381:
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.
555:
305:
132:
31:
538:. 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
924:
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.
633:
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).
582:
923:
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
655:
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
944:
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
632:
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
981:
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
380:
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
310:
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
599:
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
565:
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
636:
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
595:
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
927:
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
533:
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
624:
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
603:
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
569:
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
517:
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
958:
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
355:
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
530:" 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.
604:
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.
504:
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
479:
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
613:
939:
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
935:
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.
311:
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
1114:
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.
663:
648:
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
973:, 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.
592:
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.
932:
625:
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
1241:
ASCII format describing 3D geometry. All faces' vertices are ordered counter-clockwise, making facet normals implicit. Smooth normals are specified per vertex.
1394:
XML-based, open source, royalty-free, extensible, and interoperable; also supports color, texture, and scene information. ISO Standard 19775/19776/19777
652:, 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).
242:. Different representations of polygon meshes are used for different applications and goals. The variety of operations performed on meshes may include:
372:, 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
596:
example, every face is required to have exactly 3 vertices. However, this does not mean every vertex has the same number of surrounding faces.
570:
connected vertices rather than five. A general system must be able to handle an arbitrary number of vertices connected to any given vertex.
1544:
Open Source. Stores a tetrahedral mesh and its material properties for FEM simulation. ASCII (.veg) and binary (.vegb) formats available.
1503:
1482:
994:
for storing polygon mesh data. Each format is most effective when used for the purpose intended by its creator. Popular formats include
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Polygon meshes may be represented in a variety of ways, using different methods to store the vertex, edge and face data. These include:
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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
376:
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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do not require the four outgoing edges since these can be found by traversing from edge to face, then face to neighboring edge.
1700:
Lorensen, William E.; Cline, Harvey E. (1 August 1987). "Marching cubes: A high resolution 3D surface construction algorithm".
513:
which store vertices in a predefined table, such that traversing the table implicitly defines polygons. This is in essence the
99:
1498:
Open source, providing an ASCII mesh description for linear and polynomially interpolated elements in 1 to 3 dimensions.
255:
71:
1597:
Open, ASCII or binary format that contains many different data fields, including point data, cell data, and field data.
1316:
1633:
118:
1283:
Proprietary binary file format for storing humanoid model geometry with rigging, material, and physics information.
78:
1990:
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Bruce
Baumgart, Winged-Edge Polyhedron Representation for Computer Vision. National Computer Conference, May 1975.
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323:
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.
56:
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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
1955:
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indicates that a list comparison between two lists must be performed to accomplish the operation; and
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which are a separate 2d representation of the mesh "unfolded" to show what portion of a 2-dimensional
393:, which define separate elements of the mesh, and are useful for determining separate sub-objects for
284:
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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360:, 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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59: 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.
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ctivity". A universal format designed to prevent incompatibility.
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means the average number of vertices connected to a given vertex;
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resending the vertex data without updating the face connectivity.
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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
1010:. 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.
1845:
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1358:
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491:
469:, and a set of polygons that point to the vertices it uses.
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For a complete description of VV meshes see Smith (2006).
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A Mesh Data
Structure for Rendering and Subdivision. 2006
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1308:
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Figure 6: summary of mesh representation operations
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1307:
Binary and ASCII format originally designed to aid in
1091:
Proprietary. Binary and ASCII specifications exist.
1652:(a technique for adding detail to a polygon mesh)
669:
2008:
1608:Laboratory of Artificial Intelligence for Design
534:triangles than general polygons, especially in
397:or separate actors for non-skeletal animation.
871:Example with 10 vertices, 16 faces, 24 edges:
1872:
1735:
1733:
1699:
1693:
566:edges and faces are not easily accomplished.
437:information such as colour, tangent vectors,
258:, and many others. Algorithms also exist for
219:, but may also be more generally composed of
423:Most mesh formats also support some form of
1879:
1865:
1848:open source half-edge mesh representation.
1730:
1713:
119:Learn how and when to remove this message
1646:(a mesh can be manifold or non-manifold)
948:
643:
238:(specifically 3D computer graphics) and
130:
47:Relevant discussion may be found on the
549:
520:
2009:
783:V β f1, f2, f3, ... β v1, v2, v3, ...
709:V β e1, e2, e3, ... β v1, v2, v3, ...
706:V β e1, e2, e3, ... β v1, v2, v3, ...
703:V β f1, f2, f3, ... β v1, v2, v3, ...
640:See Baumgart (1975) for more details.
1860:
1827:
1808:
1759:"Use of Polyhedra in computer vision"
961:
853:
607:
576:
471:
459:
57:adding citations to reliable sources
24:
16:Set of polygons to define a 3D model
1886:
1525:data in separate file (.skeleton).
