Dynamic Isoline Extraction for Visualization of Streaming Data

Transcription

1 Dyamic Isolie Extractio for Visualizatio of Streamig Data Dia Goli 1, Huaya Gao Uiversity of Coecticut, Storrs, CT USA Abstract. Queries over streamig ata offer the potetial to provie timely iformatio for moer atabase applicatios, such as sesor etworks a web services. Isolie-base visualizatio of streamig ata has the potetial to be of great use i such applicatios. Dyamic (real-time) isolie extractio from the streamig ata is eee i orer to fully harvest that potetial, allowig the users to see i real time the patters a tres both spatial a temporal iheret i such ata. This is the goal of this paper. Our approach to isolie extractio is base o ata terrais, triagulate irregular etworks (TINs) where the cooriates of the vertices correspos to locatios of ata sources, a the height correspos to their reaigs. We yamically maitai such a ata terrai for the streamig ata. Furthermore, we yamically maitai a isolie (cotour) map over this yamic ata etwork. The user has the optio of cotiuously viewig either the curret shae triagulatio of the ata terrai, or the curret isolie map, or a overlay of both. For large etworks, we assume that complete recomputatio of either the ata terrai or the isolie map at every epoch is impractical. If is the umber of ata sources i the etwork, time complexity per epoch shoul be O(log ) to achieve real-time performace. To achieve this time complexity, our algorithms are base o efficiet yamic ata structures that are cotiuously upate rather tha recompute. Specifically, we use a oubly-balace iterval tree, a ew ata structure where both the tree a the ege sets of each oe are balace. As far as we kow, o oe has applie TINs for ata terrai visualizatio before this work. Our yamic isolie computatio algorithm is also ew. Experimetal results cofirm both the efficiecy a the scalability of our approach. 1 Itrouctio Queries over streamig ata offer the potetial to provie timely iformatio for moer atabase applicatios, such as sesor etworks a web services. Isolie-base visualizatio of streamig ata has the potetial to be of great use i such applicatios. Isolie (cotour) maps is particularly iformative if the streamig ata values are relate to pheomea that te to be cotiuous for ay give locatio, such as temperature, pressure or raifall i a sesor etwork. Dyamic (real-time) isolie extractio from the streamig ata is eee i orer to allow the users to see i real time the patters a tres both spatial a temporal iheret i such ata. Such isolie extractio is the goal of this paper. 1 Supporte by NSF awar

2 Our approach to isolie extractio is base o ata terrais, triagulate irregular etworks (TINs) where the (x, y)-cooriates of the vertices correspos to locatios of ata sources, a the z-cooriate correspos to their reaigs. Efficiet algorithms, especially whe implemete i harware, allow for fast shaig of TINs, which are three-imesioal. By combiig shaig with user-rive rotatio a zoomig, ata terrais provie a very user-friely way to visualize ata etworks. While the reerig of static TINs is a well-researche problem, we are cocere with yamic etworks, where ata sources may chage their reaigs over time; they may also joi the etwork, or leave the etwork. We yamically maitai a ata terrai for the streamig ata from such a etwork of ata sources. Furthermore, we yamically maitai a isolie (cotour) map over this yamic ata etwork. Isolies cosist of poits of equal value; they are most commoly use to map moutaious geography. The isolie map ca be isplaye i isolatio, or overlaye o the uerlyig TIN, proviig the user with a visualizatio that is both highly escriptive a very ituitive. For large etworks, we assume that complete recomputatio of either the ata terrai or the isolie map at every epoch is impractical. If is the umber of ata sources i the etwork, time complexity per epoch shoul be O(log ) to achieve real-time performace. To achieve this time complexity, our algorithms are base o efficiet yamic ata structures that are cotiuously upate rather tha recompute. Specifically, we use a oubly-balace iterval tree, a ew ata structure where both the tree a the ege sets of each oe are balace. Dyamic isolie maps have bee propose before i the cotext of sesor etworks [7, 11]. However, as far as we kow, o oe has applie TINs for this purpose before this work. Our yamic isolie computatio algorithm is also ew. As a result, earlier approaches prouce isolie maps that are i both more costly a less accurate. We have implemete the ata structures a algorithms propose i the paper. The user has the optio of cotiuously viewig either the curret shae triagulatio, or the curret isolie map, or a overlay of both. Experimetal results, simulatig a large etwork of raomly istribute ata sources, cofirm both the efficiecy a the scalability of our approach. Overview. We escribe ata terrais i sectio 2, a iscuss the algorithms for their computatio a yamic maiteace. I sectio 3, we give a algorithm for computig isolie maps over the ata terrai, as well as their yamic maiteace. I sectio 4 we preset our implemetatio of isolie-base visualizatio. Relate work is iscusse i sectio 5, a we coclue i sectio 6. 2 Data Terrais Our otio of a ata terrai is closely relate to the otio of a geographic terrai, commoly use i Geographic Iformatio Systems (GIS). Geographic terrais represet elevatios of sites a are static. There are two mai approaches to represet terrais i GIS. Oe is Digital Elevatio Moels (DEM), represetig it as grie ata withi some preefie itervals, which is volume-base a regular. DEMs are typically use i raster surface moels. Due to

3 the regularity of DEMs, they are ot appropriate for etworks of streamig ata sources, whose locatios are ot assume to be regular. The other represetatio is Triagulate Irregular Networks (TIN). The vertices of a TIN, sometimes calle sites, are istribute irregularly a store with their locatio (x, y) as well as their height value z as vector ata (x, y, z); TINs are typically use i vector ata moels. For a etaile survey of terrai algorithms, icluig TINs, see [17]. I this paper, we chose to use TINs to represet the state of a ata etwork. TINs are goo for visualizatio, because they ca be efficietly shae to highlight the 3D aspects of the ata. The (x, y) cooriates of the TIN s vertices correspos to the locatios of ata sources, a the z cooriates correspos to their curret value (that is beig visualize). We refer to this represetatio as ata terrais. We iitially costruct the ata terrai with the typical algorithm for TIN costructio, as i [8, 9] i O( log ) time. Sice the costructio of TIN is oly epeet o the locatio of its sites, the topology of the TIN oes ot chage with the chage of the ata values. The oly possibility for a TIN to chage is whe a ew ata source jois the etwork, or whe some ata source leaves the etwork, e.g. ue to power loss. I the followig, we escribe the algorithm for upatig the TIN whe this happes. Isertio. Whe a ew ata source is ae to the etwork, we ee to a the correspoig vertex to the ata terrai. It woul be the same algorithm as whe builig a ew ata terrai, sice it is a icremetal algorithm. As iscusse i [9], the worst case of the time performace for site isertio coul be O(). Note that we assume that ata sources are ot iserte ofte, much less frequetly tha their values are upate, givig us amortize performace of O(log ) for this operatio. Deletio. Whe a ata source leaves the etwork, we ee a local upatig algorithm to maitai our yamic TIN. Basically, this is the iverse of the icremetal isertio algorithm, but i practice there are a variety of specific cosieratios. [10] first escribe a eletio algorithm i etail, but ufortuately, it ha mistakes. The algorithm was correcte i [5], a further improve i [14]. The performace for eletio algorithm is O(k log k) where k is the umber of eighbors of the polygo iciet the vertex to be elete. Figure 1 illustrates how oe site is remove from a TIN. Fig. 1. Deletig oe site from TIN: (a) before eletio; (b) after eletio.

