392:
the same data, such as a splitting angle (polygons with normals above this threshold are either automatically treated as separate smoothing groups or some technique such as splitting or chamfering is automatically applied to the edge between them). Additionally, very high resolution meshes are less subject to issues that would require smoothing groups, as their polygons are so small as to make the need irrelevant. Further, another alternative exists in the possibility of simply detaching the surfaces themselves from the rest of the mesh. Renderers do not attempt to smooth edges across noncontiguous polygons.
566:
316:
143:
42:
549:. For certain operations it is necessary to have a fast access to topological information such as edges or neighboring faces; this requires more complex structures such as the winged-edge representation. For hardware rendering, compact, simple structures are needed; thus the corner-table (triangle fan) is commonly incorporated into low-level rendering APIs such as
935:
the vertex list. Then, from those faces, use the face list to find the vertices around them. Winged-edge meshes explicitly store nearly all information, and other operations always traverse to the edge first to get additional info. Vertex-vertex meshes are the only representation that explicitly stores the neighboring vertices of a given vertex.
644:
each end. The other edges may be traversed incrementally. The information for each edge therefore resembles a butterfly, hence "winged-edge" meshes. The above figure shows the "box-cylinder" as a winged-edge mesh. The total data for an edge consists of 2 vertices (endpoints), 2 faces (on each side), and 4 edges (winged-edge).
934:
The notation "V β f1, f2, f3, ... β v1, v2, v3, ..." describes that a traversal across multiple elements is required to perform the operation. For example, to get "all vertices around a given vertex V" using the face-vertex mesh, it is necessary to first find the faces around the given vertex V using
666:
Render dynamic meshes require slightly less storage space than standard winged-edge meshes, and can be directly rendered by graphics hardware since the face list contains an index of vertices. In addition, traversal from vertex to face is explicit (constant time), as is from face to vertex. RD meshes
955:
of static or morphing objects. Winged-edge or render dynamic meshes are used when the geometry changes, such as in interactive modeling packages or for computing subdivision surfaces. Vertex-vertex meshes are ideal for efficient, complex changes in geometry or topology so long as hardware rendering
643:
Winged-edge meshes address the issue of traversing from edge to edge, and providing an ordered set of faces around an edge. For any given edge, the number of outgoing edges may be arbitrary. To simplify this, winged-edge meshes provide only four, the nearest clockwise and counter-clockwise edges at
992:
transmit progressive changes to a mesh as a set of normal displacements from a base mesh. With this technique, a series of textures represent the desired incremental modifications. Normal meshes are compact, since only a single scalar value is needed to express displacement. However, the technique
391:
surface, the crease vertices would have incorrect normals. Thus, some way of determining where to cease smoothing is needed to group smooth parts of a mesh, just as polygons group 3-sided faces. As an alternative to providing surfaces/smoothing groups, a mesh may contain other data for calculating
321:
Objects created with polygon meshes must store different types of elements. These include vertices, edges, faces, polygons and surfaces. In many applications, only vertices, edges and either faces or polygons are stored. A renderer may support only 3-sided faces, so polygons must be constructed of
610:
For rendering, the face list is usually transmitted to the GPU as a set of indices to vertices, and the vertices are sent as position/color/normal structures (in the figure, only position is given). This has the benefit that changes in shape, but not geometry, can be dynamically updated by simply
576:
represent an object as a set of vertices connected to other vertices. This is the simplest representation, but not widely used since the face and edge information is implicit. Thus, it is necessary to traverse the data in order to generate a list of faces for rendering. In addition, operations on
647:
Rendering of winged-edge meshes for graphics hardware requires generating a Face index list. This is usually done only when the geometry changes. Winged-edge meshes are ideally suited for dynamic geometry, such as subdivision surfaces and interactive modeling, since changes to the mesh can occur
606:
