/*
* SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
* Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
*
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* and/or sell copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following conditions:
*
* The above copyright notice including the dates of first publication and
* either this permission notice or a reference to
* http://oss.sgi.com/projects/FreeB/
* shall be included in all copies or substantial portions of the Software.
*
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* OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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*/
/*
** Author: Eric Veach, July 1994.
**
*/
#ifndef __mesh_h_
#define __mesh_h_
#include "glues.h"
typedef struct GLUmesh GLUmesh;
typedef struct GLUvertex GLUvertex;
typedef struct GLUface GLUface;
typedef struct GLUhalfEdge GLUhalfEdge;
typedef struct ActiveRegion ActiveRegion; /* Internal data */
/* The mesh structure is similar in spirit, notation, and operations
* to the "quad-edge" structure (see L. Guibas and J. Stolfi, Primitives
* for the manipulation of general subdivisions and the computation of
* Voronoi diagrams, ACM Transactions on Graphics, 4(2):74-123, April 1985).
* For a simplified description, see the course notes for CS348a,
* "Mathematical Foundations of Computer Graphics", available at the
* Stanford bookstore (and taught during the fall quarter).
* The implementation also borrows a tiny subset of the graph-based approach
* use in Mantyla's Geometric Work Bench (see M. Mantyla, An Introduction
* to Sold Modeling, Computer Science Press, Rockville, Maryland, 1988).
*
* The fundamental data structure is the "half-edge". Two half-edges
* go together to make an edge, but they point in opposite directions.
* Each half-edge has a pointer to its mate (the "symmetric" half-edge Sym),
* its origin vertex (Org), the face on its left side (Lface), and the
* adjacent half-edges in the CCW direction around the origin vertex
* (Onext) and around the left face (Lnext). There is also a "next"
* pointer for the global edge list (see below).
*
* The notation used for mesh navigation:
* Sym = the mate of a half-edge (same edge, but opposite direction)
* Onext = edge CCW around origin vertex (keep same origin)
* Dnext = edge CCW around destination vertex (keep same dest)
* Lnext = edge CCW around left face (dest becomes new origin)
* Rnext = edge CCW around right face (origin becomes new dest)
*
* "prev" means to substitute CW for CCW in the definitions above.
*
* The mesh keeps global lists of all vertices, faces, and edges,
* stored as doubly-linked circular lists with a dummy header node.
* The mesh stores pointers to these dummy headers (vHead, fHead, eHead).
*
* The circular edge list is special; since half-edges always occur
* in pairs (e and e->Sym), each half-edge stores a pointer in only
* one direction. Starting at eHead and following the e->next pointers
* will visit each *edge* once (ie. e or e->Sym, but not both).
* e->Sym stores a pointer in the opposite direction, thus it is
* always true that e->Sym->next->Sym->next == e.
*
* Each vertex has a pointer to next and previous vertices in the
* circular list, and a pointer to a half-edge with this vertex as
* the origin (NULL if this is the dummy header). There is also a
* field "data" for client data.
*
* Each face has a pointer to the next and previous faces in the
* circular list, and a pointer to a half-edge with this face as
* the left face (NULL if this is the dummy header). There is also
* a field "data" for client data.
*
* Note that what we call a "face" is really a loop; faces may consist
* of more than one loop (ie. not simply connected), but there is no
* record of this in the data structure. The mesh may consist of
* several disconnected regions, so it may not be possible to visit
* the entire mesh by starting at a half-edge and traversing the edge
* structure.
*
* The mesh does NOT support isolated vertices; a vertex is deleted along
* with its last edge. Similarly when two faces are merged, one of the
* faces is deleted (see __gl_meshDelete below). For mesh operations,
* all face (loop) and vertex pointers must not be NULL. However, once
* mesh manipulation is finished, __gl_MeshZapFace can be used to delete
* faces of the mesh, one at a time. All external faces can be "zapped"
* before the mesh is returned to the client; then a NULL face indicates
* a region which is not part of the output polygon.
*/
struct GLUvertex
{
GLUvertex* next; /* next vertex (never NULL) */
GLUvertex* prev; /* previous vertex (never NULL) */
GLUhalfEdge* anEdge; /* a half-edge with this origin */
void* data; /* client's data */
/* Internal data (keep hidden) */
GLfloat coords[3]; /* vertex location in 3D */
GLfloat s, t; /* projection onto the sweep plane */
long pqHandle; /* to allow deletion from priority queue */
};
struct GLUface
{
GLUface* next; /* next face (never NULL) */
GLUface* prev; /* previous face (never NULL) */
GLUhalfEdge* anEdge; /* a half edge with this left face */
void* data; /* room for client's data */
/* Internal data (keep hidden) */
GLUface* trail; /* "stack" for conversion to strips */
GLboolean marked; /* flag for conversion to strips */
GLboolean inside; /* this face is in the polygon interior */
};
struct GLUhalfEdge
{
GLUhalfEdge* next; /* doubly-linked list (prev==Sym->next) */
GLUhalfEdge* Sym; /* same edge, opposite direction */
GLUhalfEdge* Onext; /* next edge CCW around origin */
GLUhalfEdge* Lnext; /* next edge CCW around left face */
GLUvertex* Org; /* origin vertex (Overtex too long) */
GLUface* Lface; /* left face */
/* Internal data (keep hidden) */
ActiveRegion* activeRegion; /* a region with this upper edge (sweep.c) */
int winding; /* change in winding number when crossing
from the right face to the left face */
};
#define Rface Sym->Lface
#define Dst Sym->Org
#define Oprev Sym->Lnext
#define Lprev Onext->Sym
#define Dprev Lnext->Sym
#define Rprev Sym->Onext
#define Dnext Rprev->Sym /* 3 pointers */
#define Rnext Oprev->Sym /* 3 pointers */
struct GLUmesh
{
GLUvertex vHead; /* dummy header for vertex list */
GLUface fHead; /* dummy header for face list */
GLUhalfEdge eHead; /* dummy header for edge list */
GLUhalfEdge eHeadSym; /* and its symmetric counterpart */
};
/* The mesh operations below have three motivations: completeness,
* convenience, and efficiency. The basic mesh operations are MakeEdge,
* Splice, and Delete. All the other edge operations can be implemented
* in terms of these. The other operations are provided for convenience
* and/or efficiency.
*
* When a face is split or a vertex is added, they are inserted into the
* global list *before* the existing vertex or face (ie. e->Org or e->Lface).
* This makes it easier to process all vertices or faces in the global lists
* without worrying about processing the same data twice. As a convenience,
* when a face is split, the "inside" flag is copied from the old face.
* Other internal data (v->data, v->activeRegion, f->data, f->marked,
* f->trail, e->winding) is set to zero.
*
* ********************** Basic Edge Operations **************************
*
* __gl_meshMakeEdge( mesh ) creates one edge, two vertices, and a loop.
* The loop (face) consists of the two new half-edges.
*
* __gl_meshSplice( eOrg, eDst ) is the basic operation for changing the
* mesh connectivity and topology. It changes the mesh so that
* eOrg->Onext <- OLD(eDst->Onext)
* eDst->Onext <- OLD(eOrg->Onext)
* where OLD(...) means the value before the meshSplice operation.
*
* This can have two effects on the vertex structure:
* - if eOrg->Org != eDst->Org, the two vertices are merged together
* - if eOrg->Org == eDst->Org, the origin is split into two vertices
* In both cases, eDst->Org is changed and eOrg->Org is untouched.
*
* Similarly (and independently) for the face structure,
* - if eOrg->Lface == eDst->Lface, one loop is split into two
* - if eOrg->Lface != eDst->Lface, two distinct loops are joined into one
* In both cases, eDst->Lface is changed and eOrg->Lface is unaffected.
*
* __gl_meshDelete( eDel ) removes the edge eDel. There are several cases:
* if (eDel->Lface != eDel->Rface), we join two loops into one; the loop
* eDel->Lface is deleted. Otherwise, we are splitting one loop into two;
* the newly created loop will contain eDel->Dst. If the deletion of eDel
* would create isolated vertices, those are deleted as well.
*
* ********************** Other Edge Operations **************************
*
* __gl_meshAddEdgeVertex( eOrg ) creates a new edge eNew such that
* eNew == eOrg->Lnext, and eNew->Dst is a newly created vertex.
* eOrg and eNew will have the same left face.
*
* __gl_meshSplitEdge( eOrg ) splits eOrg into two edges eOrg and eNew,
* such that eNew == eOrg->Lnext. The new vertex is eOrg->Dst == eNew->Org.
* eOrg and eNew will have the same left face.
*
* __gl_meshConnect( eOrg, eDst ) creates a new edge from eOrg->Dst
* to eDst->Org, and returns the corresponding half-edge eNew.
* If eOrg->Lface == eDst->Lface, this splits one loop into two,
* and the newly created loop is eNew->Lface. Otherwise, two disjoint
* loops are merged into one, and the loop eDst->Lface is destroyed.
*
* ************************ Other Operations *****************************
*
* __gl_meshNewMesh() creates a new mesh with no edges, no vertices,
* and no loops (what we usually call a "face").
*
* __gl_meshUnion( mesh1, mesh2 ) forms the union of all structures in
* both meshes, and returns the new mesh (the old meshes are destroyed).
*
* __gl_meshDeleteMesh( mesh ) will free all storage for any valid mesh.
*
* __gl_meshZapFace( fZap ) destroys a face and removes it from the
* global face list. All edges of fZap will have a NULL pointer as their
* left face. Any edges which also have a NULL pointer as their right face
* are deleted entirely (along with any isolated vertices this produces).
* An entire mesh can be deleted by zapping its faces, one at a time,
* in any order. Zapped faces cannot be used in further mesh operations!
*
* __gl_meshCheckMesh( mesh ) checks a mesh for self-consistency.
*/
GLUhalfEdge* __gl_meshMakeEdge(GLUmesh* mesh);
int __gl_meshSplice(GLUhalfEdge* eOrg, GLUhalfEdge* eDst);
int __gl_meshDelete(GLUhalfEdge* eDel);
GLUhalfEdge* __gl_meshAddEdgeVertex(GLUhalfEdge* eOrg);
GLUhalfEdge* __gl_meshSplitEdge(GLUhalfEdge* eOrg);
GLUhalfEdge* __gl_meshConnect(GLUhalfEdge* eOrg, GLUhalfEdge* eDst);
GLUmesh* __gl_meshNewMesh(void);
GLUmesh* __gl_meshUnion(GLUmesh* mesh1, GLUmesh* mesh2);
void __gl_meshDeleteMesh(GLUmesh* mesh);
void __gl_meshZapFace(GLUface* fZap);
#ifdef NDEBUG
#define __gl_meshCheckMesh(mesh)
#else
void __gl_meshCheckMesh(GLUmesh* mesh);
#endif
#endif /* __mesh_h_ */
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