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/*
* d2.cpp - Lifts one dimensional objects into 2d
*
* Copyright 2007 Michael Sloan <mgsloan@gmail.com>
*
* 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 "d2.h"
namespace Geom {
SBasis L2(D2<SBasis> const & a, unsigned k) { return sqrt(dot(a, a), k); }
double L2(D2<double> const & a) { return hypot(a[0], a[1]); }
D2<SBasis> multiply(Linear const & a, D2<SBasis> const & b) {
return D2<SBasis>(multiply(a, b[X]), multiply(a, b[Y]));
}
D2<SBasis> multiply(SBasis const & a, D2<SBasis> const & b) {
return D2<SBasis>(multiply(a, b[X]), multiply(a, b[Y]));
}
D2<SBasis> truncate(D2<SBasis> const & a, unsigned terms) {
return D2<SBasis>(truncate(a[X], terms), truncate(a[Y], terms));
}
unsigned sbasis_size(D2<SBasis> const & a) {
return std::max((unsigned) a[0].size(), (unsigned) a[1].size());
}
//TODO: Is this sensical? shouldn't it be like pythagorean or something?
double tail_error(D2<SBasis> const & a, unsigned tail) {
return std::max(a[0].tailError(tail), a[1].tailError(tail));
}
Piecewise<D2<SBasis> > sectionize(D2<Piecewise<SBasis> > const &a) {
Piecewise<SBasis> x = partition(a[0], a[1].cuts), y = partition(a[1], a[0].cuts);
assert(x.size() == y.size());
Piecewise<D2<SBasis> > ret;
for(unsigned i = 0; i < x.size(); i++)
ret.push_seg(D2<SBasis>(x[i], y[i]));
ret.cuts.insert(ret.cuts.end(), x.cuts.begin(), x.cuts.end());
return ret;
}
D2<Piecewise<SBasis> > make_cuts_independant(Piecewise<D2<SBasis> > const &a) {
D2<Piecewise<SBasis> > ret;
for(unsigned d = 0; d < 2; d++) {
for(unsigned i = 0; i < a.size(); i++)
ret[d].push_seg(a[i][d]);
ret[d].cuts.insert(ret[d].cuts.end(), a.cuts.begin(), a.cuts.end());
}
return ret;
}
Piecewise<D2<SBasis> > rot90(Piecewise<D2<SBasis> > const &M){
Piecewise<D2<SBasis> > result;
if (M.empty()) return M;
result.push_cut(M.cuts[0]);
for (unsigned i=0; i<M.size(); i++){
result.push(rot90(M[i]),M.cuts[i+1]);
}
return result;
}
Piecewise<SBasis> dot(Piecewise<D2<SBasis> > const &a,
Piecewise<D2<SBasis> > const &b){
Piecewise<SBasis > result;
if (a.empty() || b.empty()) return result;
Piecewise<D2<SBasis> > aa = partition(a,b.cuts);
Piecewise<D2<SBasis> > bb = partition(b,a.cuts);
result.push_cut(aa.cuts.front());
for (unsigned i=0; i<aa.size(); i++){
result.push(dot(aa.segs[i],bb.segs[i]),aa.cuts[i+1]);
}
return result;
}
Piecewise<SBasis> cross(Piecewise<D2<SBasis> > const &a,
Piecewise<D2<SBasis> > const &b){
Piecewise<SBasis > result;
if (a.empty() || b.empty()) return result;
Piecewise<D2<SBasis> > aa = partition(a,b.cuts);
Piecewise<D2<SBasis> > bb = partition(b,a.cuts);
result.push_cut(aa.cuts.front());
for (unsigned i=0; i<a.size(); i++){
result.push(cross(aa.segs[i],bb.segs[i]),aa.cuts[i+1]);
}
return result;
}
/* Replaced by remove_short_cuts in piecewise.h
//this recursively removes the shortest cut interval until none is shorter than tol.
//TODO: code this in a more efficient way!
Piecewise<D2<SBasis> > remove_short_cuts(Piecewise<D2<SBasis> > const &f, double tol){
double min = tol;
unsigned idx = f.size();
for(unsigned i=0; i<f.size(); i++){
if (min > f.cuts[i+1]-f.cuts[i]){
min = f.cuts[i+1]-f.cuts[i];
idx = int(i);
}
}
if (idx==f.size()){
return f;
}
if (f.size()==1) {
//removing this seg would result in an empty pw<d2<sb>>...
return f;
}
Piecewise<D2<SBasis> > new_f=f;
for (int dim=0; dim<2; dim++){
double v = Hat(f.segs.at(idx)[dim][0]);
//TODO: what about closed curves?
if (idx>0 && f.segs.at(idx-1).at1()==f.segs.at(idx).at0())
new_f.segs.at(idx-1)[dim][0][1] = v;
if (idx<f.size() && f.segs.at(idx+1).at0()==f.segs.at(idx).at1())
new_f.segs.at(idx+1)[dim][0][0] = v;
}
double t = (f.cuts.at(idx)+f.cuts.at(idx+1))/2;
new_f.cuts.at(idx+1) = t;
new_f.segs.erase(new_f.segs.begin()+idx);
new_f.cuts.erase(new_f.cuts.begin()+idx);
return remove_short_cuts(new_f, tol);
}
*/
//if tol>0, only force continuity where the jump is smaller than tol.
Piecewise<D2<SBasis> > force_continuity(Piecewise<D2<SBasis> > const &f,
double tol,
bool closed){
if (f.size()==0) return f;
Piecewise<D2<SBasis> > result=f;
unsigned cur = (closed)? 0:1;
unsigned prev = (closed)? f.size()-1:0;
while(cur<f.size()){
Point pt0 = f.segs[prev].at1();
Point pt1 = f.segs[cur ].at0();
if (tol<=0 || L2sq(pt0-pt1)<tol*tol){
pt0 = (pt0+pt1)/2;
for (unsigned dim=0; dim<2; dim++){
result.segs[prev][dim][0][1]=pt0[dim];
result.segs[cur ][dim][0][0]=pt0[dim];
}
}
prev = cur++;
}
return result;
}
};
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