Automated Generation of Interative 3D Exloded View Diagrams Wilmot Li 1,3 Manees Agrawala 2 Brian Curless 1 David Salesin 1,3 1 University of Wasington 2 University of California, Berkeley 3 Adobe Systems Abstrat We resent a system for reating and viewing interative exloded views of omlex 3D models. In our aroa, a 3D inut model is organized into an exlosion gra tat enodes ow arts exlode wit reset to ea oter. We resent an automati metod for omuting exlosion gras tat takes into aount art ieraries in te inut models and andles ommon lasses of interloking arts. Our system also inludes an interfae tat allows users to interatively exlore our exloded views using bot diret ontrols and iger-level interation modes. CR Categories: I.3.5 [Comuter Grais]: Comutational Geometry & Objet Modeling; I.3.8 [Comuter Grais]: Aliations Keywords: exloded view illustration, interative, visualization 1 Introdution Comlex 3D objets, su as meanial assemblies, eletroni devies, and aritetural environments, are tyially omosed of numerous arts. To onvey te internal struture of su objets, illustrators often reate exloded views in wi arts are searated (or exloded ) away from one anoter to reveal arts of interest. Well designed exloded views not only exose internal arts, tey also onvey te global struture of te deited objet and te loal satial relationsis between arts. Furtermore, unlike oter illustration teniques tat reveal internal arts in situ by removing or de-emasizing oluding geometry, su as utaways and transareny, exloded views sow te details of individual arts. However, traditional stati exloded views ave several limitations tat an make it diffiult for viewers to browse te art struture of omlex objets and fous on different subsets of arts. Sine most exloded views exose all te arts in an objet, tey often suffer from exess visual lutter. As a result, te viewer may ave to arefully inset te entire illustration to loate arts of interest. Furtermore, arts tat are lose to one anoter may end u far aart wen te objet is fully exloded, making it diffiult for te viewer to determine ow arts of interest are ositioned and oriented wit reset to te rest of te model. Finally, stati exloded views do not allow viewers to exlore satial relationsis at different levels of detail. For instane, a viewer migt first want to see ow two subassemblies fit togeter before examining teir onstituent arts. In tis aer, we resent a system for reating and viewing interative 3D exloded views tat allow users to exlore te satial relationsis between seifi arts of interest. In our aroa, we Figure 1 Exloded view diagram generated by our system. Our system instruments 3D models to enable interative exloded views. Tis illustration of a turbine model was automatially omuted to exose te user-seleted target art labeled in red. automatially determine te order and diretions in wi arts an exlode witout violating bloking onstraints (i.e., witout assing troug ea oter) and ten use tis information to imlement ig-level viewing tools tat exand and ollase arts dynamially. For instane, te user an selet target arts of interest from a list, and te system automatially generates an exloded view tat exoses te targets witout sowing every oter art in te objet (see Figure 1). Te user an ten diretly exand and ollase te exosed arts along teir exlosion diretions to better see ow tey fit togeter. Our work makes several ontributions. We resent an automati tenique for organizing 3D models into layers of exlodable arts tat andles te most ommon lasses of interloking arts. We also introdue two algoritms for exosing user-seleted target arts, one tat exlodes te neessary ortions of te model in order to make te targets visible, and one tat ombines exlosions wit te dynami utaway views desribed by Li et al. [2007]. We also resent several interative viewing tools tat allow te user to diretly exlore and browse our exloded views. 2 Related work Tere is a large amount of existing work on visualizing te internal struture of omlex 3D objets. Here, we fous on revious teniques tat rearrange rater tan remove geometry in order to exose arts of interest. A number of digital illustration systems rovide tools for reating exloded views [Adobe In. ; Agrawala et al. 2003; Driskill and Coen 1995; Li et al. 2004; Rist et al. 1994]. A limitation of most of tese systems is tat te user must manually seify te exlosion diretions and bloking relationsis for all arts in te model. A notable exetion is te work of Agrawala et al. [2003], wose teniques for generating ste-by-ste assembly instrutions automatially determine te order and diretions in wi arts an exlode witout violating bloking onstraints. We resent an automati algoritm for omuting exloded views tat extends tis work to take into aount art ieraries and to andle te most ommon ases in wi arts interlok.
Exlosion diretions Exloded view for detail Drill bit sub-assembly Figure 2 Exlosion onventions. Tis illustration of a drill inororates several exlosion onventions desribed in Setion 3.1. Image redit: Bos Tools semati Most existing systems generate exloded views tat are eiter meant to be viewed statially [Driskill and Coen 1995; Rist et al. 1994] or rovide limited interative viewing ontrols (e.g., a single knob for exanding te entire exloded view [Agrawala et al. 2003]). Sine a key goal of our system is to enable users to interatively exlore omlex 3D objets, we rovide a rier set of interations. Te viewing interfae for our system is similar to te work of Li et al. [2004], wo resent viewing tools tat allow users to diretly maniulate and sear for arts. However, teir teniques are designed for 2.5D illustrations, and tus do not automatially omute or maintain bloking onstraints between arts. Wereas traditional exloded views tyially searate arts along linear exlosion diretions, researers ave develoed visualization teniques tat exlode arts using oter tyes of transformations and/or deformations. Some of tese aroaes eel away layers of arts using non-rigid deformations [Correa et al. 2006; MGuffin et al. 2003]. Oters extend 2D fiseye teniques to exose and enlarge arts of interest in 3D senes [Carendale et al. 1997; LaMar et al. 2001; Raab and Rüger 1996; Wang et al. 2005]. Reent work by Brukner and Gröller [2006] uses a fore-based model to us oluding arts out of te way. Our work fouses on te allenges of generating more traditional exloded views. 3 Conventions from traditional illustration Te onventions desribed below were distilled from a large orus of examle illustrations taken from tenial manuals, instrutional texts on tenial illustration, and eduational books tat fous on omlex meanial assemblies [Hoyt 1981; Platt and Biesty 1996; Dennison and Jonson 2003]. 3.1 Exlosion onventions Wen reating exloded views, illustrators arefully oose te diretions in wi arts sould be searated (exlosion diretions) and ow far arts sould be offset from ea oter based on te following fators. Te examle illustration in Figure 2 inororates several of tese onventions. Bloking onstraints. Parts are exloded away from ea oter in unbloked diretions. Te resulting arrangement of arts els te viewer understand loal bloking relationsis and te relative ositions of arts. Visibility. Te offsets between arts are osen su tat all te arts of interest are visible. Comatness. Exloded views often minimize te distane arts are moved from teir original ositions to make it easier for te viewer to mentally reonstrut te model. Container Searation distane Cutaway view for ontext (a) Slit ontainer (b) Contextual utaway Figure 3 Cutting onventions for exloded views. Image redits: (a) Steen Biesty Dorling Kindersley; (b) Bill Serwood s Differential Page (www.bilzilla.org) Canonial exlosion diretions. Many objets ave a anonial oordinate frame tat may be defined by a number of fators, inluding symmetry (as in Figure 2), real-world orientation, and domainseifi onventions. In most exloded views, arts are exloded only along tese anonial axes. Restriting te number of exlosion diretions makes it easier for te viewer to interret ow ea art in te exloded view as moved from its original osition. Part ierary. In many omlex models, individual arts are groued into sub-assemblies (i.e., olletions of arts). To emasize ow arts are groued, illustrators often searate iger-level sub-assemblies from ea oter before exloding tem indeendently, as sown in Figure 2. 3.2 Cutting onventions in exloded views Illustrators often inororate uts in exloded view diagrams. Here, we desribe two ommon ways in wi uts are used. Slitting ontainers. In many omlex models, some internal arts are nested witin ontainer arts. To visualize su ontainment relationsis, illustrators often slit ontainers wit a utting lane troug te entre of te art and ten exlode te two ontainer segments away from ea oter to exose te ontained arts (see Figure 3a). To emasize tat te segments originate from te same art, te orientation of te lane is osen to minimize te distane te segments must be searated to make te internal arts visible. Contextual utaways. In some ases, a utaway view is used to rovide additional ontext for an exloded view. For examle, in Figure 3b, te utaway view (bottom) allows te viewer to see ow te sub-assembly of interest is ositioned and oriented wit reset to surrounding strutures, and te exloded view (to) exoses te sub-assembly s onstituent arts. 4 Imlementing exloded views Te minimum inut to our system is a 3D solid model wose individual arts are reresented as searate geometri objets. Te following additional information may be seified to el te system generate iger quality exloded views. Part ierary. If te inut model is organized into a ierary of sub-assemblies, our system generates ierarial exloded views tat enable exloration at any level of te art ierary. Exlosion diretions. By default, our system allows arts to exlode only in diretions arallel to te oordinate frame axes of te entire model. However, a different set of diretions may be seified as art of te inut. All of te examle illustrations sown ere were generated using te default exlosion diretions. Cutaway instrumentation. If te inut model is instrumented to enable utaway views, as desribed by Li et al. [2007], our system
Sub-assembly A a b d f e (a) Inut model g d f b a e g (b) Exlosion gra a b Sub-assembly B g d f e a b g Sub-assembly C d f (a) Hierarial inut model (b) Hierarial exlosion gra e () Exloded model Figure 4 Exlosion gra reresentation. automatially ombines exloded views wit ontextual utaways to exose user-seleted sub-assemblies. In te remainder of tis setion, we desribe a reresentation for 3D exloded views and ten resent an automati tenique for onstruting tis reresentation from te 3D inut model. 4.1 Exloded view reresentation To enable interative exloded views, our system organizes arts into a direted ayli exlosion gra, as sown in Figure 4b. Te struture of te gra defines te relative order in wi arts an be exloded witout violating bloking onstraints. In artiular, a art an exlode as long as all of its desendants in te exlosion gra ave been moved out of te way. For ea art, te gra also stores an exlosion diretion and te urrent offset of from its initial osition. We define tis initial osition wit reset to te largest of te diret arents of, wi enourages smaller arts to move togeter wit larger arts. To exand and ollase different ortions of te model, te system simly modifies te art offsets. Sine many of te omutations desribed below need to know weter arts tou, blok, or ontain ea oter, our system omutes auxiliary data strutures tat enode tese low-level satial relationsis. Contat and bloking relationsis are omuted and stored in te manner desribed by Agrawala et al. [2003]. For a given art, tese data strutures an be queried to determine all te arts tat tou and all te arts tat blok from moving in ea of te ossible exlosion diretions. We use an aroximate definition of ontainment tat is omuted as follows. For a air of arts ( 1, 2 ), our system eks weter te onvex ull of 2 is omletely inside te onvex ull of 1 and if 1 bloks 2 from moving in ea of te ossible exlosion diretions. If so, 1 is onsidered to ontain 2. Te algoritms for omuting ontat, bloking, and ontainment relationsis assume te inut model is two-sided and tat arts tat are meant to fit togeter do not interfere wit ea oter (i.e., overla beyond a small tolerane). 4.2 Construting te exlosion gra Our basi aroa for omuting exlosion gras is similar to te metod of Agrawala et al. [2003] for determining assembly sequenes. We first desribe tis algoritm before introduing two imortant extensions tat allow our system to take into aount art ieraries and andle ommon lasses of interloking arts. Basi aroa Figure 5 Hierarial exlosion gra. To onstrut te exlosion gra, we use an iterative algoritm tat removes unbloked arts from te model, one at a time, and adds tem to te gra. To begin, all model arts are inserted into a set S of ative arts. At ea iteration, te system determines te set of arts P S tat are unbloked in at least one diretion by any oter ative art. For ea art P, te system omutes te minimum distane would ave to move (in one of its unbloked diretions) to esae te bounding box of te ative arts in ontat wit. Te art i P wit te minimum esae distane is added to te gra. An edge is added from every ative art tat toues i, and te diretion used to omute te minimum esae distane is stored as te exlosion diretion for i. Finally, i is removed from S. Te algoritm terminates wen no unbloked arts an be removed from S. Using art ieraries If te model as a art ierary, our system omutes a nested olletion of exlosion gras, as sown in Figure 5. Tis aroa enables sub-assemblies at any level of te art ierary to exand and ollase indeendently. For ea sub-assembly A, te system omutes an exlosion gra by treating all of te diret ildren of A in te art ierary (wi may temselves be sub-assemblies) as atomi arts and ten alying te algoritm desribed above. Handling interloked arts In some ases, te arts in te ative set may be interloked su tat no unbloked art an be removed. Here, we desribe ow our system andles two ommon lasses of interloking arts. Slitting sub-assemblies Wen omuting te exlosion gra for a ierarial inut model, te ative set may ontain interloked sub-assemblies. In Sub-assembly A (a) Interloked (b) Slit Partial sub-assembly Figure 6 Slitting sub-assembly A. su ases, te system attemts to slit interloked sub-assemblies into smaller olletions of arts (see Figure 6). Given an interloked sub-assembly A, te system omutes te largest artial sub-assembly (i.e., subset of arts in A) tat an be searated from te remaining ative arts and ten removes tis artial sub-assembly from te set of ative arts. If tere is more tan one interloked sub-assembly, te system omutes te largest removable artial sub-assembly for ea one. Amongst tese omuted artial sub-assemblies, te smallest one is removed from te set of ative arts.
Slitting ontainers If any of te interloked arts is an atomi ontainer art wose only blokers are ontained arts, te system slits te ontainer into two segments tat are ten removed from te set of ative arts, as sown in Figure 7. To slit a ontainer, te system selets one of te andidate exlosion diretions and ten slits into two segments 1 and 2 wit a utting lane tat asses troug te bounding box entre of and wose normal is arallel to te osen exlosion diretion. Te exlosion diretion is determined in a view-deendent manner. Te system exlodes te set of ontained arts P and ten, for ea Slitting diretion Container (a) Interloked Segment 1 Cutting lane Cutting lane Segment 2 (b) Slit Figure 7 Slitting ontainer. andidate diretion, measures ow far 1 and 2 would ave to searate in order to omletely disolude and esae te 3D bounding box of P (see Figure 7b). In aordane wit te utting onventions desribed in Setion 3.2, te ontainer is slit in te diretion tat requires te smallest searation distane. If some of te arts in P are temselves ontainers, te system emasizes teir onentri ontainment relationsis by onsidering only exlosion diretions were te bounding boxes of te nested ontainers remain inside te exloded bounding box of. If none of te slitting diretions satisfy tis onstraint, te system ooses te slitting diretion tat auses te smallest total volume of nested ontainer bounding boxes to extend beyond te exloded bounding box of. 4.3 Preomutation Sine te viewing diretion an influene ow ontainer arts are slit, exlosion gras may be view-deendent. Reomuting tese data strutures on te fly as te viewoint anges an ause some lag in te viewing interfae. Instead, our system reomutes exlosion gras from te 26 viewoints tat orresond to te faes, edges and orners of an axis-aligned ube tat is entered at te model s bounding box enter and is large enoug to ensure tat te entire model is visible from ea viewoint. At viewing time, te system automatially swites to te reomuted exlosion gra losest to te urrent viewoint. 5 Viewing interative exloded views One te exlosion gra is omuted, te model an be exlored in our viewing interfae, wi rovides bot diret ontrols and iger-level interation modes to el users find arts of interest and exlore seifi ortions of te model. 5.1 Animated exand/ollase Our system allows te user to exand or ollase te entire exloded view wit a single lik. Ea art is animated to its fully exloded or ollased osition by udating its urrent offset. To ensure tat arts do not violate bloking onstraints during te animation, te system exands arts in reverse toologial order (i.e., outermost to innermost) wit reset to te exlosion gra. In oter words, te desendants of ea art are exanded before te art itself. For ierarial models, iger-level (i.e., larger) subassemblies are exanded before lower-level sub-assemblies. Te system ollases arts in te oosite order. 