1 /**
2 * \file
3 * \brief Defines S-power basis function class
4 *
5 * Authors:
6 * Nathan Hurst <njh@mail.csse.monash.edu.au>
7 * Michael Sloan <mgsloan@gmail.com>
8 *
9 * Copyright (C) 2006-2007 authors
10 *
11 * This library is free software; you can redistribute it and/or
12 * modify it either under the terms of the GNU Lesser General Public
13 * License version 2.1 as published by the Free Software Foundation
14 * (the "LGPL") or, at your option, under the terms of the Mozilla
15 * Public License Version 1.1 (the "MPL"). If you do not alter this
16 * notice, a recipient may use your version of this file under either
17 * the MPL or the LGPL.
18 *
19 * You should have received a copy of the LGPL along with this library
20 * in the file COPYING-LGPL-2.1; if not, write to the Free Software
21 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
22 * You should have received a copy of the MPL along with this library
23 * in the file COPYING-MPL-1.1
24 *
25 * The contents of this file are subject to the Mozilla Public License
26 * Version 1.1 (the "License"); you may not use this file except in
27 * compliance with the License. You may obtain a copy of the License at
28 * http://www.mozilla.org/MPL/
29 *
30 * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
31 * OF ANY KIND, either express or implied. See the LGPL or the MPL for
32 * the specific language governing rights and limitations.
33 */
35 #ifndef SEEN_SBASIS_H
36 #define SEEN_SBASIS_H
37 #include <vector>
38 #include <cassert>
39 #include <iostream>
41 #include <2geom/linear.h>
42 #include <2geom/interval.h>
43 #include <2geom/utils.h>
44 #include <2geom/exception.h>
46 //#define USE_SBASISN 1
49 #if defined(USE_SBASIS_OF)
51 #include "sbasis-of.h"
53 #elif defined(USE_SBASISN)
55 #include "sbasisN.h"
56 namespace Geom{
58 /*** An empty SBasis is identically 0. */
59 class SBasis : public SBasisN<1>;
61 };
62 #else
64 namespace Geom{
66 /*** An empty SBasis is identically 0. */
67 class SBasis{
68 std::vector<Linear> d;
69 void push_back(Linear const&l) { d.push_back(l); }
71 public:
72 // As part of our migration away from SBasis isa vector we provide this minimal set of vector interface methods.
73 size_t size() const {return d.size();}
74 Linear operator[](unsigned i) const {
75 return d[i];
76 }
77 Linear& operator[](unsigned i) { return d.at(i); }
78 Linear const* begin() const { return (Linear const*)&*d.begin();}
79 Linear const* end() const { return (Linear const*)&*d.end();}
80 Linear* begin() { return (Linear*)&*d.begin();}
81 Linear* end() { return (Linear*)&*d.end();}
82 bool empty() const {return d.empty();}
83 Linear &back() {return d.back();}
84 Linear const &back() const {return d.back();}
85 void pop_back() { d.pop_back();}
86 void resize(unsigned n) { d.resize(n);}
87 void resize(unsigned n, Linear const& l) { d.resize(n, l);}
88 void reserve(unsigned n) { d.reserve(n);}
89 void clear() {d.clear();}
90 void insert(Linear* before, const Linear* src_begin, const Linear* src_end) { d.insert(std::vector<Linear>::iterator(before), src_begin, src_end);}
91 //void insert(Linear* aa, Linear* bb, Linear* cc} { d.insert(aa, bb, cc);}
92 Linear& at(unsigned i) { return d.at(i);}
93 //void insert(Linear* before, int& n, Linear const &l) { d.insert(std::vector<Linear>::iterator(before), n, l);}
94 bool operator==(SBasis const&B) const { return d == B.d;}
95 bool operator!=(SBasis const&B) const { return d != B.d;}
96 operator std::vector<Linear>() { return d;}
