Representing Random Terrain on Resource Limited Devices

© IJIGS/Uni e si y o Wol e hamp on/EUROSIS REPRESENTING RANDOM TERRAIN ON RESOURCE LIMITED DEVICES DAMIEN MARSHALL φ , DECLAN DELANEY φ , SEAMUS MCLOONE*, TOMAS WARD* φ Depa men o Compu e Science, NUI Maynoo h Maynoo h, Co. Kilda e E-mail: [email protected] * Depa men o Elec onic Enginee ing NUI Maynoo h, Maynoo h, Co. Kilda e E-mail: omas.w[email p o ec ed]y.ie KEYWORDS Random Te ain, Pe lin Noise, Mobile De ices, Game Boy Ad ance ABSTRACT Random e ain gene a ion is he p ocedu al c ea ion o a se o da a ha ep esen s closely a belie able landscape. Common echniques o achie ing his include he use o ac als and noise. Such echniques usually equi e a la ge olume o memo y, as he geome y o he e ain needs o be calcula ed and s o ed a un ime. Gi en he limi ed memo y a ailable on mobile de ices, such as mobile elephones, he s o age o he da a equi ed o ep esen massi e e ains can be di icul . In his pape , we p opose a no el me hod o s o ing e ain da a on de ices wi h limi ed memo y. This me hod in ol es placing p e-compu ed blocks o e ain, known as e ain iles, oge he in a psuedo- andom manne as go e ned by a noise unc ion known as Pe lin noise. This allows la ge amoun s o e ain da a o be ep esen ed while s ill gi ing he appea ance o a andomly gene a ed e ain. T adi ionally, Pe lin noise is used in he p ocedu al gene a ion o ex u es and he modeling o na u ally occu ing phenomena. Using Pe lin noise, only a subse o he o e all da a gene a ed by he unc ion needs o be s o ed a any one ime. The app oach ou lined in his pape associa es a ile o e ain wi h each alue gene a ed by he Pe lin Noise unc ion, meaning ha only a subsec ion o he o al e ain is s o ed in memo y a any one ime. We show how his p ocess can be execu ed in eal ime on a esou ce limi ed de ice known as he Game Boy Ad ance, and also illus a e a signi ican educ ion in he memo y equi emen s o e ain s o age when compa ed wi h adi ional me hods. INTRODUCTION A andom e ain is a g oup o p ocedu ally calcula ed alues ha ep esen s closely a belie able landscape. They a e u ilised in all a eas o compu e science, especially compu e g aphics and games (Picko e 1995), whe e hey allow o he c ea ion o game con en wi h minimal ime o e head. Also, as e ain maps can be qui e la ge, echniques o gene a ing andom e ain, such as ac als (Dudgeon and Gopalak ishnan 1996), and models o na u ally occu ing phenomena (Kelley e al. 1988), help o minimise ixed s o age equi emen s. Howe e , his means ha such me hods usually equi e a oluminous amoun o Random Access Memo y (RAM). Wi h ecen ad ances in p ocessing powe , compu e games a e becoming mo e popula on handheld de ices (Ri e n e al. 2003). Howe e , he e a e s ill limi a ions o he amoun o a ailable RAM o such de ices, so ha he c ea ion o andomly gene a ed e ain o compu e games on such de ices can be p oblema ic. In his pape , a no el me hod based on he use o e ain iles and a pseudo andom noise known as Pe lin Noise is desc ibed (Rabino ich and Go sman 1997; Pe lin 2002) T adi ionally, Pe lin noise is used in he gene a ion o p ocedu al ex u es and he modeling o na u ally occu ing phenomena such as clouds and smoke (Ye and Lewis 1999; Hol kämpe 2003) – see Figu e 7. He e, we p opose an app oach ha associa es a ile o e ain wi h each Pe lin noise alue. A e ain ile desc ibes a squa e block o e ain da a. Using Pe lin noise, only a subse o he o e all da a gene a ed by he unc ion needs o be s o ed a any one ime. The e o e, la ge e ain maps can be ep esen ed in eal ime wi