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. It is a simple, round, solid, partially concave mathematical model of an ordinary teapot.
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.
History
Newell needed a moderately simple mathematical model of a familiar object for his work. Sandra Newell (his wife) 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 tea service by eye. Then, he went back to the lab and edited Bezier control points on a Tektronix storage tube, again by hand. While a cup, saucer, and teaspoon were digitized along with the famous teapot, only the teapot itself attained widespread usage. It is thought that a milk jug was also modelled, but the data for that seem to have been lost.
The teapot shape contains a number of elements that made it ideal for the graphics experiments of the time — it is round, contains saddle points, has a genus 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 describes 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 SIGGRAPH'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 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 Blinn 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 ZCMI (a department store in Salt Lake City, Utah) 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 in Mountain View, California where it is catalogued as "Teapot used for Computer Graphics rendering" and bears the catalogue number X00398.1984.
Applications
Versions of the teapot model, or sample scenes containing it, are distributed with or freely available for nearly every current rendering and modeling program, including AutoCAD, Lightwave 3D, POV-Ray, OpenGL, Direct3D, and 3D Studio Max. Along with the expected cubes and spheres, the GLUT library even provides the function glutSolidTeapot() as a graphics primitive, as does its Direct3D counterpart D3DX (D3DXCreateTeapot()). BeOS 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 data in various parts of the scene.
Appearances
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With the advent first of computer generated short films, and then of full length feature films, it has become something of an in joke to hide a Utah teapot somewhere in one of the film's scenes. Utah teapots can be found in Toy Story, Monsters Inc., and Disney's Beauty and the Beast, as well as in The Simpsons. It can be found in Microsoft Train Simulator, and is featured in one of the levels of the video game Super Monkey Ball 2 and in the technological demo section of Serious Sam. By using a cheat code it is possible to have a Utah teapot as an avatar in the Star Wars: Knights of the Old Republic PC game. In computers, the Utah teapot sometimes appears in the Pipes[1] screensaver shipped with Microsoft Windows.
One famous ray-traced image (by Jim Arvo and Dave Kirk, from their 1987 SigGraph paper `Fast Ray Tracing by Ray Classification.') shows six stone columns five of which are surmounted by the platonic solids (tetrahedron, cube, octahedron, dodecahedron, icosahedron) - 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 Blinn (in one of his "Project Mathematics!" videos) proves an interesting version of the Pythagorean theorem: Construct a (2D) teapot on each side of a right triangle and the area of the teapot on the hypotenuse is equal to sum of the areas of the teapots on the other two sides.
