diff options
Diffstat (limited to '')
-rw-r--r-- | src/3rdparty/2geom/include/2geom/sbasis.h | 530 |
1 files changed, 530 insertions, 0 deletions
diff --git a/src/3rdparty/2geom/include/2geom/sbasis.h b/src/3rdparty/2geom/include/2geom/sbasis.h new file mode 100644 index 0000000..5cb0e93 --- /dev/null +++ b/src/3rdparty/2geom/include/2geom/sbasis.h @@ -0,0 +1,530 @@ +/** @file + * @brief Polynomial in symmetric power basis (S-basis) + *//* + * Authors: + * Nathan Hurst <njh@mail.csse.monash.edu.au> + * Michael Sloan <mgsloan@gmail.com> + * + * Copyright (C) 2006-2007 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. + */ + +#ifndef LIB2GEOM_SEEN_SBASIS_H +#define LIB2GEOM_SEEN_SBASIS_H +#include <cassert> +#include <iostream> +#include <utility> +#include <vector> + +#include <2geom/linear.h> +#include <2geom/interval.h> +#include <2geom/utils.h> +#include <2geom/exception.h> + +//#define USE_SBASISN 1 + + +#if defined(USE_SBASIS_OF) + +#include "sbasis-of.h" + +#elif defined(USE_SBASISN) + +#include "sbasisN.h" +namespace Geom{ + +/*** An empty SBasis is identically 0. */ +class SBasis : public SBasisN<1>; + +}; +#else + +namespace Geom { + +/** + * @brief Polynomial in symmetric power basis + * @ingroup Fragments + */ +class SBasis { + std::vector<Linear> d; + void push_back(Linear const&l) { d.push_back(l); } + +public: + // As part of our migration away from SBasis isa vector we provide this minimal set of vector interface methods. + size_t size() const {return d.size();} + typedef std::vector<Linear>::iterator iterator; + typedef std::vector<Linear>::const_iterator const_iterator; + Linear operator[](unsigned i) const { + return d[i]; + } + Linear& operator[](unsigned i) { return d.at(i); } + const_iterator begin() const { return d.begin();} + const_iterator end() const { return d.end();} + iterator begin() { return d.begin();} + iterator end() { return d.end();} + bool empty() const { return d.size() == 1 && d[0][0] == 0 && d[0][1] == 0; } + Linear &back() {return d.back();} + Linear const &back() const {return d.back();} + void pop_back() { + if (d.size() > 1) { + d.pop_back(); + } else { + d[0][0] = 0; + d[0][1] = 0; + } + } + void resize(unsigned n) { d.resize(std::max<unsigned>(n, 1));} + void resize(unsigned n, Linear const& l) { d.resize(std::max<unsigned>(n, 1), l);} + void reserve(unsigned n) { d.reserve(n);} + void clear() { + d.resize(1); + d[0][0] = 0; + d[0][1] = 0; + } + void insert(iterator before, const_iterator src_begin, const_iterator src_end) { d.insert(before, src_begin, src_end);} + Linear& at(unsigned i) { return d.at(i);} + //void insert(Linear* before, int& n, Linear const &l) { d.insert(std::vector<Linear>::iterator(before), n, l);} + bool operator==(SBasis const&B) const { return d == B.d;} + bool operator!=(SBasis const&B) const { return d != B.d;} + + SBasis() + : d(1, Linear(0, 0)) + {} + explicit SBasis(double a) + : d(1, Linear(a, a)) + {} + explicit SBasis(double a, double b) + : d(1, Linear(a, b)) + {} + SBasis(SBasis const &a) + : d(a.d) + {} + SBasis(std::vector<Linear> ls) + : d(std::move(ls)) + {} + SBasis(Linear const &bo) + : d(1, bo) + {} + SBasis(Linear* bo) + : d(1, bo ? *bo : Linear(0, 0)) + {} + explicit SBasis(size_t n, Linear const&l) : d(n, l) {} + + SBasis(Coord c0, Coord c1, Coord c2, Coord c3) + : d(2) + { + d[0][0] = c0; + d[1][0] = c1; + d[1][1] = c2; + d[0][1] = c3; + } + SBasis(Coord c0, Coord c1, Coord c2, Coord c3, Coord c4, Coord c5) + : d(3) + { + d[0][0] = c0; + d[1][0] = c1; + d[2][0] = c2; + d[2][1] = c3; + d[1][1] = c4; + d[0][1] = c5; + } + SBasis(Coord c0, Coord c1, Coord c2, Coord c3, Coord c4, Coord c5, + Coord c6, Coord c7) + : d(4) + { + d[0][0] = c0; + d[1][0] = c1; + d[2][0] = c2; + d[3][0] = c3; + d[3][1] = c4; + d[2][1] = c5; + d[1][1] = c6; + d[0][1] = c7; + } + SBasis(Coord c0, Coord c1, Coord c2, Coord c3, Coord c4, Coord c5, + Coord c6, Coord c7, Coord c8, Coord c9) + : d(5) + { + d[0][0] = c0; + d[1][0] = c1; + d[2][0] = c2; + d[3][0] = c3; + d[4][0] = c4; + d[4][1] = c5; + d[3][1] = c6; + d[2][1] = c7; + d[1][1] = c8; + d[0][1] = c9; + } + + // construct from a sequence of coefficients + template <typename Iter> + SBasis(Iter first, Iter last) { + assert(std::distance(first, last) % 2 == 0); + assert(std::distance(first, last) >= 2); + for (; first != last; ++first) { + --last; + push_back(Linear(*first, *last)); + } + } + + //IMPL: FragmentConcept + typedef double output_type; + inline bool isZero(double eps=EPSILON) const { + assert(size() > 0); + for(unsigned i = 0; i < size(); i++) { + if(!(*this)[i].isZero(eps)) return false; + } + return true; + } + inline bool isConstant(double eps=EPSILON) const { + assert(size() > 0); + if(!(*this)[0].isConstant(eps)) return false; + for (unsigned i = 1; i < size(); i++) { + if(!(*this)[i].isZero(eps)) return false; + } + return true; + } + + bool isFinite() const; + inline Coord at0() const { return (*this)[0][0]; } + inline Coord &at0() { return (*this)[0][0]; } + inline Coord at1() const { return (*this)[0][1]; } + inline Coord &at1() { return (*this)[0][1]; } + + int degreesOfFreedom() const { return size()*2;} + + double valueAt(double t) const { + assert(size() > 0); + double s = t*(1-t); + double p0 = 0, p1 = 0; + for(unsigned k = size(); k > 0; k--) { + const Linear &lin = (*this)[k-1]; + p0 = p0*s + lin[0]; + p1 = p1*s + lin[1]; + } + return (1-t)*p0 + t*p1; + } + //double valueAndDerivative(double t, double &der) const { + //} + double operator()(double t) const { + return valueAt(t); + } + + std::vector<double> valueAndDerivatives(double t, unsigned n) const; + + SBasis toSBasis() const { return SBasis(*this); } + + double tailError(unsigned tail) const; + +// compute f(g) + SBasis operator()(SBasis const & g) const; + +//MUTATOR PRISON + //remove extra zeros + void normalize() { + while(size() > 1 && back().isZero(0)) + pop_back(); + } + + void truncate(unsigned k) { if(k < size()) resize(std::max<size_t>(k, 1)); } +private: + void derive(); // in place version +}; + +//TODO: figure out how to stick this in linear, while not adding an sbasis dep +inline SBasis Linear::toSBasis() const { return SBasis(*this); } + +//implemented in sbasis-roots.cpp +OptInterval bounds_exact(SBasis const &a); +OptInterval bounds_fast(SBasis const &a, int order = 0); +OptInterval bounds_local(SBasis const &a, const OptInterval &t, int order = 0); + +/** Returns a function which reverses the domain of a. + \param a sbasis function + \relates SBasis + +useful for reversing a parameteric curve. +*/ +inline SBasis reverse(SBasis const &a) { + SBasis result(a.size(), Linear()); + + for(unsigned k = 0; k < a.size(); k++) + result[k] = reverse(a[k]); + return result; +} + +//IMPL: ScalableConcept +inline SBasis operator-(const SBasis& p) { + if(p.isZero()) return SBasis(); + SBasis result(p.size(), Linear()); + + for(unsigned i = 0; i < p.size(); i++) { + result[i] = -p[i]; + } + return result; +} +SBasis operator*(SBasis const &a, double k); +inline SBasis operator*(double k, SBasis const &a) { return a*k; } +inline SBasis operator/(SBasis const &a, double k) { return a*(1./k); } +SBasis& operator*=(SBasis& a, double b); +inline SBasis& operator/=(SBasis& a, double b) { return (a*=(1./b)); } + +//IMPL: AddableConcept +SBasis operator+(const SBasis& a, const SBasis& b); +SBasis operator-(const SBasis& a, const SBasis& b); +SBasis& operator+=(SBasis& a, const SBasis& b); +SBasis& operator-=(SBasis& a, const SBasis& b); + +//TODO: remove? +/*inline SBasis operator+(const SBasis & a, Linear const & b) { + if(b.isZero()) return a; + if(a.isZero()) return b; + SBasis result(a); + result[0] += b; + return result; +} +inline SBasis operator-(const SBasis & a, Linear const & b) { + if(b.isZero()) return a; + SBasis result(a); + result[0] -= b; + return result; +} +inline SBasis& operator+=(SBasis& a, const Linear& b) { + if(a.isZero()) + a.push_back(b); + else + a[0] += b; + return a; +} +inline SBasis& operator-=(SBasis& a, const Linear& b) { + if(a.isZero()) + a.push_back(-b); + else + a[0] -= b; + return a; + }*/ + +//IMPL: OffsetableConcept +inline SBasis operator+(const SBasis & a, double b) { + if(a.isZero()) return Linear(b, b); + SBasis result(a); + result[0] += b; + return result; +} +inline SBasis operator-(const SBasis & a, double b) { + if(a.isZero()) return Linear(-b, -b); + SBasis result(a); + result[0] -= b; + return result; +} +inline SBasis& operator+=(SBasis& a, double b) { + if(a.isZero()) + a = SBasis(Linear(b,b)); + else + a[0] += b; + return a; +} +inline SBasis& operator-=(SBasis& a, double b) { + if(a.isZero()) + a = SBasis(Linear(-b,-b)); + else + a[0] -= b; + return a; +} + +SBasis shift(SBasis const &a, int sh); +SBasis shift(Linear const &a, int sh); + +inline SBasis truncate(SBasis const &a, unsigned terms) { + SBasis c; + c.insert(c.begin(), a.begin(), a.begin() + std::min(terms, (unsigned)a.size())); + return c; +} + +SBasis multiply(SBasis const &a, SBasis const &b); +// This performs a multiply and accumulate operation in about the same time as multiply. return a*b + c +SBasis multiply_add(SBasis const &a, SBasis const &b, SBasis c); + +SBasis integral(SBasis const &c); +SBasis derivative(SBasis const &a); + +SBasis sqrt(SBasis const &a, int k); + +// return a kth order approx to 1/a) +SBasis reciprocal(Linear const &a, int k); +SBasis divide(SBasis const &a, SBasis const &b, int k); + +inline SBasis operator*(SBasis const & a, SBasis const & b) { + return multiply(a, b); +} + +inline SBasis& operator*=(SBasis& a, SBasis const & b) { + a = multiply(a, b); + return a; +} + +/** Returns the degree of the first non zero coefficient. + \param a sbasis function + \param tol largest abs val considered 0 + \return first non zero coefficient + \relates SBasis +*/ +inline unsigned +valuation(SBasis const &a, double tol=0){ + unsigned val=0; + while( val<a.size() && + fabs(a[val][0])<tol && + fabs(a[val][1])<tol ) + val++; + return val; +} + +// a(b(t)) +SBasis compose(SBasis const &a, SBasis const &b); +SBasis compose(SBasis const &a, SBasis const &b, unsigned k); +SBasis inverse(SBasis a, int k); +//compose_inverse(f,g)=compose(f,inverse(g)), but is numerically more stable in some good cases... +//TODO: requires g(0)=0 & g(1)=1 atm. generalization should be obvious. +SBasis compose_inverse(SBasis const &f, SBasis const &g, unsigned order=2, double tol=1e-3); + +/** Returns the sbasis on domain [0,1] that was t on [from, to] + \param t sbasis function + \param from,to interval + \return sbasis + \relates SBasis +*/ +SBasis portion(const SBasis &t, double from, double to); +inline SBasis portion(const SBasis &t, Interval const &ivl) { return portion(t, ivl.min(), ivl.max()); } + +// compute f(g) +inline SBasis +SBasis::operator()(SBasis const & g) const { + return compose(*this, g); +} + +inline std::ostream &operator<< (std::ostream &out_file, const Linear &bo) { + out_file << "{" << bo[0] << ", " << bo[1] << "}"; + return out_file; +} + +inline std::ostream &operator<< (std::ostream &out_file, const SBasis & p) { + for(unsigned i = 0; i < p.size(); i++) { + if (i != 0) { + out_file << " + "; + } + out_file << p[i] << "s^" << i; + } + return out_file; +} + +// These are deprecated, use sbasis-math.h versions if possible +SBasis sin(Linear bo, int k); +SBasis cos(Linear bo, int k); + +std::vector<double> roots(SBasis const & s); +std::vector<double> roots(SBasis const & s, Interval const inside); +std::vector<std::vector<double> > multi_roots(SBasis const &f, + std::vector<double> const &levels, + double htol=1e-7, + double vtol=1e-7, + double a=0, + double b=1); + +//--------- Levelset like functions ----------------------------------------------------- + +/** Solve f(t) = v +/- tolerance. The collection of intervals where + * v - vtol <= f(t) <= v+vtol + * is returned (with a precision tol on the boundaries). + \param f sbasis function + \param level the value of v. + \param vtol: error tolerance on v. + \param a, b limit search on domain [a,b] + \param tol: tolerance on the result bounds. + \returns a vector of intervals. +*/ +std::vector<Interval> level_set (SBasis const &f, + double level, + double vtol = 1e-5, + double a=0., + double b=1., + double tol = 1e-5); + +/** Solve f(t)\in I=[u,v], which defines a collection of intervals (J_k). More precisely, + * a collection (J'_k) is returned with J'_k = J_k up to a given tolerance. + \param f sbasis function + \param level: the given interval of deisred values for f. + \param a, b limit search on domain [a,b] + \param tol: tolerance on the bounds of the result. + \returns a vector of intervals. +*/ +std::vector<Interval> level_set (SBasis const &f, + Interval const &level, + double a=0., + double b=1., + double tol = 1e-5); + +/** 'Solve' f(t) = v +/- tolerance for several values of v at once. + \param f sbasis function + \param levels vector of values, that should be sorted. + \param vtol: error tolerance on v. + \param a, b limit search on domain [a,b] + \param tol: the bounds of the returned intervals are exact up to that tolerance. + \returns a vector of vectors of intervals. +*/ +std::vector<std::vector<Interval> > level_sets (SBasis const &f, + std::vector<double> const &levels, + double a=0., + double b=1., + double vtol = 1e-5, + double tol = 1e-5); + +/** 'Solve' f(t)\in I=[u,v] for several intervals I at once. + \param f sbasis function + \param levels vector of 'y' intervals, that should be disjoints and sorted. + \param a, b limit search on domain [a,b] + \param tol: the bounds of the returned intervals are exact up to that tolerance. + \returns a vector of vectors of intervals. +*/ +std::vector<std::vector<Interval> > level_sets (SBasis const &f, + std::vector<Interval> const &levels, + double a=0., + double b=1., + double tol = 1e-5); + +} +#endif + +/* + 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 : +#endif |