5.2 Diret maniulation Te system also suorts te diret maniulation of arts. As te user drags a art, te system slides along its exlosion diretion and udates te urrent offset of. If te user drags ast its fully exloded or ollased osition, te system roagates te offset troug te exlosion anestors of until it enounters a art wit a different exlosion diretion. Proagating offsets in tis manner allows te user to exand or ollase an entire olletion of arts, just by dragging a single art. Tis tye of onstrained diret maniulation for exloded views was introdued in te image-based system of Li et al. [2004]. However, tat aroa does not automatially omute and enfore bloking onstraints. In our system, bloking onstraints are maintained in real time during diret maniulation. As te user drags art, te system eks for bloking arts amongst te desendants of in te exlosion gra and stos from moving if su arts are found. A single lik auses te bloking arts to move out of te way, wi allows te user to ontinue dragging. 5.3 Riffling Te viewing interfae also rovides a riffling mode, in wi arts are exloded away from adjaent ortions of te model as te user overs over tem wit te mouse. Wen te mouse moves away, te art tat was beneat te mouse returns to its initial osition. If te user liks, te seleted art remains searated as te mouse moves away. Altoug similar in feel to existing 3D fiseye viewing teniques [LaMar et al. 2001; Sonnet et al. 2004], our riffling interation restrits satial distortions to te omuted exlosion diretions. By riffling troug te model, te user an quikly isolate arts or sub-assemblies and see ow various ortions of te model an exand witout atually dragging on a art. 5.4 Automatially exosing target arts In addition to te diret ontrols desribed above, te viewing system rovides a ig-level interfae for generating exloded views tat exose user-seleted target arts. Te user just ooses te targets from a list of arts and te system automatially generates a labeled exloded view illustration. Parts are smootly animated to teir new ositions to el te user see wi ortions of te model ave been exanded and ollased. Te text labels are arranged using te aroa desribed by Ali et al. [2005]. We desribe two different teniques for generating illustrations. By default, te system exands seifi ortions of te model to exose te target arts. If te model as been instrumented for utaways (as desribed by Li et al. [2007]), te system an also generate illustrations tat ombine exlosions wit ontextual utaways. Exosing target arts wit exlosions For non-ierarial models, te algoritm works as follows. Given a set of target arts T, te system visits ea art in toologial order wit reset to te exlosion gra and moves if neessary to ensure tat no visited target art is oluded by any oter visited art. Tat is, is moved to meet te following two onditions: 1. does not olude any reviously visited target arts. 2. if T, is not oluded by any visited art. To visually isolate target arts from surrounding arts, te algoritm moves to meet two additional onditions tat ensure ea target is searated from its touing arts, even if tose touing arts do not atually olude te target: 3. is not oluded by any visited target art tat toues. 4. if T, does not olude any visited art tat toues.
Visibility frustum for target art Target art Sub-assembly A Target art Visibility frustum for target art Iteration 1: move arts witin sub-assembly A Condition 1 Condition 2 Condition 3 Condition 4 Figure 8 Conditions for moving art. For ea ondition, te target art is outlined in red. Te orange visibility frusta sow ow unwanted olusions ave been eliminated in ea ase. Condition 1: Condition 2: Condition 3: Condition 4: To move satisfy s.t. does tese not onditions, move s.t. is te not systemove erforms s.t. is not te relevant move s.t. olusion tests and if neessary, moves tat tetoues minimum distane tat toues along does not olude visited target oluded by visited art oluded by visited target olude visited art its exlosion diretion su tat all unwanted olusions are eliminated (see Figure 8). To suessfully eliminate unwanted olusions, te exlosion diretion of must not be exatly arallel to te viewing diretion. If it is arallel, te system informs te user tat one of te targets annot be exosed from tis viewoint; in ratie, su failure ases rarely arise. If is moved, its exlosion gra desendants are also moved out of te way so tat no bloking onstraints are violated. Sine te osition of a art only deends on te ositions of its exlosion gra anestors, visited targets are guaranteed to remain visible wit reset to visited arts after ea art is roessed. Tus, one every art as been roessed, te resulting exloded view will ave no oluded targets. For ierarial models, te algoritm starts by roessing te igest level sub-assembly