The
Utah teapot or
Newell teapot is a
3D3D 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-jokeAn in-joke is a joke whose humor is clear only to those people who are "inside" a social group, occupation or other community of common understanding; an esoteric joke. It is only humorous to those who know the situation behind it...
) in the
computer graphicsComputer graphics are graphics created using computers and, more generally, the representation and manipulation of pictorial data by a computer....
community. It is a
mathematical modelA mathematical model uses mathematical language to describe a system. Mathematical models are used not only in the natural sciences and engineering disciplines but also in the social sciences ; physicists, engineers, computer scientists, and economists use...
of an ordinary
teapotA teapot is a vessel used for steeping tea leaves or an 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.
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 UtahThe 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 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
storage tubeMostly 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.
The teapot shape contains a number of elements that made it ideal for the graphics experiments of the time — it is round, contains
saddle pointIn mathematics, a saddle point is a point in the domain of a function of two variables which is a stationary point but not a local extremum. At such a point, in general, the surface resembles a saddle that curves up in one direction, and curves down in a different direction...
s, has a
genusIn 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 closed simple curves without rendering the resultant manifold disconnected. It is equal to the...
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 made the mathematical data that describe 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
ACMThe Association for Computing Machinery, or ACM, 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...
SIGGRAPHSIGGRAPH 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 setA 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. It lists values for each of the variables, such as height and weight of an object or values of random numbers....
have fixed this.
The real teapot is noticeably taller than the computer model because Newell's frame buffer used non-square pixels. Rather than distorting the image, Newell's colleague
Jim BlinnJames 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.
Height scale factor was 1.3.
The original, physical teapot was purchased from
ZCMIZion's Cooperative Mercantile Institution was founded in 1868 and was America's first department store. Based in Salt Lake City, Utah, it quickly became a household name in the community. The Church of Jesus Christ of Latter-day Saints was a significant influence in the company, retaining a...
(a department store in
Salt Lake City, UtahSalt 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. Salt Lake City has a population of 181,698 as of July 1, 2008, making it the 125th largest city in the United States...
) 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 MuseumThe Computer History Museum is a museum established in 1996 in Mountain View, California, USA, when The Computer Museum sent the majority of its historical collection to Moffett Field, California, so that TCM could concentrate on computing-related exhibits for children...
in
Mountain View, CaliforniaMountain View is a city in Santa Clara County, in the U.S. state of California. The city gets its name from the views of the Santa Cruz Mountains. As of the 2000 census, the city had a total population of 70,708.-Geography:...
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
AutoCADAutoCAD is a CAD software application for 2D and 3D design and drafting, developed and sold by Autodesk, Inc. Initially released in late 1982, AutoCAD was one of the first CAD programs to run on personal computers, and notably the IBM PC...
,
HoudiniHoudini is a high-end 3D animation package developed by Side Effects Software which headquartered in Toronto, Canada. Its chief distinction from other packages is that it has been designed as a purely procedural environment...
, Lightwave 3D,
modomodo is an advanced polygon, subdivision surface, modeling, sculpting, 3D painting, animation and rendering package developed by Luxology, LLC...
,
POV-RayThe 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 MaxAutodesk 3ds Max, formerly 3D Studio MAX, is a modeling, animation and rendering package developed by Autodesk Media and Entertainment.- Early history & Releases :...
, and the APIs
OpenGLOpenGL 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
Direct3DDirect3D is part of Microsoft's DirectX API. Direct3D is only available for Microsoft's various Windows operating systems and in the open source software Wine. It is the base for the graphics API on the Xbox and Xbox 360 console systems. Direct3D is used to render three dimensional graphics in...
. Some
RenderManThe RenderMan Interface Specification, or RISpec in short, is an open API developed by Animal Logic. It was later sold to 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
GLUTThe 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 is part of Microsoft's DirectX API. Direct3D is only available for Microsoft's various Windows operating systems and in the open source software Wine. It is the base for the graphics API on the Xbox and Xbox 360 console systems. Direct3D is used to render three dimensional graphics in...
counterpart
D3DXIn 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 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 mappingBump mapping is a computer graphics technique where at each pixel, a perturbation to the surface normal of the object being rendered is looked up in a texture map and applied before the illumination calculation is done...