Face-vertex meshes improve on VV-mesh for modeling in that they allow explicit lookup of the vertices of a face, and the faces surrounding a vertex. The above figure shows the "box-cylinder" example as an FV mesh. Vertex v5 is highlighted to show the faces that surround it. Notice that, in this
938:
As the mesh representations become more complex (from left to right in the summary), the amount of information explicitly stored increases. This gives more direct, constant time, access to traversal and topology of various elements but at the cost of increased overhead and space in maintaining
544:
Each of the representations above have particular advantages and drawbacks, further discussed in Smith (2006). The choice of the data structure is governed by the application, the performance required, size of the data, and the operations to be performed. For example, it is easier to deal with
635:
explicitly represent the vertices, faces, and edges of a mesh. This representation is widely used in modeling programs to provide the greatest flexibility in dynamically changing the mesh geometry, because split and merge operations can be done quickly. Their primary drawback is large storage
614:
Modeling requires easy traversal of all structures. With face-vertex meshes it is easy to find the vertices of a face. Also, the vertex list contains a list of faces connected to each vertex. Unlike VV meshes, both faces and vertices are explicit, so locating neighboring faces and vertices is
580:
However, VV meshes benefit from small storage space and efficient morphing of shape. The above figure shows a four-sided box as represented by a VV mesh. Each vertex indexes its neighboring vertices. The last two vertices, 8 and 9 at the top and bottom center of the "box-cylinder", have four
528:
used in hardware graphics rendering. The representation is more compact, and more efficient to retrieve polygons, but operations to change polygons are slow. Furthermore, corner-tables do not represent meshes completely. Multiple corner-tables (triangle fans) are needed to represent most
969:
store faces in an ordered, yet independent, way so that the mesh can be transmitted in pieces. The order of faces may be spatial, spectral, or based on other properties of the mesh. Streaming meshes allow a very large mesh to be rendered even while it is still being
366:
set of faces. In systems that support multi-sided faces, polygons and faces are equivalent. However, most rendering hardware supports only 3- or 4-sided faces, so polygons are represented as multiple faces. Mathematically a polygonal mesh may be considered an
593:
541:" mesh represents only vertices, which point to other vertices. Both the edge and face information is implicit in the representation. However, the simplicity of the representation does not allow for many efficient operations to be performed on meshes.
615:
constant time. However, the edges are implicit, so a search is still needed to find all the faces surrounding a given face. Other dynamic operations, such as splitting or merging a face, are also difficult with face-vertex meshes.
515:
which store edges, half-edges, and vertices without any reference to polygons. The polygons are implicit in the representation, and may be found by traversing the structure. Memory requirements are similar to half-edge
490:
in which each edge points to two vertices, two faces, and the four (clockwise and counterclockwise) edges that touch them. Winged-edge meshes allow constant time traversal of the surface, but with higher storage
950:
As a general rule, face-vertex meshes are used whenever an object must be rendered on graphics hardware that does not change geometry (connectivity), but may deform or morph shape (vertex positions) such as
946:
for each of the four technique described in this article. Other representations also exist, such as half-edge and corner tables. These are all variants of how vertices, faces and edges index one another.
322:
many of these, as shown above. However, many renderers either support quads and higher-sided polygons, or are able to convert polygons to triangles on the fly, making it unnecessary to store a mesh in a
1125:
A common but outdated format with hard 16-bit limits on the number of vertices and faces. Neither standardised nor well documented, but used to be a "de facto standard" for data exchange.
659:
Winged-edge meshes are not the only representation which allows for dynamic changes to geometry. A new representation which combines winged-edge meshes and face-vertex meshes is the
984:, progressive meshes give the overall shape of the entire object, but at a low level of detail. Additional data, new edges and faces, progressively increase the detail of the mesh.
603:
represent an object as a set of faces and a set of vertices. This is the most widely used mesh representation, being the input typically accepted by modern graphics hardware.