99 SBasis() {}
100 explicit SBasis(double a) {
101 push_back(Linear(a,a));
102 }
103 explicit SBasis(double a, double b) {
104 push_back(Linear(a,b));
105 }
106 SBasis(SBasis const & a) :
107 d(a.d)
108 {}
109 SBasis(Linear const & bo) {
110 push_back(bo);
111 }
112 SBasis(Linear* bo) {
113 push_back(*bo);
114 }
115 explicit SBasis(size_t n, Linear const&l) : d(n, l) {}
117 //IMPL: FragmentConcept
118 typedef double output_type;
119 inline bool isZero() const {
120 if(empty()) return true;
121 for(unsigned i = 0; i < size(); i++) {
122 if(!(*this)[i].isZero()) return false;
123 }
124 return true;
125 }
126 inline bool isConstant() const {
127 if (empty()) return true;
128 for (unsigned i = 0; i < size(); i++) {
129 if(!(*this)[i].isConstant()) return false;
130 }
131 return true;
132 }
134 bool isFinite() const;
135 inline double at0() const {
136 if(empty()) return 0; else return (*this)[0][0];
137 }
138 inline double at1() const{
139 if(empty()) return 0; else return (*this)[0][1];
140 }
142 int degreesOfFreedom() const { return size()*2;}
144 double valueAt(double t) const {
145 double s = t*(1-t);
146 double p0 = 0, p1 = 0;
147 for(unsigned k = size(); k > 0; k--) {
148 const Linear &lin = (*this)[k-1];
149 p0 = p0*s + lin[0];
150 p1 = p1*s + lin[1];
151 }
152 return (1-t)*p0 + t*p1;
153 }
154 //double valueAndDerivative(double t, double &der) const {
155 //}
156 double operator()(double t) const {
157 return valueAt(t);
158 }
160 std::vector<double> valueAndDerivatives(double t, unsigned n) const;
162 SBasis toSBasis() const { return SBasis(*this); }
164 double tailError(unsigned tail) const;
166 // compute f(g)
167 SBasis operator()(SBasis const & g) const;
169 //MUTATOR PRISON
170 //remove extra zeros
171 void normalize() {
172 while(!empty() && 0 == back()[0] && 0 == back()[1])
173 pop_back();
174 }
176 void truncate(unsigned k) { if(k < size()) resize(k); }
177 private:
178 void derive(); // in place version
179 };
181 //TODO: figure out how to stick this in linear, while not adding an sbasis dep
182 inline SBasis Linear::toSBasis() const { return SBasis(*this); }
184 //implemented in sbasis-roots.cpp
185 OptInterval bounds_exact(SBasis const &a);
186 OptInterval bounds_fast(SBasis const &a, int order = 0);
187 OptInterval bounds_local(SBasis const &a, const OptInterval &t, int order = 0);
189 /** Returns a function which reverses the domain of a.
190 \param a sbasis function
192 useful for reversing a parameteric curve.
193 */
194 inline SBasis reverse(SBasis const &a) {
195 SBasis result(a.size(), Linear());
197 for(unsigned k = 0; k < a.size(); k++)
198 result[k] = reverse(a[k]);
199 return result;
200 }
202 //IMPL: ScalableConcept
203 inline SBasis operator-(const SBasis& p) {
204 if(p.isZero()) return SBasis();
205 SBasis result(p.size(), Linear());
207 for(unsigned i = 0; i < p.size(); i++) {
208 result[i] = -p[i];
209 }
210 return result;
211 }
212 SBasis operator*(SBasis const &a, double k);
213 inline SBasis operator*(double k, SBasis const &a) { return a*k; }
214 inline SBasis operator/(SBasis const &a, double k) { return a*(1./k); }
215 SBasis& operator*=(SBasis& a, double b);
216 inline SBasis& operator/=(SBasis& a, double b) { return (a*=(1./b)); }
218 //IMPL: AddableConcept
219 SBasis operator+(const SBasis& a, const SBasis& b);
220 SBasis operator-(const SBasis& a, const SBasis& b);
221 SBasis& operator+=(SBasis& a, const SBasis& b);
222 SBasis& operator-=(SBasis& a, const SBasis& b);
224 //TODO: remove?
