| 1 | // Created on: 2015-09-21 |
| 2 | // Copyright (c) 2015 OPEN CASCADE SAS |
| 3 | // |
| 4 | // This file is part of Open CASCADE Technology software library. |
| 5 | // |
| 6 | // This library is free software; you can redistribute it and/or modify it under |
| 7 | // the terms of the GNU Lesser General Public License version 2.1 as published |
| 8 | // by the Free Software Foundation, with special exception defined in the file |
| 9 | // OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT |
| 10 | // distribution for complete text of the license and disclaimer of any warranty. |
| 11 | // |
| 12 | // Alternatively, this file may be used under the terms of Open CASCADE |
| 13 | // commercial license or contractual agreement. |
| 14 | |
| 15 | #include <GeomEvaluator_OffsetSurface.hxx> |
| 16 | |
| 17 | #include <GeomAdaptor_HSurface.hxx> |
| 18 | #include <CSLib.hxx> |
| 19 | #include <CSLib_NormalStatus.hxx> |
| 20 | #include <Geom_BezierSurface.hxx> |
| 21 | #include <Geom_BSplineSurface.hxx> |
| 22 | #include <Geom_UndefinedValue.hxx> |
| 23 | #include <GeomAdaptor_HSurface.hxx> |
| 24 | #include <gp_Vec.hxx> |
| 25 | #include <Standard_RangeError.hxx> |
| 26 | |
| 27 | |
| 28 | IMPLEMENT_STANDARD_RTTIEXT(GeomEvaluator_OffsetSurface,GeomEvaluator_Surface) |
| 29 | |
| 30 | template<class SurfOrAdapt> |
| 31 | static void derivatives(Standard_Integer theMaxOrder, |
| 32 | Standard_Integer theMinOrder, |
| 33 | const Standard_Real theU, |
| 34 | const Standard_Real theV, |
| 35 | const SurfOrAdapt& theBasisSurf, |
| 36 | const Standard_Integer theNU, |
| 37 | const Standard_Integer theNV, |
| 38 | const Standard_Boolean theAlongU, |
| 39 | const Standard_Boolean theAlongV, |
| 40 | const Handle(Geom_BSplineSurface)& theL, |
| 41 | TColgp_Array2OfVec& theDerNUV, |
| 42 | TColgp_Array2OfVec& theDerSurf); |
| 43 | |
| 44 | |
| 45 | |
| 46 | GeomEvaluator_OffsetSurface::GeomEvaluator_OffsetSurface( |
| 47 | const Handle(Geom_Surface)& theBase, |
| 48 | const Standard_Real theOffset, |
| 49 | const Handle(Geom_OsculatingSurface)& theOscSurf) |
| 50 | : GeomEvaluator_Surface(), |
| 51 | myBaseSurf(theBase), |
| 52 | myOffset(theOffset), |
| 53 | myOscSurf(theOscSurf) |
| 54 | { |
| 55 | if (!myOscSurf.IsNull()) |
| 56 | return; // osculating surface already exists |
| 57 | |
| 58 | // Create osculating surface for B-spline and Besier surfaces only |
| 59 | if (myBaseSurf->IsKind(STANDARD_TYPE(Geom_BSplineSurface)) || |
| 60 | myBaseSurf->IsKind(STANDARD_TYPE(Geom_BezierSurface))) |
| 61 | myOscSurf = new Geom_OsculatingSurface(myBaseSurf, Precision::Confusion()); |
| 62 | } |
| 63 | |
| 64 | GeomEvaluator_OffsetSurface::GeomEvaluator_OffsetSurface( |
| 65 | const Handle(GeomAdaptor_HSurface)& theBase, |
| 66 | const Standard_Real theOffset, |
| 67 | const Handle(Geom_OsculatingSurface)& theOscSurf) |
| 68 | : GeomEvaluator_Surface(), |
| 69 | myBaseAdaptor(theBase), |
| 70 | myOffset(theOffset), |
| 71 | myOscSurf(theOscSurf) |
| 72 | { |
| 73 | } |
| 74 | |
| 75 | void GeomEvaluator_OffsetSurface::D0( |
| 76 | const Standard_Real theU, const Standard_Real theV, gp_Pnt& theValue) const |
| 77 | { |
| 78 | gp_Vec aD1U, aD1V; |
| 79 | BaseD1(theU, theV, theValue, aD1U, aD1V); |
| 80 | CalculateD0(theU, theV, theValue, aD1U, aD1V); |
| 81 | } |
| 82 | |
| 83 | void GeomEvaluator_OffsetSurface::D1( |
| 84 | const Standard_Real theU, const Standard_Real theV, |
| 85 | gp_Pnt& theValue, gp_Vec& theD1U, gp_Vec& theD1V) const |
| 86 | { |
| 87 | gp_Vec aD2U, aD2V, aD2UV; |
| 88 | BaseD2(theU, theV, theValue, theD1U, theD1V, aD2U, aD2V, aD2UV); |
| 89 | CalculateD1(theU, theV, theValue, theD1U, theD1V, aD2U, aD2V, aD2UV); |
| 90 | } |
| 91 | |
| 92 | void GeomEvaluator_OffsetSurface::D2( |
| 93 | const Standard_Real theU, const Standard_Real theV, |
| 94 | gp_Pnt& theValue, gp_Vec& theD1U, gp_Vec& theD1V, |
| 95 | gp_Vec& theD2U, gp_Vec& theD2V, gp_Vec& theD2UV) const |
| 96 | { |
| 97 | gp_Vec aD3U, aD3V, aD3UUV, aD3UVV; |
| 98 | BaseD3(theU, theV, theValue, theD1U, theD1V, |
| 99 | theD2U, theD2V, theD2UV, aD3U, aD3V, aD3UUV, aD3UVV); |
| 100 | CalculateD2(theU, theV, theValue, theD1U, theD1V, |
| 101 | theD2U, theD2V, theD2UV, aD3U, aD3V, aD3UUV, aD3UVV); |
| 102 | } |
| 103 | |
| 104 | void GeomEvaluator_OffsetSurface::D3( |
| 105 | const Standard_Real theU, const Standard_Real theV, |
| 106 | gp_Pnt& theValue, gp_Vec& theD1U, gp_Vec& theD1V, |
| 107 | gp_Vec& theD2U, gp_Vec& theD2V, gp_Vec& theD2UV, |
| 108 | gp_Vec& theD3U, gp_Vec& theD3V, gp_Vec& theD3UUV, gp_Vec& theD3UVV) const |
| 109 | { |
| 110 | BaseD3(theU, theV, theValue, theD1U, theD1V, |
| 111 | theD2U, theD2V, theD2UV, theD3U, theD3V, theD3UUV, theD3UVV); |
| 112 | CalculateD3(theU, theV, theValue, theD1U, theD1V, |
| 113 | theD2U, theD2V, theD2UV, theD3U, theD3V, theD3UUV, theD3UVV); |
| 114 | } |
| 115 | |
| 116 | gp_Vec GeomEvaluator_OffsetSurface::DN( |
| 117 | const Standard_Real theU, const Standard_Real theV, |
| 118 | const Standard_Integer theDerU, const Standard_Integer theDerV) const |
| 119 | { |
| 120 | Standard_RangeError_Raise_if(theDerU < 0, "GeomEvaluator_OffsetSurface::DN(): theDerU < 0"); |
| 121 | Standard_RangeError_Raise_if(theDerV < 0, "GeomEvaluator_OffsetSurface::DN(): theDerV < 0"); |
| 122 | Standard_RangeError_Raise_if(theDerU + theDerV < 1, |
| 123 | "GeomEvaluator_OffsetSurface::DN(): theDerU + theDerV < 1"); |
| 124 | |
| 125 | gp_Pnt aP; |
| 126 | gp_Vec aD1U, aD1V; |
| 127 | BaseD1(theU, theV, aP, aD1U, aD1V); |
| 128 | return CalculateDN(theU, theV, theDerU, theDerV, aD1U, aD1V); |
| 129 | } |
| 130 | |
| 131 | |
| 132 | void GeomEvaluator_OffsetSurface::BaseD0(const Standard_Real theU, const Standard_Real theV, |
| 133 | gp_Pnt& theValue) const |
| 134 | { |
| 135 | if (!myBaseAdaptor.IsNull()) |
| 136 | myBaseAdaptor->D0(theU, theV, theValue); |
| 137 | else |
| 138 | myBaseSurf->D0(theU, theV, theValue); |
| 139 | } |
| 140 | |
| 141 | void GeomEvaluator_OffsetSurface::BaseD1(const Standard_Real theU, const Standard_Real theV, |
| 142 | gp_Pnt& theValue, gp_Vec& theD1U, gp_Vec& theD1V) const |
| 143 | { |
| 144 | if (!myBaseAdaptor.IsNull()) |
| 145 | myBaseAdaptor->D1(theU, theV, theValue, theD1U, theD1V); |
| 146 | else |
| 147 | myBaseSurf->D1(theU, theV, theValue, theD1U, theD1V); |
| 148 | } |
| 149 | |
| 150 | void GeomEvaluator_OffsetSurface::BaseD2(const Standard_Real theU, const Standard_Real theV, |
| 151 | gp_Pnt& theValue, gp_Vec& theD1U, gp_Vec& theD1V, |
| 152 | gp_Vec& theD2U, gp_Vec& theD2V, gp_Vec& theD2UV) const |
| 153 | { |
| 154 | if (!myBaseAdaptor.IsNull()) |
| 155 | myBaseAdaptor->D2(theU, theV, theValue, theD1U, theD1V, theD2U, theD2V, theD2UV); |
| 156 | else |
| 157 | myBaseSurf->D2(theU, theV, theValue, theD1U, theD1V, theD2U, theD2V, theD2UV); |
| 158 | } |
| 159 | |
| 160 | void GeomEvaluator_OffsetSurface::BaseD3( |
| 161 | const Standard_Real theU, const Standard_Real theV, |
| 162 | gp_Pnt& theValue, gp_Vec& theD1U, gp_Vec& theD1V, |
| 163 | gp_Vec& theD2U, gp_Vec& theD2V, gp_Vec& theD2UV, |
| 164 | gp_Vec& theD3U, gp_Vec& theD3V, gp_Vec& theD3UUV, gp_Vec& theD3UVV) const |
| 165 | { |
| 166 | if (!myBaseAdaptor.IsNull()) |
| 167 | myBaseAdaptor->D3(theU, theV, theValue, theD1U, theD1V, |
| 168 | theD2U, theD2V, theD2UV, theD3U, theD3V, theD3UUV, theD3UVV); |
| 169 | else |
| 170 | myBaseSurf->D3(theU, theV, theValue, theD1U, theD1V, |
| 171 | theD2U, theD2V, theD2UV, theD3U, theD3V, theD3UUV, theD3UVV); |
| 172 | } |
| 173 | |
| 174 | |
| 175 | void GeomEvaluator_OffsetSurface::CalculateD0( |
| 176 | const Standard_Real theU, const Standard_Real theV, |
| 177 | gp_Pnt& theValue, |
| 178 | const gp_Vec& theD1U, const gp_Vec& theD1V) const |
| 179 | { |
| 180 | const Standard_Real MagTol = 1.e-9; |
| 181 | |
| 182 | // Normalize derivatives before normal calculation because it gives more stable result. |
| 183 | // There will be normalized only derivatives greater than 1.0 to avoid differences in last significant digit |
| 184 | gp_Vec aD1U(theD1U); |
| 185 | gp_Vec aD1V(theD1V); |
| 186 | Standard_Real aD1UNorm2 = aD1U.SquareMagnitude(); |
| 187 | Standard_Real aD1VNorm2 = aD1V.SquareMagnitude(); |
| 188 | if (aD1UNorm2 > 1.0) |
| 189 | aD1U /= Sqrt(aD1UNorm2); |
| 190 | if (aD1VNorm2 > 1.0) |
| 191 | aD1V /= Sqrt(aD1VNorm2); |
| 192 | |
| 193 | gp_Vec aNorm = aD1U.Crossed(aD1V); |
| 194 | if (aNorm.SquareMagnitude() > MagTol * MagTol) |
| 195 | { |
| 196 | // Non singular case. Simple computations. |
| 197 | aNorm.Normalize(); |
| 198 | theValue.SetXYZ(theValue.XYZ() + myOffset * aNorm.XYZ()); |
| 199 | } |
| 200 | else |
| 201 | { |
| 202 | const Standard_Integer MaxOrder = 3; |
| 203 | |
| 204 | Handle(Geom_BSplineSurface) L; |
| 205 | Standard_Boolean isOpposite = Standard_False; |
| 206 | Standard_Boolean AlongU = Standard_False; |
| 207 | Standard_Boolean AlongV = Standard_False; |
| 208 | if (!myOscSurf.IsNull()) |
| 209 | { |
| 210 | AlongU = myOscSurf->UOscSurf(theU, theV, isOpposite, L); |
| 211 | AlongV = myOscSurf->VOscSurf(theU, theV, isOpposite, L); |
| 212 | } |
| 213 | const Standard_Real aSign = ((AlongV || AlongU) && isOpposite) ? -1. : 1.; |
| 214 | |
| 215 | TColgp_Array2OfVec DerNUV(0, MaxOrder, 0, MaxOrder); |
| 216 | TColgp_Array2OfVec DerSurf(0, MaxOrder + 1, 0, MaxOrder + 1); |
| 217 | Standard_Integer OrderU, OrderV; |
| 218 | Standard_Real Umin = 0, Umax = 0, Vmin = 0, Vmax = 0; |
| 219 | Bounds(Umin, Umax, Vmin, Vmax); |
| 220 | |
| 221 | DerSurf.SetValue(1, 0, theD1U); |
| 222 | DerSurf.SetValue(0, 1, theD1V); |
| 223 | if (!myBaseSurf.IsNull()) |
| 224 | derivatives(MaxOrder, 1, theU, theV, myBaseSurf, 0, 0, AlongU, AlongV, L, DerNUV, DerSurf); |
| 225 | else |
| 226 | derivatives(MaxOrder, 1, theU, theV, myBaseAdaptor, 0, 0, AlongU, AlongV, L, DerNUV, DerSurf); |
| 227 | |
| 228 | gp_Dir Normal; |
| 229 | CSLib_NormalStatus NStatus; |
| 230 | CSLib::Normal(MaxOrder, DerNUV, MagTol, theU, theV, Umin, Umax, Vmin, Vmax, |
| 231 | NStatus, Normal, OrderU, OrderV); |
| 232 | if (NStatus == CSLib_InfinityOfSolutions) |
| 233 | { |
| 234 | // Replace zero derivative and try to calculate normal |
| 235 | gp_Vec aNewDU = theD1U; |
| 236 | gp_Vec aNewDV = theD1V; |
| 237 | if (ReplaceDerivative(theU, theV, aNewDU, aNewDV, MagTol * MagTol)) |
| 238 | CSLib::Normal(aNewDU, aNewDV, MagTol, NStatus, Normal); |
| 239 | } |
| 240 | |
| 241 | if (NStatus != CSLib_Defined) |
| 242 | throw Geom_UndefinedValue( |
| 243 | "GeomEvaluator_OffsetSurface::CalculateD0(): Unable to calculate normal"); |
| 244 | |
| 245 | theValue.SetXYZ(theValue.XYZ() + myOffset * aSign * Normal.XYZ()); |
| 246 | } |
| 247 | } |
| 248 | |
| 249 | void GeomEvaluator_OffsetSurface::CalculateD1( |
| 250 | const Standard_Real theU, const Standard_Real theV, |
| 251 | gp_Pnt& theValue, gp_Vec& theD1U, gp_Vec& theD1V, |
| 252 | const gp_Vec& theD2U, const gp_Vec& theD2V, const gp_Vec& theD2UV) const |
| 253 | { |
| 254 | const Standard_Real MagTol = 1.e-9; |
| 255 | |
| 256 | // Check offset side. |
| 257 | Handle(Geom_BSplineSurface) L; |
| 258 | Standard_Boolean isOpposite = Standard_False; |
| 259 | Standard_Boolean AlongU = Standard_False; |
| 260 | Standard_Boolean AlongV = Standard_False; |
| 261 | |
| 262 | // Normalize derivatives before normal calculation because it gives more stable result. |
| 263 | // There will be normalized only derivatives greater than 1.0 to avoid differences in last significant digit |
| 264 | gp_Vec aD1U(theD1U); |
| 265 | gp_Vec aD1V(theD1V); |
| 266 | Standard_Real aD1UNorm2 = aD1U.SquareMagnitude(); |
| 267 | Standard_Real aD1VNorm2 = aD1V.SquareMagnitude(); |
| 268 | if (aD1UNorm2 > 1.0) |
| 269 | aD1U /= Sqrt(aD1UNorm2); |
| 270 | if (aD1VNorm2 > 1.0) |
| 271 | aD1V /= Sqrt(aD1VNorm2); |
| 272 | |
| 273 | Standard_Boolean isSingular = Standard_False; |
| 274 | Standard_Integer MaxOrder = 0; |
| 275 | gp_Vec aNorm = aD1U.Crossed(aD1V); |
| 276 | if (aNorm.SquareMagnitude() <= MagTol * MagTol) |
| 277 | { |
| 278 | if (!myOscSurf.IsNull()) |
| 279 | { |
| 280 | AlongU = myOscSurf->UOscSurf(theU, theV, isOpposite, L); |
| 281 | AlongV = myOscSurf->VOscSurf(theU, theV, isOpposite, L); |
| 282 | } |
| 283 | |
| 284 | MaxOrder = 3; |
| 285 | isSingular = Standard_True; |
| 286 | } |
| 287 | |
| 288 | const Standard_Real aSign = ((AlongV || AlongU) && isOpposite) ? -1. : 1.; |
| 289 | |
| 290 | if (!isSingular) |
| 291 | { |
| 292 | // AlongU or AlongV leads to more complex D1 computation |
| 293 | // Try to compute D0 and D1 much simpler |
| 294 | aNorm.Normalize(); |
| 295 | theValue.SetXYZ(theValue.XYZ() + myOffset * aSign * aNorm.XYZ()); |
| 296 | |
| 297 | gp_Vec aN0(aNorm.XYZ()), aN1U, aN1V; |
| 298 | Standard_Real aScale = (theD1U^theD1V).Dot(aN0); |
| 299 | aN1U.SetX(theD2U.Y() * theD1V.Z() + theD1U.Y() * theD2UV.Z() |
| 300 | - theD2U.Z() * theD1V.Y() - theD1U.Z() * theD2UV.Y()); |
| 301 | aN1U.SetY((theD2U.X() * theD1V.Z() + theD1U.X() * theD2UV.Z() |
| 302 | - theD2U.Z() * theD1V.X() - theD1U.Z() * theD2UV.X()) * -1.0); |
| 303 | aN1U.SetZ(theD2U.X() * theD1V.Y() + theD1U.X() * theD2UV.Y() |
| 304 | - theD2U.Y() * theD1V.X() - theD1U.Y() * theD2UV.X()); |
| 305 | Standard_Real aScaleU = aN1U.Dot(aN0); |
| 306 | aN1U.Subtract(aScaleU * aN0); |
| 307 | aN1U /= aScale; |
| 308 | |
| 309 | aN1V.SetX(theD2UV.Y() * theD1V.Z() + theD2V.Z() * theD1U.Y() |
| 310 | - theD2UV.Z() * theD1V.Y() - theD2V.Y() * theD1U.Z()); |
| 311 | aN1V.SetY((theD2UV.X() * theD1V.Z() + theD2V.Z() * theD1U.X() |
| 312 | - theD2UV.Z() * theD1V.X() - theD2V.X() * theD1U.Z()) * -1.0); |
| 313 | aN1V.SetZ(theD2UV.X() * theD1V.Y() + theD2V.Y() * theD1U.X() |
| 314 | - theD2UV.Y() * theD1V.X() - theD2V.X() * theD1U.Y()); |
| 315 | Standard_Real aScaleV = aN1V.Dot(aN0); |
| 316 | aN1V.Subtract(aScaleV * aN0); |
| 317 | aN1V /= aScale; |
| 318 | |
| 319 | theD1U += myOffset * aSign * aN1U; |
| 320 | theD1V += myOffset * aSign * aN1V; |
| 321 | |
| 322 | return; |
| 323 | } |
| 324 | |
| 325 | Standard_Integer OrderU, OrderV; |
| 326 | TColgp_Array2OfVec DerNUV(0, MaxOrder + 1, 0, MaxOrder + 1); |
| 327 | TColgp_Array2OfVec DerSurf(0, MaxOrder + 2, 0, MaxOrder + 2); |
| 328 | Standard_Real Umin = 0, Umax = 0, Vmin = 0, Vmax = 0; |
| 329 | Bounds(Umin, Umax, Vmin, Vmax); |
| 330 | |
| 331 | DerSurf.SetValue(1, 0, theD1U); |
| 332 | DerSurf.SetValue(0, 1, theD1V); |
| 333 | DerSurf.SetValue(1, 1, theD2UV); |
| 334 | DerSurf.SetValue(2, 0, theD2U); |
| 335 | DerSurf.SetValue(0, 2, theD2V); |
| 336 | if (!myBaseSurf.IsNull()) |
| 337 | derivatives(MaxOrder, 2, theU, theV, myBaseSurf, 1, 1, AlongU, AlongV, L, DerNUV, DerSurf); |
| 338 | else |
| 339 | derivatives(MaxOrder, 2, theU, theV, myBaseAdaptor, 1, 1, AlongU, AlongV, L, DerNUV, DerSurf); |
| 340 | |
| 341 | gp_Dir Normal; |
| 342 | CSLib_NormalStatus NStatus; |
| 343 | CSLib::Normal(MaxOrder, DerNUV, MagTol, theU, theV, Umin, Umax, Vmin, Vmax, NStatus, Normal, OrderU, OrderV); |
| 344 | if (NStatus == CSLib_InfinityOfSolutions) |
| 345 | { |
| 346 | gp_Vec aNewDU = theD1U; |
| 347 | gp_Vec aNewDV = theD1V; |
| 348 | // Replace zero derivative and try to calculate normal |
| 349 | if (ReplaceDerivative(theU, theV, aNewDU, aNewDV, MagTol * MagTol)) |
| 350 | { |
| 351 | DerSurf.SetValue(1, 0, aNewDU); |
| 352 | DerSurf.SetValue(0, 1, aNewDV); |
| 353 | if (!myBaseSurf.IsNull()) |
| 354 | derivatives(MaxOrder, 2, theU, theV, myBaseSurf, 1, 1, AlongU, AlongV, L, DerNUV, DerSurf); |
| 355 | else |
| 356 | derivatives(MaxOrder, 2, theU, theV, myBaseAdaptor, 1, 1, AlongU, AlongV, L, DerNUV, DerSurf); |
| 357 | CSLib::Normal(MaxOrder, DerNUV, MagTol, theU, theV, Umin, Umax, Vmin, Vmax, |
| 358 | NStatus, Normal, OrderU, OrderV); |
| 359 | } |
| 360 | } |
| 361 | |
| 362 | if (NStatus != CSLib_Defined) |
| 363 | throw Geom_UndefinedValue( |
| 364 | "GeomEvaluator_OffsetSurface::CalculateD1(): Unable to calculate normal"); |
| 365 | |
| 366 | theValue.SetXYZ(theValue.XYZ() + myOffset * aSign * Normal.XYZ()); |
| 367 | |
| 368 | theD1U = DerSurf(1, 0) + myOffset * aSign * CSLib::DNNormal(1, 0, DerNUV, OrderU, OrderV); |
| 369 | theD1V = DerSurf(0, 1) + myOffset * aSign * CSLib::DNNormal(0, 1, DerNUV, OrderU, OrderV); |
| 370 | } |
| 371 | |
| 372 | void GeomEvaluator_OffsetSurface::CalculateD2( |
| 373 | const Standard_Real theU, const Standard_Real theV, |
| 374 | gp_Pnt& theValue, gp_Vec& theD1U, gp_Vec& theD1V, |
| 375 | gp_Vec& theD2U, gp_Vec& theD2V, gp_Vec& theD2UV, |
| 376 | const gp_Vec& theD3U, const gp_Vec& theD3V, const gp_Vec& theD3UUV, const gp_Vec& theD3UVV) const |
| 377 | { |
| 378 | const Standard_Real MagTol = 1.e-9; |
| 379 | |
| 380 | gp_Dir Normal; |
| 381 | CSLib_NormalStatus NStatus; |
| 382 | CSLib::Normal(theD1U, theD1V, MagTol, NStatus, Normal); |
| 383 | |
| 384 | const Standard_Integer MaxOrder = (NStatus == CSLib_Defined) ? 0 : 3; |
| 385 | Standard_Integer OrderU, OrderV; |
| 386 | TColgp_Array2OfVec DerNUV(0, MaxOrder + 2, 0, MaxOrder + 2); |
| 387 | TColgp_Array2OfVec DerSurf(0, MaxOrder + 3, 0, MaxOrder + 3); |
| 388 | |
| 389 | Standard_Real Umin = 0, Umax = 0, Vmin = 0, Vmax = 0; |
| 390 | Bounds(Umin, Umax, Vmin, Vmax); |
| 391 | |
| 392 | DerSurf.SetValue(1, 0, theD1U); |
| 393 | DerSurf.SetValue(0, 1, theD1V); |
| 394 | DerSurf.SetValue(1, 1, theD2UV); |
| 395 | DerSurf.SetValue(2, 0, theD2U); |
| 396 | DerSurf.SetValue(0, 2, theD2V); |
| 397 | DerSurf.SetValue(3, 0, theD3U); |
| 398 | DerSurf.SetValue(2, 1, theD3UUV); |
| 399 | DerSurf.SetValue(1, 2, theD3UVV); |
| 400 | DerSurf.SetValue(0, 3, theD3V); |
| 401 | //********************* |
| 402 | |
| 403 | Handle(Geom_BSplineSurface) L; |
| 404 | Standard_Boolean isOpposite = Standard_False; |
| 405 | Standard_Boolean AlongU = Standard_False; |
| 406 | Standard_Boolean AlongV = Standard_False; |
| 407 | if ((NStatus != CSLib_Defined) && !myOscSurf.IsNull()) |
| 408 | { |
| 409 | AlongU = myOscSurf->UOscSurf(theU, theV, isOpposite, L); |
| 410 | AlongV = myOscSurf->VOscSurf(theU, theV, isOpposite, L); |
| 411 | } |
| 412 | const Standard_Real aSign = ((AlongV || AlongU) && isOpposite) ? -1. : 1.; |
| 413 | |
| 414 | if (!myBaseSurf.IsNull()) |
| 415 | derivatives(MaxOrder, 3, theU, theV, myBaseSurf, 2, 2, AlongU, AlongV, L, DerNUV, DerSurf); |
| 416 | else |
| 417 | derivatives(MaxOrder, 3, theU, theV, myBaseAdaptor, 2, 2, AlongU, AlongV, L, DerNUV, DerSurf); |
| 418 | |
| 419 | CSLib::Normal(MaxOrder, DerNUV, MagTol, theU, theV, Umin, Umax, Vmin, Vmax, |
| 420 | NStatus, Normal, OrderU, OrderV); |
| 421 | if (NStatus != CSLib_Defined) |
| 422 | throw Geom_UndefinedValue( |
| 423 | "GeomEvaluator_OffsetSurface::CalculateD2(): Unable to calculate normal"); |
| 424 | |
| 425 | theValue.SetXYZ(theValue.XYZ() + myOffset * aSign * Normal.XYZ()); |
| 426 | |
| 427 | theD1U = DerSurf(1, 0) + myOffset * aSign * CSLib::DNNormal(1, 0, DerNUV, OrderU, OrderV); |
| 428 | theD1V = DerSurf(0, 1) + myOffset * aSign * CSLib::DNNormal(0, 1, DerNUV, OrderU, OrderV); |
| 429 | |
| 430 | if (!myBaseSurf.IsNull()) |
| 431 | { |
| 432 | theD2U = myBaseSurf->DN(theU, theV, 2, 0); |
| 433 | theD2V = myBaseSurf->DN(theU, theV, 0, 2); |
| 434 | theD2UV = myBaseSurf->DN(theU, theV, 1, 1); |
| 435 | } |
| 436 | else |
| 437 | { |
| 438 | theD2U = myBaseAdaptor->DN(theU, theV, 2, 0); |
| 439 | theD2V = myBaseAdaptor->DN(theU, theV, 0, 2); |
| 440 | theD2UV = myBaseAdaptor->DN(theU, theV, 1, 1); |
| 441 | } |
| 442 | |
| 443 | theD2U += aSign * myOffset * CSLib::DNNormal(2, 0, DerNUV, OrderU, OrderV); |
| 444 | theD2V += aSign * myOffset * CSLib::DNNormal(0, 2, DerNUV, OrderU, OrderV); |
| 445 | theD2UV += aSign * myOffset * CSLib::DNNormal(1, 1, DerNUV, OrderU, OrderV); |
| 446 | } |
| 447 | |
| 448 | void GeomEvaluator_OffsetSurface::CalculateD3( |
| 449 | const Standard_Real theU, const Standard_Real theV, |
| 450 | gp_Pnt& theValue, gp_Vec& theD1U, gp_Vec& theD1V, |
| 451 | gp_Vec& theD2U, gp_Vec& theD2V, gp_Vec& theD2UV, |
| 452 | gp_Vec& theD3U, gp_Vec& theD3V, gp_Vec& theD3UUV, gp_Vec& theD3UVV) const |
| 453 | { |
| 454 | const Standard_Real MagTol = 1.e-9; |
| 455 | |
| 456 | gp_Dir Normal; |
| 457 | CSLib_NormalStatus NStatus; |
| 458 | CSLib::Normal(theD1U, theD1V, MagTol, NStatus, Normal); |
| 459 | const Standard_Integer MaxOrder = (NStatus == CSLib_Defined) ? 0 : 3; |
| 460 | Standard_Integer OrderU, OrderV; |
| 461 | TColgp_Array2OfVec DerNUV(0, MaxOrder + 3, 0, MaxOrder + 3); |
| 462 | TColgp_Array2OfVec DerSurf(0, MaxOrder + 4, 0, MaxOrder + 4); |
| 463 | Standard_Real Umin = 0, Umax = 0, Vmin = 0, Vmax = 0; |
| 464 | Bounds(Umin, Umax, Vmin, Vmax); |
| 465 | |
| 466 | DerSurf.SetValue(1, 0, theD1U); |
| 467 | DerSurf.SetValue(0, 1, theD1V); |
| 468 | DerSurf.SetValue(1, 1, theD2UV); |
| 469 | DerSurf.SetValue(2, 0, theD2U); |
| 470 | DerSurf.SetValue(0, 2, theD2V); |
| 471 | DerSurf.SetValue(3, 0, theD3U); |
| 472 | DerSurf.SetValue(2, 1, theD3UUV); |
| 473 | DerSurf.SetValue(1, 2, theD3UVV); |
| 474 | DerSurf.SetValue(0, 3, theD3V); |
| 475 | |
| 476 | |
| 477 | //********************* |
| 478 | Handle(Geom_BSplineSurface) L; |
| 479 | Standard_Boolean isOpposite = Standard_False; |
| 480 | Standard_Boolean AlongU = Standard_False; |
| 481 | Standard_Boolean AlongV = Standard_False; |
| 482 | if ((NStatus != CSLib_Defined) && !myOscSurf.IsNull()) |
| 483 | { |
| 484 | AlongU = myOscSurf->UOscSurf(theU, theV, isOpposite, L); |
| 485 | AlongV = myOscSurf->VOscSurf(theU, theV, isOpposite, L); |
| 486 | } |
| 487 | const Standard_Real aSign = ((AlongV || AlongU) && isOpposite) ? -1. : 1.; |
| 488 | |
| 489 | if (!myBaseSurf.IsNull()) |
| 490 | derivatives(MaxOrder, 3, theU, theV, myBaseSurf, 3, 3, AlongU, AlongV, L, DerNUV, DerSurf); |
| 491 | else |
| 492 | derivatives(MaxOrder, 3, theU, theV, myBaseAdaptor, 3, 3, AlongU, AlongV, L, DerNUV, DerSurf); |
| 493 | |
| 494 | CSLib::Normal(MaxOrder, DerNUV, MagTol, theU, theV, Umin, Umax, Vmin, Vmax, |
| 495 | NStatus, Normal, OrderU, OrderV); |
| 496 | if (NStatus != CSLib_Defined) |
| 497 | throw Geom_UndefinedValue( |
| 498 | "GeomEvaluator_OffsetSurface::CalculateD3(): Unable to calculate normal"); |
| 499 | |
| 500 | theValue.SetXYZ(theValue.XYZ() + myOffset * aSign * Normal.XYZ()); |
| 501 | |
| 502 | theD1U = DerSurf(1, 0) + myOffset * aSign * CSLib::DNNormal(1, 0, DerNUV, OrderU, OrderV); |
| 503 | theD1V = DerSurf(0, 1) + myOffset * aSign * CSLib::DNNormal(0, 1, DerNUV, OrderU, OrderV); |
| 504 | |
| 505 | if (!myBaseSurf.IsNull()) |
| 506 | { |
| 507 | theD2U = myBaseSurf->DN(theU, theV, 2, 0); |
| 508 | theD2V = myBaseSurf->DN(theU, theV, 0, 2); |
| 509 | theD2UV = myBaseSurf->DN(theU, theV, 1, 1); |
| 510 | theD3U = myBaseSurf->DN(theU, theV, 3, 0); |
| 511 | theD3V = myBaseSurf->DN(theU, theV, 0, 3); |
| 512 | theD3UUV = myBaseSurf->DN(theU, theV, 2, 1); |
| 513 | theD3UVV = myBaseSurf->DN(theU, theV, 1, 2); |
| 514 | } |
| 515 | else |
| 516 | { |
| 517 | theD2U = myBaseAdaptor->DN(theU, theV, 2, 0); |
| 518 | theD2V = myBaseAdaptor->DN(theU, theV, 0, 2); |
| 519 | theD2UV = myBaseAdaptor->DN(theU, theV, 1, 1); |
| 520 | theD3U = myBaseAdaptor->DN(theU, theV, 3, 0); |
| 521 | theD3V = myBaseAdaptor->DN(theU, theV, 0, 3); |
| 522 | theD3UUV = myBaseAdaptor->DN(theU, theV, 2, 1); |
| 523 | theD3UVV = myBaseAdaptor->DN(theU, theV, 1, 2); |
| 524 | } |
| 525 | |
| 526 | theD2U += aSign * myOffset * CSLib::DNNormal(2, 0, DerNUV, OrderU, OrderV); |
| 527 | theD2V += aSign * myOffset * CSLib::DNNormal(0, 2, DerNUV, OrderU, OrderV); |
| 528 | theD2UV += aSign * myOffset * CSLib::DNNormal(1, 1, DerNUV, OrderU, OrderV); |
| 529 | theD3U += aSign * myOffset * CSLib::DNNormal(3, 0, DerNUV, OrderU, OrderV); |
| 530 | theD3V += aSign * myOffset * CSLib::DNNormal(0, 3, DerNUV, OrderU, OrderV); |
| 531 | theD3UUV += aSign * myOffset * CSLib::DNNormal(2, 1, DerNUV, OrderU, OrderV); |
| 532 | theD3UVV += aSign * myOffset * CSLib::DNNormal(1, 2, DerNUV, OrderU, OrderV); |
| 533 | } |
| 534 | |
| 535 | gp_Vec GeomEvaluator_OffsetSurface::CalculateDN( |
| 536 | const Standard_Real theU, const Standard_Real theV, |
| 537 | const Standard_Integer theNu, const Standard_Integer theNv, |
| 538 | const gp_Vec& theD1U, const gp_Vec& theD1V) const |
| 539 | { |
| 540 | const Standard_Real MagTol = 1.e-9; |
| 541 | |
| 542 | gp_Dir Normal; |
| 543 | CSLib_NormalStatus NStatus; |
| 544 | CSLib::Normal(theD1U, theD1V, MagTol, NStatus, Normal); |
| 545 | const Standard_Integer MaxOrder = (NStatus == CSLib_Defined) ? 0 : 3; |
| 546 | Standard_Integer OrderU, OrderV; |
| 547 | TColgp_Array2OfVec DerNUV(0, MaxOrder + theNu, 0, MaxOrder + theNu); |
| 548 | TColgp_Array2OfVec DerSurf(0, MaxOrder + theNu + 1, 0, MaxOrder + theNv + 1); |
| 549 | |
| 550 | Standard_Real Umin = 0, Umax = 0, Vmin = 0, Vmax = 0; |
| 551 | Bounds(Umin, Umax, Vmin, Vmax); |
| 552 | |
| 553 | DerSurf.SetValue(1, 0, theD1U); |
| 554 | DerSurf.SetValue(0, 1, theD1V); |
| 555 | |
| 556 | //********************* |
| 557 | Handle(Geom_BSplineSurface) L; |
| 558 | // Is there any osculatingsurface along U or V; |
| 559 | Standard_Boolean isOpposite = Standard_False; |
| 560 | Standard_Boolean AlongU = Standard_False; |
| 561 | Standard_Boolean AlongV = Standard_False; |
| 562 | if ((NStatus != CSLib_Defined) && !myOscSurf.IsNull()) |
| 563 | { |
| 564 | AlongU = myOscSurf->UOscSurf(theU, theV, isOpposite, L); |
| 565 | AlongV = myOscSurf->VOscSurf(theU, theV, isOpposite, L); |
| 566 | } |
| 567 | const Standard_Real aSign = ((AlongV || AlongU) && isOpposite) ? -1. : 1.; |
| 568 | |
| 569 | if (!myBaseSurf.IsNull()) |
| 570 | derivatives(MaxOrder, 1, theU, theV, myBaseSurf, theNu, theNv, AlongU, AlongV, L, DerNUV, DerSurf); |
| 571 | else |
| 572 | derivatives(MaxOrder, 1, theU, theV, myBaseAdaptor, theNu, theNv, AlongU, AlongV, L, DerNUV, DerSurf); |
| 573 | |
| 574 | CSLib::Normal(MaxOrder, DerNUV, MagTol, theU, theV, Umin, Umax, Vmin, Vmax, |
| 575 | NStatus, Normal, OrderU, OrderV); |
| 576 | if (NStatus != CSLib_Defined) |
| 577 | throw Geom_UndefinedValue( |
| 578 | "GeomEvaluator_OffsetSurface::CalculateDN(): Unable to calculate normal"); |
| 579 | |
| 580 | gp_Vec D; |
| 581 | if (!myBaseSurf.IsNull()) |
| 582 | D = myBaseSurf->DN(theU, theV, theNu, theNv); |
| 583 | else |
| 584 | D = myBaseAdaptor->DN(theU, theV, theNu, theNv); |
| 585 | |
| 586 | D += aSign * myOffset * CSLib::DNNormal(theNu, theNv, DerNUV, OrderU, OrderV); |
| 587 | return D; |
| 588 | } |
| 589 | |
| 590 | |
| 591 | void GeomEvaluator_OffsetSurface::Bounds(Standard_Real& theUMin, Standard_Real& theUMax, |
| 592 | Standard_Real& theVMin, Standard_Real& theVMax) const |
| 593 | { |
| 594 | if (!myBaseSurf.IsNull()) |
| 595 | myBaseSurf->Bounds(theUMin, theUMax, theVMin, theVMax); |
| 596 | else |
| 597 | { |
| 598 | theUMin = myBaseAdaptor->FirstUParameter(); |
| 599 | theUMax = myBaseAdaptor->LastUParameter(); |
| 600 | theVMin = myBaseAdaptor->FirstVParameter(); |
| 601 | theVMax = myBaseAdaptor->LastVParameter(); |
| 602 | } |
| 603 | } |
| 604 | |
| 605 | |
| 606 | Standard_Boolean GeomEvaluator_OffsetSurface::ReplaceDerivative( |
| 607 | const Standard_Real theU, const Standard_Real theV, |
| 608 | gp_Vec& theDU, gp_Vec& theDV, |
| 609 | const Standard_Real theSquareTol) const |
| 610 | { |
| 611 | Standard_Boolean isReplaceDU = theDU.SquareMagnitude() < theSquareTol; |
| 612 | Standard_Boolean isReplaceDV = theDV.SquareMagnitude() < theSquareTol; |
| 613 | Standard_Boolean isReplaced = Standard_False; |
| 614 | if (isReplaceDU ^ isReplaceDV) |
| 615 | { |
| 616 | Standard_Real aU = theU; |
| 617 | Standard_Real aV = theV; |
| 618 | Standard_Real aUMin = 0, aUMax = 0, aVMin = 0, aVMax = 0; |
| 619 | Bounds(aUMin, aUMax, aVMin, aVMax); |
| 620 | |
| 621 | // Calculate step along non-zero derivative |
| 622 | Standard_Real aStep; |
| 623 | Handle(Adaptor3d_HSurface) aSurfAdapt; |
| 624 | if (!myBaseAdaptor.IsNull()) |
| 625 | aSurfAdapt = myBaseAdaptor; |
| 626 | else |
| 627 | aSurfAdapt = new GeomAdaptor_HSurface(myBaseSurf); |
| 628 | if (isReplaceDV) |
| 629 | { |
| 630 | aStep = Precision::Confusion() * theDU.Magnitude(); |
| 631 | if (aStep > aUMax - aUMin) |
| 632 | aStep = (aUMax - aUMin) / 100.; |
| 633 | } |
| 634 | else |
| 635 | { |
| 636 | aStep = Precision::Confusion() * theDV.Magnitude(); |
| 637 | if (aStep > aVMax - aVMin) |
| 638 | aStep = (aVMax - aVMin) / 100.; |
| 639 | } |
| 640 | |
| 641 | gp_Pnt aP; |
| 642 | gp_Vec aDU, aDV; |
| 643 | // Step away from currect parametric coordinates and calculate derivatives once again. |
| 644 | // Replace zero derivative by the obtained. |
| 645 | for (Standard_Real aStepSign = -1.0; aStepSign <= 1.0 && !isReplaced; aStepSign += 2.0) |
| 646 | { |
| 647 | if (isReplaceDV) |
| 648 | { |
| 649 | aU = theU + aStepSign * aStep; |
| 650 | if (aU < aUMin || aU > aUMax) |
| 651 | continue; |
| 652 | } |
| 653 | else |
| 654 | { |
| 655 | aV = theV + aStepSign * aStep; |
| 656 | if (aV < aVMin || aV > aVMax) |
| 657 | continue; |
| 658 | } |
| 659 | |
| 660 | BaseD1(aU, aV, aP, aDU, aDV); |
| 661 | |
| 662 | if (isReplaceDU && aDU.SquareMagnitude() > theSquareTol) |
| 663 | { |
| 664 | theDU = aDU; |
| 665 | isReplaced = Standard_True; |
| 666 | } |
| 667 | if (isReplaceDV && aDV.SquareMagnitude() > theSquareTol) |
| 668 | { |
| 669 | theDV = aDV; |
| 670 | isReplaced = Standard_True; |
| 671 | } |
| 672 | } |
| 673 | } |
| 674 | return isReplaced; |
| 675 | } |
| 676 | |
| 677 | |
| 678 | |
| 679 | |
| 680 | |
| 681 | // ===================== Auxiliary functions =================================== |
| 682 | template<class SurfOrAdapt> |
| 683 | void derivatives(Standard_Integer theMaxOrder, |
| 684 | Standard_Integer theMinOrder, |
| 685 | const Standard_Real theU, |
| 686 | const Standard_Real theV, |
| 687 | const SurfOrAdapt& theBasisSurf, |
| 688 | const Standard_Integer theNU, |
| 689 | const Standard_Integer theNV, |
| 690 | const Standard_Boolean theAlongU, |
| 691 | const Standard_Boolean theAlongV, |
| 692 | const Handle(Geom_BSplineSurface)& theL, |
| 693 | TColgp_Array2OfVec& theDerNUV, |
| 694 | TColgp_Array2OfVec& theDerSurf) |
| 695 | { |
| 696 | Standard_Integer i, j; |
| 697 | gp_Pnt P; |
| 698 | gp_Vec DL1U, DL1V, DL2U, DL2V, DL2UV, DL3U, DL3UUV, DL3UVV, DL3V; |
| 699 | |
| 700 | if (theAlongU || theAlongV) |
| 701 | { |
| 702 | theMaxOrder = 0; |
| 703 | TColgp_Array2OfVec DerSurfL(0, theMaxOrder + theNU + 1, 0, theMaxOrder + theNV + 1); |
| 704 | switch (theMinOrder) |
| 705 | { |
| 706 | case 1: |
| 707 | theL->D1(theU, theV, P, DL1U, DL1V); |
| 708 | DerSurfL.SetValue(1, 0, DL1U); |
| 709 | DerSurfL.SetValue(0, 1, DL1V); |
| 710 | break; |
| 711 | case 2: |
| 712 | theL->D2(theU, theV, P, DL1U, DL1V, DL2U, DL2V, DL2UV); |
| 713 | DerSurfL.SetValue(1, 0, DL1U); |
| 714 | DerSurfL.SetValue(0, 1, DL1V); |
| 715 | DerSurfL.SetValue(1, 1, DL2UV); |
| 716 | DerSurfL.SetValue(2, 0, DL2U); |
| 717 | DerSurfL.SetValue(0, 2, DL2V); |
| 718 | break; |
| 719 | case 3: |
| 720 | theL->D3(theU, theV, P, DL1U, DL1V, DL2U, DL2V, DL2UV, DL3U, DL3V, DL3UUV, DL3UVV); |
| 721 | DerSurfL.SetValue(1, 0, DL1U); |
| 722 | DerSurfL.SetValue(0, 1, DL1V); |
| 723 | DerSurfL.SetValue(1, 1, DL2UV); |
| 724 | DerSurfL.SetValue(2, 0, DL2U); |
| 725 | DerSurfL.SetValue(0, 2, DL2V); |
| 726 | DerSurfL.SetValue(3, 0, DL3U); |
| 727 | DerSurfL.SetValue(2, 1, DL3UUV); |
| 728 | DerSurfL.SetValue(1, 2, DL3UVV); |
| 729 | DerSurfL.SetValue(0, 3, DL3V); |
| 730 | break; |
| 731 | default: |
| 732 | break; |
| 733 | } |
| 734 | |
| 735 | if (theNU <= theNV) |
| 736 | { |
| 737 | for (i = 0; i <= theMaxOrder + 1 + theNU; i++) |
| 738 | for (j = i; j <= theMaxOrder + theNV + 1; j++) |
| 739 | if (i + j > theMinOrder) |
| 740 | { |
| 741 | DerSurfL.SetValue(i, j, theL->DN(theU, theV, i, j)); |
| 742 | theDerSurf.SetValue(i, j, theBasisSurf->DN(theU, theV, i, j)); |
| 743 | if (i != j && j <= theNU + 1) |
| 744 | { |
| 745 | theDerSurf.SetValue(j, i, theBasisSurf->DN(theU, theV, j, i)); |
| 746 | DerSurfL.SetValue(j, i, theL->DN(theU, theV, j, i)); |
| 747 | } |
| 748 | } |
| 749 | } |
| 750 | else |
| 751 | { |
| 752 | for (j = 0; j <= theMaxOrder + 1 + theNV; j++) |
| 753 | for (i = j; i <= theMaxOrder + theNU + 1; i++) |
| 754 | if (i + j > theMinOrder) |
| 755 | { |
| 756 | DerSurfL.SetValue(i, j, theL->DN(theU, theV, i, j)); |
| 757 | theDerSurf.SetValue(i, j, theBasisSurf->DN(theU, theV, i, j)); |
| 758 | if (i != j && i <= theNV + 1) |
| 759 | { |
| 760 | theDerSurf.SetValue(j, i, theBasisSurf->DN(theU, theV, j, i)); |
| 761 | DerSurfL.SetValue(j, i, theL->DN(theU, theV, j, i)); |
| 762 | } |
| 763 | } |
| 764 | } |
| 765 | for (i = 0; i <= theMaxOrder + theNU; i++) |
| 766 | for (j = 0; j <= theMaxOrder + theNV; j++) |
| 767 | { |
| 768 | if (theAlongU) |
| 769 | theDerNUV.SetValue(i, j, CSLib::DNNUV(i, j, DerSurfL, theDerSurf)); |
| 770 | if (theAlongV) |
| 771 | theDerNUV.SetValue(i, j, CSLib::DNNUV(i, j, theDerSurf, DerSurfL)); |
| 772 | } |
| 773 | } |
| 774 | else |
| 775 | { |
| 776 | for (i = 0; i <= theMaxOrder + theNU+ 1; i++) |
| 777 | for (j = i; j <= theMaxOrder + theNV + 1; j++) |
| 778 | if (i + j > theMinOrder) |
| 779 | { |
| 780 | theDerSurf.SetValue(i, j, theBasisSurf->DN(theU, theV, i, j)); |
| 781 | if (i != j) |
| 782 | theDerSurf.SetValue(j, i, theBasisSurf->DN(theU, theV, j, i)); |
| 783 | } |
| 784 | for (i = 0; i <= theMaxOrder + theNU; i++) |
| 785 | for (j = 0; j <= theMaxOrder + theNV; j++) |
| 786 | theDerNUV.SetValue(i, j, CSLib::DNNUV(i, j, theDerSurf)); |
| 787 | } |
| 788 | } |
| 789 | |