📄 http:^^www.cs.wisc.edu^computer-vision^projects^visad.html
字号:
Date: Thu, 07 Nov 1996 19:22:57 GMTServer: NCSA/1.5Content-type: text/htmlLast-modified: Fri, 11 Nov 1994 18:28:26 GMTContent-length: 5347<HTML><HEAD><TITLE> VIS-AD: Data Visualization based on Lattices </TITLE></HEAD><BODY><H1> VIS-AD: Data Visualization based on Lattices </H1><BR><H2> Bill Hibbard, Brian Paul, Chuck Dyer </H2><P>We are defining a foundation for data visualization based on theidea that a visualization process is a function from a set ofdata objects, called a data model, to a set of displays, calleda display model. A prototype system called <!WA0><!WA0><!WA0><!WA0><A HREF="file://iris.ssec.wisc.edu/pub/www/visad.html">VIS-AD</A>has been implemented based upon our ideas. <P>We are guided by the following principles:<OL><LI>Scientists develop mathematical models of nature, and data objectsrepresent the objects of mathematical models. Mathematical objectsfrequently contain infinite precision real numbers and functionswith infinite domains, whereas computer data objects containfinite amounts of information and are thus approximations to themathematical objects they represent.<LI>Computer displays contain finite amounts of information (i.e.,they contain finite numbers of pixels, their colors are chosenfrom finite palettes, animation sequences contain finite numbersof frames, etc.) and are thus approximations to ideal displays.<LI>Because of the close relationship between data and computation,a data model should be appropriate for the data objects of a computationalmodel such as a programming language.<LI>The purpose of data visualization is to communicate the informationcontent of data objects. In particular, we define expressivenessconditions on the mapping from data objects to displays such thatdisplays should encode the facts about data objects, and onlythose facts.<LI>A visualization system should be complete in the sense that itimplements any function from data objects to displays satisfyingthe expressivenss conditions.</OL><P>We can define an order relation between data objects based onhow precisely they approximate mathematical objects, and wecan define an order relation between displays based on howprecisely they approximate ideal displays (i.e., based on voxelresolution, etc.). These order relations define lattices ofdata objects and displays. Therefore we can model the visualizationprocess as a function D:U --> V from a lattice U of data objectsto a lattice V of displays. We can interpret the expressivenessconditions in this context and show that D satisfies theexpressiveness conditions if and only if it is a lattice isomorphism.<P>We can define a particular lattice US appropriate for scientificdata objects. These data objects are built up from primitivevariables that we call scalars (e.g., time, latitude, radiance,and temperature) by tuple and array data type constructors(e.g., "array[time] of temperature" is a data type appropriatefor a time series of temperatures). Thus the lattice US containsthe data objects of a scientific programming language. We canalso define a particular lattice VV of displays, in which a displayis a set of voxels. Each voxel is specified by a set of graphicsprimitives that we call display scalars, e.g., a pixel's locationand size in a volume, its color, and its place in an animationsequence. <P>We can show that functions D: US --> VV satisfying the expressivenessconditions are just the class of functions defined by mappings fromthe scalars used for primitive variables in data objects to thedisplay scalars that specify graphics primitives of voxels. Ofcourse, designers of scientific displays already assume that primitive variables are mapped to graphics primitives. For example,given a data object of type "array[time] of temperature", it isnatural to display it as a graph with time along one axis andtemperature along another. The remarkable thing is that wedo not have to take this way of designing displays as an assumption,but that it is a consequence of the more fundamental expressivenessconditions.<P>We are developing and implementing a system called<!WA1><!WA1><!WA1><!WA1><A HREF="file://iris.ssec.wisc.edu/pub/visad/README">VIS-AD</A>that allows scientists to experiment with algorithms, steer theircomputations, and visualize the data objects they create in theirprograms. The lattice US defines the data objects of theVIS-AD programming language, the system implements the lattice VVof displays, and data can be displayed using any function thatsatisfies the expressiveness conditions (however, the implementationis not quite precise). Just as data flow systems define auser interface for controlling data display based on abstractionof the rendering pipeline, the VIS-AD system defines a user interfacefor controlling data display based on the abstraction ofmappings from scalars to display scalars.<P>It is possible to define data lattices for the recursively defineddata types (i.e., complex linked types such as trees) used ingeneral-purpose programming languages, and for the abstract datatypes and object classes in object-oriented programming languages.<P>Lattices provide a rigorous foundation for visualization. In particular,they can help us to develop an analytical alternative to the usualapproach of defining a visualization process D constructively bywriting a special-purpose program for computing a display D(u) fora specific data object u.</BODY></HTML>⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -