ompuferGm hIQS
`
`MU
`
`E4LLUr2nEE
`
`hihnlnlml‘uqulmulrl.1uiui.l.lulni:isl
`FILL. FUR. FIE“:- {sq-34::
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`IEEE Computer Society
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`

`

`Cgin uferGra bibs
`
`AND APPLICATIONS
`
`Articles
`
`VRM L
`
`1 7
`
`Guest Editor’s Introduction:
`
`Virtual Reality Modeling Language
`Maureen Stone
`
`Tutorial: Building Virtual Worlds
`1 8 with VRML
`David R. Nadeou
`
`VRML makes it easy to create virtual worlds. This
`tutorial reviews VRML‘s syntax and features as well
`as its world construction and animation abilities.
`
`3
`
`TerraVision ll: Visualizing Massive
`Terrain Databases in VRML
`Martin Raddy, Yvon Leclerc, Lee Mason.
`and Nat Bletter
`
`To disseminate 3D maps and spatial data over the
`Web, the authors designed massive terrain data sets
`accessible through either a VRML browser or the CUE-
`tomized TerraVision 1] browser.
`
`Large-Scale Mine Visualization
`Using VRML
`Kaitit Russ and Andrew Wetitcrell
`
`Traditionally, mine plans and sections in 2D stored
`3D information. This article shows that using VRML
`to model this information leads to new, interactive
`methods of data visualization.
`
`"Bottom, Thou Art Translated":
`45 The Making ofVRML Dream
`Stephen N. Motsuba and Bernie Roolll
`Bringing virtual theater to the Web requires 3D
`graphics, efficient networking, and strong content.
`The authors discuss the VRML Dream Project, a real-
`time Internet performance
`
`March/April 1999
`Volume 19 Number 2
`
`Published by the IEEE Computer Society
`
`Developing the VRML 97
`International Standard
`
`George S. Carson, Richard F. Fair, and
`Riki: Carey
`VRML 97 arose from a cooperative effort between the
`standards and VRML communities. The methodology
`employed applies equally well to development of
`future standards.
`
`5
`
`VRML Testing: Making VRML Worlds
`Look the Same Everywhere
`Mary Brady. Alden Dima, Len Gebase,
`Michael Kass, Carmelo Mommies-Rivera.
`and Lynne Rosentltal
`NIST tools address problems posed by testing 3D
`graphics. This article explains the test development
`strategy and design issues in developing and deliver-
`ing these testing tools.
`
`6 A Framework for Streaming Geometry
`in VRML
`André Gue'ziec, Gabriel 'l'anbin, Bill Horn,
`and Francis Lazarus
`The authors introduce a framework for streaming
`geometry in V'RML that eliminates the need to
`perform complete downloads ofgeomerric models
`before starting to display them.
`
`Dynamics Modeling and Culling
`79 Stephen Chutney. Jeffrey icitnoivski, and
`David Forsyth
`The tools described permit including large numbers
`of complex dynamic models in a VRML world easily
`and efficiently while maintaining high frame rates.
`
`'c‘ti'i Fed
`
`http://con1puter.org/egaf
`
`[SEN 0272-1716
`
`ad“...
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`
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`

`

`4 About the Cover
`
`Advancing 3]) through VRMI.
`rm the Web
`
`6 Projects in VR
`Public Speaking in Virtual
`Reality: Facing :ln Audience
`nf'Avutzn‘s
`
`10 Applications
`VizSim Technolugy Helps
`I-‘ind Oil Palmer
`
`88 Andrew Glassner's
`Notebook
`
`String Crossings
`
`96 New Products
`
`100 Advertiserf Product
`Index
`
`Computer Snciely Information, (73
`Change qucldress form. 1).
`l
`
`
`
`
`
`Microsoft Corp. Exhibit 1010
`
`Microsoft Corp. Exhibit 1010
`
`

`

`VRML
`
`This material may be protected by Copyright law (Title 17 U.S. Code)
`
`i
`
`TerraVision ll:
`
`Visualizing Massive
`Terrain Databases
`
`in VRML
`
`
`
`Martin Roddy, Yvan Leclerc, Lee iversun,
`and Nat Bietter
`SRI International
`
`To disseminate 3D maps and
`
`spatial data over the Web,
`
`we designed massive terrain
`
`in-
`Researchers haw.-
`creasingly turned to
`Virtual Reality Modeling Language
`(VRML)
`to represent geographic
`information. In VRMl..'s early days,
`the result was a few toy examples
`that did not scale well, such as
`coarse, single-resolution elevation
`grids. Today, VRML is drawing more
`serious interest from researchers
`across the spectrum, including geo-
`graphers, cartographers, geologists.
`and computer scientists, as the side-
`bar “Related Worlt" describes. As
`Theresa-Marie Rhyne noted, geo-
`graphic information system (613] and scientific visual-
`isation tools have begun to expand into each other's
`
`data sets accessible through
`
`either a VRML browser or
`
`the customized TerraVision
`
`ll browser.
`
`clomains,' and VRML offers cartographers and geogra-
`phers the potential to disseminate 3i) maps and spatial
`data over the World WideWeb. However, to date we have
`not seen useful large-scale VRML gcographicdalalmses.
`We aim to enable visualization of near plint‘nrealistic
`3D models oft-errain that can be on the order ofhun—
`dreds of gigabytes. This might incl tide different types of
`terrain imagery For particular regions. as well as site
`models and auxiliary information for ground leatures.
`The following scenario indicates the capabilities ‘
`required. Say a user wants to find a particular building III
`in a particular city. 1' lcrjotn'neyhegilis With a 3D model
`|
`oi" the earth viewed From space. This model is texture-
`‘
`mapped with satellite imagery of 100 kilometers reso-
`i
`illiit‘JI‘l—that is, each pixel in the texture map represents
`a region on the planet‘s surl’ace covering 100 ltnf. To |
`find the city, the user first rotates the earth to view the i
`
`-
`
`l
`
`
`
`Related Work
`Currently, interesting and significant work
`addresses the problem of representing geographic
`data in VRML. In the earth sciences, Kate Moore
`described the work of the Virtual Field Course
`(VFC) project,‘ which is developing software tools
`to familiarize students with fieldwork locations and
`aid data collection and analysis. The VFC project
`uses VRML and java to provide interactive 2D and
`3D views of geo~reierenced data to enhance
`students‘ cognition oi the real environment.
`The US Naval Postgraduate School ls currently
`working on a project to develop a 3D model of the
`Monterey Bay National Marine Sanctuary. They
`aim to create a VRML representation of the
`sanctuary based on raw bathymetry (below sea
`level) data for a 2.5 x 2.5 degree region of the bay.
`Their representation uses multiresolution
`techniques to deliver these large data amounts
`over a 28K modem connection.
`
`Michael Abernathy and Sam Shaw described
`their work using VRML to visualize the course fora
`197-mile relay race through the San Francisco Bay
`Area.2 They did this using standard US Geological
`Survey (USGS) 7.5 arc min digital elevation
`models (DEMs) for the terrain geometry with geo-
`referenced satellite imagery draped over the
`terrain. Their system also used Global Positioning
`System (GPS) input to create a line segment
`showing the race's course Over the VRML terrain.
`
`
`11
`Ill
`
`lli‘
`iii
`1J1
`l’l'
`{'31'
`
`References
`t!
`1. K. Moore, "Interactive Virtual EnVlronments for field
`1i
`work," British Cartographic Society Annual Syrup, 1 997:
`h
`available at http:/Mmugeog.le.ac.ukimekMrtEnv.httu.
`‘
`2. M. Abernathy and 5. Shaw, “Integrating Geographic
`J“
`Information in VRivlL Models," Proc. Third Symp. p
`VRML, ACM New York, 1998, pp. 107-114.
`0‘
`
`3!)
`
`March/April 1999
`
`Microsoft Corp.
`
`Exhibit 1010
`(Mill?!- 1 IflLiNWilClDD 3) lEli-J'J IEEE
`
`Microsoft Corp. Exhibit 1010
`
`

