Cloth Simulation. Simulation in Computer Graphics University of Freiburg WS 05/06
|
|
- Nora Cameron
- 5 years ago
- Views:
Transcription
1 Clot Smlato Smlato Comptr Grapcs Urst of Frbrg WS 05/06 D. Baraff A. Wtk. Larg stps clot smlato. Sggrap 98 pp
2 Ackoldgmt Ts sld st s basd o t follog sorcs: D. Baraff A. Wtk. Larg stps clot smlato. Sggrap 98 pp D. Macr. Ral-tm clot. Gam dlopr cofrc 000. D. Prtcard. Implmtg Baraff ad Wtk s clot smlato. ttp://frclot.gmat.ca/ 003. sorcforg. frclot proct. ttp://frclot.gmat.ca/ R. Brdso. Comptatoal aspcts of damc srfacs. PD tss Staford Urst 003.
3 Otl gomtr strtc forcs sar forcs bd forcs damc smlato stra lmtg altrat bd forcs dmostratos dscsso
4 Gomtr traglatd ms of mass pots to rprstatos of pot postos 3 orld coordats R pla coordats R orld coordats ar drg t smlato pla coordats rprst tal dformd gomtr maps from pla to orld coordats costat plaar paramtrato tm-arg orld coordats
5 Strtcg rprstd t partal drats matral s strtcd / comprssd drcto ff drcto ff Eampl.
6 Strtc of a Tragl mass pots of a tragl k dgs orld spac - k - dgs t pla s appromatd as lar fcto or a tragl ad ar costat or a tragl
7 Strtc of a Tragl solg for ad ar ot trstd st s ad to rprst ad strtc dos ot ork t dgratd tragls
8 Strtc Codto masrs strtc for a tragl ad drcto qals ro ff t tragl s strtcd / comprssd codto s gtd t t tal tragl ara A
9 Strtc Erg ad Forcs strtc rg of a tragl sr-dfd k st E st >0 f t tragl s strtcd or comprssd strtc forcs F at all mass pots of a tragl forcs ar gat gradt of t rg trms of mass pot postos
10 Strtc Forc strtc forc at pot
11 st st st st A A k C C F rrtg t drats of C trms of Strtc Forc
12 drats of ad t rspct to k 3 3 I Drats of 3 3 I 3 3 k I 3 3 I 3 3 I 3 3 k I
13 Strtc Smmar strtc s rprstd t partal drats of a psdo-mappg fcto c corts from tal plaar coordats to orld coordats strtc s cosdrd dffrt drctos strtc codto s statd pr tragl strtc rg ad strtc forcs ar drd from t cod. strtc forcs for mass pots of a tragl ar comptd sg tr postos orld spac ad tr orgal postos plaar coordats
14 Sarg sar of a tragl s masrd b cosdrg rst stat ts prodct s ro bot ctors ar ortogoal f sar occrs t scalar codto fcto C s qals t cos of t agl bt ad gtd b t tal tragl ara A C s k A T T ad ar ot ormald assmg tr magtds do ot cag sgfcatl d to strtc forcs
15 s s s s s s s s s s s C A k C C C C k C C k F forc s drd from sar rg sr-dfd k s forcs at tr tragl rtcs ar comptd basd o tr postos bot obct rprstatos Sar Forc
16 bd s masrd for pars of adact tragls t o commo dg Bd k k k
17 Bd Codto bd codto s t agl bt a tragl par Cb k θ agl ca b comptd sg sθ cosθ aga ormalato s glctd assmg t magtds do ot cag sgfcatl
18 Bd Forcs forc s drd from bd rg t sr-dfd k b C F b k b C b o gtg t tragl ara C b k b C C mplctl cosdrd b sg ormald ctors. Hor ormald ctors ar sd. b b b C b
19 to compt bot rlatos for t agl ar sd Bd Forcs - Drats C b s cos θ θ θ s θ θ cos s θ θ θ cos θ θ d to sglarts
20 Bd Forcs - Drats ~ ~ ~
21 drats of Bd Forcs - Drats 3 3 I 3 3 I
22 Bd Forcs - Drats [ ] drats of
23 drats of Bd Forcs - Drats k k k
24 drats of t dot ad t ctor prodct Bd Forcs Last Drats + } { k +
25 Smlato Loop talato grato of t tal plaar tragl ms dfto of ad coordats for all rtcs dfto of t tal loct for all rtcs dfto of mass for all rtcs dfto of k st k s for all tragls dfto of k b for all tragl pars forcs loop tragls: compt F st F s for t tr rtcs loop pars of tragls: compt F b for t for rtcs loop rtcs: compt tral forc appl or faort mrcal tgrato scm
26 Eprmtal Rslts Prtcard k st k s k b tm stp 0.0s mplct tgrato mass pots comptg tm 45 s pr smlato stp Ptm 4 3GH Baraff Wtk 4500 mass pots 0 s pr smlato stp bot mplmtatos s mplct tgrato ad cogat gradts t a ko mbr of tratos
27 Stra Lmtg [Proot Brdso] dstac dato of to adact pots lmtd to 0% of t tal dstac largr datos ar prtd b smmtrcall rplacg bot pots rald b loopg trog all pot pars corgt f prformd tratl rplacg ca b trprtd as t rslt of a tral forc global damc baor lar aglar momtm of t modl s ot flcd corrcto tm
28 Stra Lmtg [Brdso Fdk] adstmt of locts stad of postos t smlato loop prdct locts f postos basd o t prdctd locts cd t stra lmt corrct locts accordgl compt postos comptd postos basd o corrctd locts flfll t stra lmt smmtrc cags of locts mata aglar ad lar momtm of t sstm cosstt postos ad locts
29 Altrat Bd Forcs [Brdso Fdk] drato of forcs basd o t bdg agl bt ad forcs sold ot cas rgdbod moto of t for pots ad sold ot cas -pla dformatos compar df. of tral forcs k k ar forc drctos at k as to b paralll to k as to b paralll to a to b t spa of ad k 0 o cag of lar loct k as to b ortogoal to rgd bod rotato
30 Forc Drctos k k + k k
31 Forc Magtd F { k} b kb s + k b s sr-dfd θ / { k} addtoal rstc gtg t tragl aras srs dpdc from msg s s st smpl to compt θ / ± / s
32 Comparso [Baraff Wtk] - [Brdso Fdk] Baraff Wtk df codtos prcpl of rg-dr forcs srs tat rsltg forcs ar tral forcs lgat bt ot stragt-forard to mplmt Brdso Fdk df forcs forcs ar dsgd to rprst rsstac to bdg forcs ar dsgd to b tral forcs lss lgat bt practcal
33 Rlatd Approacs lk lst at t Urst Collg Lodo ttp://.cs.cl.ac.k/ rsarc/r/procts/3dctr/ clot_smlato_lks.tm Volo Talma Ebrardt Wbr Strassr Brdso Fdk Adrso Co Ko
34 Commrcal Clot Smlato.sfl.b Or clot smlator mplmts a compltl orgal tcq. sfl. sfl
35 Bod Skrts - Op Problms ralstc matrals ar rsstacs to sar strtc bdg a approprat paramtrato? stabl collso rspos cas of collsos ad slfcollsos tgt-fttg clot sarp dgs lard matral rkls m
FINITE ELEMENT METHOD: AN INTRODUCTION Uday S. Dixit Department of Mechanical Engineering, Indian Institute of Technology Guwahati , India
FIITE ELEMET METHOD: A ITRODUCTIO Uda S. Dt Dpartmt of Mchacal Egrg, Ida Isttt of Tcholog Gwahat-78 39, Ida. Itrodcto Ft lmt mthod (FEM s a mrcal mthod for solg a dffrtal or tgral qato. It has b appld
More informationThird Order Shear Deformation Theory for Modeling of Laminated Composite Plates
E X tratoal ogrss ad Eposto o Eprmtal ad ppld cacs osta sa J Trd Ordr ar Dformato Tor for odlg of Lamatd ompost lats Rastgaar agaa. aa Jaar G.* aar G. Dpartmt of cacal Egrg ad ppld cacs ort Daota tat Urst
More informationLECTURE 6 TRANSFORMATION OF RANDOM VARIABLES
LECTURE 6 TRANSFORMATION OF RANDOM VARIABLES TRANSFORMATION OF FUNCTION OF A RANDOM VARIABLE UNIVARIATE TRANSFORMATIONS TRANSFORMATION OF RANDOM VARIABLES If s a rv wth cdf F th Y=g s also a rv. If w wrt
More information3.4 Properties of the Stress Tensor
cto.4.4 Proprts of th trss sor.4. trss rasformato Lt th compots of th Cauchy strss tsor a coordat systm wth bas vctors b. h compots a scod coordat systm wth bas vctors j,, ar gv by th tsor trasformato
More informationComplex Numbers. Prepared by: Prof. Sunil Department of Mathematics NIT Hamirpur (HP)
th Topc Compl Nmbrs Hyprbolc fctos ad Ivrs hyprbolc fctos, Rlato btw hyprbolc ad crclar fctos, Formla of hyprbolc fctos, Ivrs hyprbolc fctos Prpard by: Prof Sl Dpartmt of Mathmatcs NIT Hamrpr (HP) Hyprbolc
More informationME 501A Seminar in Engineering Analysis Page 1
St Ssts o Ordar Drtal Equatos Novbr 7 St Ssts o Ordar Drtal Equatos Larr Cartto Mcacal Er 5A Sar Er Aalss Novbr 7 Outl Mr Rsults Rvw last class Stablt o urcal solutos Stp sz varato or rror cotrol Multstp
More informationRadial Distribution Function. Long-Range Corrections (1) Temperature. 3. Calculation of Equilibrium Properties. Thermodynamics Properties
. Calculato o qulbrum Prorts. hrmodamc Prorts mratur, Itral rg ad Prssur Fr rg ad tro. Calculato o Damc Prorts Duso Coct hrmal Coductvt Shar scost Irard Absorto Coct k k k mratur m v Rmmbr hrmodamcs or
More informationBinary Choice. Multiple Choice. LPM logit logistic regresion probit. Multinomial Logit
(c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 3 Bary Choc LPM logt logstc rgrso probt Multpl Choc Multomal Logt (c Pogsa Porchawssul,
More informationPreprint of the paper
Prprt o t papr "O t rsolto o t scos comprssbl lo or aros SUPG t lmt ormlatos" P. Vllao J. Prtas J. ollo J. F () CD Procgs o t ECCOMAS corc arcloa -4 Sptmbr (IS 84-8995-7-4). ttp://camos.c.s/gm Eropa Cogrss
More informationCOMPLEX NUMBERS AND ELEMENTARY FUNCTIONS OF COMPLEX VARIABLES
COMPLEX NUMBERS AND ELEMENTARY FUNCTIONS OF COMPLEX VARIABLES DEFINITION OF A COMPLEX NUMBER: A umbr of th form, whr = (, ad & ar ral umbrs s calld a compl umbr Th ral umbr, s calld ral part of whl s calld
More informationNote: Torque is prop. to current Stationary voltage is prop. to speed
DC Mach Cotrol Mathmatcal modl. Armatr ad orq f m m a m m r a a a a a dt d ψ ψ ψ ω Not: orq prop. to crrt Statoary voltag prop. to pd Mathmatcal modl. Fld magtato f f f f d f dt a f ψ m m f f m fλ h torq
More informationLecture 1: Empirical economic relations
Ecoomcs 53 Lctur : Emprcal coomc rlatos What s coomtrcs? Ecoomtrcs s masurmt of coomc rlatos. W d to kow What s a coomc rlato? How do w masur such a rlato? Dfto: A coomc rlato s a rlato btw coomc varabls.
More informationStatistical Thermodynamics Essential Concepts. (Boltzmann Population, Partition Functions, Entropy, Enthalpy, Free Energy) - lecture 5 -
Statstcal Thrmodyamcs sstal Cocpts (Boltzma Populato, Partto Fuctos, tropy, thalpy, Fr rgy) - lctur 5 - uatum mchacs of atoms ad molculs STATISTICAL MCHANICS ulbrum Proprts: Thrmodyamcs MACROSCOPIC Proprts
More informationMath Tricks. Basic Probability. x k. (Combination - number of ways to group r of n objects, order not important) (a is constant, 0 < r < 1)
Math Trcks r! Combato - umbr o was to group r o objcts, ordr ot mportat r! r! ar 0 a r a s costat, 0 < r < k k! k 0 EX E[XX-] + EX Basc Probablt 0 or d Pr[X > ] - Pr[X ] Pr[ X ] Pr[X ] - Pr[X ] Proprts
More informationPetroleum Reservoir Engineering by Non-linear Singular Integral Equations
www.ccst.org/mr Mchacal Egrg Rsarch Vol. 1 No. 1; Dcmbr 11 Ptrolm Rsrvor Egrg b No-lar Sglar Itgral Eqatos E. G. Laopolos Itrpapr Rsarch Orgazato 8 Dma Str. Aths GR - 16 7 Grc Rcv: Agst 8 11 Accpt: Sptmbr
More informationIntroduction to logistic regression
Itroducto to logstc rgrsso Gv: datast D {... } whr s a k-dmsoal vctor of ral-valud faturs or attrbuts ad s a bar class labl or targt. hus w ca sa that R k ad {0 }. For ampl f k 4 a datast of 3 data pots
More informationStochastic Control of Two-Level Nonlinear Large-Scale Systems; Part II-Interaction Balance Principle
6 IEEE Cofrc o ystms Ma ad Cybrtcs Octobr 8-6 ap aa tochastc Cotrol of o-vl olar arg-cal ystms; Part II-Itracto Balac Prcpl. adat Mmbr IEEE E. Dhgha Marvast Abstract I ths papr a to-lvl mthod for stochastc
More informationGALERKIN FINITE ELEMENT METHOD AND FINITE DIFFERENCE METHOD FOR SOLVING CONVECTIVE NON-LINEAR EQUATION
Cêca/Scc GALERKI FIITE ELEMET METHOD AD FIITE DIFFERECE METHOD FOR SOLVIG COVECTIVE O-LIEAR EQUATIO E. C. Romão a, M. D. d Campos b, ad L. F. M. d Mora b a Uvrsdad Fdral d Itabá Camps Avaçado d Itabra
More informationCourse 10 Shading. 1. Basic Concepts: Radiance: the light energy. Light Source:
Cour 0 Shadg Cour 0 Shadg. Bac Coct: Lght Sourc: adac: th lght rg radatd from a ut ara of lght ourc or urfac a ut old agl. Sold agl: $ # r f lght ourc a ot ourc th ut ara omttd abov dfto. llumato: lght
More informationPunctual State Computation Using Discrete Modeling
Pctal tat omptato sg Dscrt Modlg Dmtr Topa Mmbr AN ad ca Madac Mmbr AN Abstract T papr proposs a stal comptato mtod o t stat vctor assocatd to a crct dyamc bavor or pr-stablsd tm trvals or pctally Basd
More informationChp6. pn Junction Diode: I-V Characteristics II
Ch6. Jucto od: -V Charactrstcs 147 6. 1. 3 rvato Pror 163 Hols o th quas utral -sd For covc s sak, df coordat as, - Th, d h d' ' B.C. 164 1 ) ' ( ' / qv L P qv P P P P L q d d q J '/ / 1) ( ' ' 같은방법으로
More informationTotal Prime Graph. Abstract: We introduce a new type of labeling known as Total Prime Labeling. Graphs which admit a Total Prime labeling are
Itratoal Joural Of Computatoal Egrg Rsarch (crol.com) Vol. Issu. 5 Total Prm Graph M.Rav (a) Ramasubramaa 1, R.Kala 1 Dpt.of Mathmatcs, Sr Shakth Isttut of Egrg & Tchology, Combator 641 06. Dpt. of Mathmatcs,
More informationThree-Dimensional Theory of Nonlinear-Elastic. Bodies Stability under Finite Deformations
Appld Mathmatcal Sccs ol. 9 5 o. 43 75-73 HKAR Ltd www.m-hkar.com http://dx.do.org/.988/ams.5.567 Thr-Dmsoal Thory of Nolar-Elastc Bods Stablty udr Ft Dformatos Yu.. Dmtrko Computatoal Mathmatcs ad Mathmatcal
More informationFourier Transforms. Convolutions. Capturing what s important. Last Time. Linear Image Transformation. Invertible Transforms.
orr Trasors Rq rad: Captr 7 92 &P Adso Soc ad ra (adot o) Opt rad: Hor 7 & 8 P 8 Last T Cooto trs: a/box tr Gassa tr t drc tr Lapaca o Gassa tr Ed Dtcto Cootos Cooto s coptatoay costy ad a copx oprato
More informationASYMPTOTIC AND TOLERANCE 2D-MODELLING IN ELASTODYNAMICS OF CERTAIN THIN-WALLED STRUCTURES
AYMPTOTIC AD TOLERACE D-MODELLIG I ELATODYAMIC OF CERTAI THI-WALLED TRUCTURE B. MICHALAK Cz. WOŹIAK Dpartmt of tructural Mchacs Lodz Uvrsty of Tchology Al. Poltrchk 6 90-94 Łódź Polad Th objct of aalyss
More informationIrregular Boundary Area Computation. by Quantic Hermite Polynomial
It. J. Cotmp. Mat. Sccs, Vol. 6,, o., - Irrgular Boudar Ara Computato b Quatc Hrmt Polomal J. Karwa Hama Faraj, H.-S. Faradu Kadr ad A. Jamal Muamad Uvrst of Sulama-Collg of Scc Dpartmt of Matmatcs, Sualma,
More informationReal-time Cloth Simulation for Garment CAD
Ral-tm Cloth Smulato for Garmt CAD Napapor Mtaaphao Pzzau Kaogchayos Dpartmt of Computr Egrg Faculty of Egrg Chulalogor Uvrsty Abstract For dcads, Computr Graphcs has playd a mportat rol may ds of dsg
More informationChapter 6. pn-junction diode: I-V characteristics
Chatr 6. -jucto dod: -V charactrstcs Tocs: stady stat rsos of th jucto dod udr ald d.c. voltag. ucto udr bas qualtatv dscusso dal dod quato Dvatos from th dal dod Charg-cotrol aroach Prof. Yo-S M Elctroc
More informationIntroduction to logistic regression
Itroducto to logstc rgrsso Gv: datast D { 2 2... } whr s a k-dmsoal vctor of ral-valud faturs or attrbuts ad s a bar class labl or targt. hus w ca sa that R k ad {0 }. For ampl f k 4 a datast of 3 data
More informationVariational Approach in FEM Part II
COIUUM & FIIE ELEME MEHOD aratonal Approach n FEM Part II Prof. Song Jn Par Mchancal Engnrng, POSECH Fnt Elmnt Mthod vs. Ralgh-Rtz Mthod On wants to obtan an appromat solton to mnmz a fnctonal. On of th
More informationThe real E-k diagram of Si is more complicated (indirect semiconductor). The bottom of E C and top of E V appear for different values of k.
Modr Smcoductor Dvcs for Itgratd rcuts haptr. lctros ad Hols Smcoductors or a bad ctrd at k=0, th -k rlatoshp ar th mmum s usually parabolc: m = k * m* d / dk d / dk gatv gatv ffctv mass Wdr small d /
More information1D Lagrangian Gas Dynamics. g t
Te KT Dfferece Sceme for Te KT Dfferece Sceme for D Laraa Gas Damcs t 0 t 0 0 0 t 0 Dfferece Sceme for D Dfferece Sceme for D Laraa Gas Damcs 0 t m 0 / / F F t t 0 / / F F t 0 / F F t Dfferece Sceme for
More informationOn the Possible Coding Principles of DNA & I Ching
Sctfc GOD Joural May 015 Volum 6 Issu 4 pp. 161-166 Hu, H. & Wu, M., O th Possbl Codg Prcpls of DNA & I Chg 161 O th Possbl Codg Prcpls of DNA & I Chg Hupg Hu * & Maox Wu Rvw Artcl ABSTRACT I ths rvw artcl,
More informationOptimum Location and Angle of Inclination of Cut-off to Control Exit Gradient and Uplift Pressure Head under Hydraulic Structures
Optmum Locato ad gl of Iclato of Cut-off to Cotrol Et Gradt ad Uplft Prssur ad udr draulc Structurs Salh I. Khassaf l-saad, adr T. mm l-damarch ad adl Ch. Dh l-zraw l-kufa Uvrst, Collg of Egrg, Dpt. of
More informationu(x, t) = u 0 (x ct). This Riemann invariant u is constant along characteristics λ with x = x 0 +ct (u(x, t) = u 0 (x 0 )):
x, t, h x The Frst-Order Wave Eqato The frst-order wave advecto eqato s c > 0 t + c x = 0, x, t = 0 = 0x. The solto propagates the tal data 0 to the rght wth speed c: x, t = 0 x ct. Ths Rema varat s costat
More informationMathematical Statistics. Chapter VIII Sampling Distributions and the Central Limit Theorem
Mahmacal ascs 8 Chapr VIII amplg Dsrbos ad h Cral Lm Thorm Fcos of radom arabls ar sall of rs sascal applcao Cosdr a s of obsrabl radom arabls L For ampl sppos h arabls ar a radom sampl of s from a poplao
More informationInterval buckling analysis of steel structures using mathematical programming approach
th World ogrss o trctral ad Mltdscplary Optmsato 7 th - th, J, ydy Astrala trval bcklg aalyss of stl strctrs sg mathmatcal programmg approach D W, W ao, racs -o Uvrsty of Nw oth Wals, ydy, Astrala, d.w@sw.d.a
More informationEntropy Equation for a Control Volume
Fudamtals of Thrmodyamcs Chaptr 7 Etropy Equato for a Cotrol Volum Prof. Syoug Jog Thrmodyamcs I MEE2022-02 Thrmal Egrg Lab. 2 Q ds Srr T Q S2 S1 1 Q S S2 S1 Srr T t t T t S S s m 1 2 t S S s m tt S S
More informationChapter 4 NUMERICAL METHODS FOR SOLVING BOUNDARY-VALUE PROBLEMS
Chaptr 4 NUMERICL METHODS FOR SOLVING BOUNDRY-VLUE PROBLEMS 00 4. Varatoal formulato two-msoal magtostatcs Lt th followg magtostatc bouar-valu problm b cosr ( ) J (4..) 0 alog ΓD (4..) 0 alog ΓN (4..)
More informationSupport vector machines II
CS 75 Mache Learg Lecture Support vector maches II Mlos Hauskrecht mlos@cs.ptt.edu 539 Seott Square Learl separable classes Learl separable classes: here s a hperplae that separates trag staces th o error
More informationCBSE , ˆj. cos CBSE_2015_SET-1. SECTION A 1. Given that a 2iˆ ˆj. We need to find. 3. Consider the vector equation of the plane.
CBSE CBSE SET- SECTION. Gv tht d W d to fd 7 7 Hc, 7 7 7. Lt,. W ow tht.. Thus,. Cosd th vcto quto of th pl.. z. - + z = - + z = Thus th Cts quto of th pl s - + z = Lt d th dstc tw th pot,, - to th pl.
More informationEFFECT OF PLASMA-WALL RECOMBINATION AND TURBULENT RESISTIVITY ON THE CONDUCTIVITY IN HALL THRUSTERS
EFFEC OF PLASMA-WALL RECOMBINAION AND URBULEN RESISIVIY ON E CONDUCIVIY IN ALL RUSERS A.A. Ivaov, A.A. Ivaov Jr ad M. Bacal Laborator d Physqu t cholog ds Plasmas, Ecol Polytchqu, UMR 7648 du CNRS, 98
More informationLinear-Quadratic-Gaussian Optimization of Urban Transportation Network with Application to Sofia Traffic Optimization
BULGARIAN ACADEMY OF SCIENCES CYBERNEICS AND INFORMAION ECHNOLOGIES Volum 16 No 3 Sofa 216 Prt ISSN: 1311-972; Ol ISSN: 1314-481 DOI: 1.1515/cat-216-41 Lar-Quadratc-Gaussa Optmzato of Urba rasportato Ntwork
More informationOn the Study of Nyquist Contour Handling Sampled-Data Control System Real Poles and Zeros
Rvw Artcl O th Study of Nyqust Cotour Hadlg Sapld-Data Cotrol Syst Ral Pols ad Zros Yossaw Wrakahag* Dpartt of Elctrcal ad Coputr Egrg Faculty of Egrg Thaasat Uvrsty Ragst Capus Khlog Nug Khlog Luag Pathu
More informationTime : 1 hr. Test Paper 08 Date 04/01/15 Batch - R Marks : 120
Tim : hr. Tst Papr 8 D 4//5 Bch - R Marks : SINGLE CORRECT CHOICE TYPE [4, ]. If th compl umbr z sisfis th coditio z 3, th th last valu of z is qual to : z (A) 5/3 (B) 8/3 (C) /3 (D) o of ths 5 4. Th itgral,
More informationDifferent types of Domination in Intuitionistic Fuzzy Graph
Aals of Pur ad Appld Mathmatcs Vol, No, 07, 87-0 ISSN: 79-087X P, 79-0888ol Publshd o July 07 wwwrsarchmathscorg DOI: http://dxdoorg/057/apama Aals of Dffrt typs of Domato Itutostc Fuzzy Graph MGaruambga,
More informationIranian Journal of Mathematical Chemistry, Vol. 2, No. 2, December 2011, pp (Received September 10, 2011) ABSTRACT
Iraa Joral of Mathatcal Chstry Vol No Dcbr 0 09 7 IJMC Two Tys of Gotrc Arthtc dx of V hylc Naotb S MORADI S BABARAHIM AND M GHORBANI Dartt of Mathatcs Faclty of Scc Arak Ursty Arak 856-8-89 I R Ira Dartt
More informationMath 656 March 10, 2011 Midterm Examination Solutions
Math 656 March 0, 0 Mdtrm Eamnaton Soltons (4pts Dr th prsson for snh (arcsnh sng th dfnton of snh w n trms of ponntals, and s t to fnd all als of snh (. Plot ths als as ponts n th compl plan. Mak sr or
More informationKinematics. Redundancy. Task Redundancy. Operational Coordinates. Generalized Coordinates. m task. Manipulator. Operational point
Mapulato smatc Jot Revolute Jot Kematcs Base Lks: movg lk fed lk Ed-Effecto Jots: Revolute ( DOF) smatc ( DOF) Geealzed Coodates Opeatoal Coodates O : Opeatoal pot 5 costats 6 paametes { postos oetatos
More informationPHYS Look over. examples 2, 3, 4, 6, 7, 8,9, 10 and 11. How To Make Physics Pay PHYS Look over. Examples: 1, 4, 5, 6, 7, 8, 9, 10,
PHYS Look over Chapter 9 Sectos - Eamples:, 4, 5, 6, 7, 8, 9, 0, PHYS Look over Chapter 7 Sectos -8 8, 0 eamples, 3, 4, 6, 7, 8,9, 0 ad How To ake Phscs Pa We wll ow look at a wa of calculatg where the
More information1985 AP Calculus BC: Section I
985 AP Calculus BC: Sctio I 9 Miuts No Calculator Nots: () I this amiatio, l dots th atural logarithm of (that is, logarithm to th bas ). () Ulss othrwis spcifid, th domai of a fuctio f is assumd to b
More informationJ. Liu, Z. L. Zhang and C. Thaulow, A dynamic void growth model, Proceedings of the 11 th Int. Congress on Fracture (ICF11), Turin, Italy, March
J. Lu, Z. L. Zhag ad C. Thaulow, A dyamc vod growth modl, Procdgs of th th It. Cogrss o Fractur (ICF), Tur, Italy, March -5, 5 A YNAMIC OI GROWTH MOEL J. Lu, Z. L. Zhag ad C. Thaulow INTEF Matrals ad Chmstry
More informationChapter 5 Special Discrete Distributions. Wen-Guey Tzeng Computer Science Department National Chiao University
Chatr 5 Scal Dscrt Dstrbutos W-Guy Tzg Comutr Scc Dartmt Natoal Chao Uvrsty Why study scal radom varabls Thy aar frqutly thory, alcatos, statstcs, scc, grg, fac, tc. For aml, Th umbr of customrs a rod
More informationComputer Vision. Fourier Analysis. Computer Science Tripos Part II. Dr Christopher Town. Fourier Analysis. Fourier Analysis
Comptr Vision Comptr Scinc Tripos Part II Dr Christophr Town orir Analsis An imag can b rprsntd b a linar combination of basis fnctions: In th cas of 2D orir analsis: orir Analsis orir Analsis Th transform
More informationEE 570: Location and Navigation: Theory & Practice
EE 570: ocato ad Navgato: Thory & Practc Navgato Mathmatcs Thursay 7 F 2013 NMT EE 570: ocato ad Navgato: Thory & Practc Sld 1 of 15 Navgato Mathmatcs : Coordat Fram Trasformatos Dtrm th dtald kmatc rlatoshps
More informationLECTURE 8: Topics in Chaos Ricker Equation. Period doubling bifurcation. Period doubling cascade. A Quadratic Equation Ricker Equation 1.0. x x 4 0.
LECTURE 8: Topcs Chaos Rcker Equato (t ) = (t ) ep( (t )) Perod doulg urcato Perod doulg cascade 9....... A Quadratc Equato Rcker Equato (t ) = (t ) ( (t ) ). (t ) = (t ) ep( (t )) 6. 9 9. The perod doulg
More informationSolid State Theory Physics 545. Crystal Vibrations and Phonons
Sold Stat Thory Physcs 545 Crystal Vbratos ad Phoos Ovrvw Ioc oto ad th haroc approxato Itrodcto to vbratos ad th s of labl k, th wav vctor, dxg th Rcprocal spac rvstd Vbratos a ft oatoc lattc, cocpt of
More information07 - SEQUENCES AND SERIES Page 1 ( Answers at he end of all questions ) b, z = n
07 - SEQUENCES AND SERIES Pag ( Aswrs at h d of all qustios ) ( ) If = a, y = b, z = c, whr a, b, c ar i A.P. ad = 0 = 0 = 0 l a l
More informationOn Estimation of Unknown Parameters of Exponential- Logarithmic Distribution by Censored Data
saqartvlos mcrbata rovul akadms moamb, t 9, #2, 2015 BULLETIN OF THE GEORGIAN NATIONAL ACADEMY OF SCIENCES, vol 9, o 2, 2015 Mathmatcs O Estmato of Ukow Paramtrs of Epotal- Logarthmc Dstrbuto by Csord
More informationNumerical Method: Finite difference scheme
Numrcal Mthod: Ft dffrc schm Taylor s srs f(x 3 f(x f '(x f ''(x f '''(x...(1! 3! f(x 3 f(x f '(x f ''(x f '''(x...(! 3! whr > 0 from (1, f(x f(x f '(x R Droppg R, f(x f(x f '(x Forward dffrcg O ( x from
More informationCamera calibration & radiometry
Caera calbrato & radoetr Readg: Chapter 2, ad secto 5.4, Forsth & oce Chapter, Hor Optoal readg: Chapter 4, Forsth & oce Sept. 2, 22 MI 6.8/6.866 rofs. Freea ad Darrell Req: F 2, 5.4, H Opt: F 4 Req: F
More informationMultiple-Choice Test Runge-Kutta 4 th Order Method Ordinary Differential Equations COMPLETE SOLUTION SET
Multpl-Co Tst Rung-Kutta t Ordr Mtod Ordnar Drntal Equatons COMPLETE SOLUTION SET. To solv t ordnar drntal quaton sn ( Rung-Kutta t ordr mtod ou nd to rwrt t quaton as (A sn ( (B ( sn ( (C os ( (D sn (
More informationIntroduction to Quantum Information Processing. Overview. A classical randomised algorithm. q 3,3 00 0,0. p 0,0. Lecture 10.
Itroductio to Quatum Iformatio Procssig Lctur Michl Mosca Ovrviw! Classical Radomizd vs. Quatum Computig! Dutsch-Jozsa ad Brsti- Vazirai algorithms! Th quatum Fourir trasform ad phas stimatio A classical
More informationPriority Search Trees - Part I
.S. 252 Pro. Rorto Taassa oputatoal otry S., 1992 1993 Ltur 9 at: ar 8, 1993 Sr: a Q ol aro Prorty Sar Trs - Part 1 trouto t last ltur, w loo at trval trs. or trval pot losur prols, ty us lar spa a optal
More informationAPPLICATION OF THE DISTRIBUTED TRANSFER FUNCTION METHOD AND THE RIGID FINITE ELEMENT METHOD FOR MODELLING OF 2-D AND 3-D SYSTEMS
ODELOWIE IŻYIERSKIE ISS 896-77X 9. 97- Gc PPLICIO O HE DISRIBUED RSER UCIO EHOD D HE RIGID IIE ELEE EHOD OR ODELLIG O -D D -D SYSES RŁ HEI CEZRY ORLIKOWSKI chaca Egrg Dpartt Gdak Uvrt o choog -a: rah@pg.gda.p
More informationReview Exam II Complex Analysis
Revew Exam II Complex Aalyss Uderled Propostos or Theorems: Proofs May Be Asked for o Exam Chapter 3. Ifte Seres Defto: Covergece Defto: Absolute Covergece Proposto. Absolute Covergece mples Covergece
More informationLecture #11. A Note of Caution
ctur #11 OUTE uctos rvrs brakdow dal dod aalyss» currt flow (qualtatv)» morty carrr dstrbutos Radg: Chatr 6 Srg 003 EE130 ctur 11, Sld 1 ot of Cauto Tycally, juctos C dvcs ar formd by coutr-dog. Th quatos
More informationCentroids & Moments of Inertia of Beam Sections
RCH 614 Note Set 8 S017ab Cetrods & Momets of erta of Beam Sectos Notato: b C d d d Fz h c Jo L O Q Q = ame for area = ame for a (base) wdth = desgato for chael secto = ame for cetrod = calculus smbol
More informationElectromagnetics Research Group A THEORETICAL MODEL OF A LOSSY DIELECTRIC SLAB FOR THE CHARACTERIZATION OF RADAR SYSTEM PERFORMANCE SPECIFICATIONS
Elctromagntics Rsarch Group THEORETICL MODEL OF LOSSY DIELECTRIC SLB FOR THE CHRCTERIZTION OF RDR SYSTEM PERFORMNCE SPECIFICTIONS G.L. Charvat, Prof. Edward J. Rothwll Michigan Stat Univrsit 1 Ovrviw of
More information2.29 Numerical Fluid Mechanics Fall 2011 Lecture 23
2.29 Numrcal Flud Mchacs Fall 2011 Lctur 23 REVIEW Lcturs 22: Compl Gomtrs Grd Grato Basc cocpts ad structurd grds trtchd grds Algbrac mthods Gral coordat trasformato Dffrtal quato mthods Coformal mappg
More informationDesign of Functionally Graded Structures in Topology Optimization
EgOpt 2008 - Itratoal Cofrc o Egrg Optmzato Ro d Jaro, Brazl, 0-05 Ju 2008. Dsg of Fuctoally Gradd Structurs Topology Optmzato Sylva R. M. d Almda, Glauco H. Paulo 2, Emlo C. N. Slva 3 Uvrsdad Fdral d
More informationand one unit cell contains 8 silicon atoms. The atomic density of silicon is
Chaptr Vsualzato o th Slo Crystal (a) Plas rr to Fgur - Th 8 orr atoms ar shar by 8 ut lls a thror otrbut atom Smlarly, th 6 a atoms ar ah shar by ut lls a otrbut atoms A, 4 atoms ar loat s th ut ll H,
More informationMultipliers. Overview. Introduction. Reading. Computer Systems Laboratory. Stanford University. Copyright 2001 by Mark Horowitz
Lctr : ltplrs ptr Systs Laratry Stafrd Uvrsty hrwtz@stafrd.d pyrght 00 y ark Hrwtz H/JZ EE 7 Lctr Ovrvw adg Itrdct Thr ar ts f paprs wrtt ltplcat. Ufrtatly t s rar that th papr talks at th lgc ad crct
More informationCS 1675 Introduction to Machine Learning Lecture 12 Support vector machines
CS 675 Itroducto to Mache Learg Lecture Support vector maches Mlos Hauskrecht mlos@cs.ptt.edu 539 Seott Square Mdterm eam October 9, 7 I-class eam Closed book Stud materal: Lecture otes Correspodg chapters
More informationProblem Value Score Earned No/Wrong Rec -3 Total
GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL & COMPUTER ENGINEERING ECE6 Fall Quiz # Writt Eam Novmr, NAME: Solutio Kys GT Usram: LAST FIRST.g., gtiit Rcitatio Sctio: Circl t dat & tim w your Rcitatio
More informationBinary classification: Support Vector Machines
CS 57 Itroducto to AI Lecture 6 Bar classfcato: Support Vector Maches Mlos Hauskrecht mlos@cs.ptt.edu 539 Seott Square CS 57 Itro to AI Supervsed learg Data: D { D, D,.., D} a set of eamples D, (,,,,,
More informationCarbonyl Groups. University of Chemical Technology, Beijing , PR China;
Electroc Supplemetary Materal (ESI) for Physcal Chemstry Chemcal Physcs Ths joural s The Ower Socetes 0 Supportg Iformato A Theoretcal Study of Structure-Solublty Correlatos of Carbo Doxde Polymers Cotag
More informationLecture 14. P-N Junction Diodes: Part 3 Quantitative Analysis (Math, math and more math) Reading: Pierret 6.1
Lctur 4 - ucto ods art 3 Quattatv alyss Math, math ad mor math Radg rrt 6. Gorga Tch ECE 3040 - r. la oolttl Quattatv - od Soluto ssumtos stady stat codtos o- dgrat dog 3 o- dmsoal aalyss 4 low- lvl jcto
More information7 Finite element methods for the Euler Bernoulli beam problem
7 Fnt lmnt mtods for t Eulr Brnoull bam problm CIV-E6 Engnrng Computaton and Smulaton Contnts. Modllng prncpls and boundary alu problms n ngnrng scncs. Bascs of numrcal ntgraton and dffrntaton 3. Basc
More informationLearning from Data with Information Theoretic Criteria II
Larg from Data th Iformato Thortc Crtra II Jos C. Prcp, Ph.D. Dstgushd Profssor of Elctrcal ad Bomdcal Egrg ad BllSouth Profssor Computatoal uroegrg Laborator Uvrst of Florda http://.cl.ufl.du prcp@cl.ufl.du
More informationReliability of time dependent stress-strength system for various distributions
IOS Joural of Mathmatcs (IOS-JM ISSN: 78-578. Volum 3, Issu 6 (Sp-Oct., PP -7 www.osrjourals.org lablty of tm dpdt strss-strgth systm for varous dstrbutos N.Swath, T.S.Uma Mahswar,, Dpartmt of Mathmatcs,
More informationSurface x(u, v) and curve α(t) on it given by u(t) & v(t). Math 4140/5530: Differential Geometry
Surface x(u, v) and curve α(t) on it given by u(t) & v(t). α du dv (t) x u dt + x v dt Surface x(u, v) and curve α(t) on it given by u(t) & v(t). α du dv (t) x u dt + x v dt ( ds dt )2 Surface x(u, v)
More informationTime Domain Response of Multidegree-of-Freedom Systems with Fuzzy Characteristics to Seismic Action
CAS Itratoal Spos o Strctral ad arthqak r Octobr ddl ast chcal Uvrst Akara rk Doa Rspos of ltdr-of-frdo Ssts wth Fzz Charactrstcs to Ssc Acto AA aszad Odokz aıs Uvrst Faclt of r Dpartt of Cvl r 9 Sas/rk;
More informationEstimation of Population Variance Using a Generalized Double Sampling Estimator
r Laka Joural o Appl tatstcs Vol 5-3 stmato o Populato Varac Us a Gralz Doubl ampl stmator Push Msra * a R. Kara h Dpartmt o tatstcs D.A.V.P.G. Coll Dhrau- 8 Uttarakha Ia. Dpartmt o tatstcs Luckow Uvrst
More informationLecture 08 Multiple View Geometry 2. Prof. Dr. Davide Scaramuzza
Lctr 8 Mltpl V Gomtry Prof. Dr. Dad Scaramzza sdad@f.zh.ch Cors opcs Prncpls of mag formaton Imag fltrng Fatr dtcton Mlt- gomtry 3D Rconstrcton Rcognton Mltpl V Gomtry San Marco sqar, Vnc 4,79 mags, 4,55,57
More informationStudy on 2-tuple Linguistic Assessment Method based on Grey Cluster with Incomplete Attribute Weight Information
Procgs of 2009 IEEE Itratoal Cofrc o Systs, Ma, a Cybrtcs Sa Atoo, TX, USA - Octobr 2009 Sty o 2-tpl Lgstc Asssst Mo bas o Gry Clstr w Icoplt Attrbt Wght Iforato Cha M IEEE Mbr, Sfg L, Yaogo Dag, Jaglg
More informationEE 232 Lightwave Devices. Photodiodes
EE 3 Lgwav Dvcs Lcur 8: oocoucors a p-- ooos Rag: Cuag, Cap. 4 Isrucor: Mg C. Wu Uvrsy of Calfora, Brkly Elcrcal Egrg a Compur Sccs Dp. EE3 Lcur 8-8. Uvrsy of Calfora oocoucors ω + - x Ara w L Euval Crcu
More informationThe Double Rotation CORDIC Algorithm: New Results for VLSI Implementation of Fast Sine/Cosine Generation
he Doble Rotato CORDIC Algorthm: New Reslts for VLSI Implemetato of Fast Se/Cose eerato ze-y Sg * Chch-S Che ** Mg-Cho Shh * * Departmet of Electrcal Egeerg ** Isttte of Egeerg Scece Chg Ha Uerst, Hsch,
More informationA Monotone Process Replacement Model for a Two Unit Cold Standby Repairable System
Itrtol Jorl of Egrg Rsrch d Dlopmt -ISS: 78-67 p-iss: 78-8 www.jrd.com Volm 7 Iss 8 J 3 PP. 4-49 A Mooto Procss Rplcmt Modl for Two Ut Cold Std Rprl Sstm Dr.B.Vt Rmd Prof.A. Mllrj Rdd M. Bhg Lshm 3 Assstt
More informationThomas Whitham Sixth Form
Thomas Whitham Sith Form Pur Mathmatics Unit C Algbra Trigonomtr Gomtr Calculus Vctor gomtr Pag Algbra Molus functions graphs, quations an inqualitis Graph of f () Draw f () an rflct an part of th curv
More informationAlmost unbiased exponential estimator for the finite population mean
Almos ubasd poal smaor for f populao ma Rajs Sg, Pakaj aua, ad rmala Saa, Scool of Sascs, DAVV, Idor (M.P., Ida (rsgsa@aoo.com Flor Smaradac ar of Dparm of Mamacs, Uvrs of Mco, Gallup, USA (smarad@um.du
More informationEstimation Theory. Chapter 4
Estmato ory aptr 4 LIEAR MOELS W - I matrx form Estmat slop B ad trcpt A,,.. - WG W B A l fttg Rcall W W W B A W ~ calld vctor I gral, ormal or Gaussa ata obsrvato paramtr Ma, ovarac KOW p matrx to b stmatd,
More informationFigure 1: Schematic of a fluid element used for deriving the energy equation.
Driation of th Enrg Eation ME 7710 Enironmntal Flid Dnamics Spring 01 This driation follos closl from Bird, Start and Lightfoot (1960) bt has bn tndd to incld radiation and phas chang. W can rit th 1 st
More informationA Series Illustrating Innovative Forms of the Organization & Exposition of Mathematics by Walter Gottschalk
Math Medley #45 of Gottschalk s Gestalts A Seres Illustratg Iovatve Forms of the Orgazato & Exposto of Mathematcs by Walter Gottschalk Ifte Vstas Press PVD RI 2001 GG45-1 (30) 2001 Walter Gottschalk 500
More informationA Novel Symmetrical Heuristic Coefficient for Urban Microcellular Environments
A Novl Symmtrcal Hurstc Coffct for Urba crocllular Evromts Puspraj Sg Caua, mbr, IACSIT ad Sajay So Abstract A ovl urstc dffracto coffct s prstd wc s prfctly rcprocal ad symmtrcal. T prdcto obtad usg proposd
More informationFILTER BANK MULTICARRIER WITH LAPPED TRANSFORMS
FILTER BANK ULTICARRIER WITH LAPPED TRANSFORS aurc Bllagr, CNA Davd attra, aro Tada, Uv.Napol arch 5 Obctvs A multcarrr approach to mprov o OFD for futur wrlss systms - asychroous mult-usr accss - spctral
More informationFace Detection and Recognition. Linear Algebra and Face Recognition. Face Recognition. Face Recognition. Dimension reduction
F Dtto Roto Lr Alr F Roto C Y I Ursty O solto: tto o l trs s s ys os ot. Dlt to t to ltpl ws. F Roto Aotr ppro: ort y rry s tor o so E.. 56 56 > pot 6556- stol sp A st o s t ps to ollto o pots ts sp. F
More informationA METHOD FOR NUMERICAL EVALUATING OF INVERSE Z-TRANSFORM UDC 519.6(045)
FACTA UNIVERSITATIS Srs: Mcacs Automatc Cotrol ad Rootcs Vol 4 N o 6 4 pp 33-39 A METHOD FOR NUMERICAL EVALUATING OF INVERSE Z-TRANSFORM UDC 59645 Prdrag M Raovć Momr S Staovć Slađaa D Marovć 3 Dpartmt
More information8(4 m0) ( θ ) ( ) Solutions for HW 8. Chapter 25. Conceptual Questions
Solutios for HW 8 Captr 5 Cocptual Qustios 5.. θ dcrass. As t crystal is coprssd, t spacig d btw t plas of atos dcrass. For t first ordr diffractio =. T Bragg coditio is = d so as d dcrass, ust icras for
More informationCBSE SAMPLE PAPER SOLUTIONS CLASS-XII MATHS SET-2 CBSE , ˆj. cos. SECTION A 1. Given that a 2iˆ ˆj. We need to find
BSE SMLE ER SOLUTONS LSS-X MTHS SET- BSE SETON Gv tht d W d to fd 7 7 Hc, 7 7 7 Lt, W ow tht Thus, osd th vcto quto of th pl z - + z = - + z = Thus th ts quto of th pl s - + z = Lt d th dstc tw th pot,,
More information