Subversion Repositories Scribus

Rev

Rev 15347 | Details | Compare with Previous | Last modification | View Log | RSS feed

Rev Author Line No. Line
12065 fschmid 1
/*
2
 * piecewise.cpp - Piecewise function class
3
 *
4
 * Copyright 2007 Michael Sloan <mgsloan@gmail.com>
5
 * Copyright 2007 JF Barraud
6
 *
7
 * This library is free software; you can redistribute it and/or
8
 * modify it either under the terms of the GNU Lesser General Public
9
 * License version 2.1 as published by the Free Software Foundation
10
 * (the "LGPL") or, at your option, under the terms of the Mozilla
11
 * Public License Version 1.1 (the "MPL"). If you do not alter this
12
 * notice, a recipient may use your version of this file under either
13
 * the MPL or the LGPL.
14
 *
15
 * You should have received a copy of the LGPL along with this library
16
 * in the file COPYING-LGPL-2.1; if not, output to the Free Software
18122 mrdocs 17
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
12065 fschmid 18
 * You should have received a copy of the MPL along with this library
19
 * in the file COPYING-MPL-1.1
20
 *
21
 * The contents of this file are subject to the Mozilla Public License
22
 * Version 1.1 (the "License"); you may not use this file except in
23
 * compliance with the License. You may obtain a copy of the License at
24
 * http://www.mozilla.org/MPL/
25
 *
26
 * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
27
 * OF ANY KIND, either express or implied. See the LGPL or the MPL for
28
 * the specific language governing rights and limitations.
29
 *
30
 */
31
 
15347 fschmid 32
#include "piecewise.h"
12065 fschmid 33
#include <iterator>
34
#include <map>
35
 
36
namespace Geom {
37
 
38
Piecewise<SBasis> divide(Piecewise<SBasis> const &a, Piecewise<SBasis> const &b, unsigned k) {
39
    Piecewise<SBasis> pa = partition(a, b.cuts), pb = partition(b, a.cuts);
40
    Piecewise<SBasis> ret = Piecewise<SBasis>();
41
    assert(pa.size() == pb.size());
42
    ret.cuts = pa.cuts;
43
    for (unsigned i = 0; i < pa.size(); i++)
44
        ret.push_seg(divide(pa[i], pb[i], k));
45
    return ret;
46
}
47
 
48
Piecewise<SBasis>
49
divide(Piecewise<SBasis> const &a, Piecewise<SBasis> const &b, double tol, unsigned k, double zero) {
50
    Piecewise<SBasis> pa = partition(a, b.cuts), pb = partition(b, a.cuts);
51
    Piecewise<SBasis> ret = Piecewise<SBasis>();
52
    assert(pa.size() == pb.size());
53
    for (unsigned i = 0; i < pa.size(); i++){
54
        Piecewise<SBasis> divi = divide(pa[i], pb[i], tol, k, zero);
55
        divi.setDomain(Interval(pa.cuts[i],pa.cuts[i+1]));
56
        ret.concat(divi);
57
    }
58
    return ret;
59
}
60
Piecewise<SBasis> divide(Piecewise<SBasis> const &a, SBasis const &b, double tol, unsigned k, double zero){
61
    return divide(a,Piecewise<SBasis>(b),tol,k,zero);
62
}
63
Piecewise<SBasis> divide(SBasis const &a, Piecewise<SBasis> const &b, double tol, unsigned k, double zero){
64
    return divide(Piecewise<SBasis>(a),b,tol,k,zero);
65
}
66
Piecewise<SBasis> divide(SBasis const &a, SBasis const &b, double tol, unsigned k, double zero) {
67
    if (b.tailError(0)<2*zero){
68
        //TODO: have a better look at sgn(b).
69
        double sgn= (b(.5)<0.)?-1.:1;
70
        return Piecewise<SBasis>(Linear(sgn/zero)*a);
71
    }
72
 
73
    if (fabs(b.at0())>zero && fabs(b.at1())>zero ){
74
        SBasis c,r=a;
75
        //TODO: what is a good relative tol? atm, c=a/b +/- (tol/a)%...
76
 
77
        k+=1;
78
        r.resize(k, Linear(0,0));
79
        c.resize(k, Linear(0,0));
80
 