h a small memo y oo p in , as only he e ain iles o in e es o he use a e s o ed a any gi en ime. The p oposed me hod is implemen ed on a limi ed de ice known as a Game Boy Ad ance (www.nin endo.com), and esul s a e p esen ed o he implemen a ion We show ha signi ican sa ing can be made in e ms o memo y space equi ed when compa ed o adi ional me hods o s o ing and ep esen ing e ain. As his me hod makes no use o loa ing poin a i hme ic i is e y e icien , making i sui able o use on a wide a ie y o de ices whe e no dedica ed loa ing-poin uni is a ailable. I would be pa icula ly sui able o mobile elephones, as i allows o he gene a ion o massi e e ain maps wi h a minimal o e he ai download. This is o signi ican impo ance as la ge downloads ha e been iden i ied as a limi ing ac o in he nex gene a ion o h ee-dimensional games on mobile elephones (EDGE Magazine 2004). The es o he pape is laid ou as ollows. The nex sec ion in oduces Pe lin Noise and ou lines he sui abili y o he Game Boy Ad ance as a es bed. The Implemen a ion sec ion de ails he ealisa ion o he p oposed me hod, ollowed by a selec ion o pe o mance alues in he Resul s sec ion. Finally, he pape concludes wi h sugges ions o u u e wo k. BACKGROUND Pe lin Noise Pe lin noise is one o he mo e impo an noise unc ions (Pe lin 2002). C ea ed by Ken Pe lin, his noise has he special p ope y o appea ing andom o he pe cei e , ye © IJIGS/Uni e si y o Wol e hamp on/EUROSIS emaining en i ely con ollable. I wo ks by de ining a numbe o key poin s a se dis ances apa , and de ining he alues o he in e media e poin s p ocedu ally using in e pola ion. Any subsec ion o he da a c ea ed by he Pe lin noise unc ion can be econs uc ed, wi hou he need o s o e and gene a e he en i e da a se . In his sense, Pe lin noise can be conside ed o be quasi- andom noise. Fu he de ail ega ding an implemen a ion o Pe lin Noise is gi en in he Implemen a ion sec ion. Game Boy Ad ance Released in 2001, he Game Boy Ad ance (GBA) is he successo o he mul i-million selling Game Boy and Game Boy Colo . The mos impo an speci ica ions o he Game Boy Ad ance a e de ailed in Table 1. F om Table 1, i can be seen ha he GBA is e y limi ed in e ms o p ocessing powe and a ailable Random Access Memo y (RAM). Coupled wi h he ease o p og amming o he sys em, his makes he GBA a pe ec pla o m on which o es ou implemen a ion. In he nex sec ion, he implemen a ion de ails o he p oposed me hod a e desc ibed, and example sc eensho s o he applica ion in ac ion on he GBA a e gi en. IMPLEMENTATION In his sec ion, he me hod by which massi e e ains can be cons uc ed wi h a minimal memo y oo p in is discussed. The means by which he e ain da a is ende ed o sc een a a s able ame a e on he GBA is also in oduced. Pe lin Noise Map o Te ain Tiles The basis o he echnique desc ibed he e is wha is known as a e ain ile. A ile desc ibes a squa e block o e ain. Te ain iles a e used ex ensi ely in many popula game engines such as To que (Ma shall e al. 2004). Each ile is ypically de ined by wo g oups o da a – a heigh map, which de ails he geome y o he e ain, and a ex u e map, which de ails he colou s and shading o he e ain (Rabino ich and Go sman 1997). Figu e 1 (a) and (b) de ails examples o bo h ca ego y o maps. Bo h images in Figu e 1 we e c ea ed using he Wilbu andom e ain gene a ion applica ion (Slay on 2001). By placing hese iles oge he in a andom o de , a la ge a ea o e ain can be de ined – see Figu e 2(a). Howe e , as he ile size dec eases, he s o age cos o he o de o he iles can become expensi e, and can e en ually begin o app oach ha o he adi ional me hod o s o ing each heigh o e ain in an a ay – see Figu e 2 (b) and (c). This can make such an app oach unsui able o a limi ed memo y de ice. This p oblem can be alle ia ed using Pe lin noise o go e n he placemen o iles. As men ioned in he p e ious sec ion, any subsec ion o he da a gene a ed by a Pe lin noise unc ion can be ec ea ed gi en he same inpu alues, wi hou he need o s o e he comple e da a se gene a ed by he unc ion. The e o e, only he sec ion o da a o in e es o he iewe needs o be calcula ed and s o ed a any one ime, and i is gua an eed ha o he subsec ions o he da a will be gene a ed consis en ly wi h he same alues. The main ene o he app oach ou lined in his pape is ha by de ining a numbe o iles wi h small dimensions, and associa ing each alue gene a ed by he Pe lin noise unc ion wi h a e ain ile, hen only he small po ion o a massi e e ain map needs o gene a ed and s o ed a any one ime, hus p o iding d ama ic sa ing in e ms o compu a ion ime and memo y - see Figu e 3. In Figu e 3, each ile is ep esen ed by a di e en shade o g ay. As he use mo es abou he la ge e ain map, he subse o e ain ile da a is epopula ed o ep esen he use s immedia e en i onmen . Pe lin Noise Implemen a ion The i s aspec o he app oach explained in his pape is he manne by which he Pe lin noise map o e ain alues is gene a ed. The p ima y s ep o his p ocess is he de ini ion o a g id ha de ines he o e all layou o he map. Each alue in his g id is known as a e ain s uc u e alue. These e ain s uc u e alues a e simply andom numbe s, and a e no ela ed o any pa icula e ain ile. Ra he , hey a e used in conjunc ion wi h adjacen e ain s uc u e alues in o de o de ine in e media e e ain ile alues p ocedu ally. Each P ocesso 16Mhz Memo y 384 kiloby es Sc een Resolu ion 240 * 160 pixels A ailable Colou s 32,768 Figu e 2 (a) Fou 128*128 il es (b) Eigh 64 *64 iles. (c) Six y ou 32 * 32 iles. A dec ease in ile size inc eases de ail, bu leads o an inc ease in memo y equi emen s. Figu e 1 (a) Tex u e map (b) G ayscale Heigh Map. (a) (b) Table 1 Impo an speci ica ions o he GBA Figu e 3 Only a small subse o all he ile alues is s o ed a any one ime using a Pe lin noise unc ion. This is epopula ed as he use mo es abou he e ain. Full map o e ain alues gene a ed using Pe lin Noise Only a subse o all he e ain alues is s o ed a any one ime. (a) (b) (c) Te ain iles a e placed in a andom o de Te ain iles © IJIGS/Uni e si y o Wol e hamp on/EUROSIS o hese e ain ile alues is a e e ence o a pa icula e ain ile. Al hough his g id o e ain s uc u e alues will ha e iny dimensions, i can be hough o as being i ually la ge, as each elemen ep esen s a poin along a la ge map – see Figu e 4. So, o example, a 4 * 4 a ay, wi h a i ual dis ance o 1024 pixels be ween elemen s o he a ay, ep esen s a 4096 * 4096 pixel e ain map. Nex , he e ain s uc u e alues a e used o p ocedu ally de ine he in e media e e ain ile e e ences ha desc ibe he e ain immedia ely su ounding he use . Fi s ly, he a ea wi hin he g id o e ain s uc u e alues ha cu en ly houses he use is loca ed, and he poin s ha de ine he bounda ies o ha a ea a e eco ded. So, aking he example om abo e, i he playe was a poin (1056,3042) on a 4*4 map wi h a i ual dis ance o 1024 pixels be ween each elemen , hen he playe would be loca ed be ween he e ain s uc u e elemen s (1,2), (1,3), (2,2) and (2,3), as de ailed in Figu e 5 below. By linea ly in e pola ing be ween he wo op and he wo bo om bounding alues using he playe ’s ho izon al posi ion, and in e pola ing be ween he esul s o hese ope a ions using he playe ’s e ical posi ion, a alue which ep esen s he ile in which he use esides can be de ined – see Figu e 6. Map o Te ain Tiles T adi ionally, he alue gene a ed by his p ocess would be used in conjunc ion wi h o he gene a ed alues in o de o ep esen a ex u e o na u ally occu ing phenomena p ocedu ally, as in Figu e 7. Howe e , o his implemen a ion, each alue is ac ually a e e ence o a pa icula e ain ile. As he e will be only a limi ed numbe o e ain iles, and he gene a ed alue may exceed he o al numbe o e ain iles, he esul may ha e o be scaled. This can be achie ed using a simple modulus ope a ion. This p ocess is epea ed using he coo dina es su ounding he playe . The numbe o epe i ions equi ed will a y, depending on he size o each indi idual ile and he o e all map size equi ed. This esul s in a empo a y a ay o da a con aining e e ences o he e ain iles ha immedia ely su ound he use . An example o such an a ay is gi en in Figu e 8. Fo cla i y, each sepa a e map is ep esen ed by a di e en shade o g ay. Each colou ep esen s a map simila o ha in Figu e 1(a). Howe e , as can be seen in Figu e 8, h ough he use o his me hod alone, a se ies o dis inc pa e ns can be obse ed in he placemen o e ain iles. Such pa e ns a e exac ly wha Pe lin noise is celeb a ed o . Howe e , in he echnique unde discussion, mo e andomness is desi ed o gene a e uly andom landscapes. This is achie ed ia he use o ano he a ay o andom alues, which is popula ed along wi h he e ain s uc u e g id. The alue acqui ed by he in e pola ion p ocess is used o index in o his andom a ay, allowing o ano he laye o andomness, wi h li le compu a ion o e head. An example o he empo a y a ay o e ain ile alues p oduced using his me hod is gi en in Figu e 9. Again, o cla i y, each sepa a e map is ep esen ed by a di e en shade o g ay. Vi ual dis ance be ween e ain s uc u e alues Bounding Values Random Te ain S uc u e Value Bounding Values Playe Posi ion Vi ual dis ance be ween g id alues 0 Te ain s uc u e alues Figu e 4 A g id o e ain s uc u e alues de ines he o e all layou o he e ain. In e media e alues a e calcula ed p ocedu ally. Figu e 9 No disce nable pa e ns appea when a andom numbe look-up able is u ilised Posi ion o playe wi hin he e ain Te ain iles su ounding he playe . No pa e ns occu wi h usage o andom a ay. Random Te ain S uc u e Value Bounding Values Playe Posi ion Te ain iles su ounding he playe . Dis inc pa e ns can eme ge. Posi ion o playe wi hin he e ain Figu e 8 Only he e ain iles ha immedia ely su ound he playe a e calcula ed. The playe is loca ed a he cen e o hese iles. In e pola ion Poin S ep 1: In e pola e be ween op and bo om alues. S ep 2: In e pola e be ween esul s o S ep 1 abo e. Figu e 6 Resol ing he e ain ile alue based on he playe s posi ion and he calcula ed bounding alues. Playe Posi ion Full map o e ain alues In e media e e ain ile alues a e calcula ed p ocedu ally Figu e 5 Loca ion o a playe ’s posi ion wi hin he e ain s uc u e g id. 1 2 3 Figu e 7 An example o a adi ional ou pu om he Pe lin noise unc ion 1 2 3 © IJIGS/Uni e si y o Wol e hamp on/EUROSIS This empo a y a ay ep esen s only a small subsec ion o he o e all e ain da a. Howe e , his ac is no no iceable o he use , as he empo a y a ay o e ain ile e e ences is epopula ed when he playe eaches a ce ain dis ance om he pe ime e o he map. This a ay is hen used as inpu o he ende ing p ocess. Rende ing P ocess The ende ing p ocess uses a me hod known as ay-cas ing and oxels in o de o d aw he ele an e ain iles o he sc een in a imely ashion (K eege e al. 1998; S einbach e al. 2000). Al hough his me hod has i s limi a ions, such as only wo planes o mo emen , i allows o a pseudo h ee- dimensional e ec on esou ce-limi ed ha dwa e such he GBA, a a s able ame- a e. Figu e 10 de ails sc eensho s o he ende ing applica ion in ac ion on he GBA. Supe imposed on he images is a g id de ining he bounda ies o each e ain ile. Figu e 10 also ein o ces he ela ionship be ween e ain iles, as seen in Figu e 1 (a) and (b), and he empo a y a ay o ile e e ences as seen in Figu e 8 and 9. RESULTS Compu a ion Time As a p elimina y exe cise, he compu a ion ime equi ed o calcula e he empo a y a ay o e ain iles su ounding he playe was eco ded. This is achie ed by using an in-buil ime on he GBA ha is inc emen ed on e e y clock ick. A unning a e age o he amoun o ime in milliseconds aken o popula e he ile map is no ed. In each case, he ile map equi ed was 1024 * 1024 pixels. The es e na iga ed he en i onmen o 60 seconds, and a he end o his ime, he a e age compu a ion ime was eco ded. The esul s o his expe imen a e p esen ed in Table 2. As can be seen om Table 2, he compu a ion ime equi ed is minimal, and can be calcula ed in eal ime on he GBA. As no loa ing-poin a i hme ic is used in he calcula ion o he e ain ile alues, his p ocess is sui able o a wide ange o de ices whe e no ha dwa e suppo o loa ing poin alues is a ailable. To u he demons a e he e iciency o his app oach, he compu a ion ime equi ed o he c ea ion o a comple ely new andom map was also in es iga ed. In each case, andom maps we e gene a ed o 60 seconds, and a unning a e age o he compu a ion ime was eco ded using he in-buil GBA ime s. As his p ocess simply in ol es he egene a ion o he e ain s uc u e g id, he compu a ion ime equi ed is minimal, as de ailed in Table 3. Tile Size Tiles equi ed Time 128 * 128 pixels 8 * 8 iles <1 ms 64 * 64 pixels 16 * 16 iles 10 ms 32 * 32 pixels 32 * 32 iles 67 ms 16 * 16 pixels 64 * 64 iles 165 ms Te ain S uc u e g id dimension Time 4 * 4 g id elemen s 1. 25µs 8 * 8 g id elemen s 3.5µs 12 * 12 g id elemen s 6.625 µs 16 * 16 g id elemen s 16.5µs Memo y Usage The mos c i ical aspec o implemen ing he p oposed echnique in mobile de ices is how i exploi s he a ailable memo y. We he e o e conside memo y usage o be he mos impo an me ic by which o assess ou p oposed app oach. This will be done by pe o ming a compa a i e analysis wi h he adi ional echnique o s o ing a single la ge e ain geome y map and ex u e map. In Table 4 he memo y usage o a adi ional e ain geome y map and ex u e map is analysed. E e y elemen o each map is assumed o be a 16 bi unsigned in ege . As can be seen om Table 4, he s o age o a single andomly gene a ed map u ilises a la ge olume o memo y esou ces. The gene a ion o a small 256 * 256 pixel map equi es app oxima ely 66% o he en i e 384 KB o RAM on a GBA. As he map dimensions double, he memo y equi emen s quad uple. Nex , he s o age cos o he app oach de ailed in his pape was analysed – see Table 5. Resul s a e gi en o he cos o s o ing one hund ed e ain iles bo h in ixed s o age and in RAM. Each ile consis s o a heigh and ex u e map, and e e y elemen o a map is an unsigned 16-bi in ege . The RAM columns display he cos o s o ing he empo a y a ay o e ain ile e e ences ha is p ocedu ally gene a ed. The dimensions o his a ay a y depending on he indi idual e ain ile size. I , o example, a empo a y map o dimensions 1024 * 1024 pixels is equi ed using e ain iles o dimensions 8 * 8 pixels, hen a 128 * 128 empo a y e ain ile e e ence a ay is equi ed. Indi idual Map Size RAM 256 * 256 pixels 256 kb 512 * 512 pixels 1024 kb 1024 * 1024 pixels 4096 kb 2048 * 2048 pixels 16384 kb Figu e 10 (a) The empo a y a ay o ile alues ende ed o he sc een. Each ile is ep esen ed by a sepa a e colou . (b) The associa ed heigh and colou maps ende ed o he sc een. Table 2 The compu a ion ime equi ed o he gene a ion o a 1024 * 1024 pixel map using e ain iles o a ying size. Each alue o he empo a y a ay is a e e ence o a pa icula e ain ile (a) (b) Table 3 The compu a ion ime equi ed o he gene a ion o a new andom map is minimal as he e ain s uc u e g id size is insigni ican . Table 4 Values ep esen ing cos o s o ing ull maps in memo y. © IJIGS/Uni e si y o Wol e hamp on/EUROSIS Table 5 shows ha he amoun o RAM employed by he p oposed app oach is minimal. I he indi idual map dimensions a e inc eased in size by 100%, he amoun o RAM equi ed educes by 75% whe eas he ixed s o age equi emen s inc ease by 400%. Howe e , he cos o s o ing he e ain iles is nominal a smalle sizes, hus making hem sui able o download o e low bandwid h connec ions, such as on a mobile phone ne wo k. Rega dless o he dimensions o he o e all e ain map equi ed, he igu es p esen ed in he RAM columns o Table 5 emain cons an . This is due o he ac ha , as discussed in he Implemen a ion sec ion, only a subse o he o e all e ain map is e e s o ed, ega dless o a ia ion in he dimensions o he o e all e ain map. The e o e, any size map could be po en ially ep esen ed on a esou ce-limi ed de ice such as he Game Boy Ad ance, wi h no implica ions o he o e all memo y equi emen s. CONCLUSIONS In his pape we ha e desc ibed a me hod o ep esen ing he la ge olumes o da a equi ed o s o e a andom e ain on a de ice wi h a limi ed amoun o Random Access Memo y known as he Game Boy Ad ance. By using e ain iles and Pe lin Noise, we ha e shown how his echnique is pa icula ly sui able o de ices wi h limi ed p ocessing powe , as i makes no use o loa ing poin a i hme ic. The e o e, he e ain ile posi ions can be calcula ed easily a un ime. In addi ion, a o ally new andom e ain can be gene a ed apidly, as only he small e ain s uc u e g id needs o be epopula ed. I has also been shown ha a massi e e ain can be ep esen ed using a minimal amoun o bo h ixed and dynamic memo y. The cos equi ed o s o e he necessa y e ain iles can be small, hus making his app oach sui able o de ices wi h limi ed s o age capaci y, and slow download speeds such as mobile elephones. As only a po ion o he o e all e ain is s o ed a any one ime, he olume o memo y used is ixed, ega dless o a ia ion in he dimensions o he o e all e ain. Fu u e wo k will in ol e in es iga ing me hods o seamless blending be ween adjacen e ain iles, so as o p o ide a mo e uni o m isual expe ience o he use . 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"P ocedu al ex u e mapping on FPGAs".In 1999 ACM/SIGDA se en h in e na ional symposium on Field p og ammable ga e a ays, (Mon e ey, Cali o nia, Uni ed S a es, Feb ua y 21 - 23), ACM P ess, New Yo k, NY, USA, 112 - 120. Te ain Tile Dimensions Cos o s o e 100 Te ain Tiles RAM 256 * 256 map RAM 512 * 512 map RAM 1024 * 1024 map RAM 2048 * 2048 map 8 * 8 pixels 25 kb 2 kb 8 kb 32 kb 128 kb 16 * 16 pixels 100 kb 0.5 kb 2 kb 8 kb 32 kb 32 * 32 pixels 400 kb 0.125 kb 0.5 kb 2 kb 8 kb 64 * 64 pixels 1600 kb 0.03125 kb 0.125 kb 0.5 kb 2 kb 128 * 128 pixels 6400 kb 0.0078125 kb 0.03125 kb 0.125 kb 0.5 kb Table 5 Values ep esen ing memo y cos o s o ing he e ain iles and he cos o s o ing empo a y ile alue a ay in Random Access Memo y (RAM).