In mathematics, a plane is a two-dimensional manifold or surface that is perfectly flat. Informally it can be thought of as an infinitely vast and infinitesimally thin sheet oriented in some space.

When working in two-dimensional Euclidean space, the definite article is used, the plane, to refer to the whole space. Many fundamental tasks in geometry, trigonometry, and graphing are performed in two-dimensional space, or in other words, in the plane. A lot of mathematics can be and has been performed in the plane, notably in the areas of geometry, trigonometry, graph theory and graphing.

Euclidean geometry

In Euclidean space a plane is a surface such that, given any two distinct points on the surface, the surface also contains the unique straight line that passes through those points.

The fundamental structure of two such planes will always be the same. In mathematics this is described as topological equivalence. Informally though, it means that any two planes look the same.

A plane can be uniquely determined by any of the following (sets of) objects:

• three non-collinear points (ie. not lying on the same line)
• a line and a point not on the line
• two lines with one point of intersection
• two parallel lines

Properties

In three-dimensional Euclidean space, we may exploit the following facts that do not hold in higher dimensions:

• Two planes are either parallel or they intersect in a line.
• A line is either parallel to a plane or intersects it at a single point or is contained in the plane.
• Two lines normal (perpendicular) to the same plane must be parallel to each other.
• Two planes normal to the same line must be parallel to each other.

The plane areas of mathematics

In addition to its familiar geometric structure, with isomorphisms that are isometries with respect to the usual inner product, the plane may be viewed at various other levels of abstraction. Each level of abstraction corresponds to a specific category.

At one extreme, all geometrical and metric concepts may be dropped to leave the topological plane, which may be thought of as an idealised homotopically trivial infinite rubber sheet, which retains a notion of proximity, but has no distances. The topological plane has a concept of a linear path, but no concept of a straight line. The topological plane, or its equivalent the open disc, is the basic topological neighbourhood used to construct surfaces (or 2-manifolds) classified in low-dimensional topology. Isomorphisms of the topological plane are all continuous bijections. The topological plane is the natural context for the branch of graph theory that deals with planar graphs, and results such as the four color theorem.

The plane may also be viewed as an affine space, whose isomorphisms are combinations of translations and non-singular linear maps. From this viewpoint there are no distances, but colinearity and ratios of distances on any line are preserved.

Differential geometry views a plane as a 2-dimensional real manifold, a topological plane which is provided with a differential structure. Again in this case, there is no notion of distance, but there is now a concept of smoothness of maps, for example a differentiable or smooth path (depending on the type of differential structure applied). The isomorphisms in this case are bijections with the chosen degree of differentiability.

In the opposite direction of abstraction, we may apply a compatible field structure to the geometric plane, giving rise to the complex plane and the major area of complex analysis. The complex field has only two isomorphisms, the identity and conjugation.

In the same way as in the real case, the plane may also be viewed as the simplest, one-dimensional (over the complex numbers) complex manifold, sometimes called the complex line. However, this viewpoint contrasts sharply with the case of the plane as a 2-dimensional real manifold. The isomorphisms are all conformal bijections of the complex plane, but the only possibilities are maps that correspond to the composition of a multiplication by a complex number and a translation.

In addition, the Euclidean geometry (which has zero curvature everywhere) is not the only geometry that the plane may have. The plane may be given a spherical geometry by using the stereographic projection. This can be thought of as placing a sphere on the plane (just like a ball on the floor), removing the top point, and projecting the sphere onto the plane from this point). This is one of the projections that may be used in making a flat map of part of the Earth’s surface. The resulting geometry has constant positive curvature.

Alternatively, the plane can also be given a metric which gives it constant negative curvature giving the hyperbolic plane. The latter possibility finds an application in the theory of special relativity in the simplified case where there is one dimension of space and one of time.

A pyramid is any three-dimensional structure where the upper surfaces are triangular and converge on one point. The base of pyramids are usually quadrilateral or trilateral (but generally may be of any polygon shape), meaning that a pyramid usually has four or three sides. The measurements of these triangles uniformly classify the shape as isosceles and sometimes equilateral.

A pyramid’s design, with the majority of the weight closer to the ground, means that less material higher up on the pyramid will be pushing down from above. This allowed early civilizations to create stable monumental structures. For thousands of years, the largest structures on Earth were pyramids: first the Red Pyramid in the Dashur Necropolis and then the Great Pyramid of Khufu, the only remaining Wonder of the World. The largest pyramid ever built, by volume, is the Great Pyramid of Cholula, in the Mexican state of Puebla. This pyramid is considered the largest monument ever constructed anywhere in the world, and is still being excavated. Although the name pyramid is used across the world to describe ancient structures convention dictates that naming them such is not really correct. Technically a true pyramid has four smooth sides and the only ones that exist are those in Egypt and various other areas around the world which were based on the Egyptian model.

Egyptian pyramidsThe most famous pyramids are the Egyptian pyramids — huge structures built of brick or stone, some of which are among the largest man-made constructions. Pyramids functioned as tombs for pharaohs. In Ancient Egypt, a pyramid was referred to as mer, literally “place of ascendance.” The Great Pyramid of Giza is the largest in Egypt and one of the largest in the world. Until Lincoln Cathedral was built in 1300, it was the tallest building in the world. The base is over 13 acres in area.

The Sphinx, along with the sprawling sphinx temple, valley temple, and the base of the pyramids, were all built using 2.5 -16 ton blocks. No one to this day knows for certain how these massive monuments were built.

It is one of the Seven Wonders of the World, and the only one of the seven to survive into modern times. The Ancient Egyptians capped the peaks of their pyramids with gold and covered their faces with polished white limestone, though many of the stones used for the purpose have fallen or have been removed for other structures over the millennia.

Most Egyptians prepared for death; they tried to provide a secure resting place that would last an eternity. Although this was their wish, it did not work that way. Often the weather and tomb robbers were the main culprits that destroyed many tombs. Most tomb robbers, who were believed to be the tomb builders, often reentered the tomb after it was sealed, unwrapping the mummy and removing all amulets and stones. The coffins made of wood, which also held many precious stones, were also picked and destroyed. After destroying the tomb, many of the mummies would be taken out and burnt for fuel or sold as a souvenir product. Although tomb robbers were the main culprits, modern cultures also influenced the desecration of many mummies.

Nubian pyramids

Nubian pyramids were constructed (roughly 220 of them) at three sites in Nubia to serve as tombs for the kings and queens of Napata and Meroë.

The Nubians built far more pyramids than the Egyptians, but they are much smaller. The Nubian pyramids were constructed at a much steeper angle than Egyptian ones and were not tombs, but monuments to dead kings.

Pyramids were still being built in Nubia up to AD 300.

Mesopotamian pyramids

The Mesopotamians also built pyramids, called ziggurats. In ancient times these were brightly painted. Since they were constructed of mud-brick, little remains of them. The Biblical Tower of Babel is believed to have been a Babylonian ziggurat.

Tube may refer to:

Object

• cathode ray tube, a common component of electronics such as televisions and other displays
• cylinder (geometry), a hollow shape
• inner tube, a component of vehicular tires
• pneumatic tube, a method of transportation utilising compressed air
• test tube, a piece of laboratory equipment used in science
• Tube, An expansion bus on the BBC Micro computer
• tubing (material), used in plumbing, irrigation, and other applications
• vacuum tube, a component of electronics

Packaging

• Tube (packaging), a packaging solution for pasty and viscous goods such as toothpaste

Structural Engineering

• Tube (structure), the predominate structural system for constructing tall buildings in the United States between World War II and the 1990’s.

Transportation

• The London Underground, London’s subterranean train system.
• Transbay Tube, an underwater rail tube across the San Francisco Bay

Nature

• lava tube, found in volcanoes
• the inside of a hollow wave in surfing
• the flower tube

Media

• The Tube (TV series), a music related TV series by Channel 4 in the United Kingdom
• The Tubes, a San Francisco based rock group
• TUBE, a Japanese pop group
• Tube (game), a freeware game from Bullfrog Productions, released in 1995
• Tube (movie), a South Korean movie (튜브 (영화)).
• Tube, a children’s programme with inflatable characters on SABC, South Africa
• Tube & Berger, the alias of Dance/Electronica producers Arndt Rörig and Marco Vidovic from Germany
• YouTube, a website that allows users to upload, view, and share video clips
• Peter ‘Tubes’ Dale, aka Tubes from the Soccer AM television show.
• Pornotube

File-sharing

• Tubes (filesharing), a file-sharing program.

Theatre

• Blue Man Group’s theatrical show, “TUBES”, now called “Rewired.”