`

`the sidebar “The tsmApi Library" and is available along
`with other materials and several example VItML data sets
`at http:/owwai.st'i.comflbt't’a‘t’ision.
`
`Multlresolutlon terrain techniques
`Terrain models are typically massive. For example, the
`US Geological Survey produces digital elevation models
`(DEMs) that contain a regular grid of 1,201 x 1,20] ele-
`vation values for a 1-degree area of the earth's surface.
`Producing a simple polygonal representation of a single
`DEM creates a model with more than 1.4 million poly—
`gons. The titne required to download and render such a
`model would prohibitany real-time interaction using the
`current generation of VRML browsers.
`it therefore
`becotttes essential to tnanage level of detail (LCD).
`LCD techniques change a model's complexity based
`on some selection criteria, such as distance front the
`viewpoint or projected Screen size. The basic premise
`for these criteria is that any distant tietall that projects
`to less titan a single pixel on the screen will not generally
`be visible. To implement: this. we need a mechanism to
`simplify a data set‘s geomet 1'5; and imagery.
`Several polygon simplification algorithms work well
`for terrain. However, many oftitese are viewrindepen-
`dent techniques that force the same degree of simplifi-
`cation across
`the entire terrainf“ These
`are
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`The tsrnApl Library
`The “file Set Manager Application Program
`Interface (tsmApi) is a freely available C library
`from SRI International. The library offers
`functions for reading, writing, and generating
`terrain data used by TetraVision ll, including
`functions for generating VRML versions of the
`terrain data using the representations we
`describe in the article.
`
`Using the tsmApi library, users can create their
`own VRML geographic data sets from several
`supported input formats such as raw imagery,
`Portable Bitmap (PBM) images, and Land
`Analysis System (LAS) bitmaps. The library also
`includes SRl's fully re-entrant VRML 9? parsEr,
`which can be used to parse VRMI. 97 files
`efficiently Into memory and to write these
`Structures back out to a VRML 97 file. Other
`functions-perform transformations between
`various geographic coordinate systems, such as
`Unlveral Transverse Mercator (UTM), geodetic
`(latitude/longitude), and earthuiixed geocenttic,
`based on code from the US National imagery
`and Mapping Agency's Nimamuse product.
`Pro-compiled tsmApi distributions are available
`for his, Solaris, Linux, and other platforms. In
`addition, the full C source code is available from
`the tsmApi home page, which also includes full
`API documentation tutorials, format
`Specifications, and example source code. The
`tilitApi Web page is at http:!/www.ai.sri.comf
`tsmApl.
`
`
`
`Microsoft Corp. Exhibit 1010
`31
`IEEE Computer Graphics and Applications
`
`target region in tnore detail. As she seems into the
`region, higher resolution data, such as elevation and
`unagery, are progressively downloaded and displayed
`until she is "flying" over mountains with imagery down
`to onehmctcr resolution. Over certain parts of the i'Et'r
`rain. alternative imageries are available, such as aerial
`photographs; the user can select any intagc to view on
`top of the terrain geometry. As she approaches a built-
`up area, 3D models of buildings come into view. When
`the ttser clicks on a btt ilding, information abottt it is dis—
`played in a separate frame on the browser. Using this
`method, the user locates the target building. Through.-
`out the navigation, the user’s location is displayed via
`an act ive map interface that provides a context for the
`landscape being viewed.
`In setting ottt to achieve such capabilities, we identi-
`fied four principal design criteria:
`
`I Scalability. Our design must scale to very large data
`sets. Connnoniy, a geographic data set consists of
`many millions of polygons and many gigabytes of
`imagery.
`
`l ('fomposobiiity. Our data representation must allow
`the introduction of multiple types of gee-referenced
`data, including additional imagery, sire models. cul-
`tural features. and annotatiorts. it also must let the
`user switch between these on demand.
`
`I lifl’t‘rienqv. Users must be able to navigate the VRML.
`structures easily and efficiently using a stattdard
`VltMi. browser or a customized browser that further
`increases browsing efficiency.
`I Data interchange. We must develop genetic data rcp—
`resentations for goo—referenced data in VRML This
`will let other geographic data providers produce data
`using the same representation.
`
`Guided by these requirements, WE implemented this
`functionality in a standard VliMi. bi‘oWscr for dthn-
`loading tiara over the World Wide Web. We also devel-
`oped a custom terrain visualization package called
`'ilrrraVision ii that cart browse l'ltcsc VRMi. data struc-
`tures. Although not required to view the content,
`Tet raVision ll lets the user perform specia lizcd brovvser-
`level optimizations that offer increased efficiency and
`seamless interaction wit II the terrain data.
`
`We designed our framework to simplify terrain data
`maintenance and to let users dynamically select pill'thll-
`lat sets ofgco-t'ci‘iet'enced data. Our implementation uses
`Java scripting to extend VRML’s base functionality and
`the i5xternalAuthoring interface to offer applicationrspe
`ciitc management of the virtual geographic environment.
`To help develop standard techniques for solving geo-
`graphical representation problems in VRM1., coauthor
`Lee lverson formed and currently chairs the GeoVRMi.
`group, an official Working Group ofthe Web3D Consor-
`titttn (ltttp://'www.ai.st'i.cont/geovrml). As a service to
`the VltMl. cotntnun ity and the GcoVRMLeifot'i, we have
`made freelyavaiiable botlt the'l‘erraVision ii browser and
`all ot‘tlie tools we developed for generating VRMI. terrain
`data sets. This includes the source cotle to all of our cus-
`Iotn VRML nodes anti the tsmApi library that we use to
`generate the VRML data sets. The library is deseribed in
`
` L
`
`Microsoft Corp. Exhibit 1010
`
`

`

`VRML
`
`1 An example
`image pyramid
`showing
`(a) four differ-
`ent resolutions
`
`of an original
`image, where
`Each level is
`
`segmented into
`128 x128 pixel
`tiles, and
`(hi) how this
`structure can be
`used to alter the
`
`image resolu-
`tlon In different
`regions.
`
`
`
`or level; that is, at each higher resolution area, the tiles
`cover half the geographical area oftlte previous level.
`Using this representation, we can recursively resolve
`certain data set regions in more detail titan other
`regions. For example, Figure “lb shows the lower-right
`corner in high resolution with the surrounding regions
`displayed in progressively lower resolution. Assuming
`a tile size of 128 x 128 pixels, this example requires
`downloading and rendering only 49] Khytes (it) tiles)
`instead of the entire 3.1-Mhyte high-resolution image.
`lithe user‘s location is the bottom-right corner, then dis-
`tant imagery is rendered at lower resolution than near
`imagcry and we have achieved distance-based LOD.
`As Figure 2 shows, our image pyramids techniques
`can be applied to elevation grids and other types ofter—
`rain data. Because we use a tiled pyramid representa-
`tion for the geometry and the imagery, we cart optimize
`the amount ofclala transferred over the network, the
`number of polygons in the scene, attd the amount of
`memory required for texture maps. As a result, we need
`only fetch and display data for the region that the user
`is viewing, and only at a sufficient resolution for the
`user's viewpoint. This solution scales well to arbitrarily
`large data sets because it effectively attempts to keep
`the polygon count constant for any viewpoint.
`
`inappropriate for our application because switching to
`tire highest resolutionstill involves loading every point
`of tire original data set. Instead, we require a view-
`dependent technique that lets us vary the degree ofsitu—
`plification with respect to the current viewpoint.“ This
`is often done using a hierarchical data structure, such
`as a quad-tree. Further, the LCD algorithm must not
`require access to the entire high-resolution version of
`the data set, as that would limit as to viewing only data
`sets that can fit on the user’s local storage system. Given
`these requirements, a tiled. pyramid representation
`best suits our needs."u
`
`A pyrantid is a ntultiresolution hierarchy for a data
`set. For example, ifthe original image is 1024 x 1024
`pixels, then the pyramid might contain the original
`image along with down-so mpled versions at resolutions
`ol'512 X 512 pixels, 2.56 x 256 pixels, 128 x128 pixels,
`and so on. As Figure 1a shows, each pyramid image is
`then segmented into rectangular tiles. where all tiles
`have the some pixel dimensions A tile at a given pyra—
`mid level will thus map onto four tiles on the next high-
`
`2 Using a tiled
`pyramid struc-
`ture to repre-
`sent terrain
`
`geometry.
`Closer terrain is
`
`represented in
`higher fidelity
`(more [July
`gens) than
`distant terrain.
`
`
`
`
`
`Multlresolutlon data in VRMI.
`We introduce four types ofVRML files to represent a
`large, tiled multiresolution hierarch of the globe: tcr-
`rain tile files, feature files, geolile files. and tree files.
`Figure 3 shows these files and their relationships The
`tree files recursively itttplement the LCD hierarchy by
`inlining a single gentile file at one LOD and four higher
`resolution tree files at the next LOD. ‘l‘lte gentile l'ilE
`inlincs all of the feature and terrain tiles that covert!
`
`geographical area and LCD. A terrain tile file contains
`the neural elevation and image texture data fora given
`image, geographical area. and LOD. Feature files
`describe a geographical area’s objects, such as buildings
`and roads. We. discuss these relationships and their
`advantages below.
`
`32
`
`MarchMpril 1999
`
`Microsoft Corp. Exhibit 1010
`
`Microsoft Corp. Exhibit 1010
`
`

`

`
`
`A tree tile
`
`Hierarchy of
`geoiile files
`
`Two terrain tile
`pyramids
`
`A feature file
`
`3 The relationship between tree,
`gentile. terrain tile, and feature
`files. Unidirectional arcs represent
`lnllne links to files over the network.
`Bold rectangles delineate file
`boundaries.
`
`Tree files
`
`nee files implement part of the multi resolution hier-
`archy for the entire globe. in effect. these files are the
`glue that holds the geotiles in the quad-tree structure. A
`tree file initially loads a single geotile, but when the user
`approaches the tile, it‘s replaced with four higher—reso-
`lutiDn tree files, which in turn inline the geotiles for the
`tourquad-tree children. (At the bottom level of the tree
`hierarchy, the four geotiles are inlined directly.) The
`hierarchy of tree files must be generated only once and
`won’t generally need to be modified further—except
`perhaps to extend the tree for higher resolutions at a
`later j uncture. In the future, it might be possible to gen
`crate tree files on the fly.
`The tree files let us split the entire LOD hierarchy over
`multiple files and abso‘act the LCD structure from the
`actual terrain data. They also let us create a different
`I..DD tree depth for different global regions. For eaatt‘tv
`pie, we could have loo-km-resolution data for the
`entire globe but recursively insert higher resolution
`data for smaller regions of interest. such as a one-lun-
`rcsoiution data set for the conterminous United States
`
`and a one-m-resolutien data set for Yosemite Valley,
`California.
`
`it Would be possible to use the VRMI. Inl ine node
`to include the gentile files into the LCD hierarchy. How-
`ever, VRML 97 does [101' specify when the Universal
`Resource Locator (URL) ofan In]. ine node should be
`loaded, making thisn browser—dependent feature. Cur—
`rently. most browsers load all inline scenes at once. This
`makes good sense for small scenes with a handful of
`Inline nodes. l-Iowevet‘, ii We have a data set of 10
`U bytes, the VTtML browser will attempt to load all these
`data into memory at once. This is obviously unaccept-
`able for our application, so we must control when inline
`files are loaded and ti tilotttlcd. To do this, we developed
`
`a new node. called Quadnon, using VRML 97's
`EXTERNPROTO and scripting features. QuadLOD pro-
`vides a terrain—specific LOD capability that efficiently
`manages the loading and unloading of higher levels of
`detail. When the user enters a certain Volume around
`the tile (determined by a Proximi tySens-or) Quad—
`LOD loads only a tile‘s four higher resolution children.
`The notlealso uses a tile-caching mechanism so that tiles
`aren't needlessly reloaded. When the user approaches a
`region oftetrain. more detail is progressively loaded and
`displayed in a coarse—to—fine fashion. Most VRME.
`browsers perform nonblocking network reads so that
`the user can still interact with the some while higher
`resolution imagery and elevation loads.
`
`Gentile files
`
`Geotilo files Contain links to all data within a single
`tile. The most basic gentile includes a single terrain tile
`file for the region. However, it's possible fora gentile to
`Store linlts to multiple alternative terrain tiles, such as
`tiles referring to satellite, serial. and map imagery, as
`well as feature files for objects that exist on the terrain,
`such as buildings, roads. and annotations.
`By adding this extra layer to our global structure1 we.
`Simplify the task of maintaining and adding new data
`sets. For example, when we want to add a new image
`pyramid, we can generate the terrain tiles in isolation
`and simply link them to appropriate geotiles. (If the new
`data set requires higher resolution than the region pre-
`viously required, we also must generate new tree files.)
`In addition, because each data set is stored indepen—
`dently and referenced only via the geotiles, We can selec-
`tively display any combination of data sets. A node we
`created, GeoTi 1e, permits this selectivity by organiw
`ing the terrain tile and feature file links into sets of
`Switch nodes.
`
`Microsoft Corp . Exhibit 1010
`IEEE Computer Graphics and Applications
`33
`
`Microsoft Corp. Exhibit 1010
`
`

`

`VRML
`
`‘-' IN ‘i-ni-it- ll'l' Nun-nu-
`
`'
`
`thntacwmummfim'l'flf
`
`'I,
`
`p.“ ._
`t “it
`,s.,_ If
`I
`
`For: Burning in VILMIL
`
`H
`
`4 A tiled terrain
`model showing
`geo~referenced
`3D geometry
`overlaid for
`
`roads (orange)
`and buildings
`(yellow).
`
`Terrain rife files
`Terrain tiles contain tltc actual terrain data for a sin-
`
`gle data set tile at a particular detail level. This includes
`the elevation geometry and the texture map imagery for
`the specific terrain tile. The VRML 97‘ specification pro-
`vides us with two potential primitives for representing
`terrain geometry: the IndexedFaeaSat
`and the
`E1 evationGr id. The latter node lets the utter specify
`a grid of height values above rhcx-e plane. whereas the
`more general IndexedFaoeSet node lets the user
`define arbitrary polygons in 3D space. VRML 97"s Ele-
`vationGrid was introduced specifically to represent
`terrain models and offers a compact mecltanism to
`describe simple height field tiara. However, it has serious
`limitations that prevent us from using it, including that
`it assumes that the heights are relative to a flat plane—
`an obvious problem when dealing with curved planets.
`ElevationGric‘ia are thus useful only for modeling
`local areas, where the earth’s curvature is insignificant.
`Because we want to support global data sets, we use the
`IndexedFaceSet to build terrain geometry.
`
`Feature files
`Feature files contain VRML models for objects relat—
`ed to a region of terrain. Examples include a region's
`cultural features, such as roads and lines of communi-
`cation; weather simulations, such as clear air turbulence
`isosttrfaces and wind vectors; and other 3D data, such
`as terrain annotations.
`
`integrating terrain features proves difficult because
`features cart extend beyond tile boundaries. For exam-
`ple, a road triight cover multiple tiles, or a large building
`might sit on the boundary between two tiles. One way
`to deal with this problem is to dissect the geometry for
`all ground features along tile boundaries, forcing the
`condition that all features in a tile are contained entire-
`
`ly within that tile. Another-solution is to simply include
`a link to the same feature in all relevant geotilcs. We
`selected the latter approach because it does not cott-
`strain the cultural features to the same resolution range
`as the terrain, and it requires no modification to the fea-
`ture's geometry. However. one problem is that the
`browser Would normally load, store, and render dupli-
`cate copies of each feature for every loaded gentile in
`which it occurs. To avoid this, we have designed our
`GeoTile node. so that it keeps track ofeaelt request for
`a feature file‘s URL. We do this using static class strnc— I
`tures in a Java script. We load feature files only on first
`invocation, incrementing their reference count, and
`unload a feature file only when its reference cottnt
`returns to zero. Figure 4 shows the fusion of terrain data
`anti cultural features that results.
`Geographic coordinate systems
`VRML defines a Cartesian coordinate system for mod-
`eling objects in a 3D volume. In geographic terms, this
`gives us a geoccntric representation: a coordinate (any,
`z) is assumed to be a 3D offset [in meters] from the
`earth’s center. However, most elevation data are pro—
`
`i
`‘
`i
`
`l
`
`i
`
`vided in some geodetic or projective coordinate system.
`A geodetic coordinate system is related to the ellipsoid
`used to model the earth {such as the latitude-longitude
`system). A projective coordinate system projects the
`ellipsoid onto some simple surface, such as a cone or a
`cylinder. Examples include the I..ambert Conformal
`Conic or the Universal Transverse Mercator projections.
`Such coordinate systems were designed for different
`applications and offer particular advantages and restric-
`tions. For example, some projections can represent only i
`small-scale regions; others are conformal, offering the
`same scale in every direction; and others can be equal
`area—the projected area corresponds to the earth’s
`physical area over the entire projection. 'i'o use data in
`these different coordinate systems, we must convert
`coordinates in these systems into the VRML geocentric
`coordinate system. Descriptions for performing many
`of these transformations are available elsewhere.” The
`
`I
`
`sidebar “What Shape Is the Earth?" discusses related I
`
`representation challenges.
`
`Floating-point precision Issues
`The VRML 9'? specification defines the. Si-‘Float and
`MFloat fields to represent floating-point numbers How.
`ever, these are only sin glue-precision values; the dynamic
`range of a single-precision floating-point number isn‘t
`sufficient to store accurate geocentric coordinates. For
`example, the lEEE single-precision format defines a 23-
`hit ntant issa. This provides a resolution of approximate-
`ly six digits (2'23 = 8.39 x 10“). The earth’s diameter is
`roughly 12,700,000111, and thus we can model terrain to
`an accuracy ofonly tens or hundreds ofnieters. This accu-
`racy can‘t even represent the results front a civilian-grade
`Global Positioning System (GPS), let alone fail hfully rcp-
`rescnt ground featu res such as buildings or roads.
`MostVl’cML browsers use only single-precision arith-
`metic for modeling and matrix operations, and most
`modern graphics hardware uses only single precision.
`We must therefore implement accurate geocentric coor-
`
`34
`
`March/April 1999
`
`Microsoft Corp. Exhibit 1010
`
`Microsoft Corp. Exhibit 1010
`
`

`

`
`
`What Shape Is the Earth?
`In a computer graphics system, the simplest
`way to represent the earth is to prodUCe a sphere
`and then apply to it a texture map. This method is
`adequate for a coarse representation. However, if
`we want to model the planet down to submeter
`accuracy, We must better understand the earth's
`shrape and the coordinate systems that describe
`it.
`
`Ellipsolds
`The earth can best be modeled geometrically
`using an ellipsoid of rotation. Such an ellipsoid is
`traditionally specified by tWO of three variables: the
`semi-major axis (a), the semi-minor axis (is), and
`the inverse flattening (11f: o/ (a — in). Over the
`past 200 years, many different reference ellipsoids
`have been formulated, each defining slightly
`different values for these variables. The current US
`Department of Defense standard is defined by the
`World Geodetic System 1934 M6584), such that
`o = 6378137.0m and b = 6356752314Zm.
`
`Geolds
`
`The ellipsoid describes an ideal surface, but
`most elevation data are given relative to the
`geoid, not the ellipsoid. The geoid is the
`physically measurable surface Corresponding to
`mean sea level and is related to the earth’s
`
`gravitational field. This complex, undulating
`surface varies marginally from the ellipsoid over a
`range of roughly 100m. Once again, there are
`several slightly different geoid standards, such as
`GEOIDQO, OSU89B, and WES-84.
`
`Datum:
`
`A datum speci