lib/cpExtensions/DataStructures/QuadEdge.h

   1 #ifndef __CPEXTENSIONS__DATASTRUCTURES__QUADEDGE__H__
   2 #define __CPEXTENSIONS__DATASTRUCTURES__QUADEDGE__H__
   3
   4 #include <itkLightObject.h>
   5 #include <cpExtensions/DataStructures/QuadEdgeIterators.h>
   6
   7 namespace cpExtensions
   8   {
   9     namespace DataStructures
  10     {
  11       /**
  12        */
  13       template< typename P, typename D, bool IsPrimal = true >
  14       class QuadEdge
  15         : public itk::LightObject
  16       {
  17       public:
  18         typedef QuadEdge                        Self;
  19         typedef itk::LightObject                Superclass;
  20         typedef itk::SmartPointer< Self >       Pointer;
  21         typedef itk::SmartPointer< const Self > ConstPointer;
  22
  23         /// Vertices and faces types
  24         typedef P TPrimalGeometry;
  25         typedef D TDualGeometry;
  26
  27         /**
  28          * Dual type, basically the same type with swapped template
  29          * parameters.
  30          */
  31         typedef QuadEdge< D, P, !IsPrimal > TDual;
  32         typedef Self                        TPrimal;
  33         typedef typename TDual::Pointer     PtrDual;
  34         friend TDual;
  35
  36         /// Iterators
  37         typedef QuadEdgeIterator< TPrimal >           Iterator;
  38         typedef QuadEdgeConstIterator< TPrimal >      ConstIterator;
  39         typedef QuadEdgePointIterator< TPrimal >      PointIterator;
  40         typedef QuadEdgePointConstIterator< TPrimal > PointConstIterator;
  41
  42       public:
  43         itkNewMacro( Self );
  44         itkTypeMacro( QuadEdge, itkLightObject );
  45
  46         cpPluginsExtensionsQEAllIteratorsMacro( Onext );
  47         cpPluginsExtensionsQEAllIteratorsMacro( Lnext );
  48         cpPluginsExtensionsQEAllIteratorsMacro( Rnext );
  49         cpPluginsExtensionsQEAllIteratorsMacro( Dnext );
  50         cpPluginsExtensionsQEAllIteratorsMacro( Oprev );
  51         cpPluginsExtensionsQEAllIteratorsMacro( Lprev );
  52         cpPluginsExtensionsQEAllIteratorsMacro( Rprev );
  53         cpPluginsExtensionsQEAllIteratorsMacro( Dprev );
  54
  55       public:
  56         void CreateRings( );
  57
  58         /// First order access methods
  59         inline TPrimal* GetOnext( )
  60           { return( this->m_Onext ); }
  61         inline TDual* GetRot( )
  62           { return( this->m_Rot ); }
  63         inline const TPrimal* GetOnext( ) const
  64           { return( this->m_Onext ); }
  65         inline const TDual* GetRot( ) const
  66           { return( this->m_Rot ); }
  67
  68         /// First order configuration methods
  69         inline void SetOnext( TPrimal* e )
  70           { this->m_Onext = e; }
  71         inline void SetRot( TDual* e )
  72           { this->m_Rot = e; }
  73
  74         /// Second order accessors: around base rings
  75         inline TPrimal* GetSym( )
  76           { return( this->m_Rot->m_Rot ); }
  77         inline TDual* GetInvRot( )
  78           { return( this->m_Rot->m_Rot->m_Rot ); }
  79
  80         /// Second order accessors: neighboring topology
  81         inline TPrimal* GetLnext( )
  82           { return( this->m_Rot->m_Rot->m_Rot->m_Onext->m_Rot ); }
  83         inline TPrimal* GetRnext( )
  84           { return( this->m_Rot->m_Onext->m_Rot->m_Rot->m_Rot ); }
  85         inline TPrimal* GetDnext( )
  86           { return( this->m_Rot->m_Rot->m_Onext->m_Rot->m_Rot ); }
  87         inline TPrimal* GetOprev( )
  88           { return( this->m_Rot->m_Onext->m_Rot ); }
  89         inline TPrimal* GetLprev( )
  90           { return( this->m_Onext->m_Rot->m_Rot ); }
  91         inline TPrimal* GetRprev( )
  92           { return( this->m_Rot->m_Rot->m_Onext ); }
  93         inline TPrimal* GetDprev( )
  94           {
  95             return( this->m_Rot->m_Rot->m_Rot->m_Onext->m_Rot->m_Rot->m_Rot );
  96           }
  97
  98         /// Second order accessors: around base rings (const versions)
  99         inline const TPrimal* GetSym( ) const
 100           { return( this->m_Rot->m_Rot ); }
 101         inline const TDual* GetInvRot( ) const
 102           { return( this->m_Rot->m_Rot->m_Rot ); }
 103
 104         /// Second order accessors: neighboring topology (const versions)
 105         inline const TPrimal* GetLnext( ) const
 106           { return( this->m_Rot->m_Rot->m_Rot->m_Onext->m_Rot ); }
 107         inline const TPrimal* GetRnext( ) const
 108           { return( this->m_Rot->m_Onext->m_Rot->m_Rot->m_Rot ); }
 109         inline const TPrimal* GetDnext( ) const
 110           { return( this->m_Rot->m_Rot->m_Onext->m_Rot->m_Rot ); }
 111         inline const TPrimal* GetOprev( ) const
 112           { return( this->m_Rot->m_Onext->m_Rot ); }
 113         inline const TPrimal* GetLprev( ) const
 114           { return( this->m_Onext->m_Rot->m_Rot ); }
 115         inline const TPrimal* GetRprev( ) const
 116           { return( this->m_Rot->m_Rot->m_Onext ); }
 117         inline const TPrimal* GetDprev( ) const
 118           {
 119             return( this->m_Rot->m_Rot->m_Rot->m_Onext->m_Rot->m_Rot->m_Rot );
 120           }
 121
 122         /// Get geometry methods
 123         inline P& GetOrigin( )
 124           { return ( this->m_Origin ); }
 125         inline P& GetDestination( )
 126           { return ( this->m_Rot->m_Rot->m_Origin ); }
 127         inline D& GetRight( )
 128           { return ( this->m_Rot->m_Origin ); }
 129         inline D& GetLeft( )
 130           { return ( this->m_Rot->m_Rot->m_Rot->m_Origin ); }
 131
 132         /// Get geometry methods (const versions)
 133         inline const P& GetOrigin( ) const
 134           { return ( this->m_Origin ); }
 135         inline const P& GetDestination( ) const
 136           { return ( this->m_Rot->m_Rot->m_Origin ); }
 137         inline const D& GetRight( ) const
 138           { return ( this->m_Rot->m_Origin ); }
 139         inline const D& GetLeft( ) const
 140           { return ( this->m_Rot->m_Rot->m_Rot->m_Origin ); }
 141
 142         /// Set geometry methods
 143         inline void SetOrigin( const P& v )
 144           { this->m_Origin = v; }
 145         inline void SetDestination( const P& v )
 146           { this->m_Rot->m_Rot->m_Origin = v; }
 147         inline void SetRight( const D& v )
 148           { this->m_Rot->m_Origin = v; }
 149         inline void SetLeft( const D& v )
 150           { this->m_Rot->m_Rot->m_Rot->m_Origin = v; }
 151         inline void UnsetOrigin( )
 152           { this->m_Origin = TPrimal::NoGeometry; }
 153         inline void UnsetDestination( )
 154           { this->m_Rot->m_Rot->m_Origin = TPrimal::NoGeometry; }
 155         inline void UnsetRight( )
 156           { this->m_Rot->m_Origin = TDual::NoGeometry; }
 157         inline void UnsetLeft( )
 158           { this->m_Rot->m_Rot->m_Rot->m_Origin = TDual::NoGeometry; }
 159
 160         /**
 161          * Set the Left( ) of all the edges in the Lnext( ) ring of "this"
 162          * with the same given geometrical information.
 163          * @param  faceGeom Looks at most maxSize edges in the Lnext( ) ring.
 164          * @return Returns true on success. False otherwise.
 165          */
 166         void SetLnextRingGeometry( const D& v );
 167         void UnsetLnextRingGeometry( );
 168
 169         /// Topological queries
 170         inline bool IsIsolated( ) const
 171           { return( this == this->m_Onext ); }
 172         bool IsEdgeInOnextRing( const TPrimal* e ) const;
 173         bool IsEdgeInLnextRing( const TPrimal* e ) const;
 174         unsigned int GetOnextRingSize( ) const;
 175         unsigned int GetLnextRingSize( ) const;
 176
 177         /**
 178          * @return Returns true when "this" has no faces set on both sides.
 179          *         Return false otherwise.
 180          */
 181         inline bool IsWire( )
 182           { return( !( this->IsLeftSet( ) ) && !( this->IsRightSet( ) ) ); }
 183
 184         /**
 185          * @return Returns true when "this" is on the boundary i.e.
 186          *         one and only one of the faces is set. Return false
 187          *         otherwise.
 188          */
 189         inline bool IsAtBorder( ) const;
 190
 191         /**
 192          * @return Returns true when "this" has faces set on both sides.
 193          *         Return false otherwise.
 194          */
 195         inline bool IsInternal( ) const
 196           { return ( this->IsLeftSet( ) && this->IsRightSet( ) ); }
 197
 198         /// Geometrical queries
 199         inline bool IsOriginSet( ) const
 200           { return ( this->m_Origin != Self::NoGeometry ); }
 201         inline bool IsDestinationSet( ) const
 202           { return ( this->m_Rot->m_Rot->IsOriginSet( ) ); }
 203         inline bool IsRightSet( ) const
 204           { return ( this->m_Rot->IsOriginSet( ) ); }
 205         inline bool IsLeftSet( ) const
 206           { return ( this->m_Rot->m_Rot->m_Rot->IsOriginSet( ) ); }
 207
 208         /**
 209          * \brief Check wether edge's Origin is internal to the mesh (as
 210          * opposed to being on the boundary) by looking if all the edges
 211          * in the Onext() ring have a face set on both their Left() and
 212          * Right() side.
 213          */
 214         bool IsOriginInternal( ) const;
 215
 216         /**
 217          * Definition: an edge is said to be a boundary edge when it is
 218          * adjacent to i.e. when at least one of the faces edge->GetLeft() or
 219          * edge->GetRight() is unset.  Definition: an point is said to be a
 220          * boundary point when at least one of the edges of it's Onext() ring
 221          * is a boundary edge.
 222          *
 223          * Assume "this" edge belongs to a triangulation (i.e. it belongs to a
 224          * QEMesh which represents a 2-manifold) which possesses a boundary.
 225          * Assume "this" edge instance is a boundary edge. Let us denote by P
 226          * the point which is the origin of "this" edge i.e. P is
 227          * this->Origin().  By definition P is a boundary point.  Then AT
 228          * LEAST two [see the note below] edges of the Onext() ring of P
 229          * [which all have the point P as Origin()] are themselves boundary
 230          * edges. And among those boundary edges AT LEAST one has it's Left()
 231          * face unset.  By iterating over the Onext() ring (which defines a
 232          * local ordering on edges) this method searches for the first edge
 233          * whose Left() face is unset AND which is encountered AFTER edgeTest.
 234          *
 235          * @param edgeTest When present, this edge will be considered as
 236          *        the entry edge in the Onext() ring. When absent it shall
 237          *        be defaulted to "this" edge. (see the warning below).
 238          * @return When "this" edge is a boundary edge, return the first
 239          *         edge in "this" Onext() ring whose Left() face is unset
 240          *         AND located after edgeTest.
 241          *         When "this" edge is NOT a boundary edge the 0 is
 242          *         returned.
 243          * @warning When the Mesh possessing "this" edge is a 2-manifold
 244          *          then result of this method is unique in the sense that
 245          *          it is independent from the edgeTest parameter.
 246          *          But when the Mesh is not 2-manifold (this state can
 247          *          happen at intermediary stages of the building process,
 248          *          or during "surgical" operations on the Mesh, and
 249          *          even though the Mesh represents a triangulation)
 250          *          the result of this method is not unique in the sense
 251          *          that the result depends on the edgeTest parameter.
 252          *          Let us illusatre this dependence by considering a
 253          *          Mesh (which is a triangulation) which is not a 2-manifold.
 254          *          Assume the point P (the origin of "this" edge i.e.
 255          *          P = this->Originv()) is TWICE on the border i.e. it
 256          *          is adjacent twice to noface. We can consider the situation
 257          *          of the following diagram, which depicts some Onext()
 258          *          ring around point P:
 259          *
 260          *                       \         /                               //
 261          *                        \   *   /                                //
 262          *                        i3     b2              counter-clockwise //
 263          *                  *       \   /   NO FACE      Onext() order.    //
 264          *                           \ /                                   //
 265          *                 ----b4-----P----b1------                        //
 266          *                           /|\                                   //
 267          *               NO FACE    / | \                                  //
 268          *                         /  |  \    *  <------ a * indicates the //
 269          *                        /   |   \         the presence of a face //
 270          *                       /    |    \                               //
 271          *                     b5    i6     i7                             //
 272          *                     /   *  |  *   \                             //
 273          *                    /       |       \                            //
 274          *
 275          *          On this example, and if we assume the Onext() oder is
 276          *          represented counter-clockwise, the edges are ordered as
 277          *          follows:
 278          *             b1, b2, i3, b4, b5, i6, i7
 279          *          (when arbitrarily starting at edge b1).
 280          *          We have four Boundary edges labeled b1, b2, b4, b5 and
 281          *          we have three internal edges (i.e. non boundary edges)
 282          *          labeled i3, i6 and i7.
 283          *          Depending on edgeTest, the result of this method
 284          *          will NOT return the same edge:
 285          *            - when edgeTest == b5 (or i6 or i7 or b1) then the edge
 286          *              b1 will be returned,
 287          *            - when edgeTest == b2 (or i3 or b4) then the edge
 288          *              b4 will be returned,
 289          *          Eventually, when edgeTest is absent, the result shall
 290          *          depend on the position of "this" in the Onext() ring().
 291          *
 292          */
 293         TPrimal* GetNextBorderEdgeWithUnsetLeft( TPrimal* edge = NULL ) const;
 294
 295         /**
 296          * Assume "this->Originv()" is a boundary point P that is thrice
 297          * adjacent to noface and consider the given situation is the one
 298          * depicted by the following diagram where:
 299          *   - P is "this->Originv()" instance,
 300          *   - the * (star) indicates the presence of a face,
 301          *   - b1, b2, b3, b4, b5, b6 denote boundary edges,
 302          *   - p denotes some generic point,
 303          *   - A and B denote some specific points we want to discuss,
 304          *   - the Onext() ring order is represented counter-clockwise
 305          *     [which is coherent with the definition of edge->GetRigth()]
 306          *     i.e. the ordering of the edges is:
 307          *          b1, b2, b3, b4, b5, b6, b1...
 308          *
 309          *                    p       N       p
 310          *                   / \      O      / \                            //
 311          *                  /   \           /   \                           //
 312          *                 /     \    F    /     \       counter-clockwise  //
 313          *                /      b3   A   b2      \      Onext() ring order //
 314          *               /         \  C  /         \                        //
 315          *              /     *     \ E /     *     \                       //
 316          *             /             \ /             \                      //
 317          *             A------b4------P------b1-------B                     //
 318          *                           / \                                    //
 319          *                          /   \                                   //
 320          *             NO FACE     /     \      NO FACE                     //
 321          *                        /       \                                 //
 322          *                      b5         b6                               //
 323          *                      /     *     \                               //
 324          *                     /             \                              //
 325          *                    p---------------p                             //
 326          *
 327          * At P this Mesh doesn't represent a 2-manifold (since we are thrice
 328          * on the boundary). Nevertheless such a situation could arise in
 329          * intermediary stages (e.g. when building the Mesh, or during
 330          * surgical changes on the Mesh).
 331          *    Now, assume we are asked to build the triangle [P, A, B]. Note
 332          * that this request is not absurd since the current situation at
 333          * P isn't the one of a 2-manifold: hence when building the current
 334          * Onext() ring of P, we had not enough information to decide
 335          * wheter b4.Onext() should be b5 or b1. It is ONLY when we are
 336          * required to build the triangle [P, A, B] that we have the
 337          * additional information that b4.Onext() is indeed b1.
 338          *    When we are required to build triangle [P, A, B], we hence
 339          * need to change the Onext() ring order at P, i.e. we need to deal
 340          * with the triangle [P, b5, b6] which currently prevents
 341          * b4.Onext() to be b1. In other terms, when considering the
 342          * additional information that b4.Onext() is b1, and before
 343          * building the triangle [P, A, B], we need to reorder
 344          * the Onext() ring of P from it's current state
 345          *    b1, b2, b3, b4, b5, b6, b1...
 346          * to an order coherent with the [P, A, B] request, i.e.
 347          *     b1, b2, b5, b6, b3, b4, b1...
 348          *
 349          * In order to establish the "proper" Onext() ring at P we use
 350          * two Splice operations. The algorithm goes:
 351          *   - first disconnect the piece of the surface containing the edge
 352          *     [PB] (it would be the same process if we chose [PA]) from
 353          *     the Onext() ring at P.
 354          *   - second, re-integrate the disconnected piece at the desired
 355          *     location i.e. side by side with [PA] (respectively [PB] if
 356          *     we chose [PA] at first stage).
 357          * By "piece of surface containing the edge [PB]" we mean [all]
 358          * the triangle[s] starting at [PB] in the Onext() order and
 359          * having a left face set.
 360          *
 361          * We can illustrate this process on bit more general diagram than
 362          * the last case (where the "piece of surface containing the edge
 363          * [PB]" is constituted by two triangles) and when using
 364          * the arguments of this method (i.e. [PA] = this and [PB] = second).
 365          * The initial stage is the following (we note first=this=[PA] and
 366          * second=[PB]) where the Onext() ring order is:
 367          *     first, b2, b3, second, b5, bsplice, b7, first...
 368          *
 369          *                    p       N       A                            //
 370          *                   / \      O      / \                           //
 371          *                  /   \           /   \                          //
 372          *                 /     \    F    /     \     counter-clockwise   //
 373          *                /      b2   A  first    \    Onext() ring order  //
 374          *               /         \  C  /         \                       //
 375          *              /     *     \ E /     *     \                      //
 376          *             /             \ /             \                     //
 377          *            p-------b3------P------b7-------p                    //
 378          *                           /|\                                   //
 379          *                          / | \                                  //
 380          *          NO FACE        /  |  \      NO FACE                    //
 381          *                        /   |   \                                //
 382          *                  second   b5   bsplice                          //
 383          *                      /  *  |  *  \                              //
 384          *                     /      |      \                             //
 385          *                    B-------p-------p                            //
 386          *
 387          * The first stage, implemented as
 388          *     second->Oprev()->Splice( bsplice ),
 389          * yields the following diagram:
 390          *
 391          *                    p       N       A                            //
 392          *                   / \      O      / \                           //
 393          *                  /   \     F     /   \                          //
 394          *                 /     \    A    /     \      counter-clockwise  //
 395          *                /      b2   C  first    \     Onext() ring order //
 396          *               /         \  E  /         \                       //
 397          *              /     *     \   /     *     \                      //
 398          *             /             \ /             \                     //
 399          *            p-------b3------P------b7-------p                    //
 400          *                                                                 //
 401          *                         NO FACE                                 //
 402          *                                                                 //
 403          *                           /|\                                   //
 404          *                          / | \                                  //
 405          *                         /  |  \                                 //
 406          *                        /   |   \                                //
 407          *                  second   b5   bsplice                          //
 408          *                      /  *  |  *  \                              //
 409          *                     /      |      \                             //
 410          *                    B-------p-------p                            //
 411          *
 412          * and the second stage, implemented as
 413          *      first->Splice( bsplice ),
 414          * yields the following diagram:
 415          *
 416          *                                    A                            //
 417          *         B__        NO FACE        / \                           //
 418          *         |  \__                   /   \                          //
 419          *         |     \__               /     \       counter-          //
 420          *         |      second         first    \      clockwise for all //
 421          *         |           \__       /         \                       //
 422          *         |     *        \__   /     *     \                      //
 423          *         |                 \ /             \                     //
 424          *         p-------b5---------P------b7-------p                    //
 425          *         |               __/|\                                   //
 426          *         |     *      __/   | \                                  //
 427          *         |           /      |  \      NO FACE                    //
 428          *         |     bsplice      |   \                                //
 429          *         |   __/           b2    b3                              //
 430          *         p__/               |  *  \                              //
 431          *                NO FACE     |      \                             //
 432          *                            p-------p                            //
 433          *
 434          */
 435         inline static bool ReorderOnextRing( TPrimal* first, TPrimal* second );
 436
 437         /**
 438          * \brief Basic quad-edge topological method.
 439          *
 440          * This method describes all possible topological operations on an
 441          * edge since it is its own inverse. It works in two ways:
 442          *
 443          *   1. If this->m_Org != b->m_Org, it slice a face in two.
 444          *   2. If this->m_Org == b->m_Org, it unifies two faces.
 445          */
 446         inline static void Splice( TPrimal* a, TPrimal* b );
 447
 448       protected:
 449         QuadEdge( );
 450         virtual ~QuadEdge( );
 451
 452       public:
 453         static const TPrimalGeometry NoGeometry;
 454
 455       protected:
 456         Pointer         m_Onext;  /**< Onext ring */
 457         PtrDual         m_Rot;    /**< Rot ring */
 458         TPrimalGeometry m_Origin; /**< Geometry attached to edge's origin */
 459       };
 460
 461     } // ecapseman
 462
 463 } // ecapseman
 464
 465 #include <cpExtensions/DataStructures/QuadEdge.hxx>
 466
 467 #endif // __CPEXTENSIONS__DATASTRUCTURES__QUADEDGE__H__
 468
 469 // eof - $RCSfile$