225 /*inline SBasis operator+(const SBasis & a, Linear const & b) {
226 if(b.isZero()) return a;
227 if(a.isZero()) return b;
228 SBasis result(a);
229 result[0] += b;
230 return result;
231 }
232 inline SBasis operator-(const SBasis & a, Linear const & b) {
233 if(b.isZero()) return a;
234 SBasis result(a);
235 result[0] -= b;
236 return result;
237 }
238 inline SBasis& operator+=(SBasis& a, const Linear& b) {
239 if(a.isZero())
240 a.push_back(b);
241 else
242 a[0] += b;
243 return a;
244 }
245 inline SBasis& operator-=(SBasis& a, const Linear& b) {
246 if(a.isZero())
247 a.push_back(-b);
248 else
249 a[0] -= b;
250 return a;
251 }*/
253 //IMPL: OffsetableConcept
254 inline SBasis operator+(const SBasis & a, double b) {
255 if(a.isZero()) return Linear(b, b);
256 SBasis result(a);
257 result[0] += b;
258 return result;
259 }
260 inline SBasis operator-(const SBasis & a, double b) {
261 if(a.isZero()) return Linear(-b, -b);
262 SBasis result(a);
263 result[0] -= b;
264 return result;
265 }
266 inline SBasis& operator+=(SBasis& a, double b) {
267 if(a.isZero())
268 a = SBasis(Linear(b,b));
269 else
270 a[0] += b;
271 return a;
272 }
273 inline SBasis& operator-=(SBasis& a, double b) {
274 if(a.isZero())
275 a = SBasis(Linear(-b,-b));
276 else
277 a[0] -= b;
278 return a;
279 }
281 SBasis shift(SBasis const &a, int sh);
282 SBasis shift(Linear const &a, int sh);
284 inline SBasis truncate(SBasis const &a, unsigned terms) {
285 SBasis c;
286 c.insert(c.begin(), a.begin(), a.begin() + std::min(terms, (unsigned)a.size()));
287 return c;
288 }
290 SBasis multiply(SBasis const &a, SBasis const &b);
291 // This performs a multiply and accumulate operation in about the same time as multiply. return a*b + c
292 SBasis multiply_add(SBasis const &a, SBasis const &b, SBasis c);
294 SBasis integral(SBasis const &c);
295 SBasis derivative(SBasis const &a);
297 SBasis sqrt(SBasis const &a, int k);
299 // return a kth order approx to 1/a)
300 SBasis reciprocal(Linear const &a, int k);
301 SBasis divide(SBasis const &a, SBasis const &b, int k);
303 inline SBasis operator*(SBasis const & a, SBasis const & b) {
304 return multiply(a, b);
305 }
307 inline SBasis& operator*=(SBasis& a, SBasis const & b) {
308 a = multiply(a, b);
309 return a;
310 }
312 /** Returns the degree of the first non zero coefficient.
313 \param a sbasis function
314 \param tol largest abs val considered 0
315 \returns first non zero coefficient
316 */
317 inline unsigned
318 valuation(SBasis const &a, double tol=0){
319 unsigned val=0;
320 while( val<a.size() &&
321 fabs(a[val][0])<tol &&
322 fabs(a[val][1])<tol )
323 val++;
324 return val;
325 }
327 // a(b(t))
328 SBasis compose(SBasis const &a, SBasis const &b);
329 SBasis compose(SBasis const &a, SBasis const &b, unsigned k);
330 SBasis inverse(SBasis a, int k);
331 //compose_inverse(f,g)=compose(f,inverse(g)), but is numerically more stable in some good cases...
332 //TODO: requires g(0)=0 & g(1)=1 atm. generalization should be obvious.
333 SBasis compose_inverse(SBasis const &f, SBasis const &g, unsigned order=2, double tol=1e-3);
335 /** Returns the sbasis on domain [0,1] that was t on [from, to]
336 \param a sbasis function
337 \param from,to interval
338 \returns sbasis
340 */
341 inline SBasis portion(const SBasis &t, double from, double to) { return compose(t, Linear(from, to)); }
342 inline SBasis portion(const SBasis &t, Interval ivl) { return compose(t, Linear(ivl[0], ivl[1])); }
344 // compute f(g)
345 inline SBasis
346 SBasis::operator()(SBasis const & g) const {
347 return compose(*this, g);
348 }
350 inline std::ostream &operator<< (std::ostream &out_file, const Linear &bo) {
351 out_file << "{" << bo[0] << ", " << bo[1] << "}";
352 return out_file;
353 }
355 inline std::ostream &operator<< (std::ostream &out_file, const SBasis & p) {
356 for(unsigned i = 0; i < p.size(); i++) {
357 out_file << p[i] << "s^" << i << " + ";
358 }
359 return out_file;
360 }
362 // These are deprecated, use sbasis-math.h versions if possible
363 SBasis sin(Linear bo, int k);
364 SBasis cos(Linear bo, int k);
366 std::vector<double> roots(SBasis const & s);
367 std::vector<std::vector<double> > multi_roots(SBasis const &f,
368 std::vector<double> const &levels,
369 double htol=1e-7,
370 double vtol=1e-7,
371 double a=0,
372 double b=1);
374 }
375 #endif
377 /*
378 Local Variables:
379 mode:c++
380 c-file-style:"stroustrup"
381 c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
382 indent-tabs-mode:nil
383 fill-column:99
384 End:
385 */
386 // vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :
387 #endif