in te art ierary. Atomi arts and sub-assemblies tat do not ontain any target arts are roessed as desribed above to eliminate target olusions. However, wen te algoritm enounters a sub-assembly A tat ontains one or more target arts, te algoritm reursively roesses te arts witin A to exose tese targets. One tis reursive roedure returns, te system eks weter A (in its new onfiguration) violates bloking onstraints wit reset to any visited arts or oludes any visited targets not ontained in A. If so, te algoritm iteratively inreases te urrent offset of A and ten reeats te reursive omutation for A until no bloking onstraints are violated and all visited targets are visible (see Figure 9). At ea iteration, te urrent offset of A is inreased by one erent of te bounding box diagonal for te entire model. Te exloded views sown in Figures 1, 10a, and 10b were generated using tis algoritm. Exosing target sub-assemblies wit utaways and exlosions If te inut model is instrumented for utaways and te user selets an entire sub-assembly A as a target, te system first generates a utaway view tat exoses A in ontext and ten exlodes A away from te rest of te model troug te utaway ole. Finally, te system exlodes A itself to exose its onstituent arts (see Figure 11). To generate te utaway, te system first ooses an exlosion diretion for A. Given te viewing diretion v, te system ooses te exlosion diretion d tat allows A to esae te model s bounding box as quikly as ossible and satisfies te onstraint d v < 0. Using te metod of Li et al. [2007], te system reates a utaway tat is large enoug to allow A to exlode away from te rest of te model in diretion d. 6 Results We ave used our system to generate exloded views of several 3D models, as sown in Figures 1, 10, 11, 12, and 13. Te ipod model was downloaded from TurboSquid (www.turbosquid.om), te arm dataset is from a ommerially available model of uman anatomy reated by Zygote Media (www.zygote.om), and te rest Iteration2: move sub-assembly A Iteration 3: move arts witin sub-assembly A Figure 9 Exosing a target art witin a ierarial model. To exose te target art witin sub-assembly A, te algoritm iteratively removes target olusions witin A (iteration 1) and moves A itself to enfore bloking onstraints (iteration 2). Wen te algoritm onverges at iteration 3, te target is visible and all bloking onstraints are satisfied. of te datasets were obtained from a ubli reository for CAD models. We made a few modifiations to some of tese models before loading tem into our system. To satisfy our inut assumtions, we saled two of te transmission arts sligtly to eliminate interferenes wit adjaent arts. For te turbine, disk brake, and gri meanism examles, we omitted some of te original arts to redue te reroessing time required to omute ontat and bloking relationsis. Te ipod model was oorly segmented, so we manually groued some of te geometry into arts before loading it into our system. We reated art ieraries for te disk brake and transmission models based on te simle art grouings tat ame wit te models. For te oter CAD datasets, we reated ieraries based on te satial organization and material roerties of te arts. Te arm model as no art ierary. To generate te exloded view of te turbine sown in Figure 1, te system automatially determined ow to slit two ontainer arts: te outer sell and te exaust ousing. Te exloded views sown in Figures 1, 11, 10a, and 10b were generated automatially to exose user-seified target arts. Tese illustrations learly sow te arts of interest witout exloding unneessary ortions of te model. In addition, Figure 11 sows ow a ontextual utaway view els onvey te osition and orientation of te exloded subassembly wit reset to te rest of te model. Altoug exloded views are tyially used to illustrate manufatured objets, we also tested our system wit a musuloskeletal model of a uman arm. Sine many of te musles in te arm twist around ea oter were tey atta to bones, we manually setioned off art of te arm were te musles are less intertwined and ten used tis ortion of te dataset as te inut to our system. To emasize ow te musles are layered from te outside to te inside of te arm, we also restrited te system to use a single exlosion diretion. From tis inut, our system automatially omuted te exloded view sown in Figure 12. Table 1 reorts te number of arts and reomutation time for ea dataset. In general, omuting ontat and bloking relationsis dominates te total reomutation ost. We do not reort te ost of omuting ontainment relationsis beause ontainment tests are erformed lazily only wen te system enounters interloked arts during exlosion gra onstrution. Sine te turbine is te only dataset tat inludes ontainer arts, its exlosion gra ost inludes te time required for ontainment tests.