A sphere is a perfectly symmetrical geometrical object. In non-mathematical usage, the term is used to refer either to a round ball or to its two-dimensional surface. In mathematics, a sphere is the set of all points in three-dimensional space (R³) which are at distance r from a fixed point of that space, where r is a positive real number called the radius of the sphere. The fixed point is called the center or centre, and is not part of the sphere itself. The special case of r = 1 is called a unit sphere.

This article deals with the mathematical concept of a sphere. In physics, a sphere is an object (usually idealized for the sake of simplicity) capable of colliding or stacking with other objects which occupy space.

TerminologyPairs of points on a sphere that lie on a straight line through its center are called antipodal points. A great circle is a circle on the sphere that has the same center and radius as the sphere, and consequently divides it into two equal parts. The shortest distance between two distinct non-antipodal points on the surface and measured along the surface, is on the unique great circle passing through the two points.If a particular point on a sphere is designated as its north pole, then the corresponding antipodal point is called the south pole and the equator is the great circle that is equidistant to them. Great circles through the two poles are called lines (or meridians) of longitude, and the line connecting the two poles is called the axis of rotation. Circles on the sphere that are parallel to the equator are lines of latitude. This terminology is also used for astronomical bodies such as the planet Earth, even though it is neither spherical nor even spheroidal (see geoid).

A sphere is divided into two equal hemispheres by any plane that passes through its center. If two intersecting planes pass through its center, then they will subdivide the sphere into four lunes or biangles, the vertices of which all coincide with the antipodal points lying on the line of intersection of the planes.

Generalization to other dimensions

Spheres can be generalized to other dimensions. For any natural number n, an n-sphere, often written as Sⁿ, is the set of points in (n+1)-dimensional Euclidean space which are at distance r from a fixed point of that space, where R is, as before, a positive real number. For n> 0, the n-sphere is the simply connected n-dimensional manifold of constant, positive curvature, and can also be thought of embedded in an n+1-dimensional manifold, as the surface or boundary of a ball in the n+1-dimensional manifold.

• a 0-sphere is a pair of points on the line at ( − r,r)
• a 1-sphere is a circle of radius r
• a 2-sphere is an ordinary sphere
• a 3-sphere is a sphere in 4-dimensional Euclidean space.

A cone is a three-dimensional geometric shape bounded by a simply connected region of a plane (the base) and a surface (the lateral surface) described by the locus of all line segments joining the perimeter of the base to a point (the apex or vertex) lying off the plane of the base. In common usage in elementary geometry, “cone” usually means a right circular cone Sometimes the term “cone” refers just to the boundary, or surface, of such a solid (also known as a conic surface). In mathematical usage, the straight lines that generate the lateral surface are often considered to be indefinitely extended in both directions; thus the cone is not delimited by a base, and extends symmetrically on both sides of the apex. Such a cone (sometimes called a double cone) consists of two halves joined at the apex, each of which is known as a nappe.

The line joining the apex and the center of the base, suitably defined, is called the axis. The perimeter of the base is called the directrix, and each of the line segments between the directrix and apex is a generatrix of the lateral surface. (The term “directrix” here should not be confused with its meaning as the generator of a conic section.) A cone with its apex cut off by a plane parallel to its base is called a truncated cone or frustum.

In general, cones may have a base of any shape, and the apex may lie anywhere outside the plane of the base. Circular cones and elliptical cones have, respectively, circular and elliptical bases. A pyramid is a special type of cone with a polygonal base. If the axis of the cone is at right angles to its base then it is said to be a right cone, otherwise it is an oblique cone.

Properties

Every conic surface is ruled and developable.

A right circular cone with a generatrix at angle θ to the axis has an aperture of 2θ.

Mathematically, an elliptical conic surface is a special case of a conic section which is formed by a “conical quadric”, which is a special case of a quadric.

A cylindrical surface can be viewed as a limiting case of a conical surface whose apex is moved off to infinity in a particular direction. Indeed, in projective geometry there is no difference between the cylindrical and conical surfaces, and the two halves of the latter become a single connected surface.

In geometry, a torus is a surface of revolution generated by revolving a circle in three dimensional space about an axis coplanar with the circle, which does not touch the circle. Examples of tori include the surfaces of doughnuts and inner tubes. A circle rotated about a chord of the circle is called a torus in some contexts, but this is not a common usage in mathematics. The shape produced when a circle is rotated about a chord resembles a round cushion. Torus was the Latin word for a cushion of this shape.

Toroidal groups play an important part in the theory of compact Lie groups. This is due in part to the fact that in any compact Lie group G one can always find a maximal torus; that is, a closed subgroup which is a torus of the largest possible dimension. Such maximal tori T have a controlling role to play in theory of connected G.Automorphisms of T are easily constructed from automorphisms of the lattice Zⁿ, which are classified by integral matrices M of size n×n which are invertible with integral inverse; these are just the integral M of determinant +1 or −1. Making M act on Rⁿ in the usual way, one has the typical toral automorphism on the quotient.

The fundamental group of an n-torus is a free abelian group of rank n. The k-th homology group of an n-torus is a free abelian group of rank n choose k. It follows that the Euler characteristic of the n-torus is 0 for all n. The cohomology ring H^•(Tⁿ,Z) can be identified with the exterior algebra over the Z-module Zⁿ whose generators are the duals of the n nontrivial cycles.

Boxes are highly variable receptacles. When no shape is described, a typical rectangular box may be expected. Nevertheless, a box may have a horizontal cross section that is square, elongated, round or oval; sloped or domed top surfaces, or non-vertical sides. A box normally may be opened by raising, sliding or removing the lid, which may be hinged and/or fastened by a catch, clasp, or lock. Whatever its shape or purpose or the material of which it is fashioned, it is the direct descendant of the chest, one of the most ancient articles of domestic furniture. Its uses are innumerable, and the name, preceded by a qualifying adjective, has been given to many objects of artistic or antiquarian interest. Objects are often placed inside boxes, for a variety of reasons

 Packaging Boxes

Several types of boxes are used in packaging.

• A shipping box is often made of corrugated fiberboard (also see cardboard)
• A “set-up” box is made of non-bending paperboard (also see cardboard)
• A wooden box is related to a crate
• A carton is sometimes called a box

 Permanent boxes

Numerous types of boxes are used in permanent installations. Some types are designed to be temporarily inhabited by workers.

Permanent boxes include the following:

 Equipment boxes

• Fuse box

 Compartments

• Luxury box

 Shelters or booths

• Police box
• Signal box
• Telephone box

This is a basic method, in which one models something using only boxes, spheres, cones, cylinders and other predefined objects from the list of Predefined Standard Primitives or a list of Predefined Extended Primitives. One may also apply boolean operations, including subtract, cut and connect. For example, one can make two spheres which will work as blobs that will connect with each other. This is called blob-mesh modeling, or meta-balls.

 Predefined Standard Primitives List

• Box
• Cylinder
• Torus
• The Utah Teapot
• Cone
• Sphere
• Tube
• Pyramid
• Plane
• GeoSphere

Predefined Extended Primitives List

• Hedra
• ChamferBox
• OilTank
• Spindle
• Gengon
• Prism
• Torus knot
• ChamferCyl
• Capsule
• L-Ext
• C-Ext

Polygon modeling

Polygon modeling is more common with game design than any other modeling technique as the very specific control over individual polygons allows for extreme optimization. Also, it is relatively faster to calculate in realtime. Usually, the modeller begins with one of the 3ds max primitives, and using such tools as bevel, extrude, and polygon cut, adds detail to and refines the model. Versions 4 and up feature the Editable Polygon object, which simplifies most mesh editing operations, and provides subdivision smoothing at customizable levels.

Version 7 introduced the edit poly modifier, which allows the use of the tools available in the editable polygon object to be used higher in the modifier stack (i.e. on top of other modifications).

3ds Max is also supported by advanced 3rd party modeling tools, such as Orionflame, which allows for more freedom and ease by introducing new tools to the base package.

NURBS or Nonuniform rational B-Spline

A more advanced alternative to polygons, it gives a smoothed out surface that eliminates the straight edges of a polygon model. NURBS is a mathematically exact representation of freeform surfaces like those used for car bodies and ship hulls, which can be exactly reproduced at any resolution whenever technically needed.

