DIRECTORY G3dBasic, G3dShape, Rope; G3dWingedEdge: CEDAR DEFINITIONS ~ BEGIN Error: ERROR [code: ATOM, reason: ROPE]; Quad: TYPE ~ G3dBasic.Quad; Face: TYPE ~ G3dShape.Face; Shape: TYPE ~ G3dShape.Shape; Validity: TYPE ~ G3dShape.Validity; Vertex: TYPE ~ G3dShape.Vertex; SurfaceSequence: TYPE ~ G3dShape.SurfaceSequence; ROPE: TYPE ~ Rope.ROPE; WShape: TYPE ~ REF WShapeRep; WShapeRep: TYPE ~ RECORD [ vertexRing: WVertex NIL, edgeRing: WEdge NIL, faceRing: WFace NIL, next, previous: WShape NIL, vertexValidities: ARRAY Validity OF BOOL ALL[FALSE], -- to convert back faceValidities: ARRAY Validity OF BOOL ALL[FALSE], -- to a shape index: INT 0, clientData: REF ANY NIL ]; WFace: TYPE ~ REF WFaceRep; WFaceRep: TYPE ~ RECORD [ basicFace: Face NIL, edgeRing: WEdge NIL, next, previous: WFace NIL, index: INT 0, clientData: REF ANY NIL ]; WEdgeData: TYPE ~ REF WEdgeDataRep; WEdgeDataRep: TYPE ~ RECORD [ aCWedge, bCWedge: WEdge NIL, aCCWedge, bCCWedge: WEdge NIL, aVertex, bVertex: WVertex NIL, aFace, bFace: WFace NIL, index: INT 0, owner: WEdge NIL, clientData: REF ANY NIL ]; WEdge: TYPE ~ REF WEdgeRep; WEdgeRep: TYPE ~ RECORD [ edgeData: WEdgeData NIL, next, previous: WEdge NIL, clientData: REF ANY NIL ]; WVertex: TYPE ~ REF WVertexRep; WVertexRep: TYPE ~ RECORD [ basicVertex: Vertex NIL, edgeRing: WEdge NIL, next, previous: WVertex NIL, index: INT 0, clientData: REF ANY NIL ]; ClockDirection: TYPE ~ { cw, ccw }; WVertexProc: TYPE ~ PROC [v: WVertex]; WEdgeProc: TYPE ~ PROC [e: WEdge]; WFaceProc: TYPE ~ PROC [f: WFace]; ShapeFromWingedEdge: PROC [wShape: WShape] RETURNS [shape: Shape]; WingedEdgeFromShape: PROC [shape: Shape] RETURNS [wShape: WShape]; ApplyToFaces: PROC [wShape: WShape, ff: WFaceProc]; ApplyToEdges: PROC [wShape: WShape, ef: WEdgeProc]; ApplyToVertices: PROC [wShape: WShape, vf: WVertexProc]; NextVertexAroundFaceFromEdge: PROC [edge: WEdge, face: WFace, dir: ClockDirection] RETURNS [WVertex]; NextVertexAroundFaceFromVertex: PROC [vertex: WVertex, face: WFace, dir: ClockDirection] RETURNS [WVertex]; NextVertexAroundVertex: PROC [vertex: WVertex, face: WFace, dir: ClockDirection] RETURNS [WVertex]; VertexAcrossEdge: PROC [vertex: WVertex, edge: WEdge] RETURNS [WVertex]; NextEdgeAroundFaceFromEdge: PROC [edge: WEdge, face: WFace, dir: ClockDirection] RETURNS [WEdge]; NextEdgeAroundVertex: PROC [vertex: WVertex, edge: WEdge, dir: ClockDirection] RETURNS [WEdge]; NextEdgeAroundFaceFromVertex: PROC [vertex: WVertex, face: WFace, dir: ClockDirection] RETURNS [WEdge]; NextFaceAroundEdge: PROC [vertex: WVertex, edge: WEdge, dir: ClockDirection] RETURNS [WFace]; NextFaceAroundVertex: PROC [vertex: WVertex, face: WFace, dir: ClockDirection] RETURNS [WFace]; FaceAcrossEdge: PROC [edge: WEdge, face: WFace] RETURNS [WFace]; ApplyToVertexRing: PROC [vRing: WVertex, vf: WVertexProc]; ApplyToEdgeRing: PROC [eRing: WEdge, ef: WEdgeProc]; ApplyToFaceRing: PROC [fRing: WFace, ff: WFaceProc]; InsertVertexIntoRing: PROC [v: WVertex, vRing: WVertex] RETURNS [WVertex]; InsertCopyOfVertexIntoRing: PROC [v: WVertex, vRing: WVertex] RETURNS [WVertex]; InsertEdgeIntoRing: PROC [e: WEdge, eRing: WEdge] RETURNS [WEdge]; InsertCopyOfEdgeIntoRing: PROC [e: WEdge, eRing: WEdge] RETURNS [WEdge]; InsertFaceIntoRing: PROC [f: WFace, fRing: WFace] RETURNS [WFace]; InsertCopyOfFaceIntoRing: PROC [f: WFace, fRing: WFace] RETURNS [WFace]; ReverseEdgeRing: PROC [eRing: WEdge]; SetWings: PROC [e1, e2: WEdge]; InvertEdge: PROC [edge: WEdge]; EvertEdge: PROC [e: WEdge]; InvertWShape: PROC [wShape: WShape]; EvertWShape: PROC [wShape: WShape]; AnyVertexOnFace: PROC [face: WFace] RETURNS [WVertex]; AnyEdgeOnFace: PROC [face: WFace] RETURNS [WEdge]; AnyEdgeOnVertex: PROC [vertex: WVertex] RETURNS [WEdge]; AnyFaceOnVertex: PROC [vertex: WVertex] RETURNS [WFace]; AnyFaceOnEdge: PROC [edge: WEdge] RETURNS [WFace]; VertexNotOnFirstEdge: PROC [e1, e2: WEdge] RETURNS [WVertex]; EdgeUsingVertex: PROC [eRing: WEdge, v: WVertex] RETURNS [WEdge]; VertexFromIndex: PROC [wShape: WShape, vNum: INT] RETURNS [v: WVertex]; EdgeFromIndex: PROC [wShape: WShape, eNum: INT] RETURNS [e: WEdge]; FaceFromIndex: PROC [wShape: WShape, fNum: INT] RETURNS [f: WFace]; FaceContainingVertices: PROC [v1, v2: WVertex] RETURNS [WFace]; EdgeContainingVertices: PROC [v1, v2: WVertex] RETURNS [WEdge]; VertexContainingEdges: PROC [e1, e2: WEdge] RETURNS [WVertex]; EdgeContainingFaces: PROC [f1, f2: WFace] RETURNS [WEdge]; VertexContainingFaces: PROC [f1, f2: WFace] RETURNS [WVertex]; EdgeAdjacentToFace: PROC [edge: WEdge, face: WFace] RETURNS [BOOL]; VertexAdjacentToFace: PROC [vertex: WVertex, face: WFace] RETURNS [BOOL]; VertexAdjacentToEdge: PROC [vertex: WVertex, edge: WEdge] RETURNS [BOOL]; SpurVertex: PROC [vertex: WVertex] RETURNS [BOOL]; WireEdge: PROC [edge: WEdge] RETURNS [BOOL]; EdgesAroundVertex: PROC [vertex: WVertex] RETURNS [numEdges: INT 0]; FacesAroundVertex: PROC [vertex: WVertex] RETURNS [INT]; VerticesAroundEdge: PROC [edge: WEdge] RETURNS [INT]; FacesAroundEdge: PROC [edge: WEdge] RETURNS [INT]; VerticesAroundFace: PROC [face: WFace] RETURNS [INT]; EdgesAroundFace: PROC [face: WFace] RETURNS [numEdges: INT 0]; VerticesInWShape: PROC [wShape: WShape] RETURNS [INT]; EdgesInWShape: PROC [wShape: WShape] RETURNS [INT]; FacesInWShape: PROC [wShape: WShape] RETURNS [INT]; Genus: PROC [wShape: WShape] RETURNS [INT]; SplitEdge: PROC [wShape: WShape, edge: WEdge] RETURNS [newV: WVertex]; CollapseEdge: PROC [wShape: WShape, edge: WEdge] RETURNS [WVertex]; RemoveEdge: PROC [wShape: WShape, edge: WEdge] RETURNS [WFace]; InsertBridge: PROC [wShape: WShape, v1, v2: WVertex] RETURNS [newFace: WFace NIL, newEdge: WEdge NIL]; RemoveVertex: PROC [wShape: WShape, v1: WVertex] RETURNS [newEdge: WEdge NIL]; NewWShape: PROC RETURNS [WShape]; InsertVertexIntoShape: PROC [wShape: WShape, vetex: WVertex]; InsertEdgeIntoShape: PROC [wShape: WShape, edge: WEdge]; InsertFaceIntoShape: PROC [wShape: WShape, face: WFace]; DeleteWShape: PROC [wShape: WShape]; END.  G3dWingedEdge.mesa Copyright 1990, 1992 by Xerox Corporation. All rights reserved Glassner, March 10, 1990 6:37:23 pm PST Jules Bloomenthal July 15, 1992 5:13 pm PDT Important Note This interface is not fully implemented. However, what is implemented probably works - it has passed a number of tests. If you call an unimplemented routine, you will receive an error stating that there is no implementation yet. Please feel free to provide implementations where they are missing. Imported Types Local Types A Note on These Data Structures There is a note on the architecture of the interface at the end of this file. The general structure is that faces, edges, and vertices are stored in rings (a doubly-linked list). A WShape contains three rings, one each for faces, edges, and vertices. Each edge points to a data structure called WEdgeData, which contains the information for that edge. Each face contains an edge ring describing the edges around that face. Each vertex contains an edge ring of all edges around that vertex. All duplicate instantiations of an edge point to a single WEdgeData structure (this contains a pointer back to its "owner" in the master edge ring in the WShape). Here is a pictorial description of a WShape: [Artwork node; type 'Artwork on' to command tool] The fundamental building block in the system is the edge, represented by WEdgeData. An edge is a directed connection between two vertices (from aVertex to bVertex). Each edge separates two faces (viewing the edge as below, aFace is below and bFace is above). An edge has four "wings"; these are the first edges around the vertex encountered in the specified direction. Again referring to the figure below, on aFace we travel clockwise from the edge to reach aCWedge, and counterclockwise to reach aCCWedge; similarly for bFace and its wings, bCWedge and bCCWedge. [Artwork node; type 'Artwork on' to command tool] Much of the architecture of this interface has been designed to insulate the user from dealing directly with these data structures when executing topological and geometrical operations. Changes to the topology are rather hard to implement; because of the redundancy in the data structures, many pointers must be carefully moved, and in the right order. The most important high-level topological operations are given below under "Euler Operators"; the implementation provides details for these routines. Sometimes you may need to adjust the data structures yourself; I recommend careful study of the data types and the implementations mentioned above, followed by extensive testing; sometimes the correct pointer-stitching order is not obvious, and subtle problems can arise. If you stick to the high-level routines in this interface you should be okay. Function Types Creation / Conversion to Shapes Return a shape from a winged edge representation. Return a winged edge from a shape representation. Apply A Function To All Elements of A WShape Apply the function to all faces in the wShape Apply the function to all edges in the wShape Apply the function to all vertics in the wShape Vertex Access Procedures Walks around the face in the specified direction from the edge to return the next vertex Walks around the face in the specified direction from the vertex to return the next vertex Same as NextVertexAroundFaceFromVertex Returns the vertex across the given edge from the given vertex Edge Access Procedures Walks around the face in the given direction from the given edge Returns the next edge around the given vertex. The order of edges is unspecified and may change as edges are added and removed. Walks around the face in the given direction from the given vertex Face Access Procedures Walks around the vertex from the given edge to find the face containing the given edge Walks around the vertex from the given face to find the next face Returns the face on the other side of the given edge Ring Looping Procedures Apply the given function to each vertex in the ring Apply the given function to each edge in the ring Apply the given function to each face in the ring Construction Utility Procedures Inserts the given vertex into the ring and returns the new, updated ring Inserts a copy of the given vertex into the ring and returns the new, updated ring Inserts the given edge into the ring and returns the new, updated ring Inserts a copy of the given edge into the ring and returns the new, updated ring Inserts the given face into the ring and returns the new, updated ring Inserts the given face into the ring and returns the new, updated ring Reverses the order of edges in the ring Sets the relevant pair of wings between the two edges (1 wing each is affected) Miscellaneous A topological no-op, but useful sometimes, this reverses the direction of the edge Flips an edge over; useful for turning shapes inside-out Applies InvertEdge to each edge in the shape Applies EvertEdge to each edge in the shape Utility Returns any vertex on the given face Returns any edge on the given face Returns any edge on the given vertex Returns any face on the given vertex Returns any face on the given edge Returns the vertex on e2 not in common with e1 Returns any edge in the ring that contains the vertex Lookup Procedures Returns the vertex with the given index number Returns the edge with the given index number Returns the face with the given index number Toplogical Set Operators Returns a face containing both vertices Returns an edge containing both vertices Returns a vertex containing both edge Returns the edge common to both faces Returns a vertex common to both faces Toplogical Predicates Returns TRUE if the edge is adjacent to the face Returns TRUE if the vertex is adjacent to the face Returns TRUE if the vertex is adjacent to the edge Returns TRUE if the vertex is a spur Returns TRUE if the vertex is a wire Valencies Returns the number of edges around the given vertex Returns the number of faces around the given vertex Returns the number of vertices around the given edge Returns the number of faces around the given edge Returns the number of vertices around the given face Returns the number of edges around the given face Returns the number of vertices in the entire shape Returns the number of edges in the entire shape Returns the number of faces in the entire shape Return the topological genus of the surface (usually 2) Euler Operators Insert a new vertex in the edge and the vertex Shrink the edge down to one vertex Remove the edge and return the face subsuming the two old faces Insert a new edge between the two vertices. Usually these were created with SplitEdge. This operation creates a new face and a new edge, both of which are returned. Insert a new edge between the two vertices Node Construction Returns a new (empty) winged-edge shape Insert a new vertex into the shape Insert a new edge into the shape Insert a new face into the shape Delete the shape and all its associated data Architectural Note The basic architecture of this package is based on "The Winged Edge Geometry-Topology Model" by Pat Hanrahan. This title refers both to a library and the documentation that describes it (an unnumbered tech memo from the New York Institute of Technology Computer Graphics Lab). Further references to the winged-edge model are: Baumgart, B.G. A Polyhedron Representation for Computer Vision, Proc. NCC, 1975 Baumgart, B.G. Geometric Modeling for Computer Vision, Stanford AI Project memo 249, 1974 Hanrahan, P. 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