(a) ipod (b) Transmission () Disk brake Figure 10 Exloded views generated by our system. Te illustrations of te ipod (a) and transmission (b) were automatially generated to exose te user-seleted target arts labeled in red. Te sequene of images on te rigt sows te disk brake model exloding in stages (). Model N arts T ontat T blok T egra T total Disk brake 18 440s 195s 0.016s 635s ipod 19 215s 20s 0.016s 235s Gri meanism 20 150s 50s 0.016s 200s Arm 22 280s 40s 0.016s 320s Turbine 26 380s 200s 430s 1010s Carburetor 42 135s 45s 0.16s 180s Transmission 55 885s 835s 2.5s 1778s Table 1 Preomutation statistis. For ea model, we reort te number of arts N arts and te time (in seonds) required to omute ontats T ontat, bloking relationsis T blok, and exlosion gras T egra. Te total reomutation time T total is listed on te rigt. All timings were erformed on a MaBook Pro wit a 2.6 GHz Intel Core 2 Duo, 4GB of memory, and an nvidia GeFore 8600M GT grais ard. 7 Disussion Altoug in general our system rodues effetive exloded view diagrams for a large lass of 3D models, our aroa does ave some limitations. As mentioned earlier, te ontat, bloking, and ontainment omutations assume te inut model is two-sided and tat arts fit togeter witout interferenes. In addition, our algoritm for onstruting exlosion gras assumes tat all arts an be searated via rigid linear translations. Tus, te system is not able to searate atomi arts wit ertain omlex interloking relationsis (e.g., a srew modeled wit realisti tread geometry would ave to rotate to be removed). Altoug not all 3D models adere to tese inut assumtions, many CAD models are seifially designed to fit togeter roerly witout interferenes. Furtermore, for erformane reasons, CAD rograms tyially inlude art libraries wit stylized models of standard srews, bolts and oter fasteners tat do not ave realisti tread geometry. Figure 13 illustrates two situations in wi our aroa an generate less suessful results. Sine te bloking algoritm tat we use analyzes te normals of ontat faes to determine bloking diretions, te omutation an be sensitive to noisy or irregular surfae geometry were arts tou ea oter. For examle, in Figure 13a, te to saft exlodes sideways rater tan uwards from te to sring beause te omlexity of te sring geometry auses te system to omute te wrong bloking relationsi. Figure 13b sows a ase in wi slitting a non-ontainer art ould el larify satial relationsis. Altoug te illustration suessfully exoses te target arts, it is not obvious ow te exosed arts fit togeter witin te long ollow body. Slitting te body lengtwise Figure 11 Exloded view wit ontextual utaway. To exose te userseleted sub-assembly, te system first generates a utaway view (left) and ten exlodes te sub-assembly troug te utaway ole (rigt). and ten exloding te two alves away from ea oter would likely rovide better satial ontext for te internal arts. However, sine te arts are free to slide out of te body, te system does not onsider te body to be a ontainer art (and tus, does not inororate any uts). Finally, altoug we ave sown tat our system an generate effetive visualizations of models wit u to rougly 50 arts, tere are some allenges involved in saling our aroa to andle signifiantly more omlex models. First, exosing an internal art migt require exloding many bloking arts, wi ould result in visual lutter. We believe our aroa ould be extended wit level-ofdetail ontrols to redue te amount of lutter due to exloded arts. In addition, te ost of omuting ontat, bloking, and ontainment relationsis uts a ratial limit on te omlexity of te inut geometry. Our urrent imlementation inororates simle satial data strutures to aelerate tese omutations, but for igly omlex inut models, more effiient algoritms would likely be neessary to avoid roibitively large reomutation times. 8 Conlusions and future work In tis aer, we ave resented teniques for reating and viewing interative exloded view illustrations of 3D models omosed of many distint arts. Our ontributions inlude an automati metod for deomosing models into exlodable layers and algoritms for generating dynami exloded views tat exose user-seleted target arts. Our results demonstrate tat our aroa an be used to reate effetive interative exloded views for a variety of models.
