Version: 8.3.0
Rn.h
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1 // MEFISTO : library to compute 2D triangulation from segmented boundaries
2 //
3 // Copyright (C) 2006-2016 CEA/DEN, EDF R&D, OPEN CASCADE
4 //
5 // This library is free software; you can redistribute it and/or
6 // modify it under the terms of the GNU Lesser General Public
7 // License as published by the Free Software Foundation; either
8 // version 2.1 of the License, or (at your option) any later version.
9 //
10 // This library is distributed in the hope that it will be useful,
11 // but WITHOUT ANY WARRANTY; without even the implied warranty of
12 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 // Lesser General Public License for more details.
14 //
15 // You should have received a copy of the GNU Lesser General Public
16 // License along with this library; if not, write to the Free Software
17 // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
18 //
19 // See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
20 //
21 // File : Rn.h
22 // Module : SMESH
23 // Authors: Frederic HECHT & Alain PERRONNET
24 // Date : 13 novembre 2006
25 
26 #ifndef Rn__h
27 #define Rn__h
28 
29 #include <gp_Pnt.hxx> //Dans OpenCascade
30 #include <gp_Vec.hxx> //Dans OpenCascade
31 #include <gp_Dir.hxx> //Dans OpenCascade
32 
33 //+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
34 // BUT: Definir les espaces affines R R2 R3 R4 soit Rn pour n=1,2,3,4
35 //+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
36 // AUTEUR : Frederic HECHT ANALYSE NUMERIQUE UPMC PARIS OCTOBRE 2000
37 // MODIFS : Alain PERRONNET ANALYSE NUMERIQUE UPMC PARIS NOVEMBRE 2000
38 //...............................................................................
39 #include <iostream>
40 #include <cmath>
41 
42 
43 template<class T> inline T Abs (const T &a){return a <0 ? -a : a;}
44 template<class T> inline void Echange (T& a,T& b) {T c=a;a=b;b=c;}
45 
46 template<class T> inline T Min (const T &a,const T &b) {return a < b ? a : b;}
47 template<class T> inline T Max (const T &a,const T & b) {return a > b ? a : b;}
48 
49 template<class T> inline T Max (const T &a,const T & b,const T & c){return Max(Max(a,b),c);}
50 template<class T> inline T Min (const T &a,const T & b,const T & c){return Min(Min(a,b),c);}
51 
52 template<class T> inline T Max (const T &a,const T & b,const T & c,const T & d)
53  {return Max(Max(a,b),Max(c,d));}
54 template<class T> inline T Min (const T &a,const T & b,const T & c,const T & d)
55  {return Min(Min(a,b),Min(c,d));}
56 
57 //le type Nom des entites geometriques P L S V O
58 //===========
59 typedef char Nom[1+24];
60 
61 //le type N des nombres entiers positifs
62 //=========
63 #ifndef PCLINUX64
64 typedef unsigned long int N;
65 #else
66 typedef unsigned int N;
67 #endif
68 
69 //le type Z des nombres entiers relatifs
70 //=========
71 #ifndef PCLINUX64
72 typedef long int Z;
73 #else
74 typedef int Z;
75 #endif
76 
77 //le type R des nombres "reels"
78 //=========
79 typedef double R;
80 
81 //le type XPoint des coordonnees d'un pixel dans une fenetre
82 //==============
83 //typedef struct { short int x,y } XPoint; //en fait ce type est defini dans X11-Window
84  // #include <X11/Xlib.h>
85 //la classe R2
86 //============
87 class R2
88 {
89  friend std::ostream& operator << (std::ostream& f, const R2 & P)
90  { f << P.x << ' ' << P.y ; return f; }