81
        //assert(b.at0()!=0 && b.at1()!=0);
82
        for (unsigned i=0; i<k; i++){
83
            Linear ci = Linear(r[i][0]/b[0][0],r[i][1]/b[0][1]);
84
            c[i]=ci;
85
            r-=shift(ci*b,i);
86
        }
87
 
88
        if (r.tailError(k)<tol) return Piecewise<SBasis>(c);
89
    }
90
 
91
    Piecewise<SBasis> c0,c1;
92
    c0 = divide(compose(a,Linear(0.,.5)),compose(b,Linear(0.,.5)),tol,k);
93
    c1 = divide(compose(a,Linear(.5,1.)),compose(b,Linear(.5,1.)),tol,k);
94
    c0.setDomain(Interval(0.,.5));
95
    c1.setDomain(Interval(.5,1.));
96
    c0.concat(c1);
97
    return c0;
98
}
99
 
100
 
101
//-- compose(pw<T>,SBasis) ---------------
102
/*
103
   the purpose of the following functions is only to reduce the code in piecewise.h
104
   TODO: use a vector<pairs<double,unsigned> > instead of a map<double,unsigned>.
105
 */
106
 
107
std::map<double,unsigned> compose_pullback(std::vector<double> const &values, SBasis const &g){
108
   std::map<double,unsigned> result;
109
 
110
   std::vector<std::vector<double> > roots = multi_roots(g, values);
111
   for(unsigned i=0; i<roots.size(); i++){
112
       for(unsigned j=0; j<roots[i].size();j++){
113
           result[roots[i][j]]=i;
114
       }
115
   }
116
  // Also map 0 and 1 to the first value above(or =) g(0) and g(1).
117
  if(result.count(0.)==0){
118
      unsigned i=0;
119
      while (i<values.size()&&(g.at0()>values[i])) i++;
120
      result[0.]=i;
121
  }
122
  if(result.count(1.)==0){
123
      unsigned i=0;
124
      while (i<values.size()&&(g.at1()>values[i])) i++;
125
      result[1.]=i;
126
  }
127
  return(result);
128
}
129
 
130
int compose_findSegIdx(std::map<double,unsigned>::iterator  const &cut,
131
                       std::map<double,unsigned>::iterator  const &next,
132
                       std::vector<double>  const &levels,
133
                       SBasis const &g){
134
    double     t0=(*cut).first;
135
    unsigned idx0=(*cut).second;
136
    double     t1=(*next).first;
137
    unsigned idx1=(*next).second;
138
    assert(t0<t1);
139
    int  idx; //idx of the relevant f.segs
140
    if (std::max(idx0,idx1)==levels.size()){ //g([t0,t1]) is above the top level,
141
      idx=levels.size()-1;
142
    } else if (idx0 != idx1){                //g([t0,t1]) crosses from level idx0 to idx1,
143
      idx=std::min(idx0,idx1);
144
    } else if(g((t0+t1)/2) < levels[idx0]) { //g([t0,t1]) is a 'U' under level idx0,
145
      idx=idx0-1;
146
    } else if(g((t0+t1)/2) > levels[idx0]) { //g([t0,t1]) is a 'bump' over level idx0,
147
      idx=idx0;
148
    } else {                                 //g([t0,t1]) is contained in level idx0!...
149
      idx = (idx0==levels.size())? idx0-1:idx0;
150
    }
151
 
152
    //move idx back from levels f.cuts 
153
    idx+=1;
154
    return idx;
155
}
156
 
157
std::vector<double> roots(Piecewise<SBasis> const &f){
158
    std::vector<double> result;
159
    for (unsigned i=0; i<f.size(); i++){
160
        std::vector<double> rts=roots(f.segs[i]);
15347 fschmid 161
        rts=roots(f.segs[i]);
12065 fschmid 162
 
163
        for (unsigned r=0; r<rts.size(); r++){
164
            result.push_back(f.mapToDomain(rts[r], i));
165
        }
166
    }
167
    return result;
168
}
169
 
170
}
171
/*
172
  Local Variables:
173
  mode:c++
174
  c-file-style:"stroustrup"
175
  c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
176
  indent-tabs-mode:nil
177
  fill-column:99
178
  End:
179
*/
180
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :