1 /*
2 * sbasis.h - S-power basis function class
3 *
4 * Authors:
5 * Nathan Hurst <njh@mail.csse.monash.edu.au>
6 * Michael Sloan <mgsloan@gmail.com>
7 *
8 * Copyright (C) 2006-2007 authors
9 *
10 * This library is free software; you can redistribute it and/or
11 * modify it either under the terms of the GNU Lesser General Public
12 * License version 2.1 as published by the Free Software Foundation
13 * (the "LGPL") or, at your option, under the terms of the Mozilla
14 * Public License Version 1.1 (the "MPL"). If you do not alter this
15 * notice, a recipient may use your version of this file under either
16 * the MPL or the LGPL.
17 *
18 * You should have received a copy of the LGPL along with this library
19 * in the file COPYING-LGPL-2.1; if not, write to the Free Software
20 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
21 * You should have received a copy of the MPL along with this library
22 * in the file COPYING-MPL-1.1
23 *
24 * The contents of this file are subject to the Mozilla Public License
25 * Version 1.1 (the "License"); you may not use this file except in
26 * compliance with the License. You may obtain a copy of the License at
27 * http://www.mozilla.org/MPL/
28 *
29 * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
30 * OF ANY KIND, either express or implied. See the LGPL or the MPL for
31 * the specific language governing rights and limitations.
32 */
34 #ifndef SEEN_SBASIS_H
35 #define SEEN_SBASIS_H
36 #include <vector>
37 #include <cassert>
38 #include <iostream>
40 #include <2geom/linear.h>
41 #include <2geom/interval.h>
42 #include <2geom/utils.h>
43 #include <2geom/exception.h>
45 namespace Geom {
47 /*** An empty SBasis is identically 0. */
48 class SBasis : public std::vector<Linear>{
49 public:
50 SBasis() {}
51 explicit SBasis(double a) {
52 push_back(Linear(a,a));
53 }
54 SBasis(SBasis const & a) :
55 std::vector<Linear>(a)
56 {}
57 SBasis(Linear const & bo) {
58 push_back(bo);
59 }
60 SBasis(Linear* bo) {
61 push_back(*bo);
62 }
64 //IMPL: FragmentConcept
65 typedef double output_type;
66 inline bool isZero() const {
67 if(empty()) return true;
68 for(unsigned i = 0; i < size(); i++) {
69 if(!(*this)[i].isZero()) return false;
70 }
71 return true;
72 }
73 inline bool isConstant() const {
74 if (empty()) return true;
75 for (unsigned i = 0; i < size(); i++) {
76 if(!(*this)[i].isConstant()) return false;
77 }
78 return true;
79 }
81 bool isFinite() const;
82 inline double at0() const {
83 if(empty()) return 0; else return (*this)[0][0];
84 }
85 inline double at1() const{
86 if(empty()) return 0; else return (*this)[0][1];
87 }
89 double valueAt(double t) const {
90 double s = t*(1-t);
91 double p0 = 0, p1 = 0;
92 for(unsigned k = size(); k > 0; k--) {
93 const Linear &lin = (*this)[k-1];
94 p0 = p0*s + lin[0];
95 p1 = p1*s + lin[1];
96 }
97 return (1-t)*p0 + t*p1;
98 }
99 //double valueAndDerivative(double t, double &der) const {
100 //}
101 double operator()(double t) const {
102 return valueAt(t);
103 }
105 std::vector<double> valueAndDerivatives(double t, unsigned n) const;
107 SBasis toSBasis() const { return SBasis(*this); }
109 double tailError(unsigned tail) const;
111 // compute f(g)
112 SBasis operator()(SBasis const & g) const;
114 Linear operator[](unsigned i) const {
115 assert(i < size());
116 return std::vector<Linear>::operator[](i);
117 }
119 //MUTATOR PRISON
120 Linear& operator[](unsigned i) { return this->at(i); }
122 //remove extra zeros
123 void normalize() {
124 while(!empty() && 0 == back()[0] && 0 == back()[1])
125 pop_back();
126 }
128 void truncate(unsigned k) { if(k < size()) resize(k); }
129 private:
130 void derive(); // in place version
131 };
133 //TODO: figure out how to stick this in linear, while not adding an sbasis dep
134 inline SBasis Linear::toSBasis() const { return SBasis(*this); }
136 //implemented in sbasis-roots.cpp
137 Interval bounds_exact(SBasis const &a);
138 Interval bounds_fast(SBasis const &a, int order = 0);
139 Interval bounds_local(SBasis const &a, const Interval &t, int order = 0);
141 inline SBasis reverse(SBasis const &a) {
142 SBasis result;
143 result.reserve(a.size());
144 for(unsigned k = 0; k < a.size(); k++)
145 result.push_back(reverse(a[k]));
146 return result;
147 }
149 //IMPL: ScalableConcept
150 inline SBasis operator-(const SBasis& p) {
151 if(p.isZero()) return SBasis();
152 SBasis result;
153 result.reserve(p.size());
155 for(unsigned i = 0; i < p.size(); i++) {
156 result.push_back(-p[i]);
157 }
158 return result;
159 }
160 SBasis operator*(SBasis const &a, double k);
161 inline SBasis operator*(double k, SBasis const &a) { return a*k; }
162 inline SBasis operator/(SBasis const &a, double k) { return a*(1./k); }
163 SBasis& operator*=(SBasis& a, double b);
164 inline SBasis& operator/=(SBasis& a, double b) { return (a*=(1./b)); }
166 //IMPL: AddableConcept
167 SBasis operator+(const SBasis& a, const SBasis& b);
168 SBasis operator-(const SBasis& a, const SBasis& b);
169 SBasis& operator+=(SBasis& a, const SBasis& b);
170 SBasis& operator-=(SBasis& a, const SBasis& b);
172 //TODO: remove?
173 inline SBasis operator+(const SBasis & a, Linear const & b) {
174 if(b.isZero()) return a;
175 if(a.isZero()) return b;
176 SBasis result(a);
177 result[0] += b;
178 return result;
179 }
180 inline SBasis operator-(const SBasis & a, Linear const & b) {
181 if(b.isZero()) return a;
182 SBasis result(a);
183 result[0] -= b;
184 return result;
185 }
186 inline SBasis& operator+=(SBasis& a, const Linear& b) {
187 if(a.isZero())
188 a.push_back(b);
189 else
190 a[0] += b;
191 return a;
192 }
193 inline SBasis& operator-=(SBasis& a, const Linear& b) {
194 if(a.isZero())
195 a.push_back(-b);
196 else
197 a[0] -= b;
198 return a;
199 }
201 //IMPL: OffsetableConcept
202 inline SBasis operator+(const SBasis & a, double b) {
203 if(a.isZero()) return Linear(b, b);
204 SBasis result(a);
205 result[0] += b;
206 return result;
207 }
208 inline SBasis operator-(const SBasis & a, double b) {
209 if(a.isZero()) return Linear(-b, -b);
210 SBasis result(a);
211 result[0] -= b;
212 return result;
213 }
214 inline SBasis& operator+=(SBasis& a, double b) {
215 if(a.isZero())
216 a.push_back(Linear(b,b));
217 else
218 a[0] += b;
219 return a;
220 }
221 inline SBasis& operator-=(SBasis& a, double b) {
222 if(a.isZero())
223 a.push_back(Linear(-b,-b));
224 else
225 a[0] -= b;
226 return a;
227 }
229 SBasis shift(SBasis const &a, int sh);
230 SBasis shift(Linear const &a, int sh);
232 inline SBasis truncate(SBasis const &a, unsigned terms) {
233 SBasis c;
234 c.insert(c.begin(), a.begin(), a.begin() + std::min(terms, (unsigned)a.size()));
235 return c;
236 }
238 SBasis multiply(SBasis const &a, SBasis const &b);
239 // This performs a multiply and accumulate operation in about the same time as multiply. return a*b + c
240 SBasis multiply_add(SBasis const &a, SBasis const &b, SBasis c);
242 SBasis integral(SBasis const &c);
243 SBasis derivative(SBasis const &a);
245 SBasis sqrt(SBasis const &a, int k);
247 // return a kth order approx to 1/a)
248 SBasis reciprocal(Linear const &a, int k);
249 SBasis divide(SBasis const &a, SBasis const &b, int k);
251 inline SBasis operator*(SBasis const & a, SBasis const & b) {
252 return multiply(a, b);
253 }
255 inline SBasis& operator*=(SBasis& a, SBasis const & b) {
256 a = multiply(a, b);
257 return a;
258 }
260 //valuation: degree of the first non zero coefficient.
261 inline unsigned
262 valuation(SBasis const &a, double tol=0){
263 unsigned val=0;
264 while( val<a.size() &&
265 fabs(a[val][0])<tol &&
266 fabs(a[val][1])<tol )
267 val++;
268 return val;
269 }
271 // a(b(t))
272 SBasis compose(SBasis const &a, SBasis const &b);
273 SBasis compose(SBasis const &a, SBasis const &b, unsigned k);
274 SBasis inverse(SBasis a, int k);
275 //compose_inverse(f,g)=compose(f,inverse(g)), but is numerically more stable in some good cases...
276 //TODO: requires g(0)=0 & g(1)=1 atm. generalization should be obvious.
277 SBasis compose_inverse(SBasis const &f, SBasis const &g, unsigned order=2, double tol=1e-3);
279 inline SBasis portion(const SBasis &t, double from, double to) { return compose(t, Linear(from, to)); }
281 // compute f(g)
282 inline SBasis
283 SBasis::operator()(SBasis const & g) const {
284 return compose(*this, g);
285 }
287 inline std::ostream &operator<< (std::ostream &out_file, const Linear &bo) {
288 out_file << "{" << bo[0] << ", " << bo[1] << "}";
289 return out_file;
290 }
292 inline std::ostream &operator<< (std::ostream &out_file, const SBasis & p) {
293 for(unsigned i = 0; i < p.size(); i++) {
294 out_file << p[i] << "s^" << i << " + ";
295 }
296 return out_file;
297 }
299 // These are deprecated, use sbasis-math versions if possible
300 SBasis sin(Linear bo, int k);
301 SBasis cos(Linear bo, int k);
303 std::vector<double> roots(SBasis const & s);
304 std::vector<std::vector<double> > multi_roots(SBasis const &f,
305 std::vector<double> const &levels,
306 double htol=1e-7,
307 double vtol=1e-7,
308 double a=0,
309 double b=1);
311 }
313 /*
314 Local Variables:
315 mode:c++
316 c-file-style:"stroustrup"
317 c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
318 indent-tabs-mode:nil
319 fill-column:99
320 End:
321 */
322 // vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :
323 #endif