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b311480e | 1 | -- Created on: 1993-02-17 |

2 | -- Created by: Remi LEQUETTE | |

3 | -- Copyright (c) 1993-1999 Matra Datavision | |

973c2be1 | 4 | -- Copyright (c) 1999-2014 OPEN CASCADE SAS |

b311480e | 5 | -- |

973c2be1 | 6 | -- This file is part of Open CASCADE Technology software library. |

b311480e | 7 | -- |

973c2be1 | 8 | -- This library is free software; you can redistribute it and / or modify it |

9 | -- under the terms of the GNU Lesser General Public version 2.1 as published | |

10 | -- by the Free Software Foundation, with special exception defined in the file | |

11 | -- OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT | |

12 | -- distribution for complete text of the license and disclaimer of any warranty. | |

b311480e | 13 | -- |

973c2be1 | 14 | -- Alternatively, this file may be used under the terms of Open CASCADE |

15 | -- commercial license or contractual agreement. | |

7fd59977 | 16 | |

17 | package Precision | |

18 | ||

19 | ---Purpose: The Precision package offers a set of functions defining precision criteria | |

20 | -- for use in conventional situations when comparing two numbers. | |

21 | -- Generalities | |

22 | -- It is not advisable to use floating number equality. Instead, the difference | |

23 | -- between numbers must be compared with a given precision, i.e. : | |

24 | -- Standard_Real x1, x2 ; | |

25 | -- x1 = ... | |

26 | -- x2 = ... | |

27 | -- If ( x1 == x2 ) ... | |

28 | -- should not be used and must be written as indicated below: | |

29 | -- Standard_Real x1, x2 ; | |

30 | -- Standard_Real Precision = ... | |

31 | -- x1 = ... | |

32 | -- x2 = ... | |

33 | -- If ( Abs ( x1 - x2 ) < Precision ) ... | |

34 | -- Likewise, when ordering floating numbers, you must take the following into account : | |

35 | -- Standard_Real x1, x2 ; | |

36 | -- Standard_Real Precision = ... | |

37 | -- x1 = ... ! a large number | |

38 | -- x2 = ... ! another large number | |

39 | -- If ( x1 < x2 - Precision ) ... | |

40 | -- is incorrect when x1 and x2 are large numbers ; it is better to write : | |

41 | -- Standard_Real x1, x2 ; | |

42 | -- Standard_Real Precision = ... | |

43 | -- x1 = ... ! a large number | |

44 | -- x2 = ... ! another large number | |

45 | -- If ( x2 - x1 > Precision ) ... | |

46 | -- Precision in Cas.Cade | |

47 | -- Generally speaking, the precision criterion is not implicit in Cas.Cade. Low-level geometric algorithms accept | |

48 | -- precision criteria as arguments. As a rule, they should not refer directly to the precision criteria provided by the | |

49 | -- Precision package. | |

50 | -- On the other hand, high-level modeling algorithms have to provide the low-level geometric algorithms that they | |

51 | -- call, with a precision criteria. One way of doing this is to use the above precision criteria. | |

52 | -- Alternatively, the high-level algorithms can have their own system for precision management. For example, the | |

53 | -- Topology Data Structure stores precision criteria for each elementary shape (as a vertex, an edge or a face). When | |

54 | -- a new topological object is constructed, the precision criteria are taken from those provided by the Precision | |

55 | -- package, and stored in the related data structure. Later, a topological algorithm which analyses these objects will | |

56 | -- work with the values stored in the data structure. Also, if this algorithm is to build a new topological object, from | |

57 | -- these precision criteria, it will compute a new precision criterion for the new topological object, and write it into the | |

58 | -- data structure of the new topological object. | |

59 | -- The different precision criteria offered by the Precision package, cover the most common requirements of | |

60 | -- geometric algorithms, such as intersections, approximations, and so on. | |

61 | -- The choice of precision depends on the algorithm and on the geometric space. The geometric space may be : | |

