| 7fd59977 |
1 | -- File: LeastSquare.cdl |
| 2 | -- Created: Thu Jul 25 17:24:41 1991 |
| 3 | -- Author: Laurent PAINNOT |
| 4 | -- <lpa@topsn3> |
| 5 | ---Copyright: Matra Datavision 1991, 1992 |
| 6 | |
| 7 | |
| 8 | |
| 9 | generic class LeastSquare from AppParCurves |
| 10 | (MultiLine as any; |
| 11 | ToolLine as any) -- as ToolLine(MultiLine) |
| 12 | |
| 13 | |
| 14 | ---Purpose: This class describes the least square fitting of a |
| 15 | -- MultiLine using the Householder method from the |
| 16 | -- mathematical package. |
| 17 | -- The problem to solve is the following one: |
| 18 | -- minimizing the sum(|C(ui)- Qi|)2 where Qi are the points of |
| 19 | -- the MultiLine and C(ui) the points of the approximating |
| 20 | -- curves. |
| 21 | |
| 22 | |
| 23 | |
| 24 | uses Matrix from math, |
| 25 | Vector from math, |
| 26 | IntegerVector from math, |
| 27 | Constraint from AppParCurves, |
| 28 | MultiCurve from AppParCurves, |
| 29 | MultiBSpCurve from AppParCurves, |
| 30 | Array1OfInteger from TColStd, |
| 31 | Array1OfReal from TColStd, |
| 32 | HArray1OfInteger from TColStd, |
| 33 | HArray1OfReal from TColStd |
| 34 | |
| 35 | |
| 36 | raises NotDone from StdFail, |
| 37 | OutOfRange from Standard, |
| 38 | DimensionError from Standard, |
| 39 | NoSuchObject from Standard |
| 40 | |
| 41 | is |
| 42 | |
| 43 | Create(SSP: MultiLine; FirstPoint, LastPoint: Integer; |
| 44 | FirstCons, LastCons: Constraint; |
| 45 | Parameters: Vector from math; NbPol: Integer) |
| 46 | ---Purpose: given a MultiLine, this algorithm computes the least |
| 47 | -- square resolution using the Householder-QR method. |
| 48 | -- If the first and/or the last point is a constraint |
| 49 | -- point, the value of the tangency or curvature is |
| 50 | -- computed in the resolution. |
| 51 | -- NbPol is the number of control points wanted |
| 52 | -- for the approximating curves. |
| 53 | -- The system to solve is the following: |
| 54 | -- A X = B. |
| 55 | -- Where A is the Bernstein matrix computed with the |
| 56 | -- parameters, B the points coordinates and X the poles |
| 57 | -- solutions. |
| 58 | -- The matrix A is the same for each coordinate x, y and z |
| 59 | -- and is also the same for each MultiLine point because |
| 60 | -- they are approximated in parallel(so with the same |
| 61 | -- parameter, only the vector B changes). |
| 62 | |
| 63 | returns LeastSquare from AppParCurves |
| 64 | raises DimensionError from Standard; |
| 65 | |
| 66 | |
| 67 | |
| 68 | Create(SSP: MultiLine; FirstPoint, LastPoint: Integer; |
| 69 | FirstCons, LastCons: Constraint; NbPol: Integer) |
| 70 | ---Purpose: Initializes the fields of the object. |
| 71 | |
| 72 | returns LeastSquare; |
| 73 | |
| 74 | |
| 75 | Create(SSP: MultiLine; Knots: Array1OfReal; Mults: Array1OfInteger; |
| 76 | FirstPoint, LastPoint: Integer; |
| 77 | FirstCons, LastCons: Constraint; |
| 78 | Parameters: Vector from math; NbPol: Integer) |
| 79 | ---Purpose: given a MultiLine, this algorithm computes the least |
| 80 | -- square resolution using the Householder-QR method. |
| 81 | -- If the first and/or the last point is a constraint |
| 82 | -- point, the value of the tangency or curvature is |
| 83 | -- computed in the resolution. |