4 Efficiet algorithms, especially whe implemete i harware, allow for fast shaig of ata terrais. By combiig shaig with user-rive rotatio a zoomig, ata terrais provie a very user-friely way to visualize ata etworks. 3 Dyamic Isolie Extractio I this sectio, we escribe how to extract a isolie map from a ata terrai for a yamic ata etwork. 3.1 Iterval tree Oe aive way to extract a isolie map at a give height h irectly from the ata terrai is to traverse all the triagles i the ata terrai, itersect each oe with the plae z = h, a retur all the resultig segmets. O() time is eee for this brute-force approach, where is the umber of sites. We use iterval trees [6] to obtai a more efficiet solutio. For every ege i the TIN, this tree cotais a iterval correspoig to the ege s z-spa. Iterval trees are special biary trees; besies the key which is calle a split value, each oe also cotais a iterval list. Give the set of itervals for the z-spas of a TIN s eges, a (ubalace) iterval tree is costructe as follows. 1. Choose a split value s for the root. This value may be etermie by the first iserte iterval. For example, if (a, b) is the first iserte iterval, the the split value will be (a + b)/2. 2. Use s to partitio the itervals ito three subsets, I left, I, I right. Ay iterval (a, b) is i I if a s b; it is i I left if b < s; a it is i I right if a > s. 3. Store the itervals i I at the root; they are orgaize ito two sorte lists. Oe is the left list, where all the itervals are sorte i icreasig orer of a; the other is the right list, where all the itervals are sorte by ecreasig orer of b. 4. Recurse o I left a I right, creatig the left a right subtrees, respectively. Next, we oubly balace the tree; we use AV L trees [1] for this purpose. The first AVL tree is for the iterval tree itself, the other is for the ege lists store at the oes of the iterval tree. This eables us to provie quick upates to the tree (sectio 3.2). Figure 2 gives a example of a TIN, compose of 7 sites a 19 eges, a the correspoig iterval tree. More etails ca be fou i [16], which uses a iterval tree as the ata structure to coveietly retrieve isolie segmets. But they oly cosier static TIN, while we will give a algorithm for yamic TIN i sectio 3.2. We ow escribe the algorithm for usig a iterval tree T to create a isolie at value v. It is a recursive algorithm that begis with the root oe. Let the split value be s. If v < s the we will o the followig two thigs. First search the left list of the root, a the search the left subtree of the root recursively. If v > s the we will o the similar two thigs. First search the right list of the root, a the search the right subtree of the root recursively. We stop at the leaf oe. We fiish by escribig the etails of the algorithm for queryig the matche ege list i the left list or right list of the iterval oe, metioe briefly before. Recall

5 c e f a b g l m h 27.6 k i j 0.1 a, b, j, k, l b, l, j, k, a c, e, 6.3 c, e, f, h g, i, m m, g, i f, h a b c e f g h i j k l m Fig. 2. A example of a TIN a the correspoig balace iterval tree. that we store the ege list as a AV L tree. Take the left list as a example, we oly cosier the left evaluatio of the smaller poit of the ege. Let it be the key k of the AV L oe. We search the AV L tree recursively. If v < k, the we search the left subtree recursively. If v > k, which meas that all the eges i the left subtree are the matche eges, output them a search the right subtree recursively. Queryig the right list of the iterval oe is symmetric. Note that a iterval tree ca also be costructe for triagles, rather tha eges, of the TIN, sice a z-spa ca just as easily be efie for triagles. We ca quickly fi those triagles that itersect with the plae z = h, a avoi cosierig others. Oe such algorithm is give i [16]. I our work, we fou it more coveiet to use eges to compute isolies from the TIN istea of triagles. Note that this ki of substitutio oes ot affect the efficiecy, because of the followig fact: if there are vertices i the TIN, the umber of eges

6 a the umber of triagles are each O() [13]. Let b eote the umber of sites o the bouary of the TIN, a i be the umber of sites i the iterior; the total umber of sites is = b + i. The umber of eges is e = 2 b + 3( i 1) <= 3. The umber of triagles, let be t, woul be t = 2 6 whe > 3. Therefore, both the ege-base a the triagle-base iterval trees allow for a more efficiet algorithm to get the isolies from TIN tha the aive oe escribe at the begiig of the sectio. 3.2 Dyamic Iterval Tree I our settig, the ata values at the sources chage as time passes. Sice our iterval tree is built up o the eges of the TIN, a the z-spa of the ege is epeet o the values at the sites ajacet to the ege, a chage i these values will ecessitate a chage to the iterval tree. We begi with a built TIN a a costructe iterval tree, as escribe above. I the followig, we give a etaile escriptio of the algorithm to upate the tree after some ata source s chages its value from v 0 to v. 1. We use the TIN to fi all eges iciet with the ata source s. Sice the TIN cotais a iciece list L for each vertex, we ca fi these eges i costat time O(1). 2. For every ege e i the list L, we ee to upate its positio i the iterval tree. Suppose that the origial z-spa for e is z e, a the ew oe is z e. 3. Ru a biary search from the root to fi the oe x which cotais the iterval z e. This is oe i O(log ) time. 4. Delete z e from both the right a the left lists of x. Sice both of these lists are implemete as a staar AVL tree, the performace is O(log ). 5. Look for the oe y that shoul cotai z e, that is, its split value overlaps z e. First, check whether z e overlaps with the split value of x, i which case we ee look o further. Otherwise, begi searchig from the root of the tree, comparig z e with the split value of the oe, util we fi the oe whose split value overlaps z e or reach a leaf. The time for this is i O(log ). 6. If we fou y, the isert z e ito the right a the left lists of y. Both lists are implemete with AVL trees, a the size of each list is at most the total umber of the eges i the TIN. So this isert shoul be i O(log ). 7. If we have reache a leaf without fiig y, we isert a ew leaf ito the iterval tree to store the ew iterval. Its iterval lists will cotai just z e, a its split value will be the mipoit of z e; this is i O(1). Recall that we are usig balace (AVL) trees both for the iterval tree, a for the iterval lists withi each oe of the iterval tree. To keep the trees balace, all isertios a eletios are followe by a rebalace operatio. There exists the rebalace algorithm for AVL trees i O(log ) time [19], a it is easy to see that ouble balacig oes ot icrease the time complexity. A alterative metho is relaxe AVL tree [12]. Istea of rebalacig the tree at every upate, we relax the restrictio a accumulate a greater ifferece is heights before we ee to ajust the height of the AVL tree.