62 | -- - a "real" 2D or 3D space, where the lengths are measured in meters, millimeters, microns, inches, etc ..., or | |

63 | -- - a "parametric" space, 1D on a curve or 2D on a surface, where lengths have no dimension. | |

64 | -- The choice of precision criteria for real space depends on the choice of the product, as it is based on the accuracy | |

65 | -- of the machine and the unit of measurement. | |

66 | -- The choice of precision criteria for parametric space depends on both the accuracy of the machine and the | |

67 | -- dimensions of the curve or the surface, since the parametric precision criterion and the real precision criterion are | |

68 | -- linked : if the curve is defined by the equation P(t), the inequation : | |

69 | -- Abs ( t2 - t1 ) < ParametricPrecision | |

70 | -- means that the parameters t1 and t2 are considered to be equal, and the inequation : | |

71 | -- Distance ( P(t2) , P(t1) ) < RealPrecision | |

72 | -- means that the points P(t1) and P(t2) are considered to be coincident. It seems to be the same idea, and it | |

73 | -- would be wonderful if these two inequations were equivalent. Note that this is rarely the case ! | |

74 | -- What is provided in this package? | |

75 | -- The Precision package provides : | |

76 | -- - a set of real space precision criteria for the algorithms, in view of checking distances and angles, | |

77 | -- - a set of parametric space precision criteria for the algorithms, in view of checking both : | |

78 | -- - the equality of parameters in a parametric space, | |

79 | -- - or the coincidence of points in the real space, by using parameter values, | |

80 | -- - the notion of infinite value, composed of a value assumed to be infinite, and checking tests designed to verify | |

81 | -- if any value could be considered as infinite. | |

82 | -- All the provided functions are very simple. The returned values result from the adaptation of the applications | |

83 | -- developed by the Open CASCADE company to Open CASCADE algorithms. The main interest of these functions | |

84 | -- lies in that it incites engineers developing applications to ask questions on precision factors. Which one is to be | |

85 | -- used in such or such case ? Tolerance criteria are context dependent. They must first choose : | |

86 | -- - either to work in real space, | |

87 | -- - or to work in parametric space, | |

88 | -- - or to work in a combined real and parametric space. | |

89 | -- They must next decide which precision factor will give the best answer to the current problem. Within an application | |

90 | -- environment, it is crucial to master precision even though this process may take a great deal of time. | |

91 | ||

92 | uses | |

93 | Standard | |

94 | ||

95 | is | |

96 | ||

97 | Angular returns Real from Standard; | |

98 | ---Purpose: Returns the recommended precision value | |

99 | -- when checking the equality of two angles (given in radians). | |

100 | -- Standard_Real Angle1 = ... , Angle2 = ... ; | |

101 | -- If ( Abs( Angle2 - Angle1 ) < Precision::Angular() ) ... | |

102 | -- The tolerance of angular equality may be used to check the parallelism of two vectors : | |

103 | -- gp_Vec V1, V2 ; | |

104 | -- V1 = ... | |

105 | -- V2 = ... | |

106 | -- If ( V1.IsParallel (V2, Precision::Angular() ) ) ... | |

107 | -- The tolerance of angular equality is equal to 1.e-12. | |

108 | -- Note : The tolerance of angular equality can be used when working with scalar products or | |

109 | -- cross products since sines and angles are equivalent for small angles. Therefore, in order to | |

110 | -- check whether two unit vectors are perpendicular : | |

111 | -- gp_Dir D1, D2 ; | |

112 | -- D1 = ... | |

113 | -- D2 = ... | |

114 | -- you can use : | |

115 | -- If ( Abs( D1.D2 ) < Precision::Angular() ) ... | |

116 | -- (although the function IsNormal does exist). | |

117 | ||

118 | Confusion returns Real from Standard; | |

119 | ---Purpose: | |

120 | -- Returns the recommended precision value when | |

121 | -- checking coincidence of two points in real space. | |

122 | -- The tolerance of confusion is used for testing a 3D | |

123 | -- distance : | |

124 | -- - Two points are considered to be coincident if their | |

125 | -- distance is smaller than the tolerance of confusion. | |

126 | -- gp_Pnt P1, P2 ; | |

127 | -- P1 = ... | |

128 | -- P2 = ... | |

129 | -- if ( P1.IsEqual ( P2 , Precision::Confusion() ) ) | |

130 | -- then ... | |

131 | -- - A vector is considered to be null if it has a null length : | |

132 | -- gp_Vec V ; | |

133 | -- V = ... | |

134 | -- if ( V.Magnitude() < Precision::Confusion() ) then ... | |

135 | -- The tolerance of confusion is equal to 1.e-7. | |

136 | -- The value of the tolerance of confusion is also used to | |

137 | -- define : | |

138 | -- - the tolerance of intersection, and | |

139 | -- - the tolerance of approximation. | |

140 | -- Note : As a rule, coordinate values in Cas.Cade are not | |

141 | -- dimensioned, so 1. represents one user unit, whatever | |

142 | -- value the unit may have : the millimeter, the meter, the | |

143 | -- inch, or any other unit. Let's say that Cas.Cade | |

144 | -- algorithms are written to be tuned essentially with | |

145 | -- mechanical design applications, on the basis of the | |

146 | -- millimeter. However, these algorithms may be used with | |

147 | -- any other unit but the tolerance criterion does no longer | |

148 | -- have the same signification. | |

149 | -- So pay particular attention to the type of your application, | |

150 | -- in relation with the impact of your unit on the precision criterion. | |

151 | -- - For example in mechanical design, if the unit is the | |

152 | -- millimeter, the tolerance of confusion corresponds to a | |

153 | -- distance of 1 / 10000 micron, which is rather difficult to measure. | |

154 | -- - However in other types of applications, such as | |

155 | -- cartography, where the kilometer is frequently used, | |

156 | -- the tolerance of confusion corresponds to a greater | |

157 | -- distance (1 / 10 millimeter). This distance | |

158 | -- becomes easily measurable, but only within a restricted | |

159 | -- space which contains some small objects of the complete scene. | |

160 | ||

08cd2f6b | 161 | SquareConfusion returns Real from Standard; |

162 | ---Purpose: | |

163 | -- Returns square of Confusion. | |

164 | -- Created for speed and convenience. | |

165 | ||

7fd59977 | 166 | Intersection returns Real from Standard; |

167 | ---Purpose:Returns the precision value in real space, frequently | |

168 | -- used by intersection algorithms to decide that a solution is reached. | |

