Utah teapot
Encyclopedia
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...
computer model which has become a standard reference object (and something of an in-joke
In-joke
An in-joke, also known as an inside joke or in joke, is a joke whose humour is clear only to people who are in a particular social group, occupation, or other community of common understanding...
) in the computer graphics
Computer graphics
Computer graphics are graphics created using computers and, more generally, the representation and manipulation of image data by a computer with help from specialized software and hardware....
community. It is a mathematical model
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...
of an ordinary teapot
Teapot
A teapot is a vessel used for steeping tea leaves or a herbal mix in near-boiling water. Tea may be either in a tea bag or loose, in which case a tea strainer will be needed, either to hold the leaves as they steep or to catch the leaves inside the teapot when the tea is poured...
of fairly simple shape, which appears solid, cylindrical and partially convex. A teapot primitive is considered the equivalent of a "hello world" program, as a way to create the easiest 3D scene with a somewhat complex model acting as basic geometry reference for scene and light setup. Many libraries will even have functions dedicated to drawing teapots.
The teapot model was created in 1975 by early computer graphics researcher Martin Newell, a member of the pioneering graphics program at the University of Utah
University of Utah
The University of Utah, also known as the U or the U of U, is a public, coeducational research university in Salt Lake City, Utah, United States. The university was established in 1850 as the University of Deseret by the General Assembly of the provisional State of Deseret, making it Utah's oldest...
.
History
Newell needed a moderately simple mathematical model of a familiar object for his work. His wife Sandra Newell suggested modelling their tea service since they were sitting down to tea at the time. He got some graph paper and a pencil, and sketched the entire teapot by eye. Then he went back to the lab and edited bézierBézier
Bézier can refer to:*Pierre Bézier, French engineer and creator of Bézier curves*Bézier curve*Bézier triangle*Bézier spline*Bézier surface* The town of Béziers in France* AS Béziers Hérault, a French rugby union team...
control points on a Tektronix
Tektronix
Tektronix, Inc. is an American company best known for its test and measurement equipment such as oscilloscopes, logic analyzers, and video and mobile test protocol equipment. In November 2007, Tektronix became a subsidiary of Danaher Corporation....
storage tube
Storage tube
Mostly obsolete, a storage tube is a special monochromatic CRT whose screen has a kind of 'memory' : when a portion of the screen is illuminated by the CRT's electron gun, it stays lit until a screen erase command is given...
, again by hand.
Saddle point
In mathematics, a saddle point is a point in the domain of a function that is a stationary point but not a local extremum. The name derives from the fact that in two dimensions the surface resembles a saddle that curves up in one direction, and curves down in a different direction...
s, has a genus
Genus (mathematics)
In mathematics, genus has a few different, but closely related, meanings:-Orientable surface:The genus of a connected, orientable surface is an integer representing the maximum number of cuttings along non-intersecting closed simple curves without rendering the resultant manifold disconnected. It...
greater than zero because of the hole in the handle, can project a shadow on itself, and looks reasonable when displayed without a complex surface texture.
Newell is remembered as famously saying "Fifth from me is a teapot". This was later found to mean the number 6.
Newell made the mathematical data that described the teapot's geometry (a set of three-dimensional coordinates) publicly available, and soon other researchers began to use the same data for their computer graphics experiments. These researchers needed something with roughly the same characteristics that Newell had, and using the teapot data meant they did not have to laboriously enter geometric data for some other object. Although technical progress has meant that the act of rendering the teapot is no longer the challenge it was in 1975, the teapot continued to be used as a reference object for increasingly advanced graphics techniques.
Over the following decades, editions of computer graphics journals (such as the ACM
Association for Computing Machinery
The Association for Computing Machinery is a learned society for computing. It was founded in 1947 as the world's first scientific and educational computing society. Its membership is more than 92,000 as of 2009...
SIGGRAPH
SIGGRAPH
SIGGRAPH is the name of the annual conference on computer graphics convened by the ACM SIGGRAPH organization. The first SIGGRAPH conference was in 1974. The conference is attended by tens of thousands of computer professionals...
's quarterly) regularly featured versions of the teapot: faceted or smooth-shaded, wireframe, bumpy, translucent, refractive, even leopard-skin and furry teapots were created.
The original teapot model was never intended to be seen from below and had no surface to represent the base of the teapot; later versions of the data set
Data set
A data set is a collection of data, usually presented in tabular form. Each column represents a particular variable. Each row corresponds to a given member of the data set in question. Its values for each of the variables, such as height and weight of an object or values of random numbers. Each...
have fixed this.
The real teapot is noticeably taller (by a ratio of 4:3) compared to the computer model because Newell's frame buffer used non-square pixels. Rather than distorting the image, Newell's colleague Jim Blinn
Jim Blinn
James F. Blinn is a computer scientist who first became widely known for his work as a computer graphics expert at NASA's Jet Propulsion Laboratory , particularly his work on the pre-encounter animations for the Voyager project, his work on the Carl Sagan Cosmos documentary series and the research...
reportedly scaled the geometry to cancel out the stretching, and when the model was shared with users of other systems, the scaling stuck.
The original, physical teapot was purchased from ZCMI
Zion's Co-operative Mercantile Institution
Zions Cooperative Mercantile Institution was founded in 1868 by Brigham Young and was one of the earliest department stores in the United States...
(a department store in Salt Lake City, Utah
Salt Lake City, Utah
Salt Lake City is the capital and the most populous city of the U.S. state of Utah. The name of the city is often shortened to Salt Lake or SLC. With a population of 186,440 as of the 2010 Census, the city lies in the Salt Lake City metropolitan area, which has a total population of 1,124,197...
) in 1974. It was donated to the Boston Computer Museum in 1984 where it was on display until 1990. It now resides in the ephemera collection at the Computer History Museum
Computer History Museum
The Computer History Museum is a museum established in 1996 in Mountain View, California, USA. The Museum is dedicated to preserving and presenting the stories and artifacts of the information age, and exploring the computing revolution and its impact on our lives.-History:The museum's origins...
in Mountain View, California
Mountain View, California
-Downtown:Mountain View has a pedestrian-friendly downtown centered on Castro Street. The downtown area consists of the seven blocks of Castro Street from the Downtown Mountain View Station transit center in the north to the intersection with El Camino Real in the south...
where it is catalogued as "Teapot used for Computer Graphics rendering" and bears the catalogue number X00398.1984.
Versions of the teapot model, or sample scenes containing it, are distributed with or freely available for nearly every current rendering and modelling program and even many graphic API, including 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...
, Houdini
Houdini (software)
Houdini is a high-end 3D animation package developed by Side Effects Software which is headquartered in Toronto, Canada. It is a rewrite of the PRISMS ecosystem of standalone tools. Its chief distinction from other packages is that it has been designed as a purely procedural environment...
, Lightwave 3D, modo
Modo (software)
modo is a polygon and subdivision surface modeling, sculpting, 3D painting, animation and rendering package developed by Luxology, LLC. The program incorporates features such as n-gons, 3D painting and edge weighting, and runs on Mac OS X and Microsoft Windows platforms.-History:modo was created...
, POV-Ray
POV-Ray
The Persistence of Vision Raytracer, or POV-Ray, is a ray tracing program available for a variety of computer platforms. It was originally based on DKBTrace, written by David Kirk Buck and Aaron A. Collins. There are also influences from the earlier Polyray raytracer contributed by its author...
, 3D Studio Max
3D Studio Max
Autodesk 3ds Max, formerly 3D Studio MAX, is for making 3D animations. It was developed and produced by Autodesk Media and Entertainment. It has modeling capabilities, a flexible plugin architecture and can be used on the Microsoft Windows platform. It's frequently used by video game developers, TV...
, and the 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...
and Direct3D
Direct3D
Direct3D is part of Microsoft's DirectX application programming interface . Direct3D is available for Microsoft Windows operating systems , and for other platforms through the open source software Wine. It is the base for the graphics API on the Xbox and Xbox 360 console systems...
helper libraries. Some RenderMan
RenderMan Interface Specification
The RenderMan Interface Specification, or RISpec in short, is an open API developed by Pixar Animation Studios to describe three-dimensional scenes and turn them into digital photorealistic images...