7 Figure 3illustrates a upate to the iterval tree of Figure 2 whe the reaig of ata source s chages from to Note that all eges iciet o s ee to be checke. I this figure, we ee to upate the positio of itervals f, h, l, m, i the iterval tree. 0.1 a, b, j, k, l b, l, j, k, a c, e, f, m, h g, i c, e, f, h, m g, i a b c e f g h i j k l m Fig. 3. A upate to the iterval tree. This tree is highly ubalace; it is a sapshot after the isertio but before rebalacig. Figure 4 shows the result after balacig the iterval tree. To isert ito the iterval tree, we eee to isert a ew oe to store. After rebalacig, there are o itervals i the oe whose split value is 74.35; this ecreases the height of the iterval tree by 1, so we elete this oe. The time complexity of this algorithm is O(log ). Note that our algorithm, while sometimes aig ew oes (with sigleto iterval lists), oes ot elete ol oes whe their iterval lists become empty. We etermie experimetally that there was o beefit i oig so. Sice the ata reaigs move up a ow (rather tha mootoically icreasig or ecreasig), the empty oe is very likely to be use up at some poit; it turs out that keepig it arou for this evetuality is more time efficiet tha eletig it right away. To complete the performace aalysis of the iterval tree upate algorithm, we ee to kow how may eges are iciet o a give site s, sice each of these k eges ees to be upate separately. It ca be prove that k is ever more tha 6. We alreay kow the umber of eges is e <= 3, where is the umber of sites, oe per ata

8 32.65 b, j, l, c, e, f, g, i, m b, c, e, f, l, m, g, i, j 6.3 k, k, h h 0.1 a a a b c e f g h i j k l m Fig. 4. The upate iterval tree after rebalacig. source. Sice each ege is iciet o two sites, clearly we have: k = 2 e <= 6. We cofirme this experimetally, measurig the average of k; we fou that it was ever more tha 6, ot growig as the umber of sites icrease. Therefore, we assume that k is O(1). For each ege, we took its z-spa iterval from its ol positio a fou a appropriate ew positio to isert the iterval, rebalacig whe eee. Each of these operatios is i O(log ) time. Therefore, the overall algorithm is O(log ). 4 Performace 4.1 Assumptios Our visualizatio algorithm relies o cotiuously upatig the TIN a the correspoig iterval tree. The upates are triggere by chages to ata values, isertios (ew ata sources), or eletios (loss of a ata source). We use the amortize approach to complexity aalysis, assumig that chages to ata values happe much more ofte tha either isertios or eletios. 4.2 Experimets Our implemetatio of the visualizatio of ata terrai uses OpeGL [15], a software iterface to graphics harware. I our simulatio, we use GNU C++ with OpeGL

9 library uer Liux platform to reer the ata terrai a isolie maps. We implemete isolie extractio from ata terrais usig the algorithm escribe above. I our experimet, we starte by geeratig the iitial ata terrai from the iitial values at ata sources, usig the algorithm i sectio 2. The we costructe our iterval tree usig the algorithm i sectio 3. For the iitial values of our ata, we use the actual ata which escribes the terrai arou the Uiversity of Coecticut. As show i figure 5, we simulate a etwork of 257 ata sources eploye arou UCo which were i the regio (0, 0) (9600, 10115). The ata reaigs were the local height at that cooriate, which rage from 0 to 420 (feet). Figure 5 shows the shae ata terrai (a) before a (b) after a site lower left quarat chage its value, from 350 to Oe ca clearly see the ifferece i the shape of the two ata terrais. Fig. 5. Data terrai of UCo. (a) before chage; (b) after chage. Our ata stream cosiste of chages to the reaigs of oe site (chose at raom) at a time. As we processe the stream, we upate the TIN a the iterval trees. Figure 6 illustrates how the isolies ca be affecte by a chage to the reaig at a sigle site. It shows the TIN overlaye with the isolies; the thick lie represets the isolie value 200, a the thi lie represets the isolie value 300. Whe we chage the reaig at oe site (colore as black) from 350 i (a) to i (b), it is apparet how the isolies chages accorigly. We measure the performace of our upate algorithms escribe i sectios 2 a 3, plottig time performace agaist the umber of ata sources i the etwork,. We varie from 50 to 2500 i 50 uit itervals: {50, 100, 150,..., 2450, 2500}. Give ata sources istribute raomly i a regio (0, 0) (300, 300), we chose oe at raom a chage its reaig, upatig everythig. We repeate this 100 times, gettig the cumulative time for each i microsecos. Figure 7 (a) shows the plot we obtaie from our experimets. The logarithmic trelie through this plot has the fuctio y = (l x) , a the value of.964 for R 2 as show i Figure 7 (b). This value of R 2 shows

10 Fig. 6. Isolies from TIN, (a) before a (b) after chage. Fig. 7. Time performace vs. umber of sites, (a) without a (b) with the logarithmic trelie. that there is a 96.4% reliability of the relatioship betwee the plot a the trelie. From this picture, we ca see that our algorithm is logarithmic a scalable. This cofirms our aalysis i sectio 3. 5 Relate work The visualizatio of ata terrais ivolves much kowlege i computer graphics. A goo review of reerig techiques such as trasformatios, shaig, iterpolatio, texture mappig, ray tracig, etc., as well as the mathematics theory behi it, ca be fou i [18, 2]. Oe of the popular reerig libraries is OpeGL. It is sai to be iustry staar; it is stable, reliable, portable, extesible, scalable a easy to use. Documets are available from [15], writte by the OpeGL Architecture Review Boar, is the most authoritative oe. I our simulatio, we use GNU C++ with OpeGL uer Liux to reer our ata terrai a our isolie map. Iterval tree first was propose by Eelsbruer [6] to efficietly retrieve itervals of real lies that cotai a give query value. Cigoi et. al. [4] uses iterval tree as

11 the ata structure to extract isosurfaces. Chiag [3] escribes how to extract isosurface from volumetric ata usig iterval tree. Va Krevel [16] uses the iterval tree as the ata structure to extract isolies from TINs by associatig each triagle with the itervals of the elevatio it spas. There are several iffereces betwee that algorithm a ours. Their itervals are base o z-spas of triagles rather tha eges. They o ot use balace trees as we o. Their algorithm is ot yamic (the upate operatios are ot efie). Fially, as far as we kow, their algorithm was ever implemete. To our kowlege, o oe has escribe a algorithm to extract isolies efficietly a yamically from ata terrais as we have oe. Relate work i the sesor etwork commuity has trie to extract isolies irectly from sesor reaigs, usig ietwork protocols. For example, i [11], a isobar computatio from sesor etworks is performe as a form of aggregatio. This work assumes that every sesor is i a rectagular gri a merge these gris i-etwork. The commuicatio betwee the sesors is base o a tree. The geeral process is that each sesor gets the isobar map from its chilre, combies its ow iformatio, a ses the isobar map up to its paret. Fially, the root aggregates the isobar maps. So they ee some polygo operatios such as itersect a uio; the time complexity is O( log ), where is the umber of eges i the polygo. Wheever there are some sesors chagig their reaig, we ee to compute the isobar agai, so this approach is ot efficiet i a yamic real-time settig. 6 Coclusios Isolie-base visualizatio of streamig ata has the potetial to be of great use i moer atabase applicatios, such as sesor etworks a web services. This paper was cocere with yamic (real-time) isolie extractio from the streamig ata, so as to allowig the users to see i real time the patters a tres both spatial a temporal iheret i such ata. Our approach to isolie extractio was base o ata terrais, triagulate irregular etworks (TINs) where the cooriates of the vertices correspos to locatios of ata sources, a the height correspos to their reaigs. We yamically maitaie such a ata terrai for the streamig ata. Furthermore, we yamically maitaie a isolie (cotour) map over this yamic ata etwork. For large etworks, we assume that complete recomputatio of either the ata terrai or the isolie map at every epoch is impractical. If is the umber of ata sources i the etwork, time complexity per epoch shoul be O(log ) to achieve real-time performace. To achieve this time complexity, our algorithms are base o efficiet yamic ata structures that are cotiuously upate rather tha recompute. Specifically, we use a oubly-balace iterval tree, a ew ata structure where both the tree a the ege sets of each oe are balace. As far as we kow, o oe has applie TINs for ata terrai visualizatio before this work. Our yamic isolie computatio algorithm is also ew. Experimetal results cofirm both the efficiecy a the scalability of our approach. All our implemetatio was i GNU C++ with OpeGL library uer Liux.

12 Refereces 1. G.M. Aelso-Velskii a E.M. Lais. A algorithm for the orgaizatio of iformatio. I Soviet Math. Doclay 3, pages , Ewar Agel. Iteractive Computer Graphics: A Top-Dow Approach with OpeGL. Pearso Aiso-Wesley, Jul Yi-Je Chiag a Clauio T. Silva. I/O Optimal Isosurface Extractio. IEEE Visualizatio 97, pages , Paolo Cigoi, Paola Mario, Clauio Motai, Erico Puppo, a Roberto Scopigo. Speeig up Isosurface Extractio Usig Iterval Tree. IEEE Tras. o Visualizatio a Computer Graphics, 3, Apr.-Ju Olivier Devillers. O Deletio i Delauay Triagulatios. Proc. 15th Aual Symp. o Computatioal Geometry, pages , Ju Eelsbruer. Dyamic Data Structure for Orthogoal Itersectio Queries. Tech. Rep. F59, Ist. Iformatiosverarb. Tech. Uiv. Graz, Graz, Austria, Deborah Estri. Embee Networke Sesig for Evirometal Moitorig: Applicatios a Challeges. DIALM-POMC Joit Workshop o Fou. of Mobile Computig, Sa Diego, CA, Sep Michael Garla a Paul S. Heckbert. Fast Polygoal Approximatios of Terrais a Height Fiels. Tech. Rep. CMU-CS , Caregie Mello Uiv., Sep Leoias Guibas a Jorge Stolfi. Primitives for the Maipulatio of Geeral Subivisios a the Computatio of Voroo Diagrams. ACM Tras. o Graphics, 4(2):74 123, Marti Heller. Triagulatio Algorithms for Aaptive Terrai Moelig. Proc. 4th It l Symp. of Spatial Data Halig, pages , Joseph M. Hellerstei, Wei Hog, Samuel Mae, a Kyle Staek. Beyo Average: Towars Sophisticate Sesig with Queries. 2 It l Workshop o Iformatio Proc. i Sesor Networks (IPSN 03), Mar Kim S. Larse, Eljas Soisalo-Soiie, a Peter Wimayer. Relaxe Balace through Staar Rotatios. Workshop o Alg. a Data Structures, Charles L. Lawso. Software for C 1 Surface Iterpolatio. I Joh R. Rice, e., Mathematical Software III, Acaemic Press, NY, pages , Mir Abolfazl Mostafavi, Christopher Gol, a Maciej Dakowicz. Delete a Isert Operatios i Vorooi / Delauay Methos a Applicatios. Computers & Geoscieces, 29(4): , May Dave Shreier, Maso Woo, Jackie Neier, a Tom Davis. OpeGL Programmig Guie: The Official Guie to Learig OpeGL, Versio 1.4, 4th eitio. Aiso-Wesley, Nov Marc va Krevel. Efficiet Methos for Isolie Extractio from a Digital Elevatio Moel Base o Triagulate Irregular Networks. I 6th It l Symp. o Spatial Data Halig Proc., pages , Marc va Krevel. Digital Elevatio Moels a TIN Algorithms. Algorithmic Fou. of Geographic Iformatio Systems i LNCS (tutorials),spriger-verlag, Berli, 1340:37 78, Ala H. Watt. 3D Computer Graphics. Aiso-Wesley, Dec Mark Alle Weiss. Data Structures a Algorithm Aalysis i C. Aiso-Wesley, Jul 1997.