169 | -- This function provides an acceptable level of precision | |

170 | -- for an intersection process to define the adjustment limits. | |

171 | -- The tolerance of intersection is designed to ensure | |

172 | -- that a point computed by an iterative algorithm as the | |

173 | -- intersection between two curves is indeed on the | |

174 | -- intersection. It is obvious that two tangent curves are | |

175 | -- close to each other, on a large distance. An iterative | |

176 | -- algorithm of intersection may find points on these | |

177 | -- curves within the scope of the confusion tolerance, but | |

178 | -- still far from the true intersection point. In order to force | |

179 | -- the intersection algorithm to continue the iteration | |

180 | -- process until a correct point is found on the tangent | |

181 | -- objects, the tolerance of intersection must be smaller | |

182 | -- than the tolerance of confusion. | |

183 | -- On the other hand, the tolerance of intersection must | |

184 | -- be large enough to minimize the time required by the | |

185 | -- process to converge to a solution. | |

186 | -- The tolerance of intersection is equal to : | |

187 | -- Precision::Confusion() / 100. | |

188 | -- (that is, 1.e-9). | |

189 | ||

190 | Approximation returns Real from Standard; | |

191 | ---Purpose: Returns the precision value in real space, frequently used | |

192 | -- by approximation algorithms. | |

193 | -- This function provides an acceptable level of precision for | |

194 | -- an approximation process to define adjustment limits. | |

195 | -- The tolerance of approximation is designed to ensure | |

196 | -- an acceptable computation time when performing an | |

197 | -- approximation process. That is why the tolerance of | |

198 | -- approximation is greater than the tolerance of confusion. | |

199 | -- The tolerance of approximation is equal to : | |

200 | -- Precision::Confusion() * 10. | |

201 | -- (that is, 1.e-6). | |

202 | -- You may use a smaller tolerance in an approximation | |

203 | -- algorithm, but this option might be costly. | |

204 | ||

205 | Parametric(P : Real from Standard; T : Real from Standard) | |

206 | returns Real from Standard; | |

207 | ---Purpose: Convert a real space precision to a parametric | |

208 | -- space precision. <T> is the mean value of the | |

209 | -- length of the tangent of the curve or the surface. | |

210 | -- | |

211 | -- Value is P / T | |

212 | -- | |

213 | ---C++: inline | |

214 | ||

215 | PConfusion(T : Real from Standard) returns Real from Standard; | |

216 | ---Purpose: | |

217 | -- Returns a precision value in parametric space, which may be used : | |

218 | -- - to test the coincidence of two points in the real space, | |

219 | -- by using parameter values, or | |

220 | -- - to test the equality of two parameter values in a parametric space. | |

221 | -- The parametric tolerance of confusion is designed to | |

222 | -- give a mean value in relation with the dimension of | |

223 | -- the curve or the surface. It considers that a variation of | |

224 | -- parameter equal to 1. along a curve (or an | |

225 | -- isoparametric curve of a surface) generates a segment | |

226 | -- whose length is equal to 100. (default value), or T. | |

227 | -- The parametric tolerance of confusion is equal to : | |

228 | -- - Precision::Confusion() / 100., or Precision::Confusion() / T. | |

229 | -- The value of the parametric tolerance of confusion is also used to define : | |

230 | -- - the parametric tolerance of intersection, and | |

231 | -- - the parametric tolerance of approximation. | |

232 | -- Warning | |

233 | -- It is rather difficult to define a unique precision value in parametric space. | |

234 | -- - First consider a curve (c) ; if M is the point of | |

235 | -- parameter u and M' the point of parameter u+du on | |

236 | -- the curve, call 'parametric tangent' at point M, for the | |

237 | -- variation du of the parameter, the quantity : | |

238 | -- T(u,du)=MM'/du (where MM' represents the | |

239 | -- distance between the two points M and M', in the real space). | |

240 | -- - Consider the other curve resulting from a scaling | |

241 | -- transformation of (c) with a scale factor equal to | |

242 | -- 10. The 'parametric tangent' at the point of | |

243 | -- parameter u of this curve is ten times greater than the | |

244 | -- previous one. This shows that for two different curves, | |

245 | -- the distance between two points on the curve, resulting | |

246 | -- from the same variation of parameter du, may vary considerably. | |

247 | -- - Moreover, the variation of the parameter along the | |

248 | -- curve is generally not proportional to the curvilinear | |

249 | -- abscissa along the curve. So the distance between two | |

250 | -- points resulting from the same variation of parameter | |

251 | -- du, at two different points of a curve, may completely differ. | |

252 | -- - Moreover, the parameterization of a surface may | |

253 | -- generate two quite different 'parametric tangent' values | |

254 | -- in the u or in the v parametric direction. | |

255 | -- - Last, close to the poles of a sphere (the points which | |

256 | -- correspond to the values -Pi/2. and Pi/2. of the | |

257 | -- v parameter) the u parameter may change from 0 to | |

258 | -- 2.Pi without impacting on the resulting point. | |

259 | -- Therefore, take great care when adjusting a parametric | |

260 | -- tolerance to your own algorithm. | |

261 | ||

262 | PIntersection(T : Real from Standard) returns Real from Standard; | |

263 | ---Purpose: | |

264 | -- Returns a precision value in parametric space, which | |

265 | -- may be used by intersection algorithms, to decide that | |

266 | -- a solution is reached. The purpose of this function is to | |

267 | -- provide an acceptable level of precision in parametric | |

268 | -- space, for an intersection process to define the adjustment limits. | |

269 | -- The parametric tolerance of intersection is | |

270 | -- designed to give a mean value in relation with the | |

271 | -- dimension of the curve or the surface. It considers | |

272 | -- that a variation of parameter equal to 1. along a curve | |

273 | -- (or an isoparametric curve of a surface) generates a | |

274 | -- segment whose length is equal to 100. (default value), or T. | |

275 | -- The parametric tolerance of intersection is equal to : | |

276 | -- - Precision::Intersection() / 100., or Precision::Intersection() / T. | |

277 | ||

278 | PApproximation(T : Real from Standard) returns Real from Standard; | |

279 | ---Purpose: Returns a precision value in parametric space, which may | |

280 | -- be used by approximation algorithms. The purpose of this | |

281 | -- function is to provide an acceptable level of precision in | |

282 | -- parametric space, for an approximation process to define | |

283 | -- the adjustment limits. | |

284 | -- The parametric tolerance of approximation is | |

285 | -- designed to give a mean value in relation with the | |

286 | -- dimension of the curve or the surface. It considers | |

287 | -- that a variation of parameter equal to 1. along a curve | |

288 | -- (or an isoparametric curve of a surface) generates a | |

289 | -- segment whose length is equal to 100. (default value), or T. | |

290 | -- The parametric tolerance of intersection is equal to : | |

291 | -- - Precision::Approximation() / 100., or Precision::Approximation() / T. | |

292 | ||

293 | Parametric(P : Real from Standard) | |

294 | returns Real from Standard; | |

295 | ---Purpose: Convert a real space precision to a parametric | |

296 | -- space precision on a default curve. | |

297 | -- | |

298 | -- Value is Parametric(P,1.e+2) | |

299 | -- | |

300 | ||

301 | PConfusion returns Real from Standard; | |

302 | ---Purpose: Used to test distances in parametric space on a | |

303 | -- default curve. | |

304 | -- | |

305 | -- This is Precision::Parametric(Precision::Confusion()) | |

306 | -- | |

307 | ---C++: inline | |

308 | ||

309 | PIntersection returns Real from Standard; | |

310 | ---Purpose: Used for Intersections in parametric space on a | |

311 | -- default curve. | |

312 | -- | |

313 | -- This is Precision::Parametric(Precision::Intersection()) | |

314 | -- | |

315 | ---C++: inline | |

316 | ||

317 | PApproximation returns Real from Standard; | |

318 | ---Purpose: Used for Approximations in parametric space on a | |

319 | -- default curve. | |

320 | -- | |

321 | -- This is Precision::Parametric(Precision::Approximation()) | |

322 | -- | |

323 | ---C++: inline | |

324 | ||

325 | IsInfinite(R : Real from Standard) returns Boolean; | |

326 | ---Purpose: Returns True if R may be considered as an infinite | |

327 | -- number. Currently Abs(R) > 1e100 | |

328 | ||

329 | IsPositiveInfinite(R : Real from Standard) returns Boolean; | |

330 | ---Purpose: Returns True if R may be considered as a positive | |

331 | -- infinite number. Currently R > 1e100 | |

332 | ||

333 | IsNegativeInfinite(R : Real from Standard) returns Boolean; | |

334 | ---Purpose: Returns True if R may be considered as a negative | |

335 | -- infinite number. Currently R < -1e100 | |

336 | ||

337 | ||

338 | Infinite returns Real; | |

339 | ---Purpose: Returns a big number that can be considered as | |

340 | -- infinite. Use -Infinite() for a negative big number. | |

341 | ||

342 | end Precision; | |

343 |