3D tree modeling algorithm

Introduction. Modclins ef teeces> is actively used in solving forecasting problems. Thus, in [1] tae norecast of forestrecoveiy aftef a lite ss bniifin [2] tSo calculation of forest scnvecal iei tire: long Олту is carrigd out, the authors [3] buiie f ferssast ob inrteic hoavest using h model of vine growth. As ten same thus:, Sie bgarnnes of the growth of Tee trgg depend not only on thy bsced, but also on the growino condition,. Thot it, when building a model of a pnrticulae tree, it t :песешгбу to et^doa onO) m:c2unt climatic featseec end tire: iniSncTbe olt the t^rrmo. eLealistic models of trees can tie invO on the dasis of data obduncd from aircraft no ng active ofitcbl systems [bS—6]_ Also, tree models ate steed i- many computer games. Thr paper [7] proposes ti growth oeodvi

The f)ei)er [9, ^uggesir ide mtcracOvf wo- of modeling of а toon rvhich is dboad on the interacbon of Cih usnr wP6 thr eyclm. Ai the first stage, ihe system ccfaibr several pretending modrls frim the contouv of Cic Cen cre-atedby hoe uset.

Foom tht:os mob^h^s tbc u:>er nbkais Sbl2 most ouitable trees. ftcor :sell:cihd tides ntt еПип automaticallo processed by the суПт tc anate new cac-odahe models. Atypifaleaample is shoornin ftg. 2.

T h tin. Скь isskt 1:!Sai require moiielino ob dceo can be core diverse: tdmn computer cbmis:s do rnnhcHng the grov^tV oC itbds Ll claпtationo. Cteei^nding on tint pradlem to toe solcad, ono ne dttoit1m meSdv0 oC -oe mogntiag and itslcccloddetallcrecdosen|T0a-131.

^Lii algorh:hin for conshructing a tree in three-dhrnensional space. Ttie: Coemoioddl ts dcser'ded as a dlas-sical treeldke ilynlmic.■ chruhttcie of е; soooieinatt1s of the bcbinninj? and end of ihe nodv; in tllisnci:s;s. d: is pobl01ts So 000:1x1 this stchcthcc for aiiifCrreni O’er species and faindoribs. Oiodel-ing of irce orordb im slmilar io the tdoolaCble:oional case wPhtCccolotcOюnrottCo-aiacb₂nsodlalip1' e[t1].

Constchction of a thlcddamicnaюnal mod^l nt the inee takcsptace bi ccccfalstfgbs:

• 1.    The consiпtcSionor tkeireerrame:

• - maCetifn C'i:u dпttvth;

• 2.    Builbiiig a Cove on ix: framcandae;aly^ngiehtures.

  

  Fgt. T :a:oicoileal-):iaeccoPtal-.llclodcl

  
  

daddingcewoodns.

Рис.Т Представление модели Lorix pa0oaipi-thuppcerhii1

Fes.2. Stages oftree modeling procedure

Ftg.3. W:irehramptroemodel

Рис.З. Каркас дерева

Undec the tape smme we andsnsdanf e sec af tPree-rOmangoensl vectors with the aifrboute date for eech vector <4?

Taa algonthee for cooeioneaing a trrra model is itera-iive. Eeeh itcsatton ia a stage eS icffgrowthSfig.4t. hOut, ihetceeOg nesnosllygrowut ie theeequireO level.

Son nnw rade v is ecesienbyPePeciing frhmthesar-eni naPt й by an engle 9 and Oenoeeg шоипр it l)y an sngle ф (fog. 5). RtellnSenPrf coaoninate spstem ia used in Shigcase.

Tae rotaties hf the custpieatf myetem Ъ>у angles 9 sna ф is obiatneg from fem compousSSen oO rotations sceona the О У sna OZ axss. The oageo nf Usui is the Sellewing:

• 1)    tom abouanaaxts О Y iereoghan anglesf 9 ;

• 2)    tom abouanaaxts OZ ieceoghan angles f ф.

Tfr mafex oO ieSstiaf ef Uso tetgoahnate system iheeogh anjjh:s 9 sna ф has nfenoml:

M (9,Ф) = Mz (Ф).Му(9) =

^ees9 ■ eegф ^шф gin9 ■ eegф> ees9 ■ gin ф eegф gin9 ■ ginф ч -ginф      0       ees9  y

L,itt (9_v, ф„) - пР: roltltiun anpies oh tnp new ngpe v cplsiivf te thie escant naft й. But hPn поре u , on iti tom, ii alee rotatrУ. te hfme englene ilunntinh them (9_й, ф_u) celsiive es hfe axis OZ in hui bafa coousiank: amtem. TPey afe calculatet ley formuSss si irioniitCn:h 6em spPeri-eslcooKlUiaP; systemtoCaatesian.

Fag.4. Crcagrowtlimodclmgalgoritlim

Рйс.4. Алгоритм моделирования роста дерева

Fig.S.Ncwnodccrcalingctagc

Рис.5. Построение нового узла каркаса дерева

Рис. 6. Представление конуса в X3D

Thus, the oesuknag irtataeion laiatrixi will lie crleolated by the Permula:

M = M (9 „, ф_ц)• M (6 _v, ф _v).             (2)

Accordinyly, the erurOinaSesof lho new node v io the base Crrfesiha ccrrdinale syetem oan la calauloted hn the Permula:

(x)

( 0 )

Tv

I A )

= M.

L

,

whoro L istho looglhoO tlee newteotnude.

To viuuatize о alrolsOlmccsioaal iree model booed on Ihe constIUCled Oramnwouk, wx well uno the VRML three-Utmeosteoal image deecripteon ihwgnaae rr its dcecendant X3D [15.. A sloatgUi tiunuateo isnc is coneUuoted on the basts o)f 1Пз amme oO cads nolle. Radit sO baste - the rrtlhmoltc moao bolwooo ttie aaifa^eleru oh thn usfdnp of lho current nude uoh the netb“bor at Shir bttse. The axis cP thocone ss the vectoa oO the nude.

A airaighl homceted eonr in X3D, from a mathe-mrltcrl eohit of ninw, is a aagulaa trunuatsd fsuamid ^g.6..

Scfhnpaтfmld sedeserlOed as follows:

The oecsiso lists flue ooIco of the vorlox petols 1Ог1 make uf the Sacou aseS looses of the pyramtu. Tie uproa luoe of rnsO m pav■amid will have a uoscrtplteo:

0 12... N - 2 TV-1 -1, (4)

whoro -Iso theacoe deeariptsonepnaraSoe.

The section ifila thu ooesUinates of lhoso vorloxpoinSsssCollnws:

• ^Х1   У1   ^Zl,   yl   zl   ^Z2,   -.  ^X2 N-1   УгМ-Х   ^Z2 V-1 . ⁽⁵⁾

The foltowOig eeunocoe oe oPejris es uoed to stлeslruct lhoi;one:

• 1.    The cooroinesep of tiae baeas эте urlculated, lho c^oseal oO fee towrr bsee Iles at fee pL), wleoe L is ttie Oangho oO the lroonode.

• 2.    The angles 9 and ф for the nulf vsctrr are carcu-lrloO.

• 3.    The coordinates oO tOia cone are recalculated toting tolo account Our soiatton mahix M (9, ф) according to the slrlomohl(1).

^iir ampniilp o1U a toas uasod on thts ags

Thus, ustog tin ooio>ldcaeP apaproacr te modeling lroos, you con aiutld r irrc montl rofp uny deepeu of de-1гГ1. Frr exfmalз, fot

Conclusion. The paper proposos an alnrritlrm Con con-slrucltog a tree muacV whirs le itcratioo and end itera-ltoo ss a ^teup oO tree gcowehl rags algorShas ui based no the iuioa of modalmg a Oreo bys i^s roanuat “nrowing” to lho aaeut i aaui ivaef TOr OunO ооП CoaduPal et mu- simu-lrloO troo one pprsxximateh lay 1hcncatan conat, rXo axes cP white are the framc sectors. “of varuidii'ihuia of the cooslruclou haeeeoSmleilsnзiial model nO a tree ^he language cP ttie tlo^;crip)tioil ppf t0aro-meo2nshnlbl Imesup of 3D is usou. Uowo tlis Vovckiurp ilt)pi'oablr st ts pbseibte to mouol trees wtth sny gegree of delnO aud different cate-gortosoO saae.:

Fig.7.3D tree wlthtextures

Рис. 7. Трехмерное дерево с наложенными текстурами