1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
|
/*
* 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;
}
Piecewise<SBasis> pw_compose_inverse(SBasis const &f, SBasis const &g, unsigned order, double zero){
Piecewise<SBasis> result;
assert( f.size()>0 && g.size()>0);
SBasis g01 = g;
bool flip = ( g01.at0() > g01.at1() );
//OptInterval g_range = bounds_exact(g);
OptInterval g_range( Interval( g.at0(), g.at1() ));
g01 -= g_range->min();
g01 /= g_range->extent();
if ( flip ){
g01 *= -1.;
g01 += 1.;
}
#if 1
assert( std::abs( g01.at0() - 0. ) < zero );
assert( std::abs( g01.at1() - 1. ) < zero );
//g[0][0] = 0.;
//g[0][1] = 1.;
#endif
SBasis foginv = compose_inverse( f, g01, order, zero );
SBasis err = compose( foginv, g01) - f;
if ( err.tailError(0) < zero ){
result = Piecewise<SBasis> (foginv);
}else{
SBasis g_portion = portion( g01, Interval(0.,.5) );
SBasis f_portion = portion( f, Interval(0.,.5) );
result = pw_compose_inverse(f_portion, g_portion, order, zero);
g_portion = portion( g01, Interval(.5, 1.) );
f_portion = portion( f, Interval(.5, 1.) );
Piecewise<SBasis> result_next;
result_next = pw_compose_inverse(f_portion, g_portion, order, zero);
result.concat( result_next );
}
if (flip) {
result = reverse(result);
}
result.setDomain(*g_range);
return result;
}
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 (double rt : rts){
result.push_back(f.mapToDomain(rt, 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;
}
std::vector<Interval> level_set(Piecewise<SBasis> const &f, Interval const &level, double tol){
std::vector<Interval> result;
for (unsigned i=0; i<f.size(); i++){
std::vector<Interval> resulti = level_set( f[i], level, 0., 1., tol);
for (unsigned j=0; j<resulti.size(); j++){
double a = f.cuts[i] + resulti[j].min() * ( f.cuts[i+1] - f.cuts[i] );
double b = f.cuts[i] + resulti[j].max() * ( f.cuts[i+1] - f.cuts[i] );
Interval domj( a, b );
//Interval domj( f.mapToDomain(resulti[j].min(), i ), f.mapToDomain(resulti[j].max(), i ) );
if ( j==0 && !result.empty() && result.back().intersects(domj) ){
result.back().unionWith(domj);
}else{
result.push_back(domj);
}
}
}
return result;
}
std::vector<Interval> level_set(Piecewise<SBasis> const &f, double v, double vtol, double tol){
Interval level ( v-vtol, v+vtol );
return level_set( f, level, tol);
}
}
/*
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 :
|
