In 3D computer graphics, polygonal modeling is an approach for modeling objects by representing or approximating their surfaces using polygons. Polygonal modeling is well suited to scanline rendering and is therefore the method of choice for real-time computer graphics. Alternate methods of representing 3D objects include NURBS surfaces, subdivision surfaces, and equation-based representations used in ray tracers. To meet Wikipedias quality standards, this article or section may require cleanup. ... An open surface with X-, Y-, and Z-contours shown. ... Look up Polygon in Wiktionary, the free dictionary. ... Scanline rendering is a rendering algorithm in 3D computer graphics that works on a point-by-point basis rather than polygon-by-polygon basis. ... Real-time computer graphics is the subfield of computer graphics focused on producing and analyzing images in real time. ... NURBS, short for nonuniform rational B-spline, is a computer graphics technique for drawing curves. ... In computer graphics, subdivision surfaces are used to create smooth surfaces out of arbitrary meshes. ... A ray traced scene. ...

Geometric Theory and Polygons

The basic object used in mesh modeling is a vertex, a point in three dimensional space. Two vertices connected by a straight line become an edge. Three vertices, connected to the each other by three edges, define a triangle, which is the simplest polygon in Euclidean space. More complex polygons can be created out of multiple triangles, or as a single object with more than 3 vertices. Four sided polygons (generally referred to as quads) and triangles are the most common shapes used in polygonal modeling. A group of polygons, connected to each other by shared vertices, is generally referred to as an element. Each of the polygons making up an element is called a face. In geometry, a vertex (Latin: whirl, whirlpool; plural vertices) is a corner of a polygon (where two sides meet) or of a polyhedron (where three or more faces and an equal number of edges meet). ... This article just presents the basic definitions. ... A triangle is one of the basic shapes of geometry: a polygon with three vertices and three sides which are straight line segments. ... In mathematics, Euclidean space is a generalization of the 2- and 3-dimensional spaces studied by Euclid. ... A polygon (from the Greek poly, for many, and gonos, for angle) is a closed planar path composed of a finite number of sequential straight line segments. ...

In Euclidean geometry, any three points determine a plane. For this reason, triangles always inhabit a single plane. This is not necessarily true of more complex polygons, however. The flat nature of triangles makes it simple to determine their surface normal, a three-dimensional vector perpendicular to the triangle's edges. Surface normals are useful for determining light transport in ray tracing, and are a key component of the popular Phong shading model. Some rendering systems use vertex normals instead of surface normals to create a better-looking lighting system at the cost of more processing. Note that every triangle has two surface normals, which face away from each other. In many systems only one of these normals is considered valid – the other side of the polygon is referred to as a backface, and can be made visible or invisible depending on the programmer’s desires. Euclid Euclidean geometry is a mathematical system due to the Hellenistic mathematician Euclid of Egypt. ... In mathematics, a plane is the fundamental two-dimensional object. ... A surface normal, or just normal to a flat surface is a three-dimensional vector which is perpendicular to that surface. ... It has been suggested that Phong reflection model be merged into this article or section. ...

Many modeling programs do not strictly enforce geometric theory; for example, it is possible for two vertices to have two distinct edges connecting them, occupying the exact same spatial location. It is also possible for two vertices to exist at the same spatial coordinates, or two faces to exist at the same location. Situations such as these are usually not desired by the user, and must be fixed manually. The rewrite of this article is being devised at Talk:3D computer graphics/Temp. ...

A group of polygons which are connected together by shared vertices is referred to as a mesh. In order for a mesh to appear attractive when rendered, it is desirable that it be non-self-intersecting, meaning that no edge passes through a polygon. Another way of looking at this is that the mesh cannot pierce itself. It is also desirable that the mesh not contain any errors such as doubled vertices, edges, or faces. For some purposes it is important that the mesh be manifold – that is, that it not contain holes or singularities (locations where two distinct sections of the mesh are connected by a single vertex). Rendering is the process of generating an image from a model, by means of a software program. ... On a sphere, the sum of the angles of a triangle is not equal to 180°. A sphere is not a Euclidean space, but locally the laws of the Euclidean geometry are good approximations. ...

Construction of Polygonal Meshes

Although it is possible to construct a mesh by manually specifying vertices and faces, it is much more common to build meshes using a variety of tools. A wide variety of 3d graphics software packages are available for use in constructing polygon meshes. Modeling in LightWave. ...

One of the more popular methods of constructing meshes is box modeling, which uses two simple tools: Box modeling is a technique in 3D modeling. ...

• The subdivide tool splits faces and edges into smaller pieces by adding new vertices. For example, a square would be subdivided by adding one vertex in the center and one on each edge, creating four smaller squares.

• The extrude tool is applied to a face or a group of faces. It creates a new face of the same size and shape which is connected to each of the existing edges by a face. Thus, performing the extrude operation on a square face would create a cube connected to the surface at the location of the face.

A second common modeling method is sometimes referred to as inflation modeling or extrusion modeling. In this method, the user creates a 2d shape which traces the outline of an object from a photograph or a drawing. The user then uses a second image of the subject from a different angle and extrudes the 2d shape into 3d, again following the shape’s outline. This method is especially common for creating faces and heads. In general, the artist will model half of the head and then duplicate the vertices, invert their location relative to some plane, and connect the two pieces together. This ensures that the model will be symmetrical.

Another common method of creating a polygonal mesh is by connecting together various primitives, which are predefined polygonal meshes created by the modeling environment. Common primitives include:

• Cubes
• Pyramids
• Cylinders
• 2D primitives, such as squares, triangles, and disks
• Specialized or esoteric primitives, such as the Utah Teapot or Suzanne, Blender's monkey mascot.
• Spheres - Spheres are commonly represented in one of two ways:
  • Icospheres are icosahedrons which possess a sufficient number of triangles to resemble a sphere.
  • UV Spheres are composed of quads, and resemble the grid seen on some globes - quads are larger near the "equator" of the sphere and smaller near the "poles," eventually terminating in a single vertex.

Finally, some specialized methods of constructing high or low detail meshes exist. Sketch based modeling is a user-friendly interface for constructing low-detail models quickly, while 3d scanners can be used to create high detail meshes based on existing real-world objects in almost automatic way. These devices are very expensive, and are generally only used by researchers and industry professionals but can generate high accuracy sub-millimetric digital representations. The Utah teapot A Melitta teapot, the model of the Utah teapot The Utah teapot or Newell teapot is a 3D model which has become a standard reference object (and something of an in-joke) in the computer graphics community. ... Blender is a free 3D modeler program. ... An icosahedron [ˌaıkəsəhiːdrən] noun (plural: -drons, -dra [-drə]) is a polyhedron having 20 faces, but usually a regular icosahedron is meant. ... Sketch based modeling is a method of creating 3D models for use in 3D computer graphics applications. ... A 3D scanner is a device that analyzes a real-world object or environment to collect data on its shape and possibly color. ...

Extensions

Once a polygonal mesh has been constructed, further steps must be taken before it is useful for games, animation, etc. The model must be texture mapped to add colors and texture to the surface and it must be given an inverse kinematics skeleton for animation. Meshes can also be assigned weights and centers of gravity for use in physical simulation. Texture mapping is a method of adding realism to a computer-generated graphic. ... Inverse kinematics is the process of determining the movement of interconnected segments of a body or model. ... Dynamical simulation, in computational physics, is the simulation of systems of objects that are free to move, usually in three dimensions according to Newtons laws of dynamics, or approximations thereto. ...

In order to display a model on a computer screen outside of the modeling environment, it is necessary to store that model in one of the file formats listed below, and then use or write a program capable of loading from that format. The two main methods of displaying 3d polygon models are OpenGL and Direct3D. Both of these methods can be used with or without a graphics card. A file format is a particular way to encode information for storage in a computer file. ... OpenGL official logo OpenGL (Open Graphics Library) is a standard specification defining a cross-language cross-platform API for writing applications that produce 3D computer graphics (and 2D computer graphics as well). ... This article or section does not cite its references or sources. ... A graphics/video/display card/board/adapter is a computer component designed to convert the logical representation of visual information into a signal that can be used as input for a display medium. ...

Advantages and disadvantages

There are many disadvantages to representing an object using polygons. Polygons are incapable of accurately representing curved surfaces, so a large number of them must be used to approximate curves in a visually appealing manner. The use of complex models has a cost in lowered speed. In scanline conversion, each polygon must be converted and displayed, regardless of size, and there are frequently a large number of models on the screen at any given time. Often, programmers must use multiple models at varying levels of detail to represent the same object in order to cut down on the number of polygons being rendered. Scanline rendering is a rendering algorithm in 3D computer graphics that works on a point-by-point basis rather than polygon-by-polygon basis. ... In computer programming, level of detail involves decreasing the detail of a model or object as it moves away from the viewer. ...

The main advantage of polygons is that they are faster than other representations. While a modern graphics card can show a highly detailed scene at a frame rate of 60 frames per second or higher, raytracers, the main way of displaying non-polygonal models, are incapable of achieving an interactive frame rate (10 fps or higher) with a similar amount of detail. Frame rate, or frame frequency, is the measurement of how quickly an imaging device produces unique consecutive images called frames. ... A ray traced scene. ...

File Formats

A variety of formats are available for storing 3d polygon data. The most popular are:

• .3ds, .max, which is associated with 3D Studio Max
• .mb and .ma, which are associated with Maya
• .lwo, which is associated with Lightwave
• .obj (Wavefront's "The Adanced Visualizer")
• .C4d associated with Cinema 4D
• .dxf, .dwg, .dwf, associated with AutoCAD
• .md3, .md2, associated with the Quake series of games
• .fbx (Alias)
• .rwx (Renderware)
• .wrl (VRML 2.0)

3D Studio Max (sometimes called 3DS Max, 3DS MAX, 3ds Max, 3ds MAX, or just MAX) is a 3D modeler developed by Autodesk Media & Entertainment (formerly known as Discreet and Kinetix). ... Maya is a high-end 3D computer graphics software package by Alias but now owned by Autodesk Media & Entertainment used in the film and TV industry, as well as for computer and video games. ... LightWave (or, more properly, LightWave 3D) is a computer graphics program for 3D modeling, rendering, and animation. ... OBJ (or . ... AutoCAD 2006 drawing. ... Zombies attacking the player. ...

External links

• Free models in a variety of formats: 3dcafe
• Computer graphics latest news, reviews, tutorials and interviews: InsideCG
• Computer graphics news: CG Channel
• Computer graphics forums, reviews, and contests: CG Society
• Open Source 3d modeling program: Blender [1]
• Simple, small and open source 3D modelling program: Wings 3D [2]
• Open Source 3D modeling program: AutoQ3D [3]

Blender is a free 3D modeler program. ... Wings 3D is a free and open source polygon mesh modeler inspired by Nendo and Mirai from Izware. ... AutoQ3D is an open source OpenGL based software used for 3D modeling. ...

References

OpenGL SuperBible (3rd ed.), by Richard S Wright and Benjamin Lipchak ISBN 0672326019

OpenGL Programming Guide: The Official Guide to Learning OpenGL, Version 1.4, Fourth Edition by OpenGL Architecture Review Board ISBN 0321173481

OpenGL(R) Reference Manual : The Official Reference Document to OpenGL, Version 1.4 (4th Edition) by OpenGL Architecture Review Board ISBN 032117383X

Blender documentation: http://www.blender.org/cms/Documentation.628.0.html

Maya documentation: packaged with Alias Maya, http://www.alias.com/eng/index.shtml

See also

• Finite element analysis / method
• Polygon mesh
• Vector graphics