Polygon mesh
Encyclopedia
A polygon mesh or unstructured grid
is a collection of vertices, edges and faces that defines the shape of a polyhedral
object in 3D computer graphics
and solid modeling
. The faces usually consist of triangle
s, quadrilateral
s or other simple convex polygon
s, since this simplifies rendering
, but may also be composed of more general concave polygons, or polygons with holes.
The study of polygon meshes is a large sub-field of computer graphics and geometric modeling. Different representations of polygon meshes are used for different applications and goals. The variety of operations performed on meshes may include Boolean logic, smoothing, simplification, and many others. Network representations, "streaming" and "progressive" meshes, are used to transmit polygon meshes over a network. Volumetric meshes are distinct from polygon meshes in that they explicitly represent both the surface and volume of a structure, while polygon meshes only explicitly represent the surface (the volume is implicit). As polygonal meshes are extensively used in computer graphics, algorithms also exist for ray tracing, collision detection, and rigid-body dynamics of polygon meshes.
A vertex is a position along with other information such as color, normal vector and texture coordinates. An edge is a connection between two vertices. A face is a closed set of edges, in which a triangle face has three edges, and a quad face has four edges. A polygon is a 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 unstructured grid, or undirected graph, with addition properties of geometry, shape and topology.
Surfaces, more often called smoothing groups, 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 surface normal
s must point horizontally away from the center, while the normals of the caps must point in the +/-(0,0,1) directions. Rendered as a single, Phong-shaded
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 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.
Mesh format may or may not define other useful data. Groups may be defined which define separate elements of the mesh and are useful for determining separate sub-objects for skeletal animation
or separate actors for non-skeletal animation. Generally materials will be defined, allowing different portions of the mesh to use different shaders when rendered. Most mesh formats also suppose some form of UV coordinates which are a separate 2d representation of the mesh "unfolded" to show what portion of a 2-dimensional texture map to apply to different polygons of the mesh.
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 triangles than general polygons, especially in computational geometry
. 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 DirectX
and OpenGL
.
However, VV meshes benefit from small storage space and efficient morphing of shape. Figure 2 shows the four-sided cylinder example represented using VV meshes. Each vertex indexes its neighboring vertices. Notice that the last two vertices, 8 and 9 at the top and bottom center of the "box-cylinder", have four connected vertices rather than five. A general system must be able to handle an arbitrary number of vertices connected to any given vertex.
For a complete description of VV meshes see Smith (2006).
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. Figure 3 shows the "box-cylinder" example as an FV mesh. Vertex v5 is highlighted to show the faces that surround it. Notice that, in this example, every face is required to have exactly 3 vertices. However, this does not mean every vertex has the same number of surrounding faces.
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 resending the vertex data without updating the face connectivity.
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 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.
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 each end. The other edges may be traversed incrementally. The information for each edge therefore resembles a butterfly, hence "winged-edge" meshes. Figure 4 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).
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 locally. Traversal across the mesh, as might be needed for collision detection, can be accomplished efficiently.
See Baumgart (1975) for more details.
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 implicit (constant time), as is from face to vertex. RD meshes do not require the four outgoing edges since these can be found by traversing from edge to face, then face to neighboring edge.
RD meshes benefit from the features of winged-edge meshes by allowing for geometry to be dynamically updated.
See Tobler & Maierhofer (WSCG 2006) for more details.
In the above table, explicit indicates that the operation can be performed in constant time, as the data is directly stored; list compare indicates that a list comparison between two lists must be performed to accomplish the operation; and pair search indicates a search must be done on two indices. The notation avg(V,V) means the average number of vertices connected to a given vertex; avg(E,V) means the average number of edges connected to a given vertex, and avg(F,V) is the average number of faces connected to a given vertex.
The notation "V → f1, f2, f3, ... → 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 the vertex list. Then, from those faces, use the face list to find the vertices around them. Notice that 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.
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 indices properly.
Figure 7 shows the connectivity information 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.
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 real-time rendering 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 subdivison surfaces. Vertex-vertex meshes are ideal for efficient, complex changes in geometry or topology so long as hardware rendering is not of concern.
Progressive meshes
transmit the vertex and face data with increasing levels of detail. Unlike streaming meshes, 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.
Normal meshes 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 requires a complex series of transformations to create the displacement textures.
s for storing polygon mesh data. Each format is most effective when used for the purpose intended by its creator.
Some of these formats are presented below:
Unstructured grid
An unstructured grid is a tessellation of a part of the Euclidean plane or Euclidean space by simple shapes, such as triangles or tetrahedra, in an irregular pattern...
is a collection of vertices, edges and faces that defines the shape of a polyhedral
Polyhedron
In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...
object in 3D computer graphics
3D computer graphics
3D computer graphics are graphics that use a three-dimensional representation of geometric data that is stored in the computer for the purposes of performing calculations and rendering 2D images...
and solid modeling
Solid modeling
Solid modeling is a consistent set of principles for mathematical and computer modeling of three dimensional solids. Solid modeling is distinguished from related areas of Geometric modeling and Computer graphics by its emphasis on physical fidelity...
. The faces usually consist of triangle
Triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
s, quadrilateral
Quadrilateral
In Euclidean plane geometry, a quadrilateral is a polygon with four sides and four vertices or corners. Sometimes, the term quadrangle is used, by analogy with triangle, and sometimes tetragon for consistency with pentagon , hexagon and so on...
s or other simple convex polygon
Convex polygon
In geometry, a polygon can be either convex or concave .- Convex polygons :A convex polygon is a simple polygon whose interior is a convex set...
s, since this simplifies rendering
Rendering (computer graphics)
Rendering is the process of generating an image from a model , by means of computer programs. A scene file contains objects in a strictly defined language or data structure; it would contain geometry, viewpoint, texture, lighting, and shading information as a description of the virtual scene...
, but may also be composed of more general concave polygons, or polygons with holes.
The study of polygon meshes is a large sub-field of computer graphics and geometric modeling. Different representations of polygon meshes are used for different applications and goals. The variety of operations performed on meshes may include Boolean logic, smoothing, simplification, and many others. Network representations, "streaming" and "progressive" meshes, are used to transmit polygon meshes over a network. Volumetric meshes are distinct from polygon meshes in that they explicitly represent both the surface and volume of a structure, while polygon meshes only explicitly represent the surface (the volume is implicit). As polygonal meshes are extensively used in computer graphics, algorithms also exist for ray tracing, collision detection, and rigid-body dynamics of polygon meshes.
Elements of mesh modeling
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 many of these, as shown in Figure 1. However, many renderers either support quads and higher-sided polygons, or are able to triangulate polygons to triangles on the fly, making it unnecessary to store a mesh in a triangulated form. Also, in certain applications like head modeling, it is desirable to be able to create both 3- and 4-sided polygons.A vertex is a position along with other information such as color, normal vector and texture coordinates. An edge is a connection between two vertices. A face is a closed set of edges, in which a triangle face has three edges, and a quad face has four edges. A polygon is a 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 unstructured grid, or undirected graph, with addition properties of geometry, shape and topology.
Surfaces, more often called smoothing groups, 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 surface normal
Surface normal
A surface normal, or simply normal, to a flat surface is a vector that is perpendicular to that surface. A normal to a non-flat surface at a point P on the surface is a vector perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a...
s must point horizontally away from the center, while the normals of the caps must point in the +/-(0,0,1) directions. Rendered as a single, Phong-shaded
Phong shading
Phong shading refers to an interpolation technique for surface shading in 3D computer graphics. It is also called Phong interpolation or normal-vector interpolation shading. Specifically, it interpolates surface normals across rasterized polygons and computes pixel colors based on the interpolated...
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 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.
Mesh format may or may not define other useful data. Groups may be defined which define separate elements of the mesh and are useful for determining separate sub-objects for skeletal animation
Skeletal animation
Skeletal animation is a technique in computer animation in which a character is represented in two parts: a surface representation used to draw the character and a hierarchical set of interconnected bones used to animate the mesh...
or separate actors for non-skeletal animation. Generally materials will be defined, allowing different portions of the mesh to use different shaders when rendered. Most mesh formats also suppose some form of UV coordinates which are a separate 2d representation of the mesh "unfolded" to show what portion of a 2-dimensional texture map to apply to different polygons of the mesh.
Representations
Polygon meshes may be represented in a variety of ways, using different methods to store the vertex, edge and face data. These include:- Face-vertex meshes: A simple list of verticesVertex (graph theory)In graph theory, a vertex or node is the fundamental unit out of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges , while a directed graph consists of a set of vertices and a set of arcs...
, and a set of polygons that point to the vertices it uses. - Winged-edge meshes, in which each edge points to two vertices, two faces, and the four (clockwise and counterclockwise) edges that touch it. Winged-edge meshes allow constant time traversal of the surface, but with higher storage requirements.
- Half-edge meshes: Similar to winged-edge meshes except that only half the edge traversal information is used.
- Quad-edge meshes, 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 meshes.
- Corner-tables, which store vertices in a predefined table, such that traversing the table implicitly defines polygons. This is in essence the "triangle fan" 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 meshes.
- Vertex-vertex meshes: A "VV" 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 allows for many efficient operations to be performed on meshes.
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 triangles than general polygons, especially in computational geometry
Computational geometry
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational...
. 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 DirectX
DirectX
Microsoft DirectX is a collection of application programming interfaces for handling tasks related to multimedia, especially game programming and video, on Microsoft platforms. Originally, the names of these APIs all began with Direct, such as Direct3D, DirectDraw, DirectMusic, DirectPlay,...
and OpenGL
OpenGL
OpenGL is a standard specification defining a cross-language, cross-platform API for writing applications that produce 2D and 3D computer graphics. The interface consists of over 250 different function calls which can be used to draw complex three-dimensional scenes from simple primitives. OpenGL...
.
Vertex-vertex meshes
Vertex-vertex meshes 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 edges and faces are not easily accomplished.However, VV meshes benefit from small storage space and efficient morphing of shape. Figure 2 shows the four-sided cylinder example represented using VV meshes. Each vertex indexes its neighboring vertices. Notice that the last two vertices, 8 and 9 at the top and bottom center of the "box-cylinder", have four connected vertices rather than five. A general system must be able to handle an arbitrary number of vertices connected to any given vertex.
For a complete description of VV meshes see Smith (2006).
Face-vertex meshes
Face-vertex meshes 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.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. Figure 3 shows the "box-cylinder" example as an FV mesh. Vertex v5 is highlighted to show the faces that surround it. Notice that, in this example, every face is required to have exactly 3 vertices. However, this does not mean every vertex has the same number of surrounding faces.
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 resending the vertex data without updating the face connectivity.
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 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.
Winged-edge meshes
Introduced by Baumgart 1975, winged-edge meshes 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 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 Graphics Gems II.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 each end. The other edges may be traversed incrementally. The information for each edge therefore resembles a butterfly, hence "winged-edge" meshes. Figure 4 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).
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 locally. Traversal across the mesh, as might be needed for collision detection, can be accomplished efficiently.
See Baumgart (1975) for more details.
Render dynamic meshes
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 render dynamic mesh, which explicitly stores the vertices of a face (like FV meshes), the faces of a vertex (like FV meshes), and the faces and vertices of an edge (like winged-edge).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 implicit (constant time), as is from face to vertex. RD meshes do not require the four outgoing edges since these can be found by traversing from edge to face, then face to neighboring edge.
RD meshes benefit from the features of winged-edge meshes by allowing for geometry to be dynamically updated.
See Tobler & Maierhofer (WSCG 2006) for more details.
Summary of mesh representation
| Operation | Vertex-vertex | Face-vertex | Winged-edge | Render dynamic | |
|---|---|---|---|---|---|
| V-V | All vertices around vertex | Explicit | V → f1, f2, f3, ... → v1, v2, v3, ... | V → e1, e2, e3, ... → v1, v2, v3, ... | V → e1, e2, e3, ... → v1, v2, v3, ... |
| E-F | All edges of a face | F(a,b,c) → {a,b}, {b,c}, {a,c} | F → {a,b}, {b,c}, {a,c} | Explicit | Explicit |
| V-F | All vertices of a face | F(a,b,c) → {a,b,c} | Explicit | F → e1, e2, e3 → a, b, c | Explicit |
| F-V | All faces around a vertex | Pair search | Explicit | V → e1, e2, e3 → f1, f2, f3, ... | Explicit |
| E-V | All edges around a vertex | V → {v,v1}, {v,v2}, {v,v3}, ... | V → f1, f2, f3, ... → v1, v2, v3, ... | Explicit | Explicit |
| F-E | Both faces of an edge | List compare | List compare | Explicit | Explicit |
| V-E | Both vertices of an edge | E(a,b) → {a,b} | E(a,b) → {a,b} | Explicit | Explicit |
| Flook | Find face with given vertices | F(a,b,c) → {a,b,c} | Set intersection of v1,v2,v3 | Set intersection of v1,v2,v3 | Set intersection of v1,v2,v3 |
| Storage size | V*avg(V,V) | 3F + V*avg(F,V) | 3F + 8E + V*avg(E,V) | 6F + 4E + V*avg(E,V) | |
| Example with 10 vertices, 16 faces, 24 edges: | |||||
| 10 * 5 = 50 | 3*16 + 10*5 = 98 | 3*16 + 8*24 + 10*5 = 290 | 6*16 + 4*24 + 10*5 = 242 | ||
| Figure 6: summary of mesh representation operations | |||||
In the above table, explicit indicates that the operation can be performed in constant time, as the data is directly stored; list compare indicates that a list comparison between two lists must be performed to accomplish the operation; and pair search indicates a search must be done on two indices. The notation avg(V,V) means the average number of vertices connected to a given vertex; avg(E,V) means the average number of edges connected to a given vertex, and avg(F,V) is the average number of faces connected to a given vertex.
The notation "V → f1, f2, f3, ... → 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 the vertex list. Then, from those faces, use the face list to find the vertices around them. Notice that 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.
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 indices properly.
Figure 7 shows the connectivity information 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.
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 real-time rendering 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 subdivison surfaces. Vertex-vertex meshes are ideal for efficient, complex changes in geometry or topology so long as hardware rendering is not of concern.
Other representations
Streaming meshes 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 loaded.Progressive meshes
Progressive meshes
Progressive meshes is one of the techniques of dynamic level of detail . This technique was introduced by Hugues Hoppe in 1996. This method uses saving a model to the structure - the progressive mesh, which allows a smooth choice of detail levels depending on the current view...
transmit the vertex and face data with increasing levels of detail. Unlike streaming meshes, 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.
Normal meshes 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 requires a complex series of transformations to create the displacement textures.
File formats
There exist many different file formatFile format
A file format is a particular way that information is encoded for storage in a computer file.Since a disk drive, or indeed any computer storage, can store only bits, the computer must have some way of converting information to 0s and 1s and vice-versa. There are different kinds of formats for...
s for storing polygon mesh data. Each format is most effective when used for the purpose intended by its creator.
Some of these formats are presented below:
| File suffix | Format name | Organization(s) | Program(s) | Description |
|---|---|---|---|---|
| .raw | Raw mesh | Unknown | Various | 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 |
| .blend | Blender File Format | Blender Foundation Blender Foundation The Blender Foundation is a non-profit organization responsible for the development of Blender, an open source program for three-dimensional modeling.... |
Blender 3D Blender (software) Blender is a free and open-source 3D computer graphics software product used for creating animated films, visual effects, interactive 3D applications or video games. The current release version is 2.60, and was released on October 19, 2011... |
Open source, binary-only format |
| .fbx FBX FBX is technology and a file format owned and developed by Autodesk. It is used to provide interoperability between digital content creation applications.-History:... |
Autodesk FBX Format | Autodesk Autodesk Autodesk, Inc. is an American multinational corporation that focuses on 3D design software for use in the architecture, engineering, construction, manufacturing, media and entertainment industries. The company was founded in 1982 by John Walker, a coauthor of the first versions of the company's... |
Various | Proprietary. Binary and ASCII specifications exist. |
| .3ds .3ds 3DS is one of the file formats used by the Autodesk 3ds Max 3D modeling, animation and rendering software.It was the native file format of the old Autodesk 3D Studio DOS , which was popular until its successor replaced it in April 1996... |
3ds Max File | Autodesk Autodesk Autodesk, Inc. is an American multinational corporation that focuses on 3D design software for use in the architecture, engineering, construction, manufacturing, media and entertainment industries. The company was founded in 1982 by John Walker, a coauthor of the first versions of the company's... |
3ds Max | |
| .dae COLLADA COLLADA is a COLLAborative Design Activity for establishing an interchange file format for interactive 3D applications. COLLADA is managed by the nonprofit technology consortium, the Khronos Group.... |
Digital Asset Exchange (COLLADA) | Sony Computer Entertainment Sony Computer Entertainment Sony Computer Entertainment, Inc. is a major video game company specializing in a variety of areas in the video game industry, and is a wholly owned subsidiary and part of the Consumer Products & Services Group of Sony... , Khronos Group Khronos Group The Khronos Group is a not-for-profit member-funded industry consortium based in Beaverton, Oregon, focused on the creation of open standard, royalty-free APIs to enable the authoring and accelerated playback of dynamic media on a wide variety of platforms and devices... |
N/A | Stands for "COLLAborative Design Activity". A universal format designed to prevent incompatibility. |
| .dxf AutoCAD DXF AutoCAD DXF is a CAD data file format developed by Autodesk for enabling data interoperability between AutoCAD and other programs.... |
Drawing Exchange Format | Autodesk Autodesk Autodesk, Inc. is an American multinational corporation that focuses on 3D design software for use in the architecture, engineering, construction, manufacturing, media and entertainment industries. The company was founded in 1982 by John Walker, a coauthor of the first versions of the company's... |
AutoCAD AutoCAD AutoCAD is a software application for computer-aided design and drafting in both 2D and 3D. It is developed and sold by Autodesk, Inc. First released in December 1982, AutoCAD was one of the first CAD programs to run on personal computers, notably the IBM PC... |
|
| .obj | Wavefront OBJ | Wavefront Technologies Wavefront Technologies Wavefront Technologies was a computer graphics company that developed and sold animation software used in Hollywood motion pictures and other industries. It was founded in 1984, in Santa Barbara, California, by Bill Kovacs, Larry Barels, Mark Sylvester... |
Various | ASCII format describing 3D geometry alone. All faces' vertices are ordered counter-clockwise, thus removing the need to specify normals. |
| .ply PLY (file format) PLY is a computer file format known as the Polygon File Format or the Stanford Triangle Format.The format was principally designed to store three dimensional data from 3D scanners. It supports a relatively simple description of a single object as a list of nominally flat polygons... |
Polygon File Format | Stanford University Stanford University The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San... |
Unknown | Binary and ASCII |
| .stl STL (file format) STL is a file format native to the stereolithography CAD software created by 3D Systems. This file format is supported by many other software packages; it is widely used for rapid prototyping and computer-aided manufacturing. STL files describe only the surface geometry of a three dimensional... |
Stereolithography Stereolithography Stereolithography is an additive manufacturing technology for producing models, prototypes, patterns, and in some cases, production parts.-Technology description:... Format |
3D Systems 3D Systems 3D Systems, headquartered in Rock Hill, South Carolina, is a maker of rapid prototyping machines, notable for developing stereolithography and the STL file format.- History :... |
N/A | Binary and ASCII format originally designed to aid in "3D printing". Superseded by the AMF format. |
| .amf Additive Manufacturing File Format Additive Manufacturing File Format is an open standard for describing objects for additive manufacturing processes such as 3D printing. The official ASTM F2915standard is an XML-based format designed to allow any computer-aided design software to describe the shape and composition of any 3D object... |
Additive Manufacturing File Format | ASTM International ASTM International ASTM International, known until 2001 as the American Society for Testing and Materials , is an international standards organization that develops and publishes voluntary consensus technical standards for a wide range of materials, products, systems, and services... |
N/A | Like the STL format, but with added native color, material, and constellation support. |
| .wrl VRML VRML is a standard file format for representing 3-dimensional interactive vector graphics, designed particularly with the World Wide Web in mind... |
Virtual Reality Modeling Language | Web3D Consortium Web3D Consortium The Web3D Consortium is a not-for-profit, member-funded industry consortium whose purpose is to define and develop the X3D royalty-free open standards file format and runtime architecture to represent and communicate 3D scenes.... |
Web Browsers | ISO Standard 14772-1:1997 |
| .wrz VRML VRML is a standard file format for representing 3-dimensional interactive vector graphics, designed particularly with the World Wide Web in mind... |
VRML Compressed | Web3D Consortium Web3D Consortium The Web3D Consortium is a not-for-profit, member-funded industry consortium whose purpose is to define and develop the X3D royalty-free open standards file format and runtime architecture to represent and communicate 3D scenes.... |
Web Browsers | |
| .x3d, .x3db, .x3dv X3D X3D is the ISO standard XML-based file format for representing 3D computer graphics, the successor to the Virtual Reality Modeling Language . X3D features extensions to VRML X3D is the ISO standard XML-based file format for representing 3D computer graphics, the successor to the Virtual Reality... |
Extensible 3D | Web3D Consortium Web3D Consortium The Web3D Consortium is a not-for-profit, member-funded industry consortium whose purpose is to define and develop the X3D royalty-free open standards file format and runtime architecture to represent and communicate 3D scenes.... |
Web Browsers | ISO Standard 19775/19776/19777 |
| .x3dz, .x3dbz, .x3dvz X3D X3D is the ISO standard XML-based file format for representing 3D computer graphics, the successor to the Virtual Reality Modeling Language . X3D features extensions to VRML X3D is the ISO standard XML-based file format for representing 3D computer graphics, the successor to the Virtual Reality... |
X3D Compressed Binary | Web3D Consortium Web3D Consortium The Web3D Consortium is a not-for-profit, member-funded industry consortium whose purpose is to define and develop the X3D royalty-free open standards file format and runtime architecture to represent and communicate 3D scenes.... |
Web Browsers | |
| .c4d Cinema 4D CINEMA 4D is a 3D modeling, animation and rendering application developed by MAXON Computer GmbH of Friedrichsdorf, Germany. It is capable of procedural and polygonal/subd modeling, animating, lighting, texturing, rendering, and common features found in 3d modelling applications.- Overview:The... |
Cinema 4D File | MAXON Maxon Maxon may denote:* An electronic musical device Maxon Effects Pedals.A surname:* Bonnie Maxon American professional wrestler* William Ralph Maxon American botanist... |
CINEMA 4D Cinema 4D CINEMA 4D is a 3D modeling, animation and rendering application developed by MAXON Computer GmbH of Friedrichsdorf, Germany. It is capable of procedural and polygonal/subd modeling, animating, lighting, texturing, rendering, and common features found in 3d modelling applications.- Overview:The... |
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| .mesh | OGRE XML | OGRE Development Team | OGRE, purebasic | |
| .vtk VTK The Visualization Toolkit is an open-source, freely available software system for 3D computer graphics, image processing and visualization. VTK consists of a C++ class library and several interpreted interface layers including Tcl/Tk, Java, and Python. Kitware, whose team created and continues to... |
VTK mesh | VTK VTK The Visualization Toolkit is an open-source, freely available software system for 3D computer graphics, image processing and visualization. VTK consists of a C++ class library and several interpreted interface layers including Tcl/Tk, Java, and Python. Kitware, whose team created and continues to... , Kitware Kitware Kitware, Inc. is a technology company headquartered in Clifton Park, New York. The company specializes in the research and development of open-source software in the fields of computer vision, medical imaging, visualization, 3D data publishing and technical software development... |
VTK VTK The Visualization Toolkit is an open-source, freely available software system for 3D computer graphics, image processing and visualization. VTK consists of a C++ class library and several interpreted interface layers including Tcl/Tk, Java, and Python. Kitware, whose team created and continues to... , Paraview ParaView ParaView is an open source, freely available program for parallel, interactive, scientific visualization. It has a client–server architecture to facilitate remote visualization of datasets, and generates level of detail models to maintain interactive framerates for large datasets. It is an... |
Open, ASCII or binary format that contains many different data fields, including point data, cell data, and field data. |
See also
- Wire-frame model
- Euler operatorEuler operatorIn mathematics, Euler operators are a small set of functions to create polygon meshes. They are closed and sufficient on the set of meshes, and they are invertible.- Purpose :...
- B-rep
- SimplexSimplexIn geometry, a simplex is a generalization of the notion of a triangle or tetrahedron to arbitrary dimension. Specifically, an n-simplex is an n-dimensional polytope which is the convex hull of its n + 1 vertices. For example, a 2-simplex is a triangle, a 3-simplex is a tetrahedron,...
- Triangulation (geometry)
- ManifoldManifoldIn mathematics , a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold....
(a mesh can be manifold or non-manifold)