Point Cloud Library (PCL)  1.11.0
polynomial.hpp
1 /*
2 Copyright (c) 2006, Michael Kazhdan and Matthew Bolitho
3 All rights reserved.
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28 
29 #include "factor.h"
30 
31 #include <float.h>
32 #include <math.h>
33 
34 #include <algorithm>
35 
36 #include <cstdio>
37 #include <cstring>
38 
39 ////////////////
40 // Polynomial //
41 ////////////////
42 
43 namespace pcl
44 {
45  namespace poisson
46  {
47 
48 
49  template<int Degree>
50  Polynomial<Degree>::Polynomial(void){memset(coefficients,0,sizeof(double)*(Degree+1));}
51  template<int Degree>
52  template<int Degree2>
54  memset(coefficients,0,sizeof(double)*(Degree+1));
55  for(int i=0;i<=Degree && i<=Degree2;i++){coefficients[i]=P.coefficients[i];}
56  }
57 
58 
59  template<int Degree>
60  template<int Degree2>
62  int d=Degree<Degree2?Degree:Degree2;
63  memset(coefficients,0,sizeof(double)*(Degree+1));
64  memcpy(coefficients,p.coefficients,sizeof(double)*(d+1));
65  return *this;
66  }
67 
68  template<int Degree>
70  Polynomial<Degree-1> p;
71  for(int i=0;i<Degree;i++){p.coefficients[i]=coefficients[i+1]*(i+1);}
72  return p;
73  }
74 
75  template<int Degree>
78  p.coefficients[0]=0;
79  for(int i=0;i<=Degree;i++){p.coefficients[i+1]=coefficients[i]/(i+1);}
80  return p;
81  }
82  template<> inline double Polynomial< 0 >::operator() ( double t ) const { return coefficients[0]; }
83  template<> inline double Polynomial< 1 >::operator() ( double t ) const { return coefficients[0]+coefficients[1]*t; }
84  template<> inline double Polynomial< 2 >::operator() ( double t ) const { return coefficients[0]+(coefficients[1]+coefficients[2]*t)*t; }
85  template<int Degree>
86  double Polynomial<Degree>::operator() ( double t ) const{
87  double v=coefficients[Degree];
88  for( int d=Degree-1 ; d>=0 ; d-- ) v = v*t + coefficients[d];
89  return v;
90  }
91  template<int Degree>
92  double Polynomial<Degree>::integral( double tMin , double tMax ) const
93  {
94  double v=0;
95  double t1,t2;
96  t1=tMin;
97  t2=tMax;
98  for(int i=0;i<=Degree;i++){
99  v+=coefficients[i]*(t2-t1)/(i+1);
100  if(t1!=-DBL_MAX && t1!=DBL_MAX){t1*=tMin;}
101  if(t2!=-DBL_MAX && t2!=DBL_MAX){t2*=tMax;}
102  }
103  return v;
104  }
105  template<int Degree>
107  for(int i=0;i<=Degree;i++){if(coefficients[i]!=p.coefficients[i]){return 0;}}
108  return 1;
109  }
110  template<int Degree>
112  for(int i=0;i<=Degree;i++){if(coefficients[i]==p.coefficients[i]){return 0;}}
113  return 1;
114  }
115  template<int Degree>
116  int Polynomial<Degree>::isZero(void) const{
117  for(int i=0;i<=Degree;i++){if(coefficients[i]!=0){return 0;}}
118  return 1;
119  }
120  template<int Degree>
121  void Polynomial<Degree>::setZero(void){memset(coefficients,0,sizeof(double)*(Degree+1));}
122 
123  template<int Degree>
125  for(int i=0;i<=Degree;i++){coefficients[i]+=p.coefficients[i]*s;}
126  return *this;
127  }
128  template<int Degree>
130  for(int i=0;i<=Degree;i++){coefficients[i]+=p.coefficients[i];}
131  return *this;
132  }
133  template<int Degree>
135  for(int i=0;i<=Degree;i++){coefficients[i]-=p.coefficients[i];}
136  return *this;
137  }
138  template<int Degree>
140  Polynomial q;
141  for(int i=0;i<=Degree;i++){q.coefficients[i]=(coefficients[i]+p.coefficients[i]);}
142  return q;
143  }
144  template<int Degree>
146  Polynomial q;
147  for(int i=0;i<=Degree;i++) {q.coefficients[i]=coefficients[i]-p.coefficients[i];}
148  return q;
149  }
150  template<int Degree>
151  void Polynomial<Degree>::Scale(const Polynomial& p,double w,Polynomial& q){
152  for(int i=0;i<=Degree;i++){q.coefficients[i]=p.coefficients[i]*w;}
153  }
154  template<int Degree>
