STRING DESCRIPTIONS OF DATA FOR DISPLAY*

Transcription

1 SLAC-PUB-383 January 1968 STRING DESCRIPTIONS OF DATA FOR DISPLAY* J. E. George and W. F. Miller Compuer Science Deparmen and Sanford Linear Acceleraor Cener Sanford Universiy Sanford, California Absrac A Picure Descripion Language (PDL) and a Picure Calculus have been developed for he formal descripion and manipulaion of picures. A display program which uilizes PDL sring descripions as he principal daa srucure has been developed. This display program permis he generaion of drawings on a compuer-conrolled cahode ray ube and allows ransformaions according o he rules of he picure calculus. A descripion of he complee daa srucure for his display program is presened, and he ype of ransformaions and manipulaions possible are shown. 1. INTRODUCTION A formal sysem is being developed for describing, manipulaing, generaing and recognizing picures. This formal sysem is called he Picure Calculus (1) and consiss of wo elemens. Firs, a Picure De- scripion Language wih boh a synax and semanics and, secondly, a represenaion which permis easy use of he language. (2) The Primiives A primiive class, p, is defined as any objec wih a head and a ail. The primiive class is given a name and a specificaion of is head and ail, and is defined furher by a lis of aribues. Each aribue may ake on a se of values according o is definiion including being unspecified. For example, he primiive class for ARC has he form: 2. PICTURE CALCULUS 2.1 SYNTAX AND SEMANTICS FOR THE PICTURE DESCRIPTION A senence, LANGUAGE S, in he language is defined by: (1) S-p 1 (S <BINARY OP> S) 1 (<UNARY OP> S), (2) p is a primiive class, (3) <BINARY OP>--+1x] -( *, (4) <UNARY OP > -u I/- 1 T(o). ARC = (ARC, iniial angle, final angle, An elemen curvaure, subended angle). p of he class p has a value lis conaining specific values of he aribues in he aribue lis of he class. For example, he primiive ARC has he form: ARC = (ARC, 90, 45, - 2, 45) which is of he general form, value (p ) = (Name, Tail, Head, Aribue 1, Aribue 2,...). * Work suppored in par by he Naional Science Foundaion (Gran No. GP-7615) and in par by he U. S. Aomic Energy Commission (9h Annual Symposium of he Sociey for Informaion Display, May 22-24, 1968) -l-

2 Thus he aribue lis conains informaion on how o generae he desired picure. I is also possible for an aribue o be a lis, say of absolue or relaive co- ordinaes which give he explici represenaion of a paricular primiive Operaor Semanics In all cases: Tail (Sl <BINARY OP> S2) = Tail (Sl) Head (Sl <BINARY OP> S2) = Head (S2) The binary concaenaion operaors specify how pic- ures are composed from more basic elemens. These operaors are defined by he following illusraions: hen le Sl be and S2 be Y---h s1 s2 = /h (head o ail) SlXS2= ;crh (ail o ail) Sl-s2= -r (head o head) Sl * s2 = ph The unary operaors le S be are defined by: (ail o ail and head o head) hen -S h 9 (ail head reversal) 1s h (he blanking operaor) The hird unary operaor, T(w), is a ransformaion operaor which may ransform primiives or picures; he inen is o allow linear ransformaions such as roaion and ranslaion; possibly non-linear ransfor- maions as well. Thus he essenial elemens of he Picure Calculus are defined; however in his form, i is cumbersome o use due o he excessive use of parenheses. Two addiion- al rules for inerpreing correc his: a senence in he language will (1) Unary operaors have precedence over binary operaors, (2) A senence is inerpreed by a lef-o-righ parse wih each operaor having he smalles possible scope. For example: A + B + -C + D = (((A + B) + (- C) ) + D) 2.2 GENERAL RESULTS USING THE PICTURE CALCULUS One imporan feaure of he Picure Calculus is ha proofs abou picures are possible wih his formalism.(2) Anoher feaure is he separaion of he operaors and he primiive represenaion. A primary use is for he conversion beween a sring descripion and a graphic represenaion and he reverse. The former yields a picure generaion sysem and he laer a picure recogniion sysem. For example, B=--- h c=. h D= \ h hen, 0 =A+B+ wa*b*(c+d) Hence, insead of describing graphical conceps, a sring represenaion may be used. Currenly he Picure Calculus has been used for recogniion of paricle physics picures, generaion of picures, and for he descripion of he alphabe, ex and flow chars.(2) 3. REPRESENTATION OF PRIMITIVES The acual represenaion for primiives used in he display sysem differs somewha from he general form presened. When implemening he display program, several problems developed: (1) A need o save parially compleed picures, (2) The normal requiremen of finie sorage, (3) The aribue lis mus be explici unless an inerpreer sysem is provided for evaluaing he aribues. For pracical reasons he primiive class concep was no used; insead only specific primiives are used. However, he sysem does provide for defining new -2-

3 primiives as an explici operaion or implicily as he resul of an assignmen. One general hierarchical form is used for boh primiives and parially compleed picures when hey are saved using he assignmen funcion. This form is: primiive = (name, basic, sring, ail, head, image) where name is he primiive name, basic is rue if ail, head and image specificaions are presen, sring is he sring expression if he primiive is a parial picure, ail is he relaive ail specificaion, head is he relaive head specificaion, image are he relaive coordinaes of all he vecors which define he primiive. Thus wo ypes of primiives are defined; basic primiives have an explici vecor descripion and possibly a sring descripion, whereas, non-basic primiives (emporary variables) have a sring descripion. The general rule is o always reain he sring descripion and o condiionally reain he explici vecor represenaion if sufficien sorage is available. This explici vecor represenaion is required a some poin in he display process since he graphic display device mus be given explici vecor orders. In he display sysem, picures are consruced by forming a sring descripion of he desired form. The picure is displayed by evaluaing his sring. This evaluaion is performed in wo disinc seps: (1) All non-basic primiives mus be replaced by heir sring descripion; (2) The resulan sring is evaluaed by a lefo-righ parse uilizing a push-down sack. During he sring expansion, infinie recursion is avoided by arbirarily monioring he lengh of he expanding sring a each sep. During use of he display sysem, vecors are accumulaed a a rapid rae and require considerable sorage. The sring descripions proved o be a compac form which require considerably less sorage, however, regeneraing requires more compuer ime. Thus, he sysem uilizes sorage if available, oherwise, i uilizes ime. The presence of he sring in a parially compleed picure offers he faciliy for oher feaures imporan o a display sysem. This sring may be modified by deleion, replacemen or addiional iems may be concaenaed ono i by operaors. More imporanly, i may be re-evaluaed o reflec changes in is consiuen pars. For picure generaion, one of he main srenghs of he Picure Calculus ress in he ransformaional operaor. Currenly, he display sysem does no include his, however, i has proven useful enough o consider exensions such as he ransformaional operaor and ohers. 4. EXTENSIONS 4.1 OPERATORS AND PRIMITIVES The full generaliy of he primiive represenaion should be used for a larger sysem for wo reasons. Firs, insead of many insances of a class being mainained, only he general class need be mainained. Furher, one can hen describe classes of picures and illusrae paricular members by selecing insances of he consiuen primiives. Secondly, his resuls in a greaer degree of generaliy in he manner in which he operaors are applied. For example, consider he case of he *I operaor wih one argumen absoluely specified and he second argumen a primiive class. The requiremen of maching beween he ail and he head of boh argumens will resul in an insance of he class of he second argumen being seleced. This is similar o he way a human draws a line beween wo poins. The ransformaional operaor discussed so far is wha is ermed a saic operaor; i.e., i is applied once per occurrence in he evaluaion. Anoher ype which has proved useful in oher sysems (3) is he dynamic or coninuous ransformaional operaor. This is generally referenced o real ime and used o illusrae moion which under proper use gives he effec of deph. This can be accommodaed easily wihin he Picure -3-

4 Calculus by allowing anoher argumen r ; hus T(w, T) would represen a ransformaion T(w) applied a aime incremen of T. Thus, modeling of problems where moion is imporan is possible. 4.2 MULTIPLE TAIL HEAD PICTURES So far picures have been resriced o having precisely one ail and one head. Alhough many picures may be consruced in his manner, i is very inconvenien for some applicaions. For example, circui schemaics are very difficul because many elemens have more han wo erminals (ransisors have 3, ransformers have 4, ec.). A generalizaion of he represenaion and of he operaors will solve his problem. Consider he ail and head in he primiive represen- aion o be a lis of ails and heads. Furher, le he operaors apply as previously, excep ha hey coninue unil he shores lis used by ha operaor is ex- haused or while maches are allowable. e.g., le A = 2-h2 B= 1- hl 3 -h3 h c hen C + B = anda-(c+b)= h2 i c= h2 hl h3 1 Yhl 22L+ 3 -h3 Two addiional operaors will be required for his generalized sysem: (1) An operaorfor reordering ails and heads, (2) An operaor for deleing or insering ails and heads. hl The deleion and inserion can be performed by he operaors and he normal definiions of: Head (Sl COP> S2) = Head (52) Tail (Sl COP> S2) = Tail (Sl) In he example, an objec wih no ail was used. Thus, an objec in his generalized sysem is somehing wih a ail lis and a head lis eiher or boh of which may be null. 4.3 TOPOLOGICAL CONCEPTS Topological conceps such as inside, adjacen and above are considerably more difficul. The basic limiaion of he Picure Calculus is ha i defines he synacic srucure of a picure; he Picure Descripion Language does no formally include opological conceps. These conceps can be viewed as he meaning of a picure. To include hese conceps requires he implemenaion of a specialized recogniion sysem in conjuncion wih a drawing sysem. Alhough possible, i is currenly viewed as oo resricive a case for curren implemenaion. This illusraes ha he Picure Calculus is sufficien for describing synacical srucure and possibly simple opological conceps which are included in he primiives; i is no very convenien for describing complex opological conceps wihou he inclusion of concep recognizers. 4.4 STRING OPERATIONS Wih a sring descripion for picures several naural ideas are suggesed. The firs are canonical forms and he possibiliy for a specificaion of similariy of picures. Preliminary work on a canonical ree farm(4) mdicaes promise for similariy comparisons. The curren problem is he recogniion of meaningless blank operaions wihin he sring. Inuiively, one would desire wo picures o be similar if hey have he same ail and head and he same visible srucure. The second desirable iem is he condiional replacemen of sub-srings. A powerful operaion would be o allow a es for a lis of sub-srings and if all are presen hen o subsiue anoher lis for hose occurrences. This is he ype of operaion which proved useful in FLIP.(5) This is easily accomplished wihin -4-

5 he presen display program since i was implemened (6) Jerome Feldman, Firs Thoughs on Grammaical in PL/l primarily uilizing sring operaions. Inference, Sanford Arificial Inelligence Memo No. 4.5 COMBINED GENERATION RECOGNITION SYSTEM Currenly, he recogniion sysem and he generaion sysem are disinc and separae sysems. The recog- niion sysem requires a synax for he class of picures o be recognized and a se of recognizers for he base primiives. The consolidaion of hese wo sysems o provide an ineracive paern recogniion sysem seems aracive. The basic idea is o uilize he generaion sysem o help in specifying he synax for a class of picures by generaing example members. For his o be successful, a grammar inference heurisic is essenial and work is progressing in his area. (6) 55, Sanford Universiy, Sanford, California (Augus 11, 1967). 5. CONCLUSION The Picure Calculus has proven convenien and powerful for generaing, describing, manipulaing and recognizing a large class of picures. Furher, desirable exensions have resuled in very lile basic surface modificaion o he Picure Calculus, hus indicaing is usefulness. References (1) W. F. Miller and Alan C. Shaw, A Picure Calculus, SLAC-PUB-358, Sanford Linear Acceleraor Cener, Sanford Universiy, Sanford, California (presened a he conference on Emerging Conceps in Compuer Graphics, Universiy of Illinois, Urbana, Illinois, November 5-8, 1967). (2) Alan C. Shaw, The Formal Descripion and Parsing of Picures, Ph.D. Thesis, Sanford Universiy, Sanford, California (in press). (3) I. E. Suherland, Compuer Graphics, Daamaion, (May 12, 1966) pp (4) I. Carlbom, Algorihms for Transforming PDL Expressions ino Sandard Form and Ino a Primiive Connecion Marix, CGTM 38, Compuaion Group, Sanford Linear Acceleraor Cener, Sanford Universiy, Sanford, California. (5) Warren Teielman, Pilo: A Sep Toward Man- Compuer Symbiosis, M.I.T. Projec MAC, MAC- TR-32, (Sepember 1966) pp