624:
636:
requirements and increased complexity due to maintaining many indices. A good discussion of implementation issues of Winged-edge meshes may be found in the book
1252:
ASCII format describing 3D geometry. All faces' vertices are ordered counter-clockwise, making facet normals implicit. Smooth normals are specified per vertex.
2037:
1405:
XML-based, open source, royalty-free, extensible, and interoperable; also supports color, texture, and scene information. ISO Standard 19775/19776/19777
663:, which explicitly stores both, the vertices of a face and faces of a vertex (like FV meshes), and the faces and vertices of an edge (like winged-edge).
253:. Different representations of polygon meshes are used for different applications and goals. The variety of operations performed on meshes may include:
1889:
383:, are useful, but not required to group smooth regions. Consider a cylinder with caps, such as a soda can. For smooth shading of the sides, all
607:
example, every face is required to have exactly 3 vertices. However, this does not mean every vertex has the same number of surrounding faces.
581:
connected vertices rather than five. A general system must be able to handle an arbitrary number of vertices connected to any given vertex.
1555:
Open Source. Stores a tetrahedral mesh and its material properties for FEM simulation. ASCII (.veg) and binary (.vegb) formats available.
1005:
for storing polygon mesh data. Each format is most effective when used for the purpose intended by its creator. Popular formats include
468:
Polygon meshes may be represented in a variety of ways, using different methods to store the vertex, edge and face data. These include:
266:
1327:
1058:
Open, ASCII-only format. Each line contains 3 vertices, separated by spaces, to form a triangle, like so: X1 Y1 Z1 X2 Y2 Z2 X3 Y3 Z3
1644:
129:
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must point horizontally away from the center, while the normals of the caps must point straight up and down. Rendered as a single,
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2001:
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do not require the four outgoing edges since these can be found by traversing from edge to face, then face to neighboring edge.
1711:
Lorensen, William E.; Cline, Harvey E. (1 August 1987). "Marching cubes: A high resolution 3D surface construction algorithm".
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which store vertices in a predefined table, such that traversing the table implicitly defines polygons. This is in essence the
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1509:
Open source, providing an ASCII mesh description for linear and polynomially interpolated elements in 1 to 3 dimensions.
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1608:
Open, ASCII or binary format that contains many different data fields, including point data, cell data, and field data.
674:
315:
1138:
258:
242:
1294:
Proprietary binary file format for storing humanoid model geometry with rigging, material, and physics information.
89:
1966:
1767:
Bruce
Baumgart, Winged-Edge Polyhedron Representation for Computer Vision. National Computer Conference, May 1975.
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A position (usually in 3D space) along with other information such as color, normal vector and texture coordinates.
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locally. Traversal across the mesh, as might be needed for collision detection, can be accomplished efficiently.
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RD meshes benefit from the features of winged-edge meshes by allowing for geometry to be dynamically updated.
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Open Source. Binary (.mesh) and ASCII (.mesh.xml) format available. Includes data for vertex animation and
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to apply to different polygons of the mesh. It is also possible for meshes to contain other such vertex
323:
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indicates that a list comparison between two lists must be performed to accomplish the operation; and
440:
which are a separate 2d representation of the mesh "unfolded" to show what portion of a 2-dimensional
404:, which define separate elements of the mesh, and are useful for determining separate sub-objects for
1063:
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of a structure, while polygon meshes only explicitly represent the surface (the volume is implicit).
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with polygon meshes. If the mesh's edges are rendered instead of the faces, then the model becomes a
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Similar to winged-edge meshes except that only half the edge traversal information is used. (see
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indicates that the operation can be performed in constant time, as the data is directly stored;
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Open source parallel adaptive unstructured 3D meshes for PDE based simulation workflows.
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are distinct from polygon meshes in that they explicitly represent both the surface and
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Like the STL format, but with added native color, material, and constellation support.
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371:, or undirected graph, with additional properties of geometry, shape and topology.
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requires a complex series of transformations to create the displacement textures.
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transmit the vertex and face data with increasing levels of detail. Unlike
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On Vertex-Vertex Meshes and Their Use in
Geometric and Biological Modeling
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will be defined, allowing different portions of the mesh to use different
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70: in this article. Unsourced material may be challenged and removed.
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means the average number of edges connected to a given vertex, and
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ASCII data format that describes a hierarchical tree of entities.
1162:
ctivity". A universal format designed to prevent incompatibility.
923:
means the average number of vertices connected to a given vertex;
611:
resending the vertex data without updating the face connectivity.
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1185:
There are two dgn file formats: pre-version 8 and version 8 (V8)
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indicates a search must be done on two indices. The notation
1021:. A table of some more of these formats is presented below:
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is the average number of faces connected to a given vertex.
622:
591:
564:
1856:
502:
480:, and a set of polygons that point to the vertices it uses.
584:
For a complete description of VV meshes see Smith (2006).
1799:
A Mesh Data
Structure for Rendering and Subdivision. 2006
901:
Figure 6: summary of mesh representation operations
1318:
Binary and ASCII format originally designed to aid in
1102:
Proprietary. Binary and ASCII specifications exist.
1959:
1933:
1905:
1663:(a technique for adding detail to a polygon mesh)
1619:Laboratory of Artificial Intelligence for Design
545:triangles than general polygons, especially in
408:or separate actors for non-skeletal animation.
882:Example with 10 vertices, 16 faces, 24 edges:
1883:
1746:
1744:
577:edges and faces are not easily accomplished.
448:information such as colour, tangent vectors,
269:, and many others. Algorithms also exist for
230:, but may also be more generally composed of
8:
434:Most mesh formats also support some form of
1890:
1876:
1868:
1859:open source half-edge mesh representation.
1023:
1724:
130:Learn how and when to remove this message
1657:(a mesh can be manifold or non-manifold)
684:
249:(specifically 3D computer graphics) and
141:
58:Relevant discussion may be found on the
1703:
794:V β f1, f2, f3, ... β v1, v2, v3, ...
720:V β e1, e2, e3, ... β v1, v2, v3, ...
717:V β e1, e2, e3, ... β v1, v2, v3, ...
714:V β f1, f2, f3, ... β v1, v2, v3, ...
651:See Baumgart (1975) for more details.
1770:"Use of Polyhedra in computer vision"
864:
7:
68:adding citations to reliable sources
27:Set of polygons to define a 3D model
1536:data in separate file (.skeleton).
1332:Additive Manufacturing File Format
350:A closed set of edges, in which a
342:A connection between two vertices.
25:
2038:Computer graphics data structures
1353:Virtual Reality Modeling Language
777:V β e1, e2, e3 β f1, f2, f3, ...
1135:Digital Asset Exchange (COLLADA)
1081:Open source, binary-only format
791:V β {v,v1}, {v,v2}, {v,v3}, ...
631:Introduced by Baumgart in 1975,
314:
40:
1863:Polygon Mesh Processing Library
731:F(a,b,c) β {a,b}, {b,c}, {a,c}
245:meshes is a large sub-field of
51:needs additional citations for
1713:ACM SIGGRAPH Computer Graphics
1198:Robert McNeel & Associates
848:Find face with given vertices
681:Summary of mesh representation
569:Figure 2. Vertex-vertex meshes
456:, etc (sometimes also called
1:
1987:Principles of Grid Generation
860:Set intersection of v1,v2,v3
857:Set intersection of v1,v2,v3
854:Set intersection of v1,v2,v3
673:See Tobler & Maierhofer (
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627:Figure 4. Winged-edge meshes
596:Figure 3. Face-vertex meshes
198:that defines the shape of a
1139:Sony Computer Entertainment
1001:There exist many different
708:All vertices around vertex
259:Constructive solid geometry
2064:
1776:. May 1975. Archived from
1364:ISO Standard 14772-1:1997
788:All edges around a vertex
768:All faces around a vertex
400:Some mesh formats contain
298:Several methods exist for
29:
1797:Tobler & Maierhofer,
1546:Vega FEM tetrahedral mesh
900:
896:6*16 + 4*24 + 10*5 = 242
893:3*16 + 8*24 + 10*5 = 290
881:
828:Both vertices of an edge
757:F β e1, e2, e3 β a, b, c
687:
226:), since this simplifies
218:(quads), or other simple
1946:Parallel mesh generation
1687:Triangulation (geometry)
1457:LightWave 3D object File
1283:Polygon Movie Maker data
944:connectivity information
734:F β {a,b}, {b,c}, {a,c}
677:2006) for more details.
1967:Chew's second algorithm
1640:Boundary representation
1219:Drawing Exchange Format
748:All vertices of a face
354:has three edges, and a
1530:Morph target animation
1245:Wavefront Technologies
808:Both faces of an edge
628:
597:
570:
547:computational geometry
157:
1951:Stretched grid method
1522:OGRE Development Team
1415:X3D Compressed Binary
1411:.x3dz, .x3dbz, .x3dvz
960:Other representations
877:6F + 4E + V*avg(E,V)
874:3F + 8E + V*avg(E,V)
655:Render dynamic meshes
626:
595:
568:
145:
2028:3D computer graphics
1824:"Simplicial complex"
907:In the above table,
728:All edges of a face
574:Vertex-vertex meshes
561:Vertex-vertex meshes
533:Vertex-vertex meshes
162:3D computer graphics
64:improve this article
2048:Geometry processing
1997:Ruppert's algorithm
1982:Marching tetrahedra
1972:Image-based meshing
1941:Laplacian smoothing
1735:10.1145/37402.37422
1266:Stanford University
1262:Polygon File Format
1091:Autodesk FBX Format
1068:Blender File Format
956:is not of concern.
953:real-time rendering
942:Figure 7 shows the
851:F(a,b,c) β {a,b,c}
751:F(a,b,c) β {a,b,c}
661:render dynamic mesh
279:rigid-body dynamics
275:collision detection
236:polygons with holes
206:usually consist of
172:is a collection of
1840:Weisstein, Eric W.
1821:Weisstein, Eric W.
1534:Skeletal animation
1390:.x3d, .x3db, .x3dv
1336:ASTM International
1072:Blender Foundation
975:Progressive meshes
939:indices properly.
633:winged-edge meshes
629:
619:Winged-edge meshes
601:Face-vertex meshes
598:
588:Face-vertex meshes
571:
472:Face-vertex meshes
406:skeletal animation
379:More often called
358:has four edges. A
251:geometric modeling
158:
2015:
2014:
2007:Unstructured grid
1631:
1630:
1305:Stereolithography
1273:Binary and ASCII
1172:MicroStation File
905:
904:
890:3*16 + 10*5 = 98
476:A simple list of
369:unstructured grid
289:Volumetric meshes
247:computer graphics
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16:(Redirected from
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1667:Polygon modeling
1661:Mesh subdivision
1419:Web3D Consortium
1398:Web3D Consortium
1378:Web3D Consortium
1357:Web3D Consortium
1024:
982:streaming meshes
965:Streaming meshes
871:3F + V*avg(F,V)
685:
638:Graphics Gems II
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510:Quad-edge meshes
496:Half-edge meshes
381:smoothing groups
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1525:OGRE, purebasic
1501:GMsh Developers
1374:VRML Compressed
1176:Bentley Systems
1033:Organization(s)
999:
989:
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834:E(a,b) β {a,b}
831:E(a,b) β {a,b}
700:Render dynamic
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267:simplification
216:quadrilaterals
166:solid modeling
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79:"Polygon mesh"
62:. Please help
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18:Polygonal mesh
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49:This article
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19:
2002:Tessellation
1992:Regular grid
1915:Polygon mesh
1914:
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1827:
1793:
1782:. Retrieved
1778:the original
1774:baumgart.org
1773:
1763:
1716:
1712:
1706:
1505:GMsh Project
1466:LightWave 3D
1423:Web Browsers
1402:Web Browsers
1382:Web Browsers
1361:Web Browsers
1181:MicroStation
1159:
1155:
1151:
1150:Stands for "
1112:3ds Max File
1039:Description
1003:file formats
1000:
997:File formats
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913:list compare
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887:10 * 5 = 50
771:Pair search
697:Winged-edge
694:Face-vertex
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53:verification
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1925:Volume mesh
1672:Polygonizer
1480:RPI SCOREC
1477:SCOREC apf
1030:Format name
1027:File suffix
917:pair search
868:V*avg(V,V)
485:Winged-edge
452:to control
450:weight maps
442:texture map
306:algorithm.
271:ray tracing
2022:Categories
1784:2005-08-29
1698:References
1650:Hypergraph
1311:3D Systems
1286:Yu Higuchi
1195:Rhino File
1077:Blender 3D
1036:Program(s)
688:Operation
416:Generally
234:, or even
200:polyhedral
90:newspapers
30:See also:
1848:MathWorld
1829:MathWorld
1721:CiteSeerX
1498:Gmsh Mesh
1444:CINEMA 4D
1154:borative
840:Explicit
837:Explicit
820:Explicit
817:Explicit
800:Explicit
797:Explicit
780:Explicit
774:Explicit
760:Explicit
754:Explicit
740:Explicit
737:Explicit
711:Explicit
454:animation
446:attribute
418:materials
412:materials
356:quad face
263:smoothing
228:rendering
208:triangles
204:The faces
120:June 2009
60:talk page
1857:OpenMesh
1682:T-spline
1655:Manifold
1634:See also
1604:Paraview
1587:VTK mesh
1552:Vega FEM
1519:OGRE XML
1223:Autodesk
1116:Autodesk
1095:Autodesk
1048:Raw mesh
929:avg(F,V)
925:avg(E,V)
921:avg(V,V)
909:explicit
503:OpenMesh
478:vertices
458:channels
375:surfaces
364:coplanar
310:Elements
202:object.
176:vertices
148:low poly
1960:Related
1934:Methods
1677:Simplex
1595:Kitware
1270:Various
1249:Various
1228:AutoCAD
1121:3ds Max
1099:Various
1055:Various
1052:Unknown
970:loaded.
551:DirectX
529:meshes.
516:meshes.
422:shaders
360:polygon
326:form.
243:polygon
155:dolphin
104:scholar
1723:
1461:NewTek
1307:Format
1158:esign
1064:.blend
1017:, and
845:Flook
555:OpenGL
402:groups
396:groups
330:vertex
293:volume
277:, and
224:n-gons
106:
99:
92:
85:
77:
1623:LAI4D
1515:.mesh
1474:.smb
1439:Maxon
1152:COLLA
362:is a
111:JSTOR
97:books
1613:.l4d
1583:.vtk
1542:.veg
1494:.msh
1484:PUMI
1453:.lwo
1431:.c4d
1370:.wrz
1349:.wrl
1328:.amf
1315:Many
1300:.stl
1279:.pmd
1258:.ply
1237:.obj
1215:.dwg
1211:.dxf
1191:.3dm
1168:.dgn
1131:.dae
1108:.3ds
1087:.fbx
1044:.raw
1019:.stl
1015:.obj
1011:.dae
1007:.fbx
825:V-E
805:F-E
785:E-V
765:F-V
745:V-F
725:E-F
705:V-V
675:WSCG
553:and
346:face
338:edge
193:face
189:and
184:edge
168:, a
164:and
83:news
1803:PDF
1801:. (
1756:PDF
1754:, (
1731:doi
1600:VTK
1591:VTK
1566:Z3d
1562:z3d
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1320:CNC
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261:),
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160:In
66:by
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