-compliant renderers support the teapot as a built-in geometry by calling
RiGeometry("teapot", RI_NULL). Along with the expected cubes and spheres, the GLUTOpenGL Utility Toolkit
The OpenGL Utility Toolkit is a library of utilities for OpenGL programs, which primarily perform system-level I/O with the host operating system. Functions performed include window definition, window control, and monitoring of keyboard and mouse input...
library even provides the function
glutSolidTeapot as a graphics primitive, as does its Direct3DDirect3D
Direct3D is part of Microsoft's DirectX application programming interface . Direct3D is available for Microsoft Windows operating systems , and for other platforms through the open source software Wine. It is the base for the graphics API on the Xbox and Xbox 360 console systems...
counterpart D3DX
D3dx
In computing, D3DX is a high level API library which is written to supplement Microsoft's Direct3D graphics API. The D3DX library was introduced in Direct3D 7, and subsequently was improved in Direct3D 9...
(
D3DXCreateTeapot). Mac OS X Tiger and Leopard also include the teapot as part of Quartz ComposerQuartz Composer
Quartz Composer is a node-based visual programming language provided as part of the Xcode development environment in Mac OS X for processing and rendering graphical data....
; Leopard's teapot supports bump mapping
Bump mapping
Bump mapping is a technique in computer graphics for simulating bumps and wrinkles on the surface of an object. This is achieved by perturbing the surface normals of the object and using the perturbed normal during lighting calculations. The result is an apparently bumpy surface rather than a...
. BeOS
BeOS
BeOS is an operating system for personal computers which began development by Be Inc. in 1991. It was first written to run on BeBox hardware. BeOS was optimized for digital media work and was written to take advantage of modern hardware facilities such as symmetric multiprocessing by utilizing...
included a small demo of a rotating 3D teapot, intended to show off the platform's multimedia facilities.
Teapot scenes are commonly used for renderer self-tests and benchmarks.
Appearances
With the advent first of computer generated short films, and then of full length feature films, it has become something of an in-jokeIn-joke
An in-joke, also known as an inside joke or in joke, is a joke whose humour is clear only to people who are in a particular social group, occupation, or other community of common understanding...
to hide a Utah teapot somewhere in one of the film's scenes. For example, in the movie Toy Story
Toy Story
Toy Story is a 1995 American computer-animated film released by Walt Disney Pictures. It is Pixar's first feature film as well as the first ever feature film to be made entirely with CGI. The film was directed by John Lasseter and featuring the voices of Tom Hanks and Tim Allen...
the Utah teapot appears in a short tea-party scene. The Utah teapot sometimes appears in the "Pipes" screensaver
Screensaver
A screensaver is a type of computer program initially designed to prevent phosphor burn-in on CRT and plasma computer monitors by blanking the screen or filling it with moving images or patterns when the computer is not in use...
shipped with Microsoft Windows
Microsoft Windows
Microsoft Windows is a series of operating systems produced by Microsoft.Microsoft introduced an operating environment named Windows on November 20, 1985 as an add-on to MS-DOS in response to the growing interest in graphical user interfaces . Microsoft Windows came to dominate the world's personal...
, but only in versions prior to Windows XP, and has been included in the "polyhedra" Xscreensaver
XScreenSaver
XScreenSaver is a collection of about two hundred free screensavers for Unix and Mac OS X computers. It was created by Jamie Zawinski in 1992 and is still maintained by him....
hack since 2008. The teapot also appears in The Simpsons
The Simpsons
The Simpsons is an American animated sitcom created by Matt Groening for the Fox Broadcasting Company. The series is a satirical parody of a middle class American lifestyle epitomized by its family of the same name, which consists of Homer, Marge, Bart, Lisa and Maggie...
episode Treehouse of Horror VI
Treehouse of Horror VI
"Treehouse of Horror VI" is the sixth episode of The Simpsons seventh season and the sixth episode in the Treehouse of Horror series. It first aired on the Fox network in the United States on October 29, 1995, and contains three self-contained segments...
in which Homer discovers the "third dimension".