.
BeOSBeOS was 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. In particular, the
Teapot in a stadium benchmark and problem concern the difficulty of rendering a scene with drastically different geometrical density and scale of data in various parts of the scene.
Appearances
With the advent first of computer generated short films, and then of full length feature films, it has become something of an
in-jokeAn in-joke is a joke whose humor is clear only to those people who are "inside" a social group, occupation or other community of common understanding; an esoteric joke. It is only humorous to those who know the situation behind it...
to hide a Utah teapot somewhere in one of the film's scenes. For example, in the movie
Toy StoryToy Story is a 1995 American computer-animated family/buddy film, directed by John Lasseter and featuring the voices of Tom Hanks and Tim Allen. The film was co-produced by Ralph Guggenheim and Bonnie Arnold and was distributed by Buena Vista Distribution. It was written by Joss Whedon, Andrew...
the Utah teapot appears in a short tea-party scene. The Utah teapot sometimes appears in the "Pipes"
screensaverA 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 WindowsMicrosoft Windows is a series of software operating systems and graphical user interfaces produced by Microsoft. Microsoft first introduced an operating environment named Windows in November 1985 as an add-on to MS-DOS in response to the growing interest in graphical user interfaces...
, but only in versions prior to Windows XP, and has been included in the "polyhedra"
XscreensaverXScreenSaver is a collection of several hundred free screensavers for Unix and MacOS computers. It was created by Jamie Zawinski in 1992 and is still maintained by him....
hack since 2008. The teapot also appears in
The SimpsonsThe Simpsons is an American animated television 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 eponymous family, which consists of Homer, Marge, Bart, Lisa, and Maggie...
episode
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
SIGGRAPHSIGGRAPH 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 solidIn 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 (
tetrahedronIn 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...
,
cubeIn 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...
,
octahedronIn 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.It is a 3-dimensional cross polytope.-Dimensions:...
,
dodecahedronIn geometry, a dodecahedron is any polyhedron with twelve faces, but usually a regular dodecahedron is meant: a Platonic solid. It is composed of 12 regular pentagonal faces, with three meeting at each vertex, and is represented by the Schläfli symbol {5,3}. It has 20 vertices and 30 edges...
,
icosahedronIn geometry, an icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of five Platonic solids....
) - and the sixth column has 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 BlinnJames 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!" videos) proves an amusing (but
trivialIn mathematics, the adjective trivial is frequently used for objects that have a very simple structure...
) version of the
Pythagorean theoremIn 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 triangleA right triangle or right-angled triangle is a triangle in which one angle is a right angle .-Terminology:...
and the area of the teapot on the
hypotenuseA hypotenuse is the longest side of a right 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 lengths of the...
is equal to the sum of the areas of the teapots on the other two sides.
See also
- Virtual model
A Virtual Model, in the general sense, is a model of a physical object. This model is a digital description of the object that can be used in a computer simulation or Virtual Reality....
- Trojan Room coffee pot
The Trojan Room coffee pot was the inspiration for the world's first webcam. The coffee pot was located in the so-called Trojan Room within the old Computer Laboratory of the University of Cambridge in Cambridge, England...
- Stanford Bunny
The Stanford Bunny is a computer graphics 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;...
- Stanford Dragon
The Stanford Dragon is a computer graphics test model created with a Cyberware 3030 MS at Stanford University.The Dragon consists of data describing 871,414 triangles determined by 3D scanning a real figurine...
- Lenna
Lenna or Lena is the name given to a standard test image originally cropped from a Playboy magazine centerfold picture of Lena Söderberg, a Swedish model who posed nude for the November 1972 issue...
- Cornell Box
The 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...
- Hello World
External links