155  void Polynomial<Degree>::AddScaled(const Polynomial& p1,double w1,const Polynomial& p2,double w2,Polynomial& q){
156  for(int i=0;i<=Degree;i++){q.coefficients[i]=p1.coefficients[i]*w1+p2.coefficients[i]*w2;}
157  }
158  template<int Degree>
159  void Polynomial<Degree>::AddScaled(const Polynomial& p1,double w1,const Polynomial& p2,Polynomial& q){
160  for(int i=0;i<=Degree;i++){q.coefficients[i]=p1.coefficients[i]*w1+p2.coefficients[i];}
161  }
162  template<int Degree>
163  void Polynomial<Degree>::AddScaled(const Polynomial& p1,const Polynomial& p2,double w2,Polynomial& q){
164  for(int i=0;i<=Degree;i++){q.coefficients[i]=p1.coefficients[i]+p2.coefficients[i]*w2;}
165  }
166 
167  template<int Degree>
169  for(int i=0;i<=Degree;i++){q.coefficients[i]=p1.coefficients[i]-p2.coefficients[i];}
170  }
171  template<int Degree>
173  out=in;
174  for(int i=0;i<=Degree;i++){out.coefficients[i]=-out.coefficients[i];}
175  }
176 
177  template<int Degree>
179  Polynomial q=*this;
180  for(int i=0;i<=Degree;i++){q.coefficients[i]=-q.coefficients[i];}
181  return q;
182  }
183  template<int Degree>
184  template<int Degree2>
187  for(int i=0;i<=Degree;i++){for(int j=0;j<=Degree2;j++){q.coefficients[i+j]+=coefficients[i]*p.coefficients[j];}}
188  return q;
189  }
190 
191  template<int Degree>
193  {
194  coefficients[0]+=s;
195  return *this;
196  }
197  template<int Degree>
199  {
200  coefficients[0]-=s;
201  return *this;
202  }
203  template<int Degree>
205  {
206  for(int i=0;i<=Degree;i++){coefficients[i]*=s;}
207  return *this;
208  }
209  template<int Degree>
211  {
212  for(int i=0;i<=Degree;i++){coefficients[i]/=s;}
213  return *this;
214  }
215  template<int Degree>
217  {
218  Polynomial<Degree> q=*this;
219  q.coefficients[0]+=s;
220  return q;
221  }
222  template<int Degree>
224  {
225  Polynomial q=*this;
226  q.coefficients[0]-=s;
227  return q;
228  }
229  template<int Degree>
231  {
232  Polynomial q;
233  for(int i=0;i<=Degree;i++){q.coefficients[i]=coefficients[i]*s;}
234  return q;
235  }
236  template<int Degree>
238  {
239  Polynomial q;
240  for( int i=0 ; i<=Degree ; i++ ) q.coefficients[i] = coefficients[i]/s;
241  return q;
242  }
243  template<int Degree>
245  {
246  Polynomial q=*this;
247  double s2=1.0;
248  for(int i=0;i<=Degree;i++){
249  q.coefficients[i]*=s2;
250  s2/=s;
251  }
252  return q;
253  }
254  template<int Degree>
256  {
258  for(int i=0;i<=Degree;i++){
259  double temp=1;
260  for(int j=i;j>=0;j--){
261  q.coefficients[j]+=coefficients[i]*temp;
262  temp*=-t*j;
263  temp/=(i-j+1);
264  }
265  }
266  return q;
267  }
268  template<int Degree>
269  void Polynomial<Degree>::printnl(void) const{
270  for(int j=0;j<=Degree;j++){
271  printf("%6.4f x^%d ",coefficients[j],j);
272  if(j<Degree && coefficients[j+1]>=0){printf("+");}
273  }
274  printf("\n");
275  }
276  template<int Degree>
277  void Polynomial<Degree>::getSolutions(double c,std::vector<double>& roots,double EPS) const
278  {
279  double r[4][2];
280  int rCount=0;
281  roots.clear();
282  switch(Degree){
283  case 1:
284  rCount=Factor(coefficients[1],coefficients[0]-c,r,EPS);
285  break;
286  case 2:
287  rCount=Factor(coefficients[2],coefficients[1],coefficients[0]-c,r,EPS);
288  break;
289  case 3:
290  rCount=Factor(coefficients[3],coefficients[2],coefficients[1],coefficients[0]-c,r,EPS);
291  break;
292  // case 4:
293  // rCount=Factor(coefficients[4],coefficients[3],coefficients[2],coefficients[1],coefficients[0]-c,r,EPS);
294  // break;
295  default:
296  printf("Can't solve polynomial of degree: %d\n",Degree);
297  }
298  for(int i=0;i<rCount;i++){
299  if(fabs(r[i][1])<=EPS){
300  roots.push_back(r[i][0]);
301  }
302  }
303  }
304  template< > inline