| 84 | -- Deg is the degree wanted for the approximating curves. |
| 85 | -- The system to solve is the following: |
| 86 | -- A X = B. |
| 87 | -- Where A is the BSpline functions matrix computed with |
| 88 | -- <parameters>, B the points coordinates and X the poles |
| 89 | -- solutions. |
| 90 | -- The matrix A is the same for each coordinate x, y and z |
| 91 | -- and is also the same for each MultiLine point because |
| 92 | -- they are approximated in parallel(so with the same |
| 93 | -- parameter, only the vector B changes). |
| 94 | |
| 95 | returns LeastSquare from AppParCurves |
| 96 | raises DimensionError from Standard; |
| 97 | |
| 98 | |
| 99 | |
| 100 | Create(SSP: MultiLine; Knots: Array1OfReal; Mults: Array1OfInteger; |
| 101 | FirstPoint, LastPoint: Integer; |
| 102 | FirstCons, LastCons: Constraint; NbPol: Integer) |
| 103 | ---Purpose: Initializes the fields of the object. |
| 104 | |
| 105 | returns LeastSquare; |
| 106 | |
| 107 | |
| 108 | |
| 109 | Init(me: in out; SSP: MultiLine; FirstPoint, LastPoint: Integer) |
| 110 | ---Purpose: is used by the constuctors above. |
| 111 | |
| 112 | is static protected; |
| 113 | |
| 114 | |
| 115 | Perform(me: in out; Parameters: Vector) |
| 116 | ---Purpose: Is used after having initialized the fields. |
| 117 | -- The case "CurvaturePoint" is not treated in this method. |
| 118 | |
| 119 | is static; |
| 120 | |
| 121 | |
| 122 | Perform(me: in out; Parameters: Vector; |
| 123 | l1, l2: Real) |
| 124 | ---Purpose: Is used after having initialized the fields. |
| 125 | |
| 126 | is static; |
| 127 | |
| 128 | |
| 129 | ---------------------------------------------------------------------- |
| 130 | -- for the two following methods, vectors <V> must be constructed |
| 131 | -- as follow: |
| 132 | -- V(v1x, v1y, v1z, ....., vnx, vny, vnz, v1x, v1y, ....., vmx, vmy) |
| 133 | -- 3d curve 3d curve 2d curve 2d curve |
| 134 | -- |
| 135 | -- the length of V must be Nb3dpoints*3 + Nb2dpoints*2 |
| 136 | |
| 137 | |
| 138 | Perform(me: in out; Parameters: Vector; |
| 139 | V1t, V2t: Vector; |
| 140 | l1, l2: Real) |
| 141 | ---Purpose: Is used after having initialized the fields. |
| 142 | --- <V1t> is the tangent vector at the first point. |
| 143 | --- <V2t> is the tangent vector at the last point. |
| 144 | is static; |
| 145 | |
| 146 | Perform(me: in out; Parameters: Vector; |
| 147 | V1t, V2t, V1c, V2c: Vector; |
| 148 | l1, l2: Real) |
| 149 | ---Purpose: Is used after having initialized the fields. |
| 150 | --- <V1t> is the tangent vector at the first point. |
| 151 | --- <V2t> is the tangent vector at the last point. |
| 152 | --- <V1c> is the tangent vector at the first point. |
| 153 | --- <V2c> is the tangent vector at the last point. |
| 154 | |
| 155 | is static; |
| 156 | |
| 157 | |
| 158 | ------------------------------- |
| 159 | --- Result methods: |
| 160 | ------------------------------- |
| 161 | |
| 162 | |
| 163 | IsDone(me) |
| 164 | ---Purpose: returns True if all has been correctly done. |
| 165 | |
| 166 | returns Boolean |
| 167 | is static; |
| 168 | |
| 169 | |
| 170 | BezierValue(me: in out) |
| 171 | ---Purpose: returns the result of the approximation, i.e. all the |
| 172 | -- Curves. |
| 173 | -- An exception is raised if NotDone. |
| 174 | |
| 175 | returns MultiCurve from AppParCurves |
| 176 | raises NotDone from StdFail, |
| 177 | NoSuchObject from Standard |
| 178 | is static; |
| 179 | |
| 180 | |
| 181 | BSplineValue(me: in out) |
| 182 | ---Purpose: returns the result of the approximation, i.e. all the |
| 183 | -- Curves. |
| 184 | -- An exception is raised if NotDone. |
| 185 | ---C++: return const & |
| 186 | |
| 187 | returns MultiBSpCurve from AppParCurves |
| 188 | raises NotDone from StdFail, |
| 189 | NoSuchObject from Standard |
| 190 | is static; |
| 191 | |
| 192 | |
| 193 | FunctionMatrix(me) |
| 194 | ---Purpose: returns the function matrix used to approximate the |
| 195 | -- set. |
| 196 | ---C++: return const & |
| 197 | |
| 198 | returns Matrix from math |
| 199 | raises NotDone from StdFail |
| 200 | is static; |
| 201 | |
| 202 | |
| 203 | |
| 204 | DerivativeFunctionMatrix(me) |
| 205 | ---Purpose: returns the derivative function matrix used |
| 206 | -- to approximate the set. |
| 207 | ---C++: return const & |
| 208 | |
| 209 | returns Matrix from math |
| 210 | raises NotDone from StdFail |
| 211 | is static; |
| 212 | |
| 213 | |
| 214 | ErrorGradient(me: in out; Grad: in out Vector; |
| 215 | F: in out Real; MaxE3d, MaxE2d: in out Real) |
| 216 | ---Purpose: returns the maximum errors between the MultiLine |
| 217 | -- and the approximation curves. F is the sum of the square |
| 218 | -- distances. Grad is the derivative vector of the |
| 219 | -- function F. |
| 220 | |
| 221 | is static; |
| 222 | |
| 223 | |
| 224 | Distance(me: in out) |
| 225 | ---Purpose: returns the distances between the points of the |
| 226 | -- multiline and the approximation curves. |
| 227 | ---C++: return const& |
| 228 | |
| 229 | returns Matrix from math |
| 230 | is static; |
| 231 | |
| 232 | |
| 233 | Error(me: in out; F: in out Real; |
| 234 | MaxE3d, MaxE2d: in out Real) |
| 235 | ---Purpose: returns the maximum errors between the MultiLine |
| 236 | -- and the approximation curves. F is the sum of the square |
| 237 | -- distances. |
| 238 | |
| 239 | is static; |
| 240 | |
| 241 | |
| 242 | FirstLambda(me) |
| 243 | ---Purpose: returns the value (P2 - P1)/ V1 if the first point |
| 244 | -- was a tangency point. |
| 245 | |
| 246 | returns Real |
| 247 | is static; |
| 248 | |
| 249 | |
| 250 | LastLambda(me) |
| 251 | ---Purpose: returns the value (PN - PN-1)/ VN if the last point |
| 252 | -- was a tangency point. |
| 253 | |
| 254 | returns Real |
| 255 | is static; |
| 256 | |
| 257 | |
| 258 | Points(me) |
| 259 | ---Purpose: returns the matrix of points value. |
| 260 | ---C++: return const& |
| 261 | |
| 262 | returns Matrix |
| 263 | is static; |
| 264 | |
| 265 | |
| 266 | Poles(me) |
| 267 | ---Purpose: returns the matrix of resulting control points value. |
| 268 | ---C++: return const& |
| 269 | |
| 270 | returns Matrix |
| 271 | is static; |
| 272 | |
| 273 | |
| 274 | KIndex(me) |
| 275 | ---Purpose: Returns the indexes of the first non null values of |
| 276 | -- A and DA. |
| 277 | -- The values are non null from Index(ieme point) +1 |
| 278 | -- to Index(ieme point) + degree +1. |
| 279 | ---C++: return const& |
| 280 | |
| 281 | returns IntegerVector |
| 282 | is static; |
| 283 | |
| 284 | |
| 285 | |
| 286 | ------------------------------- |
| 287 | --- internal methods: |
| 288 | ------------------------------- |
| 289 | |
| 290 | NbBColumns(me; SSP: MultiLine) |
| 291 | ---Purpose: returns the number of second member columns. |
| 292 | -- Is used internally to initialize the fields. |
| 293 | returns Integer |
| 294 | is static protected; |
| 295 | |
| 296 | |
| 297 | TheFirstPoint(me; FirstCons: Constraint; FirstPoint: Integer) |
| 298 | ---Purpose: returns the first point beeing fitted. |
| 299 | returns Integer |
| 300 | is static protected; |
| 301 | |
| 302 | |
| 303 | TheLastPoint(me; LastCons: Constraint; LastPoint: Integer) |
| 304 | ---Purpose: returns the last point beeing fitted. |
| 305 | returns Integer |
| 306 | is static protected; |
| 307 | |
| 308 | |
| 309 | Affect(me: in out; SSP: MultiLine; Index: Integer; |
| 310 | Cons: in out Constraint; Vt, Vc: in out Vector) |
| 311 | ---Purpose: Affects the fields in the case of a constraint point. |
| 312 | is static protected; |
| 313 | |
| 314 | |
| 315 | ComputeFunction(me: in out; Parameters: Vector) |
| 316 | ---Purpose: |
| 317 | is static protected; |
| 318 | |
| 319 | |
| 320 | SearchIndex(me: in out; Index: in out IntegerVector) |
| 321 | is static protected; |
| 322 | |
| 323 | |
| 324 | MakeTAA(me: in out; TheA, TheB: in out Vector) |
| 325 | ---Purpose: computes internal matrixes for the resolution |
| 326 | is static protected; |
| 327 | |
| 328 | MakeTAA(me: in out; TheA: in out Vector) |
| 329 | ---Purpose: computes internal matrixes for the resolution |
| 330 | is static protected; |
| 331 | |
| 332 | MakeTAA(me: in out; TheA: in out Vector; TheB: in out Matrix) |
| 333 | ---Purpose: computes internal matrixes for the resolution |
| 334 | is static protected; |
| 335 | |
| 336 | fields |
| 337 | |
| 338 | |
| 339 | FirstConstraint : Constraint from AppParCurves; |
| 340 | LastConstraint : Constraint from AppParCurves; |
| 341 | SCU: MultiBSpCurve from AppParCurves; |
| 342 | myknots: HArray1OfReal from TColStd; |
| 343 | mymults: HArray1OfInteger from TColStd; |
| 344 | mypoles: Matrix from math; |
| 345 | A: Matrix from math; |
| 346 | DA: Matrix from math; |
| 347 | B2: Matrix from math; |
| 348 | mypoints: Matrix from math; |
| 349 | Vflatknots: Vector from math; |
| 350 | Vec1t: Vector from math; |
| 351 | Vec1c: Vector from math; |
| 352 | Vec2t: Vector from math; |
| 353 | Vec2c: Vector from math; |
| 354 | theError: Matrix from math; |
| 355 | myindex: IntegerVector from math; |
| 356 | |
| 357 | ERR3d: Real; |
| 358 | ERR2d: Real; |
| 359 | lambda1: Real; |
| 360 | lambda2: Real; |
| 361 | |
| 362 | FirstP: Integer; |
| 363 | LastP: Integer; |
| 364 | Nlignes: Integer; |
| 365 | Ninc: Integer; |
| 366 | NA: Integer; |
| 367 | myfirstp: Integer; |
| 368 | mylastp: Integer; |
| 369 | resinit: Integer; |
| 370 | resfin: Integer; |
| 371 | nbP2d: Integer; |
| 372 | nbP: Integer; |
| 373 | |
| 374 | nbpoles: Integer; |
| 375 | deg: Integer; |
| 376 | |
| 377 | done: Boolean; |
| 378 | iscalculated : Boolean; |
| 379 | isready : Boolean; |
| 380 | end LeastSquare; |
| 381 | |
projects / occt.git / blame