unsigned int k = 0; k <= k_max; ++k)
- draw_field(F, p + (k*R.step3())*E_3, q + (k*R.step3())*E_3,
- i_max, j_max, VECTOR, scale);
- }
-
- // Solutions of ODE systems
- // start at time 0
- void ode_plot (P F(double, double), const P& start,
- double t_max, unsigned int n)
- {
- euler_plot(surface_map(F), start, 0, t_max, n);
- }
-
- void ode_plot (P F(double, double, double), const P& start,
- double t_max, unsigned int num_pts)
- {
- euler_plot(space_map(F), start, 0, t_max, num_pts);
- }
-
- // arbitrary start time
- void ode_plot (P F(double, double), const P& start,
- double t_min, double t_max, unsigned int num_pts)
- {
- euler_plot(surface_map(F), start, t_min, t_max, num_pts);
- }
-
- void ode_plot (P F(double, double, double), const P& start,
- double t_min, double t_max, unsigned int num_pts)
- {
- euler_plot(space_map(F), start, t_min, t_max, num_pts);
- }
-
-
- // flow x0 under field for specified time
- P flow (P F(double, double), const P& start, double t_max,
- unsigned int n)
- {
- return euler_flow(surface_map(F), start, t_max, n);
- }
-
- P flow (P F(double, double, double), const P& start, double t_max,
- unsigned int n)
- {
- return euler_flow(space_map(F), start, t_max, n);
- }
-
-
- void riemann_sum(double f(double), double a, double b,
- unsigned int n, epix_integral_type TYPE)
- {
- const double dx((b-a)/n);
-
- for (unsigned int i=0; i < n; ++i)
- {
- double x(a + i*dx);
-
- switch (TYPE) {
-
- case LEFT:
- rect(P(x, f(x)), P(x+dx,0));
- break;
-
- case RIGHT:
- rect(P(x, 0), P(x+dx, f(x+dx)));
- break;
-
- case UPPER:
- rect(P(x, 0), P(x+dx, sup(f, x, x+dx)));
- break;
-
- case LOWER:
- rect(P(x, 0), P(x+dx, inf(f, x, x+dx)));
- break;
-
- case TRAP:
- quad(P(x, 0), P(x+dx, 0), P(x+dx, f(x+dx)), P(x, f(x)));
- break;
-
- case MIDPT:
- rect(P(x, 0), P(x+dx, f(x+0.5*dx)));
- break;
-
- default:
- ;
-
- } // end of switch(TYPE)
- }
- } // end of riemann_sum()
-
-
- // Jay Belanger's shaded plotting functions -- December 1, 2002
- // Re-implemented using paths, July 16, 2004
- // " for Version 1.2, June 2007
- void shadeplot(double f1(double), double f2(double),
- double t_min, double t_max, unsigned int num_pts)
- {
- // build contour
- path boundary(f1, t_min, t_max, num_pts);
- path graph2(f2, t_min, t_max, num_pts);
-
- path right_edge(P(t_max, f1(t_max)), P(t_max, f2(t_max)));
- path left_edge(P(t_min, f2(t_min)), P(t_min, f1(t_min)));
-
- boundary += right_edge;
- boundary -= graph2;
- boundary += left_edge;
-
- boundary.close().fill();
- boundary.draw();
- } // end of shadeplot
-
- void shadeplot(double f(double), double t_min, double t_max,
- unsigned int num_pts)
- {
- shadeplot(f, zero, t_min, t_max, num_pts);
- }
-} // end of namespace