306  {
307  Polynomial p;
308  p.coefficients[0] = 1.;
309  return p;
310  }
311  template< int Degree > inline
313  {
314  Polynomial p;
315  if( i>0 )
316  {
318  p -= _p;
319  p.coefficients[0] += _p(1);
320  }
321  if( i<Degree )
322  {
324  p += _p;
325  }
326  return p;
327  }
328 
329  }
330 }
pcl::poisson::Polynomial::operator-=
Polynomial & operator-=(const Polynomial &p)
Definition: polynomial.hpp:134
pcl
Definition: convolution.h:46
pcl::poisson::Polynomial::addScaled
Polynomial & addScaled(const Polynomial &p, double scale)
Definition: polynomial.hpp:124
pcl::poisson::Polynomial::operator-
Polynomial operator-(void) const
Definition: polynomial.hpp:178
pcl::poisson::Polynomial
Definition: polynomial.h:40
pcl::poisson::Polynomial::getSolutions
void getSolutions(double c, std::vector< double > &roots, double EPS) const
Definition: polynomial.hpp:277
pcl::poisson::Polynomial::printnl
void printnl(void) const
Definition: polynomial.hpp:269
pcl::poisson::Polynomial::Scale
static void Scale(const Polynomial &p, double w, Polynomial &q)
Definition: polynomial.hpp:151
pcl::poisson::Polynomial::operator*=
Polynomial & operator*=(double s)
Definition: polynomial.hpp:204
pcl::poisson::Polynomial::BSplineComponent
static Polynomial BSplineComponent(int i)
Definition: polynomial.hpp:312
pcl::poisson::Polynomial::operator!=
int operator!=(const Polynomial &p) const
Definition: polynomial.hpp:111
pcl::poisson::Polynomial::isZero
int isZero(void) const
Definition: polynomial.hpp:116
pcl::poisson::Polynomial::integral
Polynomial< Degree+1 > integral(void) const
Definition: polynomial.hpp:76
pcl::poisson::Polynomial::operator()
double operator()(double t) const
Definition: polynomial.hpp:86
pcl::poisson::Factor
PCL_EXPORTS int Factor(double a1, double a0, double roots[1][2], double EPS)
pcl::poisson::Polynomial::operator+
Polynomial operator+(const Polynomial &p) const
Definition: polynomial.hpp:139
pcl::poisson::Polynomial::operator/
Polynomial operator/(double s) const
Definition: polynomial.hpp:237
pcl::poisson::Polynomial::Subtract
static void Subtract(const Polynomial &p1, const Polynomial &p2, Polynomial &q)
Definition: polynomial.hpp:168
pcl::poisson::Polynomial::scale
Polynomial scale(double s) const
Definition: polynomial.hpp:244
pcl::poisson::Polynomial::derivative
Polynomial< Degree-1 > derivative(void) const
Definition: polynomial.hpp:69
pcl::poisson::Polynomial::operator==
int operator==(const Polynomial &p) const
Definition: polynomial.hpp:106
pcl::poisson::Polynomial::operator=
Polynomial & operator=(const Polynomial< Degree2 > &p)
pcl::poisson::Polynomial::integral
double integral(double tMin, double tMax) const
Definition: polynomial.hpp:92
pcl::poisson::Polynomial::coefficients
double coefficients[Degree+1]
Definition: polynomial.h:42
pcl::poisson::Polynomial::AddScaled
static void AddScaled(const Polynomial &p1, double w1, const Polynomial &p2, double w2, Polynomial &q)
Definition: polynomial.hpp:155
pcl::poisson::Polynomial::shift
Polynomial shift(double t) const
Definition: polynomial.hpp:255
pcl::poisson::Polynomial::Negate
static void Negate(const Polynomial &in, Polynomial &out)
Definition: polynomial.hpp:172
pcl::poisson::Polynomial::Polynomial
Polynomial(void)
Definition: polynomial.hpp:50
pcl::poisson::Polynomial::operator*
Polynomial< Degree+Degree2 > operator*(const Polynomial< Degree2 > &p) const
Definition: polynomial.hpp:185
pcl::poisson::Polynomial::operator+=
Polynomial & operator+=(const Polynomial &p)
Definition: polynomial.hpp:129
pcl::poisson::Polynomial::operator/=
Polynomial & operator/=(double s)
Definition: polynomial.hpp:210
pcl::poisson::Polynomial::setZero
void setZero(void)
Definition: polynomial.hpp:121