piecewise.cpp revision 90a3966dd44e306d23febc15ebd65cde07d7a4dd
/*
* piecewise.cpp - Piecewise function class
*
* Copyright 2007 Michael Sloan <mgsloan@gmail.com>
* Copyright 2007 JF Barraud
*
* 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, output 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 <2geom/piecewise.h>
#include <iterator>
#include <map>
namespace Geom {
Piecewise<SBasis> divide(Piecewise<SBasis> const &a, Piecewise<SBasis> const &b, unsigned k) {
Piecewise<SBasis> pa = partition(a, b.cuts), pb = partition(b, a.cuts);
Piecewise<SBasis> ret = Piecewise<SBasis>();
assert(pa.size() == pb.size());
ret.cuts = pa.cuts;
for (unsigned i = 0; i < pa.size(); i++)
ret.push_seg(divide(pa[i], pb[i], k));
return ret;
}
Piecewise<SBasis>
divide(Piecewise<SBasis> const &a, Piecewise<SBasis> const &b, double tol, unsigned k, double zero) {
Piecewise<SBasis> pa = partition(a, b.cuts), pb = partition(b, a.cuts);
Piecewise<SBasis> ret = Piecewise<SBasis>();
assert(pa.size() == pb.size());
for (unsigned i = 0; i < pa.size(); i++){
Piecewise<SBasis> divi = divide(pa[i], pb[i], tol, k, zero);
divi.setDomain(Interval(pa.cuts[i],pa.cuts[i+1]));
ret.concat(divi);
}
return ret;
}
Piecewise<SBasis> divide(Piecewise<SBasis> const &a, SBasis const &b, double tol, unsigned k, double zero){
return divide(a,Piecewise<SBasis>(b),tol,k,zero);
}
Piecewise<SBasis> divide(SBasis const &a, Piecewise<SBasis> const &b, double tol, unsigned k, double zero){
return divide(Piecewise<SBasis>(a),b,tol,k,zero);
}
Piecewise<SBasis> divide(SBasis const &a, SBasis const &b, double tol, unsigned k, double zero) {
if (b.tailError(0)<2*zero){
//TODO: have a better look at sgn(b).
double sgn= (b(.5)<0.)?-1.:1;
return Piecewise<SBasis>(Linear(sgn/zero)*a);
}
if (fabs(b.at0())>zero && fabs(b.at1())>zero ){
SBasis c,r=a;
//TODO: what is a good relative tol? atm, c=a/b +/- (tol/a)%...
k+=1;
r.resize(k, Linear(0,0));
c.resize(k, Linear(0,0));
//assert(b.at0()!=0 && b.at1()!=0);
for (unsigned i=0; i<k; i++){
Linear ci = Linear(r[i][0]/b[0][0],r[i][1]/b[0][1]);
c[i]=ci;
r-=shift(ci*b,i);
}
if (r.tailError(k)<tol) return Piecewise<SBasis>(c);
}
Piecewise<SBasis> c0,c1;
c0 = divide(compose(a,Linear(0.,.5)),compose(b,Linear(0.,.5)),tol,k);
c1 = divide(compose(a,Linear(.5,1.)),compose(b,Linear(.5,1.)),tol,k);
c0.setDomain(Interval(0.,.5));
c1.setDomain(Interval(.5,1.));
c0.concat(c1);
return c0;
}
//-- compose(pw<T>,SBasis) ---------------
/*
the purpose of the following functions is only to reduce the code in piecewise.h
TODO: use a vector<pairs<double,unsigned> > instead of a map<double,unsigned>.
*/
std::map<double,unsigned> compose_pullback(std::vector<double> const &values, SBasis const &g){
std::map<double,unsigned> result;
std::vector<std::vector<double> > roots = multi_roots(g, values);
for(unsigned i=0; i<roots.size(); i++){
for(unsigned j=0; j<roots[i].size();j++){
result[roots[i][j]]=i;
}
}
// Also map 0 and 1 to the first value above(or =) g(0) and g(1).
if(result.count(0.)==0){
unsigned i=0;
while (i<values.size()&&(g.at0()>values[i])) i++;
result[0.]=i;
}
if(result.count(1.)==0){
unsigned i=0;
while (i<values.size()&&(g.at1()>values[i])) i++;
result[1.]=i;
}
return(result);
}
int compose_findSegIdx(std::map<double,unsigned>::iterator const &cut,
std::map<double,unsigned>::iterator const &next,
std::vector<double> const &levels,
SBasis const &g){
double t0=(*cut).first;
unsigned idx0=(*cut).second;
double t1=(*next).first;
unsigned idx1=(*next).second;
assert(t0<t1);
int idx; //idx of the relevant f.segs
if (std::max(idx0,idx1)==levels.size()){ //g([t0,t1]) is above the top level,
idx=levels.size()-1;
} else if (idx0 != idx1){ //g([t0,t1]) crosses from level idx0 to idx1,
idx=std::min(idx0,idx1);
} else if(g((t0+t1)/2) < levels[idx0]) { //g([t0,t1]) is a 'U' under level idx0,
idx=idx0-1;
} else if(g((t0+t1)/2) > levels[idx0]) { //g([t0,t1]) is a 'bump' over level idx0,
idx=idx0;
} else { //g([t0,t1]) is contained in level idx0!...
idx = (idx0==levels.size())? idx0-1:idx0;
}
//move idx back from levels f.cuts
idx+=1;
return idx;
}
std::vector<double> roots(Piecewise<SBasis> const &f){
std::vector<double> result;
for (unsigned i=0; i<f.size(); i++){
std::vector<double> rts=roots(f.segs[i]);
for (unsigned r=0; r<rts.size(); r++){
result.push_back(f.mapToDomain(rts[r], i));
}
}
return result;
}
std::vector<std::vector<double> > multi_roots(Piecewise<SBasis> const &f, std::vector<double> const &values) {
std::vector<std::vector<double> > result(values.size());
for (unsigned i=0; i<f.size(); i++) {
std::vector<std::vector<double> > rts = multi_roots(f.segs[i], values);
for(unsigned j=0; j<rts.size(); j++) {
for(unsigned r=0; r<rts[j].size(); r++){
result[j].push_back(f.mapToDomain(rts[j][r], i));
}
}
}
return result;
}
}
/*
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:encoding=utf-8:textwidth=99 :