952:
496:
482:
13:
1321:Additive Manufacturing File Format
611:
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339:A closed set of edges, in which a
331:A connection between two vertices.
14:
2048:
2027:Computer graphics data structures
1801:
1342:Virtual Reality Modeling Language
766:V β e1, e2, e3 β f1, f2, f3, ...
415:
1124:Digital Asset Exchange (COLLADA)
1070:Open source, binary-only format
975:
780:V β {v,v1}, {v,v2}, {v,v3}, ...
620:Introduced by Baumgart in 1975,
507:
303:
29:
1852:Polygon Mesh Processing Library
985:
720:F(a,b,c) β {a,b}, {b,c}, {a,c}
234:meshes is a large sub-field of
40:needs additional citations for
1780:
1750:
1702:ACM SIGGRAPH Computer Graphics
1187:Robert McNeel & Associates
837:Find face with given vertices
670:Summary of mesh representation
558:Figure 2. Vertex-vertex meshes
445:, etc (sometimes also called
1:
1976:Principles of Grid Generation
1686:
849:Set intersection of v1,v2,v3
846:Set intersection of v1,v2,v3
843:Set intersection of v1,v2,v3
662:See Tobler & Maierhofer (
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616:Figure 4. Winged-edge meshes
585:Figure 3. Face-vertex meshes
399:
187:that defines the shape of a
7:
1622:
1128:Sony Computer Entertainment
990:There exist many different
697:All vertices around vertex
362:
298:
248:Constructive solid geometry
10:
2053:
1765:. May 1975. Archived from
1353:ISO Standard 14772-1:1997
777:All edges around a vertex
757:All faces around a vertex
389:Some mesh formats contain
287:Several methods exist for
18:
1948:
1922:
1894:
1786:Tobler & Maierhofer,
1535:Vega FEM tetrahedral mesh
889:
885:6*16 + 4*24 + 10*5 = 242
882:3*16 + 8*24 + 10*5 = 290
870:
817:Both vertices of an edge
746:F β e1, e2, e3 β a, b, c
676:
383:
317:
215:), since this simplifies
207:(quads), or other simple
1935:Parallel mesh generation
1676:Triangulation (geometry)
1446:LightWave 3D object File
1272:Polygon Movie Maker data
933:connectivity information
723:F β {a,b}, {b,c}, {a,c}
666:2006) for more details.
1956:Chew's second algorithm
1629:Boundary representation
1208:Drawing Exchange Format
737:All vertices of a face
343:has three edges, and a
333:
325:
1519:Morph target animation
1234:Wavefront Technologies
797:Both faces of an edge
617:
586:
559:
536:computational geometry
146:
1940:Stretched grid method
1511:OGRE Development Team
1404:X3D Compressed Binary
1400:.x3dz, .x3dbz, .x3dvz
949:Other representations
866:6F + 4E + V*avg(E,V)
863:3F + 8E + V*avg(E,V)
644:Render dynamic meshes
615:
584:
557:
134:
2017:3D computer graphics
1813:"Simplicial complex"
896:In the above table,
717:All edges of a face
563:Vertex-vertex meshes
550:Vertex-vertex meshes
522:Vertex-vertex meshes
151:3D computer graphics
53:improve this article
2037:Geometry processing
1986:Ruppert's algorithm
1971:Marching tetrahedra
1961:Image-based meshing
1930:Laplacian smoothing
1724:10.1145/37402.37422
1255:Stanford University
1251:Polygon File Format
1080:Autodesk FBX Format
1057:Blender File Format
945:is not of concern.
942:real-time rendering
931:Figure 7 shows the
840:F(a,b,c) β {a,b,c}
740:F(a,b,c) β {a,b,c}
650:render dynamic mesh
268:rigid-body dynamics
264:collision detection
225:polygons with holes
195:usually consist of
161:is a collection of
1829:Weisstein, Eric W.
1810:Weisstein, Eric W.
1523:Skeletal animation
1379:.x3d, .x3db, .x3dv
1325:ASTM International
1061:Blender Foundation
964:Progressive meshes
928:indices properly.
622:winged-edge meshes
618:
608:Winged-edge meshes
590:Face-vertex meshes
587:
577:Face-vertex meshes
560:
461:Face-vertex meshes
395:skeletal animation
368:More often called
347:has four edges. A
240:geometric modeling
147:
2004:
2003:
1996:Unstructured grid
1620:
1619:
1294:Stereolithography
1262:Binary and ASCII
1161:MicroStation File
894:
893:
879:3*16 + 10*5 = 98
465:A simple list of
358:unstructured grid
278:Volumetric meshes
236:computer graphics
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1656:Polygon modeling
1650:Mesh subdivision
1408:Web3D Consortium
1387:Web3D Consortium
1367:Web3D Consortium
1346:Web3D Consortium
1013:
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971:streaming meshes
954:Streaming meshes
860:3F + V*avg(F,V)
674:
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627:Graphics Gems II
529:
499:Quad-edge meshes
485:Half-edge meshes
370:smoothing groups
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221:concave polygons
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1558:Oleg Melashenko
1514:OGRE, purebasic
1490:GMsh Developers
1363:VRML Compressed
1165:Bentley Systems
1022:Organization(s)
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823:E(a,b) β {a,b}
820:E(a,b) β {a,b}
689:Render dynamic
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209:convex polygons
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293:marching cubes
256:simplification
205:quadrilaterals
155:solid modeling
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68:"Polygon mesh"
51:. Please help
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64:Find sources:
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38:This article
36:
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27:
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1991:Tessellation
1981:Regular grid
1904:Polygon mesh
1903:
1835:
1816:
1782:
1771:. Retrieved
1767:the original
1763:baumgart.org
1762:
1752:
1705:
1701:
1695:
1494:GMsh Project
1455:LightWave 3D
1412:Web Browsers
1391:Web Browsers
1371:Web Browsers
1350:Web Browsers
1170:MicroStation
1148:
1144:
1140:
1139:Stands for "
1101:3ds Max File
1028:Description
992:file formats
989:
986:File formats
970:
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902:list compare
901:
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895:
876:10 * 5 = 50
760:Pair search
686:Winged-edge
683:Face-vertex
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42:verification
39:
1914:Volume mesh
1661:Polygonizer
1469:RPI SCOREC
1466:SCOREC apf
1019:Format name
1016:File suffix
906:pair search
857:V*avg(V,V)
474:Winged-edge
441:to control
439:weight maps
431:texture map
295:algorithm.
260:ray tracing
2011:Categories
1773:2005-08-29
1687:References
1639:Hypergraph
1300:3D Systems
1275:Yu Higuchi
1184:Rhino File
1066:Blender 3D
1025:Program(s)
677:Operation
405:Generally
223:, or even
189:polyhedral
79:newspapers
19:See also:
1837:MathWorld
1818:MathWorld
1710:CiteSeerX
1487:Gmsh Mesh
1433:CINEMA 4D
1143:borative
829:Explicit
826:Explicit
809:Explicit
806:Explicit
789:Explicit
786:Explicit
769:Explicit
763:Explicit
749:Explicit
743:Explicit
729:Explicit
726:Explicit
700:Explicit
443:animation
435:attribute
407:materials
401:materials
345:quad face
252:smoothing
217:rendering
197:triangles
193:The faces
109:June 2009
49:talk page
1846:OpenMesh
1671:T-spline
1644:Manifold
1623:See also
1593:Paraview
1576:VTK mesh
1541:Vega FEM
1508:OGRE XML
1212:Autodesk
1105:Autodesk
1084:Autodesk
1037:Raw mesh
918:avg(F,V)
914:avg(E,V)
910:avg(V,V)
898:explicit
492:OpenMesh
467:vertices
447:channels
364:surfaces
353:coplanar
299:Elements
191:object.
165:vertices
137:low poly
1949:Related
1923:Methods
1666:Simplex
1584:Kitware
1259:Various
1238:Various
1217:AutoCAD
1110:3ds Max
1088:Various
1044:Various
1041:Unknown
959:loaded.
540:DirectX
518:meshes.
505:meshes.
411:shaders
349:polygon
315:form.
232:polygon
144:dolphin
93:scholar
1712:
1450:NewTek
1296:Format
1147:esign
1053:.blend
1006:, and
834:Flook
544:OpenGL
391:groups
385:groups
319:vertex
282:volume
266:, and
213:n-gons
95:
88:
81:
74:
66:
1612:LAI4D
1504:.mesh
1463:.smb
1428:Maxon
1141:COLLA
351:is a
100:JSTOR
86:books
1602:.l4d
1572:.vtk
1531:.veg
1483:.msh
1473:PUMI
1442:.lwo
1420:.c4d
1359:.wrz
1338:.wrl
1317:.amf
1304:Many
1289:.stl
1268:.pmd
1247:.ply
1226:.obj
1204:.dwg
1200:.dxf
1180:.3dm
1157:.dgn
1120:.dae
1097:.3ds
1076:.fbx
1033:.raw
1008:.stl
1004:.obj
1000:.dae
996:.fbx
814:V-E
794:F-E
774:E-V
754:F-V
734:V-F
714:E-F
694:V-V
664:WSCG
542:and
335:face
327:edge
182:face
178:and
173:edge
157:, a
153:and
72:news
1792:PDF
1790:. (
1745:PDF
1743:, (
1720:doi
1589:VTK
1580:VTK
1555:Z3d
1551:z3d
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250:),
203:),
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