91  friend std::istream& operator >> (std::istream& f, R2 & P)
92  { f >> P.x >> P.y ; return f; }
93 
94  friend std::ostream& operator << (std::ostream& f, const R2 * P)
95  { f << P->x << ' ' << P->y ; return f; }
96  friend std::istream& operator >> (std::istream& f, R2 * P)
97  { f >> P->x >> P->y ; return f; }
98 
99 public:
100  R x,y; //les donnees
101 
102  R2 () :x(0),y(0) {} //les constructeurs
103  R2 (R a,R b) :x(a),y(b) {}
104  R2 (R2 A,R2 B) :x(B.x-A.x),y(B.y-A.y) {} //vecteur defini par 2 points
105 
106  R2 operator+(R2 P) const {return R2(x+P.x,y+P.y);} // Q+P possible
107  R2 operator+=(R2 P) {x += P.x;y += P.y; return *this;}// Q+=P;
108  R2 operator-(R2 P) const {return R2(x-P.x,y-P.y);} // Q-P
109  R2 operator-=(R2 P) {x -= P.x;y -= P.y; return *this;} // Q-=P;
110  R2 operator-()const {return R2(-x,-y);} // -Q
111  R2 operator+()const {return *this;} // +Q
112  R operator,(R2 P)const {return x*P.x+y*P.y;} // produit scalaire (Q,P)
113  R operator^(R2 P)const {return x*P.y-y*P.x;} // produit vectoriel Q^P
114  R2 operator*(R c)const {return R2(x*c,y*c);} // produit a droite P*c
115  R2 operator*=(R c) {x *= c; y *= c; return *this;}
116  R2 operator/(R c)const {return R2(x/c,y/c);} // division par un reel
117  R2 operator/=(R c) {x /= c; y /= c; return *this;}
118  R & operator[](int i) {return (&x)[i];} // la coordonnee i
119  R2 orthogonal() {return R2(-y,x);} //le vecteur orthogonal dans R2
120  friend R2 operator*(R c,R2 P) {return P*c;} // produit a gauche c*P
121 };
122 
123 
124 //la classe R3
125 //============
126 class R3
127 {
128  friend std::ostream& operator << (std::ostream& f, const R3 & P)
129  { f << P.x << ' ' << P.y << ' ' << P.z ; return f; }
130  friend std::istream& operator >> (std::istream& f, R3 & P)
131  { f >> P.x >> P.y >> P.z ; return f; }
132 
133  friend std::ostream& operator << (std::ostream& f, const R3 * P)
134  { f << P->x << ' ' << P->y << ' ' << P->z ; return f; }
135  friend std::istream& operator >> (std::istream& f, R3 * P)
136  { f >> P->x >> P->y >> P->z ; return f; }
137 
138 public:
139  R x,y,z; //les 3 coordonnees
140 
141  R3 () :x(0),y(0),z(0) {} //les constructeurs
142  R3 (R a,R b,R c):x(a),y(b),z(c) {} //Point ou Vecteur (a,b,c)
143  R3 (R3 A,R3 B):x(B.x-A.x),y(B.y-A.y),z(B.z-A.z) {} //Vecteur AB
144 
145  R3 (gp_Pnt P) : x(P.X()), y(P.Y()), z(P.Z()) {} //Point d'OpenCascade
146  R3 (gp_Vec V) : x(V.X()), y(V.Y()), z(V.Z()) {} //Vecteur d'OpenCascade
147  R3 (gp_Dir P) : x(P.X()), y(P.Y()), z(P.Z()) {} //Direction d'OpenCascade
148 
149  R3 operator+(R3 P)const {return R3(x+P.x,y+P.y,z+P.z);}
150  R3 operator+=(R3 P) {x += P.x; y += P.y; z += P.z; return *this;}
151  R3 operator-(R3 P)const {return R3(x-P.x,y-P.y,z-P.z);}
152  R3 operator-=(R3 P) {x -= P.x; y -= P.y; z -= P.z; return *this;}
153  R3 operator-()const {return R3(-x,-y,-z);}
154  R3 operator+()const {return *this;}
155  R operator,(R3 P)const {return x*P.x+y*P.y+z*P.z;} // produit scalaire
156  R3 operator^(R3 P)const {return R3(y*P.z-z*P.y ,P.x*z-x*P.z, x*P.y-y*P.x);} // produit vectoriel
157  R3 operator*(R c)const {return R3(x*c,y*c,z*c);}
158  R3 operator*=(R c) {x *= c; y *= c; z *= c; return *this;}
159  R3 operator/(R c)const {return R3(x/c,y/c,z/c);}
160  R3 operator/=(R c) {x /= c; y /= c; z /= c; return *this;}
161  R & operator[](int i) {return (&x)[i];}
162  friend R3 operator*(R c,R3 P) {return P*c;}
163 
164  R3 operator=(gp_Pnt P) {return R3(P.X(),P.Y(),P.Z());}
165  R3 operator=(gp_Dir P) {return R3(P.X(),P.Y(),P.Z());}
166 
167  friend gp_Pnt gp_pnt(R3 xyz) { return gp_Pnt(xyz.x,xyz.y,xyz.z); }
168  //friend gp_Pnt operator=() { return gp_Pnt(x,y,z); }
169  friend gp_Dir gp_dir(R3 xyz) { return gp_Dir(xyz.x,xyz.y,xyz.z); }
170 
171  bool DansPave( R3 & xyzMin, R3 & xyzMax )
172  { return xyzMin.x<=x && x<=xyzMax.x &&
173  xyzMin.y<=y && y<=xyzMax.y &&
174  xyzMin.z<=z && z<=xyzMax.z; }
175 };
176 
177 //la classe R4
178 //============
179 class R4: public R3
180 {
181  friend std::ostream& operator <<(std::ostream& f, const R4 & P )
182  { f << P.x << ' ' << P.y << ' ' << P.z << ' ' << P.omega; return f; }
183  friend istream& operator >>(istream& f, R4 & P)
184  { f >> P.x >> P.y >> P.z >> P.omega ; return f; }
185 
186  friend std::ostream& operator <<(std::ostream& f, const R4 * P )
187  { f << P->x << ' ' << P->y << ' ' << P->z << ' ' << P->omega; return f; }
188  friend istream& operator >>(istream& f, R4 * P)
189  { f >> P->x >> P->y >> P->z >> P->omega ; return f; }
190 
191 public:
192  R omega; //la donnee du poids supplementaire
193 
194  R4 () :omega(1.0) {} //les constructeurs
195  R4 (R a,R b,R c,R d):R3(a,b,c),omega(d) {}
196  R4 (R4 A,R4 B) :R3(B.x-A.x,B.y-A.y,B.z-A.z),omega(B.omega-A.omega) {}
197 
198  R4 operator+(R4 P)const {return R4(x+P.x,y+P.y,z+P.z,omega+P.omega);}
199  R4 operator+=(R4 P) {x += P.x;y += P.y;z += P.z;omega += P.omega;return *this;}
200  R4 operator-(R4 P)const {return R4(x-P.x,y-P.y,z-P.z,omega-P.omega);}
201  R4 operator-=(R4 P) {x -= P.x;y -= P.y;z -= P.z;omega -= P.omega;return *this;}
202  R4 operator-()const {return R4(-x,-y,-z,-omega);}
203  R4 operator+()const {return *this;}
204  R operator,(R4 P)const {return x*P.x+y*P.y+z*P.z+omega*P.omega;} // produit scalaire
205  R4 operator*(R c)const {return R4(x*c,y*c,z*c,omega*c);}
206  R4 operator*=(R c) {x *= c; y *= c; z *= c; omega *= c; return *this;}
207  R4 operator/(R c)const {return R4(x/c,y/c,z/c,omega/c);}
208  R4 operator/=(R c) {x /= c; y /= c; z /= c; omega /= c; return *this;}
209  R & operator[](int i) {return (&x)[i];}
210  friend R4 operator*(R c,R4 P) {return P*c;}
211 };
212 
213 //quelques fonctions supplementaires sur ces classes
214 //==================================================
215 inline R Aire2d(const R2 A,const R2 B,const R2 C){return (B-A)^(C-A);}
216 inline R Angle2d(R2 P){ return atan2(P.y,P.x);}
217 
218 inline R Norme2_2(const R2 & A){ return (A,A);}
219 inline R Norme2(const R2 & A){ return sqrt((A,A));}
220 inline R NormeInfinie(const R2 & A){return Max(Abs(A.x),Abs(A.y));}
221 
222 inline R Norme2_2(const R3 & A){ return (A,A);}
223 inline R Norme2(const R3 & A){ return sqrt((A,A));}
224 inline R NormeInfinie(const R3 & A){return Max(Abs(A.x),Abs(A.y),Abs(A.z));}
225 
226 inline R Norme2_2(const R4 & A){ return (A,A);}
227 inline R Norme2(const R4 & A){ return sqrt((A,A));}
228 inline R NormeInfinie(const R4 & A){return Max(Abs(A.x),Abs(A.y),Abs(A.z),Abs(A.omega));}
229 
230 inline R2 XY(R3 P) {return R2(P.x, P.y);} //restriction a R2 d'un R3 par perte de z
231 inline R3 Min(R3 P, R3 Q)
232 {return R3(P.x<Q.x ? P.x : Q.x, P.y<Q.y ? P.y : Q.y, P.z<Q.z ? P.z : Q.z);} //Pt de xyz Min
233 inline R3 Max(R3 P, R3 Q)
234 {return R3(P.x>Q.x ? P.x : Q.x, P.y>Q.y ? P.y : Q.y, P.z>Q.z ? P.z : Q.z);} //Pt de xyz Max
235 
236 #endif