multi-resolution terrain depiction on an embedded 2d/3d synthetic vision system

te

cularly, todatabasesy to ensure

by using ation data

rmined at) can beirements.represen-

aviationation, andknowledgesB, DO-254,

Aerospace Science and Technology 9 (2005) 517–524

www.elsevier.com/locate/aesc

Multi-resolution terrain depiction on an embedded2D/3D synthetic vision system✩

Thorsten Wiesemanna,∗, Jens Schiefelea, Wolfgang Kubbatb

a Advanced Business Development, Jeppesen GmbH, Frankfurter Strasse 233, 63263 Neu-Isenburg, Germanyb Darmstadt University of Technology, Flight Systems and Control, Germany

Received 25 February 2003; accepted 3 January 2005

Available online 17 March 2005

Abstract

Many of today’s and tomorrow’s aviation applications demand accurate and reliable digital terrain elevation databases. Partienhance a pilot’s situation awareness with future 3D Synthetic Vision Systems (SVS), accurate, reliable, and hi-resolution terrainare required to offer a realistic and reliable terrain depiction. On the other hand, optimized or reduced terrain models are necessarreal-time rendering and computing performance.

In this paper a method for adaptive terrain meshing and depiction for SVS is presented. The initial data set is decomposedwavelet like transform, resulting in terrain coefficients and delta values to represent the terrain data in an optimized multi-resolustructure. By examining the coefficients and delta values, an adaptive surface approximation for various Level-of-Detail is deteruntime. Constraints for the Level-of-Detail approximation (like max. approximation error or degree of topography preservationassigned and changed at runtime. This results in an adaptive terrain depiction suitable to the current operational SVS display requ

Additionally, the dyadic scaling of the transform is used to build a hierarchical quad-tree representation for the terrain data. Thistation enhances fast interactive computations and real-time rendering methods.

The multi-resolution terrain concept is integrated into a hi-level certifiable 2D/3D scene graph rendering system. It runs on ancertifiable embedded rendering graphics board. The optimized combination of multi-resolution terrain data, scene graph organizgraphics board allows it to handle dynamically terrain models up to 3 arc second post spacing. The system and data processing acstandard certification rules for terrain database requirements, aeronautical data processing and software development (DO-178DO-200A, and DO-276). 2005 Published by Elsevier SAS.

Keywords:Adaptive terrain depiction; Synthetic vision system; Multi-resolution; Level-of-detail; Synthetic terrain databases; Realtime rendering

nic)

aseVS).on-re

02.173

entim-

NDter-ion

beresnalaseralcer-

1. Introduction

Modern glass cockpits are equipped with an electroPrimary Flight Display (PFD) and Navigation Display (NDas primary flight guidance displays. A concept to incresituation awareness are Synthetic Vision Systems (SSVS are particularly developed to reduce the risk of Ctrolled Flight Into Terrain (CFIT) and support the futu

✩ This article was presented at the German Aerospace Congress 20* Corresponding author. Tel.: +49 6102 508480; cellular: +49

9067369; fax: +49 6102 508463.
E-mail address:[email protected] (T. Wiesemann).
1270-9638/$ – see front matter 2005 Published by Elsevier SAS.doi:10.1016/j.ast.2005.01.010

concept of free flight [1,2,4,5,14,20]. Most SVS supplemconventional PFD symbols by an abstracted perspectiveage of surrounding terrain and airports. Conventionalsymbols are overlaid by a two-dimensional depiction ofrain, obstacles and airports [1,13,14]. Virtual informatsuch as a “tunnel in the sky” or a landing channel canintegrated as well [1,13,14,20]. Combining all these featuSVS has high pilot acceptance rates [13]. The InternatioFederation of Airline Pilots (IFALPA) has declared SVSa requirement for future cockpits. Meanwhile, also sevaviation equipment manufacturers have started realizing
tifiable graphics boards and computers [5].

518 T. Wiesemann et al. / Aerospace Science and Technology 9 (2005) 517–524

ableially

F),cen-5].ndtalta-req-

hile,iallyn-ac-

to-ingrmsuireal-5].so-

eralt re-anthi-nce

asch-

in are-orkingthe-s, ind inept

om-der

me.

romtiveiouslti-,16,bletiontheech-

on

so-

all

s forVS.s areva-ictedion.ivede-

ionl re-rraintedur-raftted

letsings isachherly

ech-ap-nsnif-rainear-ta-riesd inility

As basis for any SVS reliable databases and certifidatabase processing are a prerequisite [9,15,21]. Especduring final approach procedures, Low-Level Flights (LLor free flight maneuvers the terrain database plays atral role for any terrain alert and warning system [2Even further developments for Terrain Following (TF) aTerrain Avoidance (TA) applications during InstrumenMeteorological Conditions (IMC) are based on terrain dabases [19]. Therefore, hi-resolution terrain data are a preuisite to provide a reliable and useable system. Meanwthese databases exist for larger parts of the globe. Especwith the Shuttle Radar Topographic Mission (SRTM), cosistent and hi-resolution terrain with 90 m by 90 m post sping will be publicly available within the next years [5,25].

However, hi-resolution terrain cannot be depicted withday’s real-time graphics machines [21,25]. Simply depictthe huge amount of available terrain polygons outperfoeven any high-end graphics board. Therefore, SVS reqperformance optimized terrain models for a real-time visuization, but still providing reliable and accurate data [18,2Fig. 1 shows exemplary the trade-off between terrain relution (data quality) and rendering performance of sevterrain models. For example, an optimal terrain data segarding data quality would be a terrain model complito ED98/DO276 specifications (Fig. 1, symbolizing aquality data set). Nevertheless, the rendering performaof this model would be worse within any SVS (Fig. 1,low performance data set). In the last years various teniques were introduced to reduce digital terrain modelssafe and reliable manner. In Fig. 1 this is exemplarily repsented by the reduced grid and Triangular Irregular Netw(TIN) models, which are calculated from the correspondhi-res terrain model as a reduced approximation. Neverless, these techniques only provide static terrain modelwhich resolution and accuracy are constrained or limiteadvance [18,21,25]. Especially, for the free flight concthis is inappropriate.

In this paper a new approach is described to accplish the contradictory demands of needed accuracy, rening performance, and dynamic adjustment during runti

Fig. 1. Trade-off between data quality and rendering performance.

,

,

-

Based on polygonal surface approximation techniques fthe scientific visualization area, a new method for adapterrain meshing and depiction in SVS is presented. Varmethods are known from literature which cope with muresolution methods for surface approximations [6–9,1117,23,24]. In order to treat complex terrain data in a reliaand efficient way, we propose a wavelet like decomposiwhich is applied to the initial data set. To encompass withrequirements of a SVS, we adapted standard wavelet tniques [10,11,24] to the following constraints:

• provide a reliable and accurate decomposition;• provide full control over the introduced approximati

error;• provide a reliable and safe terrain depiction at any re

lution level;• provide a multi-resolution representation with a sm

amount of data needed.

The proposed decomposition has some major advantagemulti-resolution terrain management and depiction in SFirst of all, decomposed and reconstructed terrain modelrepresented by maximum coefficients for all terrain eletion approximations. Hence, any reconstructed and depterrain model represents always an “aviation safe” versThe multi-resolution functionality itself supports an adaptrefinement of the terrain data to various needs. Terrainpiction by means of resolution or introduced approximaterror can be responsive to a chosen field of view or locagion of interest. This can be used to have an adaptive temodel with respect to the current aircraft position. Depicterrain has a minimum approximation error nearby the crent aircraft position and increasing errors at higher aircdistances. In addition, flight critical regions can be depicat higher resolutions permanently.

2. Terrain decomposition and reconstruction for SVS

As an alternative to the classic Fourier analysis waveare a mathematical toolkit for hierarchically decomposfunctions. The basic idea behind all hierarchical methodto represent functions with a collection of coefficients, eof which provides some limited information about both tposition and the frequency of the function [24]. In the ea1990s, wavelet decompositions became a well known tnique for multi-resolution methods in Computer Graphicplications [8,9,11]. In contrast to other hierarchical functiolike the Fourier transformation wavelets have some sigicant advantages in practice. Especially for a SVS terrepresentation these are remarkable. This includes lintime complexity for very fast algorithms (real-time computions), the possibility to represent finite and aperiodic se(elevation grids), the scarcity of coefficients encounterepractice (amount of data storage), and the ideal adaptab
to various mathematical algorithms and functions [24].

T. Wiesemann et al. / Aerospace Science and Technology 9 (2005) 517–524 519

re-h one an4].de-nal-setsrid;olor

s oree

po-al.

sicaxi-ainal-

de-

irstnc-t, aedeat-

ithnd

enith

sult-y theor-Theoesededap-i-re-

theelyrixithinltere al-inal

n athenc-

.seeof

iven

ord-ed

To apply a wavelet like decomposition to terrain repsentation and depiction in SVS we based our researcstandard techniques used for images. Stollnitz et al. givexcellent overview of wavelets for Computer Graphic [2Using the overview of Stollnitz et al. we adapted thescribed methods to the requirements of a SVS. The aogy of images and terrain data is obvious: both dataare 21

2-dimensional; they are based on an equidistant geach element has an additional datum assigned to (cor elevation). Nevertheless, the constraints for waveletmulti-resolution analysis in SVS are notably different (salso bullets in Section 1).

A theoretical outline of the proposed terrain decomsition was already explained in detail in Wiesemann et[26,27]. Recalling this shortly, Fig. 2 illustrates the baidea using a standard terrain decomposition with a mmum filter bank. To obtain the decomposition of a terrtile, the transform is applied to each row and column,

(a)

(b)

Fig. 2. (a) Maximum decomposition of a terrain tile. (b) Original and
composed terrain tile.
ternating between them during transform calculations. Fone step of horizontal pair wise maximization and differeing on the height values in each row is performed. Nexvertical pair wise maximization and differencing is applito each column of the previous horizontal results. By reping this process recursively, a complete decomposition wone height value (maximum elevation for the whole tile) a2n × 2m − 1 detail coefficients is computed.

Fig. 2 tabulates the original elevation values for a givexample terrain tile and the resulting decomposition wdetail coefficients. The subsequent detail coefficients reing from the separate computation steps are indicated bdifferent background colors (Fig. 2(b)). Note that no infmation has been gained or lost by the decomposition.original elevation matrix had 16 coefficients and so dthe transform. Hence, the same amount of data is neto represent the finest resolution as well as the differentproximations. Additionally, starting with the overall maxmum elevation value, the terrain representation can beconstructed to any resolution by recursively subtractingdetail coefficients from the lower-resolution versions. Sola coefficient itself and the index position within the mathave to be considered to reconstruct a certain part wthe tile. Furthermore, due to the usage of a maximum fibank, reconstructed elevation posts at any resolution arways representing maximum elevation values of the origterrain model.

The corresponding maximum coefficients (cji ) and detail

coefficients (dji ) at recursion levelj with index i are given

by:

cji := max

(cj+12i , c

j+12i+1

), d

ji = c

j+12i − c

j+12i+1,

i = 0, . . . ,2j − 1; j = log2 n.

The mathematical basis for the decomposition is built ostandard Haar wavelet technique [12,24]. We adaptedcorresponding one-dimensional scaling and wavelet futions to our maximum filter bank, resulting in aSafety Ter-rain Delta Coefficients (STDC)set of delta functions [28]For a detailed derivation and explanation of the STDCWiesemann et al. [26,28]. Principally, the scaling functionthe STDC is based on the commonly used Box Basis gby [24]:

φji (x) := φ(2j x − i),

where

φ(x) :={

1 for 0� x < 1,0 otherwise,

with i denoting the index of an elevation post within a rowcolumn andj denoting the recursion level. The corresponing maximum delta coefficients for the STDC are definby:

ψji (x) := ψ

(2j x − i,sgn(dj

i )),

i = 0, . . . ,2j − 1; j = log2 n,


va-nc-

x-orsin-tailde-

e isox-of a

rgegiesflat

sedco-d isde-odecov-henfol-andoachom-

an

ownor-tifyagece

ma-umre-um

itudencertains or

ith

ca-

s, intlyfores

de-tain

ionfer-),

ssredn-l-ing

intstionec-

port

ntsIn

ingted

heil.

where

ψ(x, s) :=

0 for 0� x < 12 ands = 1,

1 for 0� x < 12 ands = −1,

−1 for 12 � x < 1 ands = 1,

0 for 12 � x < 1 ands = −1,

0 otherwise,

and

sgn(d) :={

1 for d � 0,

−1 for d < 0.

Transformed to the two-dimensional basis of terrain eletion data, the appropriate scaling and delta coefficient futions are defined by [24,26]:

φφjrc(x, y) := φφ(2j x − r,2j y − c),

φψjrc(x, y, s) := φψ(2j x − r,2j y − c, s),

ψφjrc(x, y, s) := ψφ(2j x − r,2j y − c, s),

ψψjrc(x, y, s1, s2) := ψψ(2j x − r,2j y − c, s1, s2),

where

φφ(x, y) := φ(x)φ(y),

φψ(x, y, s) := φ(x)ψ(y, s),

ψφ(x, y, s) := ψ(x, s)φ(y),

ψψ(x, y, s1, s2) := ψ(x, s1)ψ(y, s2),

with row and column translations denoted by subscriptr andc respectively.

Additionally to the standard decomposition with the maimum filter bank, we considered introduced vertical errwithin the multi-resolution models using the additionalformation included in the detail coefficients. Since the decoefficients of the wavelet decomposition represent theviation between two adjacent elevation posts, the valuidentical to the introduced altitude error during each apprimation step. This means, the greater the absolute valuedetail coefficient the higher the relative vertical error. Ladeviations correspond to mountainous or rough topolowith extensive terrain slopes; small values characterizeor smooth surfaces.

Given that the multi-resolution terrain model is suppoto be integrated into a SVS, the magnitudes of detailefficients are taken into account. One common methonormalizing the detail coefficients and sorting them bycreasing magnitude [3,11]. Normalization is required to cthe relationship between magnitude and correspondingerage of any detail coefficient. The reconstruction can tbe performed by applying the highest coefficients first,lowed by the coefficients with decreasing magnitudebreaking at a predefined epsilon. Nevertheless, this apprrequires additional and time extensive reconstruction cputations, but by providing at each reconstruction step
optimal relative approximation to the original model.
To go a step further for SVS we are interested to knthe absolute error values for any depicted terrain data,malizing and sorting is insufficient. Nevertheless, to idenan absolute altitude error for any multi-resolution coverfurther information is needed. To simplify and to enhanthe online computations, we decided to store some infortion additionally: the terrain is decomposed with a minimfilter bank in parallel as well. Hence, the difference of aconstructed terrain cell between the maximum and minimapproximation can be used to determine the absolute alterror. During reconstruction computations each differevalue is used to decide whether a terrain quad at a cerecursion level has to be subdivided into finer resolutionnot.

Fig. 3 displays various reconstructed terrain models wdifferent maximum error bounds.

Drawback of this method is the extra amount of datapacity needed. For a terrain tile with 2n × 2n original ele-vation posts additional 2n × 2n−1 detail coefficients for theminimum decomposition have to be stored. Neverthelespractice many detail coefficients turn out to be zero (slighrecognizable in Fig. 3(d)). This is even more remarkabletopologies with small gradients. By omitting these valuin the data file but saving the supplemental minimumtail coefficients the needed capacity is limited to a cerextent.

Prior to the implementation of the terrain reconstructalgorithms we analyzed the potential requirements of difent SVS applications like a Primary Flight Display (PFDNavigation Display (ND), or Vertical Situation AwareneDisplay (VSAD). Various constraints concerning a requidata quality and resolution were identified. Any recostructed terrain resolution (Level-of-Detail) of distinct eevation posts shall be dependent at least on the followconstraints:

• maximum approximation error;• desired frame rate (rendering performance);• current aircraft position;• current viewing direction and field of view;• terrain topography;• regions of interest;• selected display mode, range, and flight phase.

Fig. 4 represents exemplarily terrain resolution constrafor a PFD. First, the area nearby the current aircraft posiis depicted at a higher resolution than terrain farer away. Sond, a local region of interest like the area around an airis depicted at a higher resolution as well.

In Fig. 5 three different terrain reconstruction constraifor a desired terrain resolution in a ND are shown.Fig. 5(a) the resolution is constrained to the underlytopography only. Mountainous regions are reconstrucwith a higher resolution than flat locations, minimizing toverall approximation error for the current Level-of-Deta
Fig. 5(b) is an ND equivalent to the PFD constraints men-


rentay.

ownn-

ad-pic-ya ton orcho-po-s of

blesinter-Thisct toumandion,onsingac-fine

n-

(a)

(b)

(c)

(d)

Fig. 3. Different approximations of a terrain tile using maximum error

Fig. 4. Terrain resolution constraints for a PFD.

(a) (b) (c)

Fig. 5. Terrain resolution constraints for a ND.

tioned above: high terrain resolutions nearby the curaircraft position; coarser resolutions at areas farer awFig. 5(c) represents a combination of the constraints shin Figs. 5(a) and (b). Additionally, the resolution is depedent on the current selected zoom level of the ND.

As a conclusion, the realized STDC has some majorvantages for multi-resolution terrain management and detion in SVS. First of all, the multi-resolution functionalititself supports an adaptive refinement of the terrain datvarious needs. Terrain depiction by means of resolutiointroduced approximation error can be responsive to asen field of view. Moreover, the defined STDC decomsition and data management helps to define local regioninterest. The dyadic scaling of the wavelet transform enaa hierarchical quad-tree organization and enhances fastactive computations and real-time rendering methods.can be used to have an adaptive terrain model with respethe current aircraft position. Depicted terrain has a minimapproximation error nearby the current aircraft positionincreasing errors at higher aircraft distances. In additflight critical regions can be depicted at higher resolutipermanently. For an optimal approximation of underlyterrain topography the detail coefficients are taken intocount, reconstructing areas with high terrain slopes to aresolution level and plane areas to coarser levels.

3. Implementation

For the realization of the STDC in a SVS enviro
bounds. ment, the architecture shown in Fig. 6 was designed and


Fig. 6. Architecture of the STDC components.

di-ion)tec-ent.roced in

ismtem

-of6)

cial-n,S.or

red

ta is

rain. 6ode

per-rrainintoon-teds ameledre-ainberor-

implemented. Since the multi-resolution technique isvided into a pre-processing (terrain data decompositand runtime part (terrain data reconstruction), the architure is separated into an offline and an online componSource terrain databases are decomposed via a data psor and the resulting transformed STDC terrain is storean Onboard Aviation Database(OA-DB). This OA-DB isloaded onto the aircraft through a data loader mechanand theDatabase Server Application Management Sys(DBSAMS).

For the runtime part, severalDatabase Server Applications (DBSA) are dedicated to handle the reconstructionterrain approximations. In the given architecture (Fig.three separate DBSA reconstruct terrain models speized for PFD, ND and VSAD, respectively. Synchronizatiomanagement and data access is handled by the DBSAM

For displaying reconstructed terrain data in PFD, NDVSAD, the appropriate terrain approximation is transferto theCockpit Display System(CDS). A final optimizationfor the used graphics engine is computed and terrain dafinally rendered.

The various constraints used for reconstructing terapproximations are indicated in the lower part of Fig(see also bullets in Section 2). This includes selected mand zoom range as pilot inputs for the ND. Since the oated ND range influences directly the representable teresolution per pixel, the selected zoom range is takenaccount. Therefore, the maximum recursion level is ctrolled by this value at a first instance, preventing a depicresolution would be beneath a displayable pixel size. Asecond limitation, the currently achieved rendering frarate is transferred from the CDS to the ODS and handby the DBSA’s. As soon as the frame rate is below aquired minimum, the resolution of the corresponding terrapproximation is adapted dynamically to a smaller numof terrain polygons, resulting in a higher rendering perf
mance. Third, position and heading are fed to the ODS from
s-

(a)

(b)

Fig. 7. ND with integrated terrain database. (a) ND with standard DTED-0.
(b) ND with optimized STDC for 10 nm.


um

ndD

aintssedre-berre-

ori-r 3DI is

r-h anbe-

iss-allm).d dedel

theso-the

-0, byictedforein-is

n.d on

lier,cted

ainso-lso

reas

D.ND

er-Notthe

mesox-

Fig. 8. Different STDC resolutions dependent on topography and maximaltitude error.

the avionics bus, to include current aircraft position aviewing direction into reconstruction calculations for PFand ND. Nevertheless, besides the three system constrthe strategy of the dynamic terrain reconstruction is baon a maximum altitude error margin additionally. As asult, an optimal compromise between resolution, numof rendered polygons, and introduced error margins isalized.

The realized implementation is based on an objectented scene graph philosophy to manage and rendevector data. The used scene graph with it’s hi-level APdescribed in Schiefele et al. [22] in more detail.

In Fig. 7 two ND implementations with integrated terain data are displayed. The advantage of the STDC witadaptive and dynamic multi-resolution terrain depictioncomes obvious. Since the required frame rate for a NDabout 15 Hz within a SVS, only DTED-0 (30 arc sec reolution) as static terrain data fulfills this requirement atrelevant zoom ranges (ranging from 160 nm down to 10 nTherefore, the 30 arc sec resolution has to be used anpicted if the system is restricted to a static terrain mo(Fig. 7(a)).

In contrast, the dynamic resolution adaptation ofSTDC technique to different zoom levels optimizes its relution to each individual zoom level. At a 160 nm rangeresolution of the STDC corresponds exactly to the DTEDmodel to satisfy the required frame rate as well. Howeverselecting smaller zoom ranges the ratio between the depterrain coverage and useable resolution changes. Thereby zooming in the resolution can be increased, still mataining the required frame rate. In Fig. 7(b) the STDCreconstructed up to a 3 arc sec resolution. The rendered im-
age is still updated with about 17 Hz.
,

-

,

Fig. 9. STDC integrated in a PFD.

In Fig. 8 two examples of a ND with STDC are showThe image represents the adaptive reconstruction basethe underlying terrain topography. As mentioned earmountainous areas with high terrain slopes are reconstruto a higher resolution. At the right side of Fig. 8 the terrmodel is depicted as a wireframe model. The different relutions and resulting polygons are clearly recognizable. Athe different depiction between flat and mountainous abecomes obvious.

Finally, Fig. 9 illustrates the STDC integrated in a PFThe shown scenario corresponds to the one shown in thein the upper part of Fig. 8. Also recognizable are the diffent resolutions used to approximate the terrain model.shown are the dynamic resolution changes resultant tomovement of the aircraft: The closer a terrain area becoto the current aircraft position the finer the terrain is appr
imated.


ngther-olu-tiveax-aine toer-tionhicsnne

ys:hetic7–

ht997,

u-.98,

withnal

elet.ing

oc.

EU-

ing,

ma-sual-

the-

k-any,

ys,

44:light

ad-

g of

eci-etic

ionetic

ap-on

asesA,

ener-roc.

re-

ph-CA,

ataand

andced

air-En-

nde-nde-005,

4. Conclusion

A multi-resolution terrain depiction was realized usian aviation safe approximation of terrain models. Withmulti-resolution functionality a dynamic adjustment of terain resolution to various constraints was achieved. Restion, accuracy and number of terrain polygons are adapto the stated requirements of a SVS display. With the mimum filter bank of the terrain decomposition a safe terrrepresentation and depiction is constantly achieved. Duthe multi-resolution functionality real-time capable rending is possible. Furthermore, due to the online reconstructechnique different applications, architectures or graphardware can be supported in a most advantageous ma

References

[1] C. Below, H. von Viebahn, M. Hammer, 4D flight guidance displaan approach to flight safety enhancement, in: Proc. SPIE: SyntVision for Vehicle Guidance and Control, vol. 2463, 1995, pp. 13145.

[2] C. Below, H. von Viebahn, M. Purpus, Flight tests of the 4D fligguidance display, in: Proc. SPIE: Enhanced and Synthetic Vision 1vol. 3088, 1997, pp. 74–80.

[3] G. Beylkin, R. Coifman, V. Rikhlin, Fast wavelet transforms and nmerical algorithms I, Comm. Pure Appl. Math. 44 (1991) 141–183

[4] P. Brooks, Highways in the sky, Aerospace International, May 19pp. 12–19.

[5] D. Damjanovic, J. Schiefele, Enhancing general aviation safetysynthetic vision systems, in: Proc. Institute of Navigation’s NatioTechnical Meeting, 2000.

[6] R. DeVore, B. Jawerth, B. Lucier, Image compression through wavtransform coding, IEEE Trans. Inform. Theory 38 (1992) 719–746

[7] M. Duchaineau, et al., ROAMing terrain: real-time optimally adaptmeshes, in: Proc. IEEE Visualization ’97, 1997.

[8] M. Eck, et al., Multiresolution analysis for arbitrary meshes, in: PrSIGGRAPH 95, ACM, 1995, pp. 173–182.

[9] EUROCAE ED-98, User Requirements for Terrain and Obstacles,ROCAE, 2001.

[10] M. Gross, R. Gatti, O. Staadt, Fast multiresolution surface meshin: Proc. IEEE Visualization ’95, 1995, pp. 135–142.

[11] M. Gross, O. Staadt, R. Gatti, Efficient triangular surface approxition using wavelets and quadtree data structures, IEEE Trans. Viization Comput. Graph. 2 (1996) 130–143.

r.

[12] A. Haar, Zur Theorie der orthogonalen Funktionen Systeme, Mamatische Annalen 69 (1910) 331–371.

[13] M. Hammer, M. Gross, R. Kaufhold, Natürliche Displays im Cocpit, DGLR Fachausschuß Anthropotechnik, Braunschweig, Germ1994.

[14] A. Helmetag, R. Kaufhold, M. Purpus, 3D flight guidance displaCEAS Symposium Free Flight, Amsterdam, 1997.

[15] W. Kearse, et al., RTCA special committee 193/EUROCAE WGairport and terrain database acquisition for aviation applications, FSafety Foundation Conference, Athens, 2001.

[16] L. Kobbelt, A subdivision scheme for smooth interpolation of qumesh data, in: Proc. Eurographics, 1998.

[17] P. Lindstrom, et al., Real-time, continuous level of detail renderinheight fields, in: Proc. SIGGRAPH 96, ACM, 1996, pp. 109–118.

[18] L. May, J. Schiefele, H. Raabe, Controlled digital elevation data dmation for flight applications, in: Proc. SPIE: Enhanced and SynthVision 1998, vol. 3364, 1998, pp. 34–44.

[19] F. Mehler, Integrated navigation, flight guidance, and synthetic vissystem for low-level flight, in: Proc. SPIE: Enhanced and SynthVision 2000, vol. 4023, 2000, pp. 72–80.

[20] G. Sachs, H. Moller, K. Dobler, Synthetic vision experiments forproach and taxiing in poor visibility, in: Proc. SPIE: Synthetic Visifor Vehicle Guidance and Control, vol. 2463, 1995, pp. 128–136.

[21] J. Schiefele, et al., Safety relevant navigation and certifiable databfor 3D synthetic vision systems, 17th DASC in Motion, Bellevue, W1998.

[22] J. Schiefele, et al., Mass data graphics requirements for symbol gators: example 2D airport navigation and 3D terrain function, in: PSPIE: Enhanced and Synthetic Vision 2002, vol. 4713, 2002.

[23] O. Staadt, M. Gross, R. Weber, Multiresolution compression andconstruction, in: Proc. IEEE Visualization ’97, 1997, pp. 337–346.

[24] E. Stollnitz, T. DeRose, D. Salesin, Wavelets for Computer Graics: Theory and Applications, Morgan Kaufmann, San Francisco,1996.

[25] T. Wiesemann, et al., Controlled decimation of digital elevation dand subsequent in-flight verification, in: Proc. SPIE: EnhancedSynthetic Vision 2000, vol. 4023, 2000, pp. 40–51.

[26] T. Wiesemann, J. Schiefele, W. Kubbat, Adaptive surface meshingmulti-resolution terrain depiction for SVS, in: Proc. SPIE: Enhanand Synthetic Vision 2001, vol. 4363, 2001, pp. 112–123.

[27] T. Wiesemann, J. Schiefele, Multi-resolution terrain depiction andport navigation function on an embedded SVS, in: Proc. SPIE:hanced and Synthetic Vision 2002, vol. 4713, 2002.

[28] T. Wiesemann, Konzeption und Entwicklung eines adaptiven Gelämodells zur progressiven Übertragung und Darstellung von Gelädaten in 3D-Flugführungsanzeigen, Dissertation TU-Darmstadt, 2in press.

multi-resolution terrain depiction on an embedded 2d/3d synthetic vision system

Documents