| 1 | // Copyright (c) 1999-2014 OPEN CASCADE SAS |
| 2 | // |
| 3 | // This file is part of Open CASCADE Technology software library. |
| 4 | // |
| 5 | // This library is free software; you can redistribute it and/or modify it under |
| 6 | // the terms of the GNU Lesser General Public License version 2.1 as published |
| 7 | // by the Free Software Foundation, with special exception defined in the file |
| 8 | // OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT |
| 9 | // distribution for complete text of the license and disclaimer of any warranty. |
| 10 | // |
| 11 | // Alternatively, this file may be used under the terms of Open CASCADE |
| 12 | // commercial license or contractual agreement. |
| 13 | |
| 14 | #include <ChFi2d_AnaFilletAlgo.hxx> |
| 15 | |
| 16 | #include <gp_Ax3.hxx> |
| 17 | #include <gp_Circ.hxx> |
| 18 | #include <gp_Lin2d.hxx> |
| 19 | #include <gp_Circ2d.hxx> |
| 20 | |
| 21 | #include <Standard_TypeMismatch.hxx> |
| 22 | |
| 23 | #include <BRepBuilderAPI_MakeEdge.hxx> |
| 24 | #include <BRepBuilderAPI_MakeWire.hxx> |
| 25 | #include <BRepBuilderAPI_MakeFace.hxx> |
| 26 | |
| 27 | #include <GeomAPI_ExtremaCurveCurve.hxx> |
| 28 | #include <IntAna2d_AnaIntersection.hxx> |
| 29 | #include <ShapeAnalysis_Wire.hxx> |
| 30 | #include <Geom_Circle.hxx> |
| 31 | |
| 32 | #include <BRepAdaptor_Curve.hxx> |
| 33 | #include <BRep_Tool.hxx> |
| 34 | |
| 35 | #include <TopoDS.hxx> |
| 36 | #include <TopoDS_Iterator.hxx> |
| 37 | |
| 38 | #include <ProjLib.hxx> |
| 39 | #include <TopExp.hxx> |
| 40 | #include <ElSLib.hxx> |
| 41 | |
| 42 | // Compute the flag: CW || CCW |
| 43 | static Standard_Boolean isCW(const BRepAdaptor_Curve& AC) |
| 44 | { |
| 45 | const Standard_Real f = AC.FirstParameter(); |
| 46 | const Standard_Real l = AC.LastParameter(); |
| 47 | Handle(Geom_Circle) circle = Handle(Geom_Circle)::DownCast(AC.Curve().Curve()); |
| 48 | gp_Pnt start = AC.Value(f); |
| 49 | gp_Pnt end = AC.Value(l); |
| 50 | gp_Pnt center = AC.Circle().Location(); |
| 51 | gp_Ax3 plane = AC.Circle().Position(); |
| 52 | |
| 53 | // Get point on circle at half angle |
| 54 | gp_Pnt m; |
| 55 | circle->D0(0.5 * (f + l), m); |
| 56 | |
| 57 | // Compare angles between vectors to middle point and to the end point. |
| 58 | gp_Vec startv(center, start), endv(center, end), middlev(center, m); |
| 59 | double middlea = startv.AngleWithRef(middlev, plane.Direction()); |
| 60 | while(middlea < 0.0) |
| 61 | middlea += 2.0 * M_PI; |
| 62 | double enda = startv.AngleWithRef(endv, plane.Direction()); |
| 63 | while(enda < 0.0) |
| 64 | enda += 2.0 * M_PI; |
| 65 | |
| 66 | Standard_Boolean is_cw = middlea > enda ? Standard_True : Standard_False; |
| 67 | return is_cw; |
| 68 | } |
| 69 | |
| 70 | // Equality of points computed through square distance between the points. |
| 71 | static Standard_Boolean IsEqual(const gp_Pnt& p1, const gp_Pnt& p2) |
| 72 | { |
| 73 | return p1.SquareDistance(p2) < Precision::SquareConfusion(); |
| 74 | } |
| 75 | static Standard_Boolean IsEqual(const gp_Pnt2d& p1, const gp_Pnt2d& p2) |
| 76 | { |
| 77 | return p1.SquareDistance(p2) < Precision::SquareConfusion(); |
| 78 | } |
| 79 | |
| 80 | // An empty constructor. |
| 81 | // Use the method Init() to initialize the class. |
| 82 | ChFi2d_AnaFilletAlgo::ChFi2d_AnaFilletAlgo() |
| 83 | { |
| 84 | |
| 85 | } |
| 86 | |
| 87 | // An constructor. |
| 88 | // It expects two edges having a common point of type: |
| 89 | // - segment |
| 90 | // - arc of circle. |
| 91 | ChFi2d_AnaFilletAlgo::ChFi2d_AnaFilletAlgo(const TopoDS_Wire& theWire, |
| 92 | const gp_Pln& thePlane) |
| 93 | { |
| 94 | Init(theWire, thePlane); |
| 95 | } |
| 96 | |
| 97 | // A constructor. |
| 98 | // It expects two edges having a common point of type: |
| 99 | // - segment |
| 100 | // - arc of circle. |
| 101 | ChFi2d_AnaFilletAlgo::ChFi2d_AnaFilletAlgo(const TopoDS_Edge& theEdge1, |
| 102 | const TopoDS_Edge& theEdge2, |
| 103 | const gp_Pln& thePlane) |
| 104 | { |
| 105 | // Make a wire consisting of two edges. |
| 106 | Init(theEdge1, theEdge2, thePlane); |
| 107 | } |
| 108 | |
| 109 | // Initializes the class by a wire consisting of two edges. |
| 110 | void ChFi2d_AnaFilletAlgo::Init(const TopoDS_Wire& theWire, const gp_Pln& thePlane) |
| 111 | { |
| 112 | plane = thePlane; |
| 113 | TopoDS_Iterator itr(theWire); |
| 114 | for (; itr.More(); itr.Next()) |
| 115 | { |
| 116 | if (e1.IsNull()) |
| 117 | e1 = TopoDS::Edge(itr.Value()); |
| 118 | else if (e2.IsNull()) |
| 119 | e2 = TopoDS::Edge(itr.Value()); |
| 120 | } |
| 121 | if (e1.IsNull() || e2.IsNull()) |
| 122 | Standard_TypeMismatch::Raise("The algorithm expects a wire consisting of two linear or circular edges."); |
| 123 | |
| 124 | // Left neighbour. |
| 125 | BRepAdaptor_Curve AC1(e1); |
| 126 | if (AC1.GetType() != GeomAbs_Line && AC1.GetType() != GeomAbs_Circle) |
| 127 | Standard_TypeMismatch::Raise("A segment or an arc of circle is expected."); |
| 128 | |
| 129 | TopoDS_Vertex v1, v2; |
| 130 | TopExp::Vertices(e1, v1, v2, Standard_True); |
| 131 | if (v1.IsNull() || v2.IsNull()) |
| 132 | Standard_Failure::Raise("An infinite edge."); |
| 133 | |
| 134 | gp_Pnt P1 = BRep_Tool::Pnt(v1); |
| 135 | gp_Pnt P2 = BRep_Tool::Pnt(v2); |
| 136 | gp_Pnt2d p1 = ProjLib::Project(thePlane, P1); |
| 137 | gp_Pnt2d p2 = ProjLib::Project(thePlane, P2); |
| 138 | p1.Coord(x11, y11); |
| 139 | p2.Coord(x12, y12); |
| 140 | |
| 141 | segment1 = true; |
| 142 | if (AC1.GetType() == GeomAbs_Circle) |
| 143 | { |
| 144 | segment1 = false; |
| 145 | gp_Circ c = AC1.Circle(); |
| 146 | |
| 147 | gp_Pnt2d loc = ProjLib::Project(thePlane, c.Location()); |
| 148 | loc.Coord(xc1, yc1); |
| 149 | |
| 150 | radius1 = c.Radius(); |
| 151 | cw1 = isCW(AC1); |
| 152 | } |
| 153 | |
| 154 | // Right neighbour. |
| 155 | BRepAdaptor_Curve AC2(e2); |
| 156 | if (AC2.GetType() != GeomAbs_Line && AC2.GetType() != GeomAbs_Circle) |
| 157 | Standard_TypeMismatch::Raise("A segment or an arc of circle is expected."); |
| 158 | |
| 159 | TopExp::Vertices(e2, v1, v2, Standard_True); |
| 160 | if (v1.IsNull() || v2.IsNull()) |
| 161 | Standard_Failure::Raise("An infinite edge."); |
| 162 | |
| 163 | P1 = BRep_Tool::Pnt(v1); |
| 164 | P2 = BRep_Tool::Pnt(v2); |
| 165 | p1 = ProjLib::Project(thePlane, P1); |
| 166 | p2 = ProjLib::Project(thePlane, P2); |
| 167 | p1.Coord(x21, y21); |
| 168 | p2.Coord(x22, y22); |
| 169 | |
| 170 | segment2 = true; |
| 171 | if (AC2.GetType() == GeomAbs_Circle) |
| 172 | { |
| 173 | segment2 = false; |
| 174 | gp_Circ c = AC2.Circle(); |
| 175 | |
| 176 | gp_Pnt2d loc = ProjLib::Project(thePlane, c.Location()); |
| 177 | loc.Coord(xc2, yc2); |
| 178 | |
| 179 | radius2 = c.Radius(); |
| 180 | cw2 = isCW(AC2); |
| 181 | } |
| 182 | } |
| 183 | |
| 184 | // Initializes the class by two edges. |
| 185 | void ChFi2d_AnaFilletAlgo::Init(const TopoDS_Edge& theEdge1, const TopoDS_Edge& theEdge2, |
| 186 | const gp_Pln& thePlane) |
| 187 | { |
| 188 | // Make a wire consisting of two edges. |
| 189 | |
| 190 | // Get common point. |
| 191 | TopoDS_Vertex v11, v12, v21, v22; |
| 192 | TopExp::Vertices(theEdge1, v11, v12, Standard_True); |
| 193 | TopExp::Vertices(theEdge2, v21, v22, Standard_True); |
| 194 | if (v11.IsNull() || v12.IsNull() || v21.IsNull() || v22.IsNull()) |
| 195 | Standard_Failure::Raise("An infinite edge."); |
| 196 | |
| 197 | gp_Pnt p11 = BRep_Tool::Pnt(v11); |
| 198 | gp_Pnt p12 = BRep_Tool::Pnt(v12); |
| 199 | gp_Pnt p21 = BRep_Tool::Pnt(v21); |
| 200 | gp_Pnt p22 = BRep_Tool::Pnt(v22); |
| 201 | |
| 202 | gp_Pnt pcommon; |
| 203 | if (IsEqual(p11, p21) || IsEqual(p11, p22)) |
| 204 | { |
| 205 | pcommon = p11; |
| 206 | } |
| 207 | else if (IsEqual(p12, p21) || IsEqual(p12, p22)) |
| 208 | { |
| 209 | pcommon = p12; |
| 210 | } |
| 211 | else |
| 212 | Standard_Failure::Raise("The edges have no common point."); |
| 213 | |
| 214 | // Reverse the edges in case of need (to construct a wire). |
| 215 | Standard_Boolean is1stReversed(Standard_False), is2ndReversed(Standard_False); |
| 216 | if (IsEqual(pcommon, p11)) |
| 217 | is1stReversed = Standard_True; |
| 218 | else if (IsEqual(pcommon, p22)) |
| 219 | is2ndReversed = Standard_True; |
| 220 | |
| 221 | // Make a wire. |
| 222 | BRepBuilderAPI_MakeWire mkWire; |
| 223 | if (is1stReversed) |
| 224 | mkWire.Add(TopoDS::Edge(theEdge1.Reversed())); |
| 225 | else |
| 226 | mkWire.Add(theEdge1); |
| 227 | if (is2ndReversed) |
| 228 | mkWire.Add(TopoDS::Edge(theEdge2.Reversed())); |
| 229 | else |
| 230 | mkWire.Add(theEdge2); |
| 231 | if (!mkWire.IsDone()) |
| 232 | Standard_Failure::Raise("Can't make a wire."); |
| 233 | |
| 234 | const TopoDS_Wire& W = mkWire.Wire(); |
| 235 | Init(W, thePlane); |
| 236 | } |
| 237 | |
| 238 | // Calculates a fillet. |
| 239 | Standard_Boolean ChFi2d_AnaFilletAlgo::Perform(const Standard_Real radius) |
| 240 | { |
| 241 | Standard_Boolean bRet(false); |
| 242 | if (e1.IsNull() || e2.IsNull() || |
| 243 | radius < Precision::Confusion()) |
| 244 | { |
| 245 | return bRet; |
| 246 | } |
| 247 | |
| 248 | // Fillet definition. |
| 249 | Standard_Real xc = 0.0, yc = 0.0; |
| 250 | Standard_Real start = 0.0, end = 0.0; // parameters on neighbours |
| 251 | Standard_Real xstart = DBL_MAX, ystart = DBL_MAX; // point on left neighbour |
| 252 | Standard_Real xend = DBL_MAX, yend = DBL_MAX; // point on right neighbour |
| 253 | Standard_Boolean cw = Standard_False; |
| 254 | |
| 255 | // Analytical algorithm works for non-intersecting arcs only. |
| 256 | // Check arcs on self-intersection. |
| 257 | Standard_Boolean isCut(Standard_False); |
| 258 | if (!segment1 || !segment2) |
| 259 | { |
| 260 | BRepBuilderAPI_MakeWire mkWire(e1, e2); |
| 261 | if (mkWire.IsDone()) |
| 262 | { |
| 263 | const TopoDS_Wire& W = mkWire.Wire(); |
| 264 | BRepBuilderAPI_MakeFace mkFace(plane); |
| 265 | if (mkFace.IsDone()) |
| 266 | { |
| 267 | const TopoDS_Face& F = mkFace.Face(); |
| 268 | ShapeAnalysis_Wire analyzer(W, F, Precision::Confusion()); |
| 269 | if (analyzer.CheckSelfIntersection() == Standard_True) |
| 270 | { |
| 271 | // Cut the edges at the point of intersection. |
| 272 | isCut = Standard_True; |
| 273 | if (!Cut(plane, e1, e2)) |
| 274 | { |
| 275 | return Standard_False; |
| 276 | } |
| 277 | } |
| 278 | } |
| 279 | } |
| 280 | }// a case of segment - segment |
| 281 | |
| 282 | // Choose the case. |
| 283 | BRepAdaptor_Curve AC1(e1), AC2(e2); |
| 284 | if (segment1 && segment2) |
| 285 | { |
| 286 | bRet = SegmentFilletSegment(radius, xc, yc, cw, start, end); |
| 287 | } |
| 288 | else if (segment1 && !segment2) |
| 289 | { |
| 290 | bRet = SegmentFilletArc(radius, xc, yc, cw, start, end, xend, yend); |
| 291 | } |
| 292 | else if (!segment1 && segment2) |
| 293 | { |
| 294 | bRet = ArcFilletSegment(radius, xc, yc, cw, start, end, xstart, ystart); |
| 295 | } |
| 296 | else if (!segment1 && !segment2) |
| 297 | { |
| 298 | bRet = ArcFilletArc(radius, xc, yc, cw, start, end); |
| 299 | } |
| 300 | |
| 301 | if (!bRet) |
| 302 | return Standard_False; |
| 303 | |
| 304 | // Invert the fillet for left-handed plane. |
| 305 | if (plane.Position().Direct() == Standard_False) |
| 306 | cw = !cw; |
| 307 | |
| 308 | // Construct a fillet. |
| 309 | // Make circle. |
| 310 | gp_Pnt center = ElSLib::Value(xc, yc, plane); |
| 311 | const gp_Dir& normal = plane.Position().Direction(); |
| 312 | gp_Circ circ(gp_Ax2(center, cw ? -normal : normal), radius); |
| 313 | |
| 314 | // Fillet may only shrink a neighbour edge, it can't prolongate it. |
| 315 | const Standard_Real delta1 = AC1.LastParameter() - AC1.FirstParameter(); |
| 316 | const Standard_Real delta2 = AC2.LastParameter() - AC2.FirstParameter(); |
| 317 | if (!isCut && (start > delta1 || end > delta2)) |
| 318 | { |
| 319 | // Check a case when a neighbour edge almost disappears: |
| 320 | // try to reduce the fillet radius for a little (1.e-5 mm). |
| 321 | const Standard_Real little = 100.0 * Precision::Confusion(); |
| 322 | const Standard_Real d1 = fabs(start - delta1); |
| 323 | const Standard_Real d2 = fabs(end - delta2); |
| 324 | if (d1 < little || d2 < little) |
| 325 | { |
| 326 | if (segment1 && segment2) |
| 327 | { |
| 328 | bRet = SegmentFilletSegment(radius - little, xc, yc, cw, start, end); |
| 329 | } |
| 330 | else if (segment1 && !segment2) |
| 331 | { |
| 332 | bRet = SegmentFilletArc(radius - little, xc, yc, cw, start, end, xend, yend); |
| 333 | } |
| 334 | else if (!segment1 && segment2) |
| 335 | { |
| 336 | bRet = ArcFilletSegment(radius - little, xc, yc, cw, start, end, xstart, ystart); |
| 337 | } |
| 338 | else if (!segment1 && !segment2) |
| 339 | { |
| 340 | bRet = ArcFilletArc(radius - little, xc, yc, cw, start, end); |
| 341 | } |
| 342 | if (bRet) |
| 343 | { |
| 344 | // Invert the fillet for left-handed planes. |
| 345 | if (plane.Position().Direct() == Standard_False) |
| 346 | cw = !cw; |
| 347 | |
| 348 | // Make the circle again. |
| 349 | center = ElSLib::Value(xc, yc, plane); |
| 350 | circ.SetLocation(center); |
| 351 | circ.SetRadius(radius - little); |
| 352 | } |
| 353 | else |
| 354 | { |
| 355 | return Standard_False; |
| 356 | } |
| 357 | } |
| 358 | else |
| 359 | { |
| 360 | return Standard_False; |
| 361 | } |
| 362 | } |
| 363 | if (bRet) |
| 364 | { |
| 365 | // start: (xstart, ystart) - pstart. |
| 366 | gp_Pnt pstart; |
| 367 | if (xstart != DBL_MAX) |
| 368 | { |
| 369 | pstart = ElSLib::Value(xstart, ystart, plane); |
| 370 | } |
| 371 | else |
| 372 | { |
| 373 | if (e1.Orientation() == TopAbs_FORWARD) |
| 374 | pstart = AC1.Value(AC1.LastParameter() - start); |
| 375 | else |
| 376 | pstart = AC1.Value(AC1.FirstParameter() + start); |
| 377 | } |
| 378 | // end: (xend, yend) -> pend. |
| 379 | gp_Pnt pend; |
| 380 | if (xend != DBL_MAX) |
| 381 | { |
| 382 | pend = ElSLib::Value(xend, yend, plane); |
| 383 | } |
| 384 | else |
| 385 | { |
| 386 | if (e2.Orientation() == TopAbs_FORWARD) |
| 387 | pend = AC2.Value(AC2.FirstParameter() + end); |
| 388 | else |
| 389 | pend = AC2.Value(AC2.LastParameter() - end); |
| 390 | } |
| 391 | |
| 392 | // Make arc. |
| 393 | BRepBuilderAPI_MakeEdge mkEdge(circ, pstart, pend); |
| 394 | bRet = mkEdge.IsDone(); |
| 395 | if (bRet) |
| 396 | { |
| 397 | fillet = mkEdge.Edge(); |
| 398 | |
| 399 | // Limit the neighbours. |
| 400 | // Left neighbour. |
| 401 | gp_Pnt p1, p2; |
| 402 | shrinke1.Nullify(); |
| 403 | if (e1.Orientation() == TopAbs_FORWARD) |
| 404 | { |
| 405 | p1 = AC1.Value(AC1.FirstParameter()); |
| 406 | p2 = pstart; |
| 407 | } |
| 408 | else |
| 409 | { |
| 410 | p1 = pstart; |
| 411 | p2 = AC1.Value(AC1.LastParameter()); |
| 412 | } |
| 413 | if (segment1) |
| 414 | { |
| 415 | BRepBuilderAPI_MakeEdge mkSegment1; |
| 416 | mkSegment1.Init(AC1.Curve().Curve(), p1, p2); |
| 417 | if (mkSegment1.IsDone()) |
| 418 | shrinke1 = mkSegment1.Edge(); |
| 419 | } |
| 420 | else |
| 421 | { |
| 422 | BRepBuilderAPI_MakeEdge mkCirc1; |
| 423 | mkCirc1.Init(AC1.Curve().Curve(), p1, p2); |
| 424 | if (mkCirc1.IsDone()) |
| 425 | shrinke1 = mkCirc1.Edge(); |
| 426 | } |
| 427 | |
| 428 | // Right neighbour. |
| 429 | shrinke2.Nullify(); |
| 430 | if (e1.Orientation() == TopAbs_FORWARD) |
| 431 | { |
| 432 | p1 = pend; |
| 433 | p2 = AC2.Value(AC2.LastParameter()); |
| 434 | } |
| 435 | else |
| 436 | { |
| 437 | p1 = AC2.Value(AC2.FirstParameter()); |
| 438 | p2 = pend; |
| 439 | } |
| 440 | if (segment2) |
| 441 | { |
| 442 | BRepBuilderAPI_MakeEdge mkSegment2; |
| 443 | mkSegment2.Init(AC2.Curve().Curve(), p1, p2); |
| 444 | if (mkSegment2.IsDone()) |
| 445 | shrinke2 = mkSegment2.Edge(); |
| 446 | } |
| 447 | else |
| 448 | { |
| 449 | BRepBuilderAPI_MakeEdge mkCirc2; |
| 450 | mkCirc2.Init(AC2.Curve().Curve(), p1, p2); |
| 451 | if (mkCirc2.IsDone()) |
| 452 | shrinke2 = mkCirc2.Edge(); |
| 453 | } |
| 454 | |
| 455 | bRet = !shrinke1.IsNull() && !shrinke2.IsNull(); |
| 456 | }// fillet edge is done |
| 457 | }// shrinking is good |
| 458 | |
| 459 | return bRet; |
| 460 | } |
| 461 | |
| 462 | // Retrieves a result (fillet and shrinked neighbours). |
| 463 | const TopoDS_Edge& ChFi2d_AnaFilletAlgo::Result(TopoDS_Edge& theE1, TopoDS_Edge& theE2) |
| 464 | { |
| 465 | theE1 = shrinke1; |
| 466 | theE2 = shrinke2; |
| 467 | return fillet; |
| 468 | } |
| 469 | |
| 470 | // WW5 method to compute fillet. |
| 471 | // It returns a constructed fillet definition: |
| 472 | // center point (xc, yc) |
| 473 | // point on the 1st segment (xstart, ystart) |
| 474 | // point on the 2nd segment (xend, yend) |
| 475 | // is the arc of fillet clockwise (cw = true) or counterclockwise (cw = false). |
| 476 | Standard_Boolean ChFi2d_AnaFilletAlgo::SegmentFilletSegment(const Standard_Real radius, |
| 477 | Standard_Real& xc, Standard_Real& yc, |
| 478 | Standard_Boolean& cw, |
| 479 | Standard_Real& start, Standard_Real& end) |
| 480 | { |
| 481 | // Make normalized vectors at p12. |
| 482 | gp_Pnt2d p11(x11, y11); |
| 483 | gp_Pnt2d p12(x12, y12); |
| 484 | gp_Pnt2d p22(x22, y22); |
| 485 | |
| 486 | // Check length of segments. |
| 487 | if (IsEqual(p12, p11) || IsEqual(p12, p22)) |
| 488 | { |
| 489 | return Standard_False; |
| 490 | } |
| 491 | |
| 492 | // Make vectors. |
| 493 | gp_Vec2d v1(p12, p11); |
| 494 | gp_Vec2d v2(p12, p22); |
| 495 | v1.Normalize(); |
| 496 | v2.Normalize(); |
| 497 | |
| 498 | // Make bisectrissa. |
| 499 | gp_Vec2d bisec = 0.5 * (v1 + v2); |
| 500 | |
| 501 | // Check bisectrissa. |
| 502 | if (bisec.SquareMagnitude() < Precision::SquareConfusion()) |
| 503 | return Standard_False; |
| 504 | |
| 505 | // Normalize the bisectrissa. |
| 506 | bisec.Normalize(); |
| 507 | |
| 508 | // Angle at bisectrissa. |
| 509 | Standard_Real beta = v1.Angle(bisec); |
| 510 | |
| 511 | // Length along the bisectrissa till the center of fillet. |
| 512 | Standard_Real L = radius / sin(fabs(beta)); |
| 513 | |
| 514 | // Center point of fillet. |
| 515 | gp_Pnt2d pc = p12.Translated(L * bisec); |
| 516 | pc.Coord(xc, yc); |
| 517 | |
| 518 | // Shrinking length along segments. |
| 519 | start = sqrt(L * L - radius * radius); |
| 520 | end = start; |
| 521 | |
| 522 | // Orientation of fillet. |
| 523 | cw = beta > 0.0; |
| 524 | return Standard_True; |
| 525 | } |
| 526 | |
| 527 | // A function constructs a fillet between a segment and an arc. |
| 528 | Standard_Boolean ChFi2d_AnaFilletAlgo::SegmentFilletArc(const Standard_Real radius, |
| 529 | Standard_Real& xc, Standard_Real& yc, |
| 530 | Standard_Boolean& cw, |
| 531 | Standard_Real& start, Standard_Real& end, |
| 532 | Standard_Real& xend, Standard_Real& yend) |
| 533 | { |
| 534 | // Make a line parallel to the segment at the side of center point of fillet. |
| 535 | // This side may be defined through making a bisectrissa for vectors at p12 (or p21). |
| 536 | |
| 537 | // Make 2D points. |
| 538 | gp_Pnt2d p12(x12, y12); |
| 539 | gp_Pnt2d p11(x11, y11); |
| 540 | gp_Pnt2d pc2(xc2, yc2); |
| 541 | |
| 542 | // Check length of segment. |
| 543 | if (p11.SquareDistance(p12) < gp::Resolution()) |
| 544 | return Standard_False; |
| 545 | |
| 546 | // Make 2D vectors. |
| 547 | gp_Vec2d v1(p12, p11); |
| 548 | gp_Vec2d v2(p12, pc2); |
| 549 | |
| 550 | // Rotate the arc vector to become tangential at p21. |
| 551 | if (cw2) |
| 552 | v2.Rotate(+M_PI_2); |
| 553 | else |
| 554 | v2.Rotate(-M_PI_2); |
| 555 | |
| 556 | // If vectors coincide (segment and arc are tangent), |
| 557 | // the algorithm doesn't work... |
| 558 | Standard_Real angle = v1.Angle(v2); |
| 559 | if (fabs(angle) < Precision::Angular()) |
| 560 | return Standard_False; |
| 561 | |
| 562 | // Make a bissectrisa of vectors at p12. |
| 563 | v2.Normalize(); |
| 564 | v1.Normalize(); |
| 565 | gp_Vec2d bisec = 0.5 * (v1 + v2); |
| 566 | |
| 567 | // If segment and arc look in opposite direction, |
| 568 | // no fillet is possible. |
| 569 | if (bisec.SquareMagnitude() < gp::Resolution()) |
| 570 | return Standard_False; |
| 571 | |
| 572 | // Define an appropriate point to choose center of fillet. |
| 573 | bisec.Normalize(); |
| 574 | gp_Pnt2d nearp = p12.Translated(radius * bisec); |
| 575 | gp_Lin2d nearl(p12, bisec); |
| 576 | |
| 577 | // Make a line parallel to segment and |
| 578 | // passing near the "near" point. |
| 579 | gp_Vec2d d1(v1); |
| 580 | gp_Lin2d line(p11, -d1); |
| 581 | d1.Rotate(M_PI_2); |
| 582 | line.Translate(radius * d1); |
| 583 | if (line.Distance(nearp) > radius) |
| 584 | line.Translate(-2.0 * radius * d1); |
| 585 | |
| 586 | // Make a circle of radius of the arc +/- fillet radius. |
| 587 | gp_Ax2d axes(pc2, gp::DX2d()); |
| 588 | gp_Circ2d circ(axes, radius2 + radius); |
| 589 | if (radius2 > radius && circ.Distance(nearp) > radius) |
| 590 | circ.SetRadius(radius2 - radius); |
| 591 | |
| 592 | // Calculate intersection of the line and the circle. |
| 593 | IntAna2d_AnaIntersection intersector(line, circ); |
| 594 | if (!intersector.IsDone() || !intersector.NbPoints()) |
| 595 | return Standard_False; |
| 596 | |
| 597 | // Find center point of fillet. |
| 598 | Standard_Integer i; |
| 599 | Standard_Real minDist = DBL_MAX; |
| 600 | for (i = 1; i <= intersector.NbPoints(); ++i) |
| 601 | { |
| 602 | const IntAna2d_IntPoint& intp = intersector.Point(i); |
| 603 | const gp_Pnt2d& p = intp.Value(); |
| 604 | |
| 605 | Standard_Real d = nearl.Distance(p); |
| 606 | if (d < minDist) |
| 607 | { |
| 608 | minDist = d; |
| 609 | p.Coord(xc, yc); |
| 610 | } |
| 611 | } |
| 612 | |
| 613 | // Shrink of segment. |
| 614 | gp_Pnt2d pc(xc, yc); |
| 615 | Standard_Real L2 = pc.SquareDistance(p12); |
| 616 | const Standard_Real Rf2 = radius * radius; |
| 617 | start = sqrt(L2 - Rf2); |
| 618 | |
| 619 | // Shrink of arc. |
| 620 | gp_Vec2d pcc(pc2, pc); |
| 621 | end = fabs(gp_Vec2d(pc2, p12).Angle(pcc)); |
| 622 | |
| 623 | // Duplicate the information on shrink the arc: |
| 624 | // calculate a point on the arc coinciding with the end of fillet. |
| 625 | line.SetLocation(pc2); |
| 626 | line.SetDirection(pcc); |
| 627 | circ.SetLocation(pc2); |
| 628 | circ.SetRadius(radius2); |
| 629 | intersector.Perform(line, circ); |
| 630 | if (!intersector.IsDone() || !intersector.NbPoints()) |
| 631 | return Standard_False; |
| 632 | |
| 633 | xend = DBL_MAX; |
| 634 | yend = DBL_MAX; |
| 635 | for (i = 1; i <= intersector.NbPoints(); ++i) |
| 636 | { |
| 637 | const IntAna2d_IntPoint& intp = intersector.Point(i); |
| 638 | const gp_Pnt2d& p = intp.Value(); |
| 639 | |
| 640 | const Standard_Real d2 = p.SquareDistance(pc); |
| 641 | if (fabs(d2 - Rf2) < Precision::Confusion()) |
| 642 | { |
| 643 | p.Coord(xend, yend); |
| 644 | break; |
| 645 | } |
| 646 | } |
| 647 | |
| 648 | // Orientation of the fillet. |
| 649 | angle = v1.Angle(v2); |
| 650 | cw = angle > 0.0; |
| 651 | return Standard_True; |
| 652 | } |
| 653 | |
| 654 | // A function constructs a fillet between an arc and a segment. |
| 655 | Standard_Boolean ChFi2d_AnaFilletAlgo::ArcFilletSegment(const Standard_Real radius, |
| 656 | Standard_Real& xc, Standard_Real& yc, |
| 657 | Standard_Boolean& cw, |
| 658 | Standard_Real& start, Standard_Real& end, |
| 659 | Standard_Real& xstart, Standard_Real& ystart) |
| 660 | { |
| 661 | // Make a line parallel to the segment at the side of center point of fillet. |
| 662 | // This side may be defined through making a bisectrissa for vectors at p12 (or p21). |
| 663 | |
| 664 | // Make 2D points. |
| 665 | gp_Pnt2d p12(x12, y12); |
| 666 | gp_Pnt2d p22(x22, y22); |
| 667 | gp_Pnt2d pc1(xc1, yc1); |
| 668 | |
| 669 | // Check length of segment. |
| 670 | if (p12.SquareDistance(p22) < gp::Resolution()) |
| 671 | return Standard_False; |
| 672 | |
| 673 | // Make 2D vectors. |
| 674 | gp_Vec2d v1(p12, pc1); |
| 675 | gp_Vec2d v2(p12, p22); |
| 676 | |
| 677 | // Rotate the arc vector to become tangential at p21. |
| 678 | if (cw1) |
| 679 | v1.Rotate(-M_PI_2); |
| 680 | else |
| 681 | v1.Rotate(+M_PI_2); |
| 682 | |
| 683 | // If vectors coincide (segment and arc are tangent), |
| 684 | // the algorithm doesn't work... |
| 685 | Standard_Real angle = v1.Angle(v2); |
| 686 | if (fabs(angle) < Precision::Angular()) |
| 687 | return Standard_False; |
| 688 | |
| 689 | // Make a bisectrissa of vectors at p12. |
| 690 | v1.Normalize(); |
| 691 | v2.Normalize(); |
| 692 | gp_Vec2d bisec = 0.5 * (v1 + v2); |
| 693 | |
| 694 | // If segment and arc look in opposite direction, |
| 695 | // no fillet is possible. |
| 696 | if (bisec.SquareMagnitude() < gp::Resolution()) |
| 697 | return Standard_False; |
| 698 | |
| 699 | // Define an appropriate point to choose center of fillet. |
| 700 | bisec.Normalize(); |
| 701 | gp_Pnt2d nearPoint = p12.Translated(radius * bisec); |
| 702 | gp_Lin2d nearLine(p12, bisec); |
| 703 | |
| 704 | // Make a line parallel to segment and |
| 705 | // passing near the "near" point. |
| 706 | gp_Vec2d d2(v2); |
| 707 | gp_Lin2d line(p22, -d2); |
| 708 | d2.Rotate(M_PI_2); |
| 709 | line.Translate(radius * d2); |
| 710 | if (line.Distance(nearPoint) > radius) |
| 711 | line.Translate(-2.0 * radius * d2); |
| 712 | |
| 713 | // Make a circle of radius of the arc +/- fillet radius. |
| 714 | gp_Ax2d axes(pc1, gp::DX2d()); |
| 715 | gp_Circ2d circ(axes, radius1 + radius); |
| 716 | if (radius1 > radius && circ.Distance(nearPoint) > radius) |
| 717 | circ.SetRadius(radius1 - radius); |
| 718 | |
| 719 | // Calculate intersection of the line and the big circle. |
| 720 | IntAna2d_AnaIntersection intersector(line, circ); |
| 721 | if (!intersector.IsDone() || !intersector.NbPoints()) |
| 722 | return Standard_False; |
| 723 | |
| 724 | // Find center point of fillet. |
| 725 | Standard_Integer i; |
| 726 | Standard_Real minDist = DBL_MAX; |
| 727 | for (i = 1; i <= intersector.NbPoints(); ++i) |
| 728 | { |
| 729 | const IntAna2d_IntPoint& intp = intersector.Point(i); |
| 730 | const gp_Pnt2d& p = intp.Value(); |
| 731 | |
| 732 | Standard_Real d = nearLine.Distance(p); |
| 733 | if (d < minDist) |
| 734 | { |
| 735 | minDist = d; |
| 736 | p.Coord(xc, yc); |
| 737 | } |
| 738 | } |
| 739 | |
| 740 | // Shrink of segment. |
| 741 | gp_Pnt2d pc(xc, yc); |
| 742 | Standard_Real L2 = pc.SquareDistance(p12); |
| 743 | const Standard_Real Rf2 = radius * radius; |
| 744 | end = sqrt(L2 - Rf2); |
| 745 | |
| 746 | // Shrink of arc. |
| 747 | gp_Vec2d pcc(pc1, pc); |
| 748 | start = fabs(gp_Vec2d(pc1, p12).Angle(pcc)); |
| 749 | |
| 750 | // Duplicate the information on shrink the arc: |
| 751 | // calculate a point on the arc coinciding with the start of fillet. |
| 752 | line.SetLocation(pc1); |
| 753 | line.SetDirection(pcc); |
| 754 | circ.SetLocation(pc1); |
| 755 | circ.SetRadius(radius1); |
| 756 | intersector.Perform(line, circ); |
| 757 | if (!intersector.IsDone() || !intersector.NbPoints()) |
| 758 | return Standard_False; |
| 759 | |
| 760 | xstart = DBL_MAX; |
| 761 | ystart = DBL_MAX; |
| 762 | for (i = 1; i <= intersector.NbPoints(); ++i) |
| 763 | { |
| 764 | const IntAna2d_IntPoint& intp = intersector.Point(i); |
| 765 | const gp_Pnt2d& p = intp.Value(); |
| 766 | |
| 767 | const Standard_Real d2 = p.SquareDistance(pc); |
| 768 | if (fabs(d2 - Rf2) < Precision::SquareConfusion()) |
| 769 | { |
| 770 | p.Coord(xstart, ystart); |
| 771 | break; |
| 772 | } |
| 773 | } |
| 774 | |
| 775 | // Orientation of the fillet. |
| 776 | angle = v2.Angle(v1); |
| 777 | cw = angle < 0.0; |
| 778 | return Standard_True; |
| 779 | } |
| 780 | |
| 781 | // WW5 method to compute fillet: arc - arc. |
| 782 | // It returns a constructed fillet definition: |
| 783 | // center point (xc, yc) |
| 784 | // shrinking parameter of the 1st circle (start) |
| 785 | // shrinking parameter of the 2nd circle (end) |
| 786 | // if the arc of fillet clockwise (cw = true) or counterclockwise (cw = false). |
| 787 | Standard_Boolean ChFi2d_AnaFilletAlgo::ArcFilletArc(const Standard_Real radius, |
| 788 | Standard_Real& xc, Standard_Real& yc, |
| 789 | Standard_Boolean& cw, |
| 790 | Standard_Real& start, Standard_Real& end) |
| 791 | { |
| 792 | // Make points. |
| 793 | const gp_Pnt2d pc1(xc1, yc1); |
| 794 | const gp_Pnt2d pc2(xc2, yc2); |
| 795 | const gp_Pnt2d p12(x12, y12); |
| 796 | |
| 797 | // Make vectors at p12. |
| 798 | gp_Vec2d v1(pc1, p12); |
| 799 | gp_Vec2d v2(pc2, p12); |
| 800 | |
| 801 | // Rotate the vectors so that they are tangent to circles at p12. |
| 802 | if (cw1) |
| 803 | v1.Rotate(+M_PI_2); |
| 804 | else |
| 805 | v1.Rotate(-M_PI_2); |
| 806 | if (cw2) |
| 807 | v2.Rotate(-M_PI_2); |
| 808 | else |
| 809 | v2.Rotate(+M_PI_2); |
| 810 | |
| 811 | // Make a "check" point for choosing an offset circle. |
| 812 | v1.Normalize(); |
| 813 | v2.Normalize(); |
| 814 | gp_Vec2d bisec = 0.5 * (v1 + v2); |
| 815 | if (bisec.SquareMagnitude() < gp::Resolution()) |
| 816 | return Standard_False; |
| 817 | |
| 818 | const gp_Pnt2d checkp = p12.Translated(radius * bisec); |
| 819 | const gp_Lin2d checkl(p12, bisec); |
| 820 | |
| 821 | // Make two circles of radius r1 +/- r and r2 +/- r |
| 822 | // with center point equal to pc1 and pc2. |
| 823 | // Arc 1. |
| 824 | gp_Ax2d axes(pc1, gp::DX2d()); |
| 825 | gp_Circ2d c1(axes, radius1 + radius); |
| 826 | if (radius1 > radius && c1.Distance(checkp) > radius) |
| 827 | c1.SetRadius(radius1 - radius); |
| 828 | // Arc 2. |
| 829 | axes.SetLocation(pc2); |
| 830 | gp_Circ2d c2(axes, radius2 + radius); |
| 831 | if (radius2 > radius && c2.Distance(checkp) > radius) |
| 832 | c2.SetRadius(radius2 - radius); |
| 833 | |
| 834 | // Calculate an intersection point of these two circles |
| 835 | // and choose the one closer to the "check" point. |
| 836 | IntAna2d_AnaIntersection intersector(c1, c2); |
| 837 | if (!intersector.IsDone() || !intersector.NbPoints()) |
| 838 | return Standard_False; |
| 839 | |
| 840 | // Find center point of fillet. |
| 841 | gp_Pnt2d pc; |
| 842 | Standard_Real minDist = DBL_MAX; |
| 843 | for (int i = 1; i <= intersector.NbPoints(); ++i) |
| 844 | { |
| 845 | const IntAna2d_IntPoint& intp = intersector.Point(i); |
| 846 | const gp_Pnt2d& p = intp.Value(); |
| 847 | |
| 848 | Standard_Real d = checkp.SquareDistance(p); |
| 849 | if (d < minDist) |
| 850 | { |
| 851 | minDist = d; |
| 852 | pc = p; |
| 853 | } |
| 854 | } |
| 855 | pc.Coord(xc, yc); |
| 856 | |
| 857 | // Orientation of fillet. |
| 858 | Standard_Real angle = v1.Angle(v2); |
| 859 | if (fabs(angle) < Precision::Angular()) |
| 860 | { |
| 861 | angle = gp_Vec2d(pc, pc1).Angle(gp_Vec2d(pc, pc2)); |
| 862 | cw = angle < 0.0; |
| 863 | } |
| 864 | else |
| 865 | { |
| 866 | cw = angle > 0.0; |
| 867 | } |
| 868 | |
| 869 | // Shrinking of circles. |
| 870 | start = fabs(gp_Vec2d(pc1, p12).Angle(gp_Vec2d(pc1, pc))); |
| 871 | end = fabs(gp_Vec2d(pc2, p12).Angle(gp_Vec2d(pc2, pc))); |
| 872 | return Standard_True; |
| 873 | } |
| 874 | |
| 875 | // Cuts intersecting edges of a contour. |
| 876 | Standard_Boolean ChFi2d_AnaFilletAlgo::Cut(const gp_Pln& thePlane, TopoDS_Edge& theE1, TopoDS_Edge& theE2) |
| 877 | { |
| 878 | gp_Pnt p; |
| 879 | Standard_Boolean found(Standard_False); |
| 880 | Standard_Real param1 = 0.0, param2 = 0.0; |
| 881 | Standard_Real f1, l1, f2, l2; |
| 882 | Handle(Geom_Curve) c1 = BRep_Tool::Curve(theE1, f1, l1); |
| 883 | Handle(Geom_Curve) c2 = BRep_Tool::Curve(theE2, f2, l2); |
| 884 | GeomAPI_ExtremaCurveCurve extrema(c1, c2, f1, l1, f2, l2); |
| 885 | if (extrema.NbExtrema()) |
| 886 | { |
| 887 | Standard_Integer i, nb = extrema.NbExtrema(); |
| 888 | for (i = 1; i <= nb; ++i) |
| 889 | { |
| 890 | const Standard_Real d = extrema.Distance(i); |
| 891 | if (d < Precision::Confusion()) |
| 892 | { |
| 893 | extrema.Parameters(i, param1, param2); |
| 894 | if (fabs(l1 - param1) > Precision::Confusion() && |
| 895 | fabs(f2 - param2) > Precision::Confusion()) |
| 896 | { |
| 897 | found = Standard_True; |
| 898 | extrema.Points(i, p, p); |
| 899 | break; |
| 900 | } |
| 901 | } |
| 902 | } |
| 903 | } |
| 904 | |
| 905 | if (found) |
| 906 | { |
| 907 | BRepBuilderAPI_MakeEdge mkEdge1(c1, f1, param1); |
| 908 | if (mkEdge1.IsDone()) |
| 909 | { |
| 910 | theE1 = mkEdge1.Edge(); |
| 911 | |
| 912 | BRepBuilderAPI_MakeEdge mkEdge2(c2, param2, l2); |
| 913 | if (mkEdge2.IsDone()) |
| 914 | { |
| 915 | theE2 = mkEdge2.Edge(); |
| 916 | |
| 917 | gp_Pnt2d p2d = ProjLib::Project(thePlane, p); |
| 918 | p2d.Coord(x12, y12); |
| 919 | x21 = x12; |
| 920 | y21 = y12; |
| 921 | return Standard_True; |
| 922 | } |
| 923 | } |
| 924 | } |
| 925 | return Standard_False; |
| 926 | } |