Figure 12 Exloded view of arm. To reate tis visualization, we setioned off a ortion of te arm to exlode. Witin tis ortion, our system automatially omuted te layering relationsis between te musles. We onlude by mentioning a few areas for future work: Inferring arts to exose. Our system allows users to diretly seify target arts to exose. In some ases, sowing additional arts an rovide more ontext for te seifi arts of interest. It would be interesting to exlore teniques tat automatially infer wi additional arts to exose based on te user-seleted targets. Continuous measure of bloking. It is diffiult to detet te orret bloking relationsis for 3D models tat ontain interfering arts. One otential aroa for andling su models would be to onstrut exloded views based on some ontinuous measure of te amount of bloking between arts. Automati guidelines. Guidelines an be useful for larifying ow exloded arts fit bak togeter. Altoug some revious work [Agrawala et al. 2003] as been done on omuting guideline laement automatially, furter investigation is required to identify and imlement all of te onventions tat illustrators use to reate effetive guidelines. Aknowledgments Te autors want to tank Saron Lin for er work on te label layout omonent of te system. We also tank François Crétien, Doug Jonson, and Dave Kasik for teir feedbak on te use of CAD tenology in industry. Tis work was suorted by NSF grants CCF-0643552 and EIA-0321235, te Alfred P. Sloan Foundation, te University of Wasington Animation Resear Labs, te Wasington Resear Foundation, Adobe, Mirosoft, and Pixar. Referenes ADOBE INC. Arobat 3D. AGRAWALA, M., PHAN, D., HEISER, J., HAYMAKER, J., KLINGNER, J., HANRAHAN, P., AND TVERSKY, B. 2003. Designing effetive ste-by-ste assembly instrutions. ACM Transations on Grais 22, 3 (July), 828 837. ALI, K., HARTMANN, K., AND STROTHOTTE, T. 2005. Label layout for interative 3D illustrations. In WCSG Journal, 1 8. BRUCKNER, S., AND GROLLER, M. 2006. Exloded views for volume data. IEEE Transations on Visualization and Comuter Grais 12, 5 (Set./Ot.), 1077 1084. CARPENDALE, M. S. T., COWPERTHWAITE, D. J., AND FRAC- CHIA, F. D. 1997. Extending distortion viewing from 2D to (a) Carburetor (b) Gri meanism Figure 13 Less suessful results. Due to te omlexity of te sring geometry, te system omutes te wrong bloking relationsi for te to saft in te arburetor model (a). In te exloded view of te gri meanism (b), it may be ard for te viewer to understand ow te igligted target arts fit togeter inside of te long ollow body. 3D. IEEE Comuter Grais and Aliations: Seial Issue on Information Visualization 17, 4, 42 51. CORREA, C., SILVER, D., AND CHEN, M. 2006. Feature aligned volume maniulation for illustration and visualization. IEEE Transations on Visualization and Comuter Grais 12, 5 (Set./Ot.), 1069 1076. DENNISON, J. A., AND JOHNSON, C. D. 2003. Tenial Illustration: Teniques and Aliations. Goodeart-Wilox. DRISKILL, E., AND COHEN, E. 1995. Interative design, analysis and illustration of assemblies. In Proeedings of te Symosium on Interative 3D Grais. HOYT, W. A. 1981. Comlete Car Care Manual. Reader s Digest. LAMAR, E., HAMANN, B., AND JOY, K. I. 2001. A magnifiation lens for interative volume visualization. In 9t Paifi Conferene on Comuter Grais and Aliations, 223 232. LI, W., AGRAWALA, M., AND SALESIN, D. H. 2004. Interative image-based exloded view diagrams. In Proeedings of Grais Interfae 04. LI, W., RITTER, L., AGRAWALA, M., CURLESS, B., AND SALESIN, D. 2007. Interative utaway illustrations of omlex 3D models. ACM Transations on Grais 26, 3 (July), 31:1 31:11. MCGUFFIN, M. J., TANCAU, L., AND BALAKRISHNAN, R. 2003. Using deformations for browsing volumetri data. In Proeedings of IEEE Visualization 2003, 401 408. PLATT, R., AND BIESTY, S. Exlosions. DK Cildren. 1996. Steen Biesty s Inredible RAAB, A., AND RÜGER, M. 1996. 3D-ZOOM: interative visualization of strutures and relations in omlex grais. In 3D image analysis and syntesis, 87 93. RIST, R., KRÜGER, A., SCHNEIDER, G., AND ZIMMERMANN, D. 1994. AWI: A workben for semi-automated illustration design. In Proeedings of Advaned Visual Interfaes 94. SONNET, H., CARPENDALE, S., AND STROTHOTTE, T. 2004. Integrating exanding annotations wit a 3D exlosion robe. In Proeedings of ACM AVI 2004, 63 70. WANG, L., ZHAO, Y., MUELLER, K., AND KAUFMAN, A. E. 2005. Te magi volume lens: An interative fous+ontext tenique for volume rendering. In Proeedings of IEEE Visualization 2005, 367 374.