Surface tool/Editable patch object

Surface tool was originally a 3rd party plugin, but Kinetix acquired and included this feature since version 3.0. The surface tool is for creating common 3ds max’s splines, and then applying a modifier called “surface.” This modifier makes a surface from every 3 or 4 vertices in a grid. This is often seen as an alternative to ‘Mesh’ or ‘Nurbs’ modeling, as it enables a user to interpolate curved sections with straight geometry (for example a hole through a box shape). Although the surface tool is a useful way to generate parametrically accurate geometry, it lacks the ’surface properties’ found in the similar Edit Patch modifier, which enables a user to maintain the original parametric geometry whilst being able to adjust “smoothing groups” between faces.

3ds Max is one of the most widely-used off the shelf 3D animation programs by content creation professionals. It has strong modeling capabilities, a flexible plugin architecture and a long heritage on the Microsoft Windows platform. It is mostly used by video game developers, TV commercial studios and architectural visualisation studios. It is also used for movie effects and movie previsualisation.

In addition to its modeling and animation tools, the latest version of 3ds Max also features advanced shaders (such as ambient occlusion and subsurface scattering), dynamic simulation, particle systems, radiosity, normal map creation and rendering, global illumination, an intuitive and fully-customizable user interface, its own scripting language and much more. There is also a plethora of specialized renderer plugins that can be bought separately, such as V-Ray, Brazil r/s , Maxwell, FryRender and finalRender.

3ds Max is a full-featured 3D graphics application developed by Autodesk Media and Entertainment. It runs on the Win32 and Win64 platforms. As of July 2007, 3ds Max is in its Tenth version generation.

The original 3D Studio product was created for the DOS platform by the Yost Group and published by Autodesk. Autodesk purchased the product at its second release mark and internalized development entirely over the next two releases. After 3D Studio Release 4, the product was ported to the Windows NT platform, and originally named “3D Studio MAX.” This version was also originally created by the Yost Group. It was released by Kinetix, which was at that time Autodesk’s division of media and entertainment. Later, the product name was changed to “3ds max” (all lower case) to better comply with the naming conventions of Discreet, a Montreal-based software company which Autodesk had purchased. At release 8, the product was again branded with the Autodesk logo, and the name was again changed to “3ds Max”

Some of the most popular and heavily used general purpose 3D modelers on the market include:

• 3D Studio Max
• Alias
• Blender (open source)
• LightWave
• Maya
• Cinema 4D
• MilkShape 3D
• Softimage|XSI
• trueSpace
• ZBrush

Some free modelers available via the Internet include:

• Anim8or
• Art of Illusion
• AutoQ3D
• Blender (open source)
• DeleD (lite version is offered for free)
• K-3D (open source)
• Quake 2 Modeler
• ShapeShop
• SketchUp
• SmoothTeddy
• TopMod
• Wings 3D (open source)
• Zanoza Modeler

A 3D modeler is a 3D computer graphics software application used to visually produce polygonal 3D models, or the title of a professional who uses the software to produce 3D models. The 3D model is most often described by a geometric mesh of triangles or other polygons located in 3D space, with other popular descriptive models including NURBS and subdivision surface models. This article is about 3D modeling software.

Features

Many 3D modelers are general-purpose and can be used to produce models of various real-world entities, from plants to automobiles to people. Some are specially designed to model certain objects, such as chemical compounds or internal organs.

3D modelers allow users to create and alter models via their 3D mesh. Users can add, subtract, stretch and otherwise change the mesh to their desire. Models can be viewed from a variety of angles, usually simultaneously. Models can be rotated and the view can be zoomed in and out.

3D modelers can export their models to files, which can then be imported into other applications. Many modelers allow importers and exporters to be plugged-in, so they can read and write data in the native formats of other applications.

Most 3D modelers contain a number of related features, such as ray tracers and other rendering alternatives and texture mapping facilities. Some also contain features that support or allow animation of models. Some may be able to generate full-motion video of a series of rendered scenes

Uses

3D modelers are used in a wide variety of industries. The medical industry uses them to create detailed models of organs. The movie industry uses them to create and manipulate characters and objects for animated and real-life motion pictures. The video game industry uses them to create assets for video games. The science sector uses them to create highly detailed models of chemical compounds. The architecture industry uses them to create models of proposed buildings and landscapes. The engineering community uses them to design new devices, vehicles and structures as well as a host of other uses

Maya is the culmination of three 3D software lines: Wavefront’s The Advanced Visualizer (in California), Thomson Digital Image (TDI) Explore (in France) and Alias’ Power Animator (in Canada). In 1993 Wavefront purchased TDI, and in 1995 Silicon Graphics Incorporated (SGI) purchased both Alias and Wavefront (due to pressure from Microsoft’s purchase of Softimage earlier that year) and combined them into one working company, producing a single package from their collective source code. In the mid-1990s, the most popular pipeline in Hollywood films was a combination of tools: Alias Studio for modeling, Softimage for animation, and PhotoRealistic RenderMan for rendering. This combination was used for numerous films, such as Jurassic Park, The Abyss and Terminator 2: Judgment Day. The combined company was referred to as Alias|Wavefront. It took Alias|Wavefront two more years after the merger to release the highly anticipated Maya.

Both Alias and Wavefront were working on their next-generation of software at the time of the merger. Alias had taken a Macintosh product, “Alias Sketch!”, moved it to the SGI platform and added many features to it. The code name for this project was “Maya”, the Sanskrit term for “illusion.” The first scene ever animated with Maya was the cave-mouth from Disney’s “Aladdin”.

After much discussion it was decided to adopt Alias’ “Maya” architecture, and merge Wavefront’s code with it.

In the early days of development, Maya used Tcl as the scripting language. After the merger, there was debate amongst those who supported Tcl, Perl and Sophia. Sophia was much faster than the others and won out. However, once error checking was added, it ended up being equally slow.

Upon its release in 1998, Alias|Wavefront discontinued all previous animation-based software lines including Alias Power Animator, encouraging consumers to upgrade to Maya. It succeeded in expanding its product line to take over a great deal of market share, with leading visual effects companies such as Industrial Light and Magic and Tippett Studio switching from Softimage to Maya for the animation software.

Later Alias|Wavefront was renamed Alias. In 2005 Alias was sold by the cash-strapped SGI to the Teachers’ pension fund of Ontario and the private equity investment firm Accel-KKR. In October 2005, Alias was sold again, this time to Autodesk, and on January 10, 2006, Autodesk completed the acquisition and Alias Maya is now known as Autodesk Maya.

Maya has been used to animate popular television shows. It is used in combination with CorelDRAW to animate the cartoon South Park, and has been used to make 3D segments on Futurama and games such as Xenosaga and Resident Evil. Every episode of VeggieTales after Larry-Boy and the Rumor Weed was animated using Maya. It is now used to do the 3D modeling in Channel 4’s Grand Designs.

Maya has also been Crystal Dynamics (US game designers) main software, creating top titles like; Tomb Raider: Legend – Prince of Persia and Tomb Raider remake of Tomb Raider: Anniversary. The software was also used to create top sim game The Sims

A feature that makes Maya ever more powerful is that you can connect anything to anything. E.g. you can use a color intensity of a shader to control the movement of a door opening and closing. To control the node based system of maya, fully reconfigurable user interface can be scripted with MEL script code which can be dropped onto a shelf to create a new icon that executes that code)

With the release of Maya 8.5 support for the Python scripting language has been included. “This popular open-source programming language helps accelerate facility-specific custom script development and plug-in prototyping, better extending and automating Maya production pipelines

Maya unlimited version comes with a set of tools not available in the Maya complete version.

Maya Fluid

A realistic fluid simulator (effective for smoke, fire, clouds and explosions, added in Maya 4.5)

Maya Classic Cloth

Cloth simulation to automatically simulate clothing and fabrics moving realistically over an animated character. The Maya Cloth toolset has been upgraded in every version of Maya released after Spiderman 2. Alias worked with Sony Pictures Imageworks to get Maya Cloth up to scratch for that production, and all those changes have been implemented, although the big studios opted to use third party plugins such as Syflex instead of the (relatively) cumbersome Maya Cloth.

Maya Fur

Animal fur simulation similar to Maya Hair. It can be used to simulate other fur-like objects, such as grass.

Maya Hair

A simulator for realistic-looking human hair implemented using curves and PaintEffects. These are also known as dynamic curves.

Maya Live

A set of motion tracking tools for CG matching to clean plate footage.

Maya Cloth

Added in version 8.5, nCloth is the first implementation of Maya Nucleus, Autodesk’s simulation framework. nCloth gives the artist further control of cloth and material simulations.

Shading

Like most 3D programs, Maya includes a number of parameterized shading models to define an object’s visual properties, including Lambert, Blinn, Phong, and anisotropic shaders. Depending on which shading model is used, the parameters affect attributes such as the surface’s color, reflective properties, and transparency, with the goal of simulating the appearance of real-life materials such as metal, stone, wood, and skin. Shaders can also incorporate bump maps, which create the illusion of surface textures.

Toon Shading

Toon shading creates the look of 2D cel or cartoon animation using 3D modeling and animation software. Elements of the “toon” look include profile lines (outlines), border lines, crease lines, intersection lines, and solid color shading. Combined, these elements recreate the look of traditional animation’s “ink and paint” technique, where ink refers to lines and paint refers to shading.

Lighting

In the real world, when light shines on a surface, the parts of the surface facing toward the light source appear illuminated, and the parts of the surface facing away from the light source appear dark. If one object is located between a second object and the light source, the first object casts a shadow onto the second object.

PaintEffects

A component of Maya used to paint brush strokes and particle effects on a 2D canvas or on or between 3D geometry. Paint Effects can be used as a traditional paint program to paint images on a canvas, to paint repeatable textures applied to 3D geometry in scenes, or to paint in 3D space

’’Paint Effects’’integrates 2D painting tools into a 3D rendering environment. Libraries include numerous trees, grasses, and plants which can be painted to ‘grow’ off the surface of an object.

Mental ray

Native mental ray renderer.

RenderMan for Maya

In 2005, Pixar released its highly anticipated RenderMan for Maya renderer which incorporates the full RenderMan Pro Server features into a native Maya plugin. The workflow involves the use of Maya materials converted into RenderMan .

Maya features a particle system for handling masses like steam and water drops. Dynamic fields allow adding gravity, wind and vortexes, allowing for effects such as blowing leaves or even tornados. Special tools give artists the ability to brush and style particles like hair and fur.

An artist may create rigid body geometric objects which collide automatically without explicit animation, as well as soft body objects which can ripple and bend, like flags and cloth.

Maya effects are built-in programs that make it easy for users to create complex animation effects such as smoke, fire and realistic water effects, with many options and attributes for tuning the results.

Keyframe Animation

This is the essential, fundamental form of computer animation. The model is placed in a starting pose or position, and a keyframe is set. Some frames later, another keyframe is set, and the model is moved as desired. This process is repeated as many times as needed. The animation software interpolates the motion needed to move the model smoothly between the keyframes. What this means is that if the animator keys a box, and moves the box across the room in the next keyframe, when the scene is scrubbed or viewed, the box will glide across the floor instead of jumping from frame to frame. This applies to anything in the scene – moving fingers, eyelids, moving lips, etc.

Nonlinear Animation

After animating a character with keyframes or motion capture, you can collect its animation data into a single, editable sequence. This animation sequence is called an animation clip.

In Maya, there are two types of clip: source clips and regular clips. Maya preserves and protects a character’s original animation curves by storing them in source clips. You do not use source clips to animate your characters. Instead, you use copies or instances of source clips called regular clips to animate your characters nonlinearly.

Moving, manipulating, and blending regular clips to produce a smooth series of motions for a character is the basis of nonlinear animation. The tool with which you manage all these aspects of a character’s nonlinear animation is the Trax Editor.

Path Animation

A path animation controls the position and rotation of an object along a curve. A NURBS curve cannot be designated as a motion path. An object must first be attached to the curve for it to become a path curve. You can also generate motion paths by animating objects using motion path keys.

Motion Capture Animation

Skeletons

Skeletons are hierarchical, articulated structures that let you pose and animate bound models. A skeleton provides a deformable model with a similar underlying structure as the human skeleton gives the human body.

Just like in the human body, the location of joints and the number of joints you add to a skeleton determine how the skeleton’s bound model or `body’ moves. When you bind a model to a skeleton, it is called skinning. The process of making a skeleton or bones, refining the joints, using IK or FK, putting handles on the joints so animators can manipulate them, and over all making the model ready for animation is called “Rigging”

Forward Kinematics

The reverse of Inverse Kinematics (IK), Forward Kinematics (FK) is an animation method that involves moving each joint without the restriction of an expected final position. Thus, the ‘goal’ is to move a joint (or series of joints) as desired, and the final pose is a consequence of those movements. Forward Kinematics is often used for finely-tuned joint movement (such as hands & fingers), as it allows for more complete control over posing. For more information, see Forward kinematic animation.

Inverse Kinematics

The reverse of Forward Kinematics, Inverse Kinematics is a method that involves defining a final pose, and generating joint movement as needed to reach that pose. Thus, the ‘goal’ is for all joints to be in a final pose, and the individual joint movements are a consequence of getting to that final pose. Joints must have carefully defined limits to their possible motion for Inverse Kinematics to work well, or the joints can end up ‘flopping’ before reaching the goal pose. Inverse Kinematics is often used for large limb movement (such as walking, reaching, etc.). For more information, see Inverse kinematic animation and Inverse kinematics.

Full Body IK Solver

When Alias bought Kaydara, Maya got an upgrade, from Kaydara Motion Builder, with a full body IK solver (FBIK Solver) which simulates real body kinematics. The package comes with a biped and a quadruped FBIK sample.

Skinning

’’Skinning’’ is the process of setting up a character’s model so that it can be deformed by a skeleton. For more information on skeletons, see What are skeletons?. You skin a model by binding a skeleton to the model. You can bind a model to a skeleton by a variety of skinning methods, including smooth skinning and rigid skinning. Smooth skinning and rigid skinning are direct skinning methods. You can also use indirect skinning methods, which combine the use of lattice or wrap deformers with either smooth or rigid skinning.

Constraints

’’Constraints’’ enable you to constrain the position, orientation, or scale of an object to other objects. Further, with constraints you can impose specific limits on objects and automate animation processes.

Character Sets

In Maya, a character set is a node that brings together into a set all the attributes of any collection of objects that you want to animate together. The character set could be anything: a well-armed robot, an automobile, or even some seemingly unrelated collection of objects. Maya enables you to bring together all the attributes together in a character node, so you only have to select one node, the character node, when you want to animate all the various attributes.

Deformers

’’deformers‘’ are high-level tools that you can use to manipulate (when modeling) or drive (when animating) the low-level components of a target geometry. In other software packages, the terms modifiers and space warps are used to refer to what Maya calls deformers. The following are the many types of deformers: Blend Shape deformer, Lattice deformer, Cluster deformer, Nonlinear deformers, Sculpt deformer, Soft Modification deformer, Jiggle deformer, Wire deformer, Wrinkle deformer, Wrap deformer, Point On Curve deformer.

Maya is a high-end 3D computer graphics and 3D modeling software package originally developed by Alias Systems Corporation, but now owned by Autodesk as part of the Media and Entertainment division. Autodesk acquired the software in October 2005 upon purchasing Alias. Maya is used in the film and TV industry, as well as for computer and video games.In 2003, Maya (then owned by Alias) won an Academy Award “for scientific and technical achievement”, citing use “on nearly every feature using 3-D computer-generated images

Overview

Maya is a popular, proprietary integrated node-based 3D software suite, evolved from Alias PowerAnimator. The software is released in two versions: Maya Complete (the less powerful package) and Maya Unlimited. Maya Personal Learning Edition (PLE) is available at no cost for non-commercial use, although rendered images are watermarked.

Maya was developed by Alias. It was originally released for the IRIX operating system, and subsequently ported to the Microsoft Windows, Linux and Mac OS X operating systems. IRIX support was discontinued after the release of version 6.5. When Autodesk acquired Alias in October 2005, they continued Maya development. The latest version, 8.5 Service Pack 1, was released in June 2007.

An important feature of Maya is its openness to third-party software, which can strip the software completely of its standard appearance and, using only the kernel, can transform it into a highly customized version of the software. Apart from its intrinsic power and flexibility, this feature in itself made Maya appealing to large studios which tend to write custom code for their productions using the provided software development kit.

A Tcl-like powerful, cross-platform scripting language called Maya Embedded Language (MEL) is provided not only as a scripting language, but as means to customize Maya’s core functionality (much of the environment and tools are written in the language). Additionally, user interactions are implemented and recorded as MEL scripting code which users can store on a toolbar, allowing animators to add functionality without experience in C or C++ programming and compilers, though that option is provided with the software development kit. Support for Python scripting was added in version 8.5.

The core of Maya itself is written in C++

Project files, including all geometry and animation data, are stored as sequences of MEL operations which can be optionally saved as a ‘human readable’ file (.ma, for Maya ASCII), editable in any text editor outside of the Maya environment which allows for a tremendous level of flexibility when working with external tools.

A pie menu called Hotbox provides instant access to a majority of features in Maya at the press of a key.