One famous ray-traced image (by Jim Arvo and Dave Kirk, from their 1987 SIGGRAPH
SIGGRAPH
SIGGRAPH is the name of the annual conference on computer graphics convened by the ACM SIGGRAPH organization. The first SIGGRAPH conference was in 1974. The conference is attended by tens of thousands of computer professionals...
paper "Fast Ray Tracing by Ray Classification") shows six stone columns, five of which are surmounted by the platonic solid
Platonic solid
In geometry, a Platonic solid is a convex polyhedron that is regular, in the sense of a regular polygon. Specifically, the faces of a Platonic solid are congruent regular polygons, with the same number of faces meeting at each vertex; thus, all its edges are congruent, as are its vertices and...
s (tetrahedron
Tetrahedron
In geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids...
, cube
Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and...
, octahedron
Octahedron
In geometry, an octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex....
, dodecahedron, icosahedron
Icosahedron
In geometry, an icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids....
). The sixth column supports a teapot. The image is titled "The Six Platonic Solids" – which has led some people to call the teapot a "Teapotahedron". This image appeared on the covers of several books and journals.
Jim Blinn
Jim Blinn
James F. Blinn is a computer scientist who first became widely known for his work as a computer graphics expert at NASA's Jet Propulsion Laboratory , particularly his work on the pre-encounter animations for the Voyager project, his work on the Carl Sagan Cosmos documentary series and the research...
(in one of his "Project MATHEMATICS!
Project MATHEMATICS!
Project Mathematics! , is a series of educational video modules and accompanying workbooks for teachers, developed to help teach the principles of mathematics to high school students.-Overview:...
" videos) proves an amusing (but trivial
Trivial (mathematics)
In mathematics, the adjective trivial is frequently used for objects that have a very simple structure...
) version of the Pythagorean theorem
Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle...
: Construct a (2D) teapot on each side of a right triangle
Right triangle
A right triangle or right-angled triangle is a triangle in which one angle is a right angle . The relation between the sides and angles of a right triangle is the basis for trigonometry.-Terminology:The side opposite the right angle is called the hypotenuse...
and the area of the teapot on the hypotenuse
Hypotenuse
In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the...
is equal to the sum of the areas of the teapots on the other two sides.
The teapot also makes an appearance in the Technology Test level of the Serious Engine, where it's used to demonstrate many of the engine characteristics.
In addition, the teapot is a spawnable object in the physics simulator Universe Sandbox
Universe Sandbox
Universe Sandbox is an interactive space gravity simulator. Using Universe Sandbox, one can see the effects of gravity on objects in the universe and run scale simulations of our Solar System, various galaxies or other simulations, while at the same time, interacting and maintaining control over...
, more-or-less to scale with the other entities in the program.
See also
- 3D modeling3D modelingIn 3D computer graphics, 3D modeling is the process of developing a mathematical representation of any three-dimensional surface of object via specialized software. The product is called a 3D model...
- Stanford BunnyStanford BunnyThe Stanford Bunny is a computer graphics 3D test model developed by Greg Turk and Marc Levoy in 1994 at Stanford University.The Bunny consists of data describing 69,451 triangles determined by 3D scanning a ceramic figurine of a rabbit. The data can be used to test various graphics algorithms;...
- Suzanne (3D model)
- Cornell BoxCornell BoxThe Cornell Box is a test aimed at determining the accuracy of rendering software by comparing the rendered scene with an actual photograph of the same scene. It was created by Cindy M. Goral, Kenneth E. Torrance, Donald P...
- Russell's teapotRussell's teapotIn 1958 Russell elaborated on the analogy as a reason for his own atheism:- Analysis :Peter Atkins said that the point of Russell's teapot is that no one can prove a negative, and therefore Occam's razor suggests that the more simple theory should trump the more complex theory...
- List of common 3D test models
- LennaLennaLenna or Lena is the name given to a 512 x 512 pixel standard test image originally cropped from the centerfold of November 1972 issue of Playboy magazine. It is a picture of Lena Söderberg, a Swedish model, shot by photographer Dwight Hooker...
