4 An Incremental Strategy for the Fast Transmission of Multi-Resolution 63 façade elements. Three different kinds of structures can be identified, for which appropriate reduction methods are defined: extrusion or intrusion, offset, and cor- ner (see Fig. 4.5). Fig. 4.5. Elimination of short facade S n : offset (a), intrusion/extrusion (b) and corner (c) (based on Sester et al., 2004b) These operators are interesting in a client-server context with limited resources by reducing the amount of transferred data. Generalised dataset can be sent before a more detailed one. Furthermore such operators guarantee the “sharing of geome- tries” which is essential in an incremental strategy. Consequences on incremental transitions between different levels of detail If we observe results of these operators on different representations of regions and polylines, we can deduce the different changes to perform on an object in order to rebuild its more generalised or detailed representation. Case of simplified polylines: In consequence of the simplification process, eliminated points need to be inserted in the generalised representation of the poly- line in a refinement transition and must be removed from the most detailed one during a generalisation transformation. In this last case a choice must be done be- tween conservation of shared points or removal of details. Moreover, vertices can be moved between different LoDs, for example in order to respect the topological relations with neighboring objects: coordinates of these points must be changed during a refinement or generalisation transition. Case of simplified regions: In generalisation transition, vertices can be either kept (for the common points), removed (for the details), or moved (for preserving parallelism and rectangularity properties of building). In refinement transition, vertices can be either moved or introduced (for adding details). These generalisation operators are expected to be performed on the server side and followed by a process of increment creation. A formalism has been defined in order to consider different object resolutions and transformations between them. 64 Jean-Michel FOLLIN, Alain BOUJU 4.3 MR data and MR data transfer models 4.3.1 Data model A multiresolution data model adapted to limitations of mobile context has been defined in Follin, et al. (2005b). The data organization is based on the traditional definition of a geographic map: objects are grouped into layers and a sequence (or overlay) of layers forms a map (Tomlinson, 1967). As representations of objects vary according to the level of detail, we consider different LoD objects grouped into different LoD layers. Increments allow navigation through these different LoD objects and in this way reuse of available LoD representations on the client- side. In order to reduce volume of data transferred from server to client, incre- ments are sent if their size is less important than the size of LoD objects. Layer and object A layer, noted l, is a collection of objects associated with a description of their at- tributes. Each layer corresponds to a specific theme (e.g. transportation network or buildings) that can be decomposed in different LoD layers. A map is defined as a succession of thematic layers which aims to be manipulated and visualized at a specific scale (Follin, et al. 2005b). An object entity is defined by the quadruplet ),,,( J gto where: x o: unique identifier, x t: last time of modification (timestamp value), x g: location and geometrical description (modelled by one among six two-dimensional geographical objects of spatial domain G : Point, Polyline or Region for simple objects, and MultiPoint, MultiPolyline and MultiRegion for collections of objects), x J: alphanumeric values n J J J J ,,, 21  accessed through the set of object’s attributes n aaa ,,, 21  (for instance, the name of a street). LoD layer and LoD object LoD layers of a layer l correspond to the definitions of l’s objects in the scale ranges where they exist. A layer l can be seen as a serie of n LoD layers. LoD ob- jects included in LoD layers can be matched (i.e. linked) between the two or more consecutive levels where they are represented. The matching configuration corre- sponds to the number of matched LoD representations of the same real world enti- ties (when objects are represented at two different LoDs). Three different matching cases are distinguished in Ai et al. (2001): 1:1, 1:n and n:m matching case. In our works only the 1:1 and 1:0 matching cases have been considered, i.e. the cases where 1 LoD representation of an object is mapped to 1 4 An Incremental Strategy for the Fast Transmission of Multi-Resolution 65 representation of the same object at a different and consecutive LoD or where it is not linked to other object (because it has been deleted between the two LoDs). Only these matching configurations are studied because use of incremental opera- tors seems only relevant for these cases: more complex matching configurations should involve more complex increments which are less interesting. The linking is based on identifier o of the object’s different representations. Some solutions to match objects with various link cardinalities have been studied in Hampe et al. (2003). A LoD representation or LoD object is an object o version defined for a level i in adequacy with a scale interval. It will be noted i o . The below described concept of increment is applied to polylines but can also be valid for regions. Indeed a region can be defined as a closed polyline: its boundary. A polyline noted P is defined as a sequence of vertices ^` n VV ,, 1  such that each couple  11 , i VV defines a segment >@ 11 , i VV . As we deal with multiple representations of same polylines, we use the following definition: a vertex j i V is a vertex V at index i of a polyline P j . For example, we consider two LoDs of a polyline in Fig. 4.6: a detailed and a simplified one. We can notice that vertices of P n with indexes 1 and 4, i.e. n V 1 and n V 4 have the same coordinates that vertices of P n+1 with indexes 1 and 2, i.e. 1 1 n V and 1 2 n V . We define the vertices which have the same coordinates, i.e. are matched, in the two LoD representations P n and P n+1 as shared (or matched) vertices. The set of matched vertices is used during the creation of increment and recon- struction of the polyline. Increment An increment allows performing changes on LoD object o n in order to rebuild its representation o n-1 or o n+1 . An increment point corresponds to a couple   j ii Vop , where a geometrical op- erator op i is combined with a manipulated vertex j i V . An increment is defined as an ordered list of increment points. The increment allowing transition from o n to o n+1 (resp. o n-1 ) will be noted   1nnoInc n o, (resp.   1nnoInc n o, ). 66 Jean-Michel FOLLIN, Alain BOUJU Fig. 4.6. Vertices of two LoD representations of a same polyline Four geometrical operators are considered: x insert: puts a vertex V which is only present in the most detailed polyline P n-1 at the index i of the less detailed one P n during a transition from LoD n to LoD n - 1 (noted 1nn o ). It manipulates the index and coordinates of a vertex. x keep: keeps a vertex V n shared by P n and P n+1 at index i of P n , x remove: removes a vertex V n only present at index i of P n , x move: changes the coordinates of a vertex V in a polyline P n . It manipulates index and coordinates shifts of a vertex for a given transition 1nn o or 1nn o . Geