The main principles of formation of dynamic bar graph representation using display with a matrix electric connection of elements have been considered in this work. Applying the theory of sets we formalized a synthesis of symbols and obtained logic operators describing a formation of a visual image at the display information area. Offered and analysed is the information model for the bar graph form of information representation using the scale with scanning along the columns (elder digits) of the element matrix

Bushma, A.V.

Sypko, N.I.

Semiconductor Physics Quantum Electronics & Optoelectronics

Наукова електронна бібліотека періодичних видань НАН України (Vernadsky National Library of Ukraine)

193' 2002, Institute of Semiconductor Physics, National Academy of Sciences of UkraineSemiconductor Physics, Quantum Electronics & Optoelectronics. 2002. V. 5, N 2. P. 193-196.PACS: 85.60.Bt, 42.79.KrModel of dynamic indication in the bar graph formA.V. Bushma,  N.I. SypkoInstitute of Semiconductor Physics, NAS of Ukraine, 45 prospect Nauky, 03128 Kyiv, UkrainePhone: +380 (44) 265-6188; fax: +380 (44) 265-5430; e-mail: bushma@isp.kiev.uaAbstract. The main principles of formation of dynamic bar graph representation using dis-play with a matrix electric connection of elements have been considered in this work. Apply-ing the theory of sets we formalized a synthesis of symbols and obtained logic operatorsdescribing a formation of a visual image at the display information area. Offered and ana-lysed is the information model for the bar graph form of information representation usingthe scale with scanning along the columns (elder digits) of the element matrix.Keywords: indication in bar graph form, dynamic control, display, modeling, multielementbar graph array, array connection of elements, information area, theory of sets, logical opera-tor.Paper received 08.04.02; revised manuscript received 31.05.02; accepted for publication 25.06.02.1. IntroductionThe main information amount coming to a man from tech-nical means is transferred by the sight. Indication facili-ties transform coming information into a visual form.These convert data into visual images in accord with adefinite system of rules that are determined by an infor-mation model (IM). When developing information-meas-uring systems, they use IM that represent the essence ofreal processes and states of controlled objects in the bestway using special coded images [1, 2].Among IM widely used in measuring technique, loca-tion means and communication systems, the particularplace in occupied by the bar graph display [3]. It is causedby the fact that such a way of data output provides simplyrecognized and effective image representation of infor-mation. Using this IM, annunciation in the indicator in-formation area is determined both by its length and posi-tion of reading out end of an optical non-uniformity rela-tively to scale marks. It can be, for instance, a luminousline at the scale of an indicator based on active elements.A combination of the bar graph IM with digit methods ofdata processing provides high reliability of informationtransfer to an operator from indication means.2. Design of imaging means with the bar graphindication formDisplays with multi-element scales enable to providehighly informative and discret indication. It determinedthe considerable practical interest to them in varioustypes of measuring systems [1]. It is indicative of displayswith multi-element (more than 15-20) scales that two-co-ordinated matrix electrical connection of elements is used.As a result, the amount of controlling buses is consider-ably reduced, which increases reliability of an imagingunit as a whole. However, this electrical scheme of thedisplay causes some supplementary difficulties when re-alizing a control circuit, as it does not enable to simulta-neously excite an arbitrary group of information areaelements (IAE). Besides, there arise undesirable condi-tions of exciting unchosen IAE, which is caused by si-multaneous supplying contacts of element groups withelectric signals. This parasitic illumination worsens qual-ity of visual symbols formed [2].Harnessing the dynamic methods for an image syn-thesis at display panels enables to overcome these limita-tions restricting IAE integration into groups. It is obvi-ous that in the case, the necessary group of elements isdivided by sub-groups, elements of which allow simulta-194 SQO, 5(2), 2002A.V. Bushma et al.: Model of dynamic indication in the bar graph formneous excitation. Elimination or essential reducing theparasitic illumination caused by unchosen elements isprovided here by using IAE with threshold characteris-tics and unipolar conductivity as well as the respectivealgorithm of their excitation [2, 3].The analysis of logic-time regularities characteriz-ing the synthesis of IM for indication in the bar graphform at the multi-element scale display used inoptoelectronic information-measuring systems is repre-sented in this work.3. Modelling the dynamic bar graph datarepresentationInformation is transferred to an operator using νS  sym-bols that in their visual form represent data upon the con-trolled value. The set of symbols used in determined byIM and forms its alphabet ΩIM. A display unit provides asynthesis of all IM symbols in its information area. Thesecan be determined as a set=ΩBG{ }BGBG 1)(BGBG2BG1 ,,,,,, ll SSSSS −= KK ν(1)where  ΩBG is the alphabet of the bar graph IM;BGνS  is the ν -th symbol, with l,1=ν ;l is the IM alphabet length.The alphbet length equal to the amount of differentsymbols in IM is determined by the finite set of allowablestates in the display information area. A symbol image isformed from excited discrete display elements by the con-trol circuit in accord with IM. The set A of display ele-ments ai is described as{ }ppi a,a,,a,,a,aA 121 −= KK ,  (2)where p is a total amount of elements comprised by thedisplay information area; pi ,1= .In an electrical representation, the display elementsai are usually two-terminals. In multi-element displays,these, as a rule, are connected by a two-coordinated ma-trix, while their spatial location is determined by topol-ogy of IM used. The bar graph form of information rep-resentation assumes presence of a weight function)( ii aϖϖ =  intrinsic to each IAE ai. Obviously, its valueis related to the element position in the display informa-tion area and is in proportion to the i number in the scale.Therefore, we assume that the set A is absolutely ordered[4]. In this set, the weight function is determined and theinequality )()( 1+< jj aa ϖϖ  is valid for all)1(,1 −= pj . Information read-out is performed in ac-cordance with the weight function value relatively to scalemarks that serve as a multi-channel measure [1].Symbols BGνS  are synthesized from ai elements in-corporated into the A  set determined by expression (2).Therefore, each visual symbol from the set BGΩ , de-scribed by (1), can be supplied with one-to-one corre-spondence of a definite IM subset of ai elements from theset A. IM of the bar graph form data representation ischaracterized by formation of a continuous visual imageconsisting of excited elements. The synthesized line ofIAE begins from the element possessing the lowest valueof the weight function. The end of the line is determinedby IAE with the weight function corresponding to theimaged meaning of information. Let us assume that thesymbol corresponding to the zeroth value of an input sig-nal has the positional number 1=í . Then, using the uni-fication operator one can writeBGνS ⇔ Uνν1BG==iiaA ={ }νν a,a,,a,,a,a i 121 −= KK ,     (3)where BGνA  is a subset of the set A , which forms thevisual BGνS  symbol image in the display information area.In accord with the operator (3), the synthesis of sym-bols in the display information area is possible only atseries connection of two-terminal elements or when usingone common electrode. The display matrix electricalscheme does not allow to simultaneously excite all IAEthat belong to the set BGνA , corresponding to the sym-bol BGνS . Therefore, used is the dynamic formation ofthe visual image BGνS  for the number of series timeintervals (cycles). Their amount is determined by IM andcorresponds to conventional principles of scanning thedisplay elements. In doing so, each of l IAE sets BGνA ,corresponding to l symbols of the alphabet ΩBG, is di-vided by the number of uncrossed subsets excited withindifferent cycles of BGνS  symbol formation==DBGBG νν AA{ }rrq AAAAA BG1BGBG2BG1 BG ,,,,,, ννννν −= KK , (4)where DBGνA  is the set identical to BGνA  and is its dy-namic equivalent;qA BGν is a subset of the set DBGνA  consisting of elements ai,which corresponds to the q-th cycle of formation of thedynamic visual  BGνS  symbol representation, with,∅==IrqA11BGν  and rq ,1= ;r is an amount of cycles necessary to synthesize the visualsymbol image.An obligatory condition to create a stable observableimage of any visual symbol is to exceed a critical flickerfrequency of SS Tf 1=  by a frequency of image regen-eration [3]. In this case, each group of ai elements, incor-porated into the set qA BGν  is excited during every symbolrecovering period within the time range rTSg =τ .Then from (3), taking (4) into account, one can obtainthe generalized IM for the dynamic bar graph form datarepresentationA.V. Bushma et al.: Model of dynamic indication in the bar graph form195SQO, 5(2), 2002BGνS ⇔ggqttqttrqqTii AaAsττννν+=−+=====)1(1BG1DBG UU ,  (5)where Ts is the peroid of BGíS  symbol formation in thedisplay information area.4. The information model for the bar graphform data representation based on scanningalong matrix element columnsAn information area of a multi-element bar graph dis-play consisting of p elements corresponding to (2), froman electrical viewpoint, can be built, as a rule, in theform of two-coordinate matrix comprising n groups withm elements in each one where (m⋅n=p). As a result, thisunit is some multi-terminal with (m+n) outputs. Everycommon bus for a group of elements that are located neareach other in the information area is the output terminalof one of n elder digits. The respective value of the weightfunction is determined by the position of this group rela-tively to the scale marks. Every common output terminalfor elements with the same number in all groups serves asa bus for one of m younger digits. The relative value ofthe weight function for these buses is determined by posi-tions of group elements connected with them. It followsthereof that the element xyi aa =  possesses the number yin the group number x with n,x 1= , m,y 1= . In such acase, its positional number in the scale is determined bythe expression yxmi +⋅= . Then for ν-th IAE one canwrite that in the matrix it occupies ( )mmy ννν Ε⋅−=position in the group with the number ( ) 1+Ε= mx νν ,where E is Entire. As a consequence, the operator (3) formatrix connection of display elements can be written inthe following formBGνS ⇔( )( )==Ε⋅−=+Ε==mimiymixixyaA11BG Uνν{ }νν a,a,,a,,a,a xy 121 −= KK .    (6)The algorithm for scanning the IAE matrix determinesthe specific appearance of qA BGν  groups of ai elementsrepresented by (4). One of the typical variants to form theimage when using two-coordinate matrix scheme of elec-trical connections of display elements is scanning alongthe columns (groups) [2]. In this case, the amount of qA BGνelements incorporated into the DBGνA  set described in (4),and the amount of formation cycles for the model (5) isequal to r=n. It is obvious that within any cycle, the arbi-trary amount of elements related to one switched-on col-umn of the matrix elder digits can be excited. This aielement set can be described as===Uuyxyx aA1BG{ }xuuxxyxx a,a,,a,,a,a )1(21 −= KK , (7)where xA BGν  is the set of excited elements related to thecolumn number x when representing information in thebar graph form and scanning the IAE along matrix col-umns;u is an amount of excited elements in the column with, ingeneral case, mu ,0= .Our analysis of expressions (5), (6) and (7) shows thatthe synthesis of all elements of the alphabet ΩBG resultsin formation of n sets xA BGν , that is for scanning the ma-trix of IAE along columns in the model (5) we used xq = .There are three possible variants to create xA BGν with dif-ferent analytical description, namely: when the numberof excited elements in the column 0=u , mu =  andmu <<0 .Then, starting from the generalized model (5) andtaking into account (6) and (7), IM for the bar graphrepresentation of data in the display with matrix electri-cal connection of IAE can be represented as,2 )1(11)1(11 )1(11BG1DBGBG∅====⇔+Ε=+=−+=+Ε+Ε=+=−+=Ε−=Ε=+=−+====UUUU UUUU UUUnmxxttxttmmxxttxttmmyxymxxttxttmyxyTnxxTiiggggggAaaAaASssνττννττνννττννννwhere t is a flowing time for dynamic formation of thesymbol image;∅A  is an empty set.It is noteworthy that IM (8) describing BGνS  symbolformation in a dynamical mode for n  cycles can be char-acterized by three time intervals. During the first onecorresponding to cycles from the first one up to(8)196 SQO, 5(2), 2002A.V. Bushma et al.: Model of dynamic indication in the bar graph form( )mq νΕ=1  all elements of the first q1 matrix columnsare excited. During the second interval equal by its dura-tion to one cycle, elements of the column with the number( ) 12 +Ε= mq ν  are transfered to an excited state. Theiramount can be changed from unity up to  m in depend-ency on a reproduced symbol. In third period that isformed by cycles with numbers from ( ) 22 +Ε= mq ν  ton, excitation of IAE is not made. It corresponds to forma-tion of empty sets ∅A  of elements in respective matrixcolumns.5. ConclusionsThus, we have considered principles of formation of thedynamic bar graph data representation in a display. Basedon the theory of sets, offered is a formalized descriptionsuitable to synthesize symbols from elements of linearscale information area. Obtained are the logical opera-tors that model the process of formation of a visual imageat the bar graph display with matrix connection of ele-ments. Offered and analysed is IM with the bar graphform of imaging information at the scale with scanningalong columns (elder digits) of the two-coordinate ele-ment matrix.Represented results creates an analytical basis to re-search and comprehensively optimize functional, struc-tural and general-circuit simulations of units for infor-mation output in optoelectronic information-measuringsystems. It will enable to increase efficiency of displaydevices as well as simplify their integration into auto-mated means of controlling the complex objects and tech-nological processes.References1. P.P. Ornatsky, Theoretical principles of information-measur-ing techniques. (in Russian), Kyiv, Vyshcha shkola, 1983,455 p.2. F.M. Yablonsky, Yu.V. Troitsky, Means for imaging infor-mation (in Russian). Moscow, Vysshaya shkola, 1985, 200 p.3. Stan Gage, Mark Hodapp, Dave Evans, Hans Sorensen.Optoelectronics application manual. McGraw-Hill Book Com-pany, New York, 1977.4. V.P. Sigorsky, Mathematics for engineers (in Russian), Kyiv,Tekhnika, 1975, 768 p.

Model of dynamic indication in the bar graph form

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Model of dynamic indication in the bar graph form

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Наукова електронна бібліотека періодичних видань НАН України (Vernadsky National Library of Ukraine)