Adding upstream version 1.0.2.upstream/1.0.2upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 337 insertions, 0 deletions

diff --git a/src/2geom/polynomial.cpp b/src/2geom/polynomial.cpp
new file mode 100644
index 0000000..e853b9a
--- /dev/null
+++ b/src/2geom/polynomial.cpp
@@ -0,0 +1,337 @@
+/**
+ * \file
+ * \brief Polynomial in canonical (monomial) basis
+ *//*
+ * Authors:
+ *    MenTaLguY <mental@rydia.net>
+ *    Krzysztof Kosiński <tweenk.pl@gmail.com>
+ * 
+ * Copyright 2007-2015 Authors
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it either under the terms of the GNU Lesser General Public
+ * License version 2.1 as published by the Free Software Foundation
+ * (the "LGPL") or, at your option, under the terms of the Mozilla
+ * Public License Version 1.1 (the "MPL"). If you do not alter this
+ * notice, a recipient may use your version of this file under either
+ * the MPL or the LGPL.
+ *
+ * You should have received a copy of the LGPL along with this library
+ * in the file COPYING-LGPL-2.1; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * You should have received a copy of the MPL along with this library
+ * in the file COPYING-MPL-1.1
+ *
+ * The contents of this file are subject to the Mozilla Public License
+ * Version 1.1 (the "License"); you may not use this file except in
+ * compliance with the License. You may obtain a copy of the License at
+ * http://www.mozilla.org/MPL/
+ *
+ * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
+ * OF ANY KIND, either express or implied. See the LGPL or the MPL for
+ * the specific language governing rights and limitations.
+ */
+
+#include <algorithm>
+#include <2geom/polynomial.h>
+#include <2geom/math-utils.h>
+#include <math.h>
+
+#ifdef HAVE_GSL
+#include <gsl/gsl_poly.h>
+#endif
+
+namespace Geom {
+
+#ifndef M_PI
+# define M_PI 3.14159265358979323846
+#endif
+
+Poly Poly::operator*(const Poly& p) const {
+    Poly result; 
+    result.resize(degree() +  p.degree()+1);
+    
+    for(unsigned i = 0; i < size(); i++) {
+        for(unsigned j = 0; j < p.size(); j++) {
+            result[i+j] += (*this)[i] * p[j];
+        }
+    }
+    return result;
+}
+
+/*double Poly::eval(double x) const {
+    return gsl_poly_eval(&coeff[0], size(), x);
+    }*/
+
+void Poly::normalize() {
+    while(back() == 0)
+        pop_back();
+}
+
+void Poly::monicify() {
+    normalize();
+    
+    double scale = 1./back(); // unitize
+    
+    for(unsigned i = 0; i < size(); i++) {
+        (*this)[i] *= scale;
+    }
+}
+
+
+#ifdef HAVE_GSL
+std::vector<std::complex<double> > solve(Poly const & pp) {
+    Poly p(pp);
+    p.normalize();
+    gsl_poly_complex_workspace * w 
+        = gsl_poly_complex_workspace_alloc (p.size());
+       
+    gsl_complex_packed_ptr z = new double[p.degree()*2];
+    double* a = new double[p.size()];
+    for(unsigned int i = 0; i < p.size(); i++)
+        a[i] = p[i];
+    std::vector<std::complex<double> > roots;
+    //roots.resize(p.degree());
+    
+    gsl_poly_complex_solve (a, p.size(), w, z);
+    delete[]a;
+     
+    gsl_poly_complex_workspace_free (w);
+     
+    for (unsigned int i = 0; i < p.degree(); i++) {
+        roots.push_back(std::complex<double> (z[2*i] ,z[2*i+1]));
+        //printf ("z%d = %+.18f %+.18f\n", i, z[2*i], z[2*i+1]);
+    }    
+    delete[] z;
+    return roots;
+}
+
+std::vector<double > solve_reals(Poly const & p) {
+    std::vector<std::complex<double> > roots = solve(p);
+    std::vector<double> real_roots;
+    
+    for(unsigned int i = 0; i < roots.size(); i++) {
+        if(roots[i].imag() == 0) // should be more lenient perhaps
+            real_roots.push_back(roots[i].real());
+    }
+    return real_roots;
+}
+#endif
+
+double polish_root(Poly const & p, double guess, double tol) {
+    Poly dp = derivative(p);
+    
+    double fn = p(guess);
+    while(fabs(fn) > tol) {
+        guess -= fn/dp(guess);
+        fn = p(guess);
+    }
+    return guess;
+}
+
+Poly integral(Poly const & p) {
+    Poly result;
+    
+    result.reserve(p.size()+1);
+    result.push_back(0); // arbitrary const
+    for(unsigned i = 0; i < p.size(); i++) {
+        result.push_back(p[i]/(i+1));
+    }
+    return result;
+
+}
+
+Poly derivative(Poly const & p) {
+    Poly result;
+    
+    if(p.size() <= 1)
+        return Poly(0);
+    result.reserve(p.size()-1);
+    for(unsigned i = 1; i < p.size(); i++) {
+        result.push_back(i*p[i]);
+    }
+    return result;
+}
+
+Poly compose(Poly const & a, Poly const & b) {
+    Poly result;
+    
+    for(unsigned i = a.size(); i > 0; i--) {
+        result = Poly(a[i-1]) + result * b;
+    }
+    return result;
+    
+}
+
+/* This version is backwards - dividing taylor terms
+Poly divide(Poly const &a, Poly const &b, Poly &r) {
+    Poly c;
+    r = a; // remainder
+    
+    const unsigned k = a.size();
+    r.resize(k, 0);
+    c.resize(k, 0);
+
+    for(unsigned i = 0; i < k; i++) {
+        double ci = r[i]/b[0];
+        c[i] += ci;
+        Poly bb = ci*b;
+        std::cout << ci <<"*" << b << ", r= " << r << std::endl;
+        r -= bb.shifted(i);
+    }
+    
+    return c;
+}
+*/
+
+Poly divide(Poly const &a, Poly const &b, Poly &r) {
+    Poly c;
+    r = a; // remainder
+    assert(b.size() > 0);
+    
+    const unsigned k = a.degree();
+    const unsigned l = b.degree();
+    c.resize(k, 0.);
+    
+    for(unsigned i = k; i >= l; i--) {
+        //assert(i >= 0);
+        double ci = r.back()/b.back();
+        c[i-l] += ci;
+        Poly bb = ci*b;
+        //std::cout << ci <<"*(" << b.shifted(i-l) << ") = " 
+        //          << bb.shifted(i-l) << "     r= " << r << std::endl;
+        r -= bb.shifted(i-l);
+        r.pop_back();
+    }
+    //std::cout << "r= " << r << std::endl;
+    r.normalize();
+    c.normalize();
+    
+    return c;
+}
+
+Poly gcd(Poly const &a, Poly const &b, const double /*tol*/) {
+    if(a.size() < b.size())
+        return gcd(b, a);
+    if(b.size() <= 0)
+        return a;
+    if(b.size() == 1)
+        return a;
+    Poly r;
+    divide(a, b, r);
+    return gcd(b, r);
+}
+
+
+
+
+std::vector<Coord> solve_quadratic(Coord a, Coord b, Coord c)
+{
+    std::vector<Coord> result;
+
+    if (a == 0) {
+        // linear equation
+        if (b == 0) return result;
+        result.push_back(-c/b);
+        return result;
+    }
+
+    Coord delta = b*b - 4*a*c;
+
+    if (delta == 0) {
+        // one root
+        result.push_back(-b / (2*a));
+    } else if (delta > 0) {
+        // two roots
+        Coord delta_sqrt = sqrt(delta);
+
+        // Use different formulas depending on sign of b to preserve
+        // numerical stability. See e.g.:
+        // http://people.csail.mit.edu/bkph/articles/Quadratics.pdf
+        int sign = b >= 0 ? 1 : -1;
+        Coord t = -0.5 * (b + sign * delta_sqrt);
+        result.push_back(t / a);
+        result.push_back(c / t);
+    }
+    // no roots otherwise
+
+    std::sort(result.begin(), result.end());
+    return result;
+}
+
+
+std::vector<Coord> solve_cubic(Coord a, Coord b, Coord c, Coord d)
+{
+    // based on:
+    // http://mathworld.wolfram.com/CubicFormula.html
+
+    if (a == 0) {
+        return solve_quadratic(b, c, d);
+    }
+    if (d == 0) {
+        // divide by x
+        std::vector<Coord> result = solve_quadratic(a, b, c);
+        result.push_back(0);
+        std::sort(result.begin(), result.end());
+        return result;
+    }
+
+    std::vector<Coord> result;
+
+    // 1. divide everything by a to bring to canonical form
+    b /= a;
+    c /= a;
+    d /= a;
+
+    // 2. eliminate x^2 term: x^3 + 3Qx - 2R = 0
+    Coord Q = (3*c - b*b) / 9;
+    Coord R = (-27 * d + b * (9*c - 2*b*b)) / 54;
+
+    // 3. compute polynomial discriminant
+    Coord D = Q*Q*Q + R*R;
+    Coord term1 = b/3;
+
+    if (D > 0) {
+        // only one real root
+        Coord S = cbrt(R + sqrt(D));
+        Coord T = cbrt(R - sqrt(D));
+        result.push_back(-b/3 + S + T);
+    } else if (D == 0) {
+        // 3 real roots, 2 of which are equal
+        Coord rroot = cbrt(R);
+        result.reserve(3);
+        result.push_back(-term1 + 2*rroot);
+        result.push_back(-term1 - rroot);
+        result.push_back(-term1 - rroot);
+    } else {
+        // 3 distinct real roots
+        assert(Q < 0);
+        Coord theta = acos(R / sqrt(-Q*Q*Q));
+        Coord rroot = 2 * sqrt(-Q);
+        result.reserve(3);
+        result.push_back(-term1 + rroot * cos(theta / 3));
+        result.push_back(-term1 + rroot * cos((theta + 2*M_PI) / 3));
+        result.push_back(-term1 + rroot * cos((theta + 4*M_PI) / 3));
+    }
+
+    std::sort(result.begin(), result.end());
+    return result;
+}
+
+
+/*Poly divide_out_root(Poly const & p, double x) {
+    assert(1);
+    }*/
+
+} //namespace Geom
+
+/*
+  Local Variables:
+  mode:c++
+  c-file-style:"stroustrup"
+  c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
+  indent-tabs-mode:nil
+  fill-column:99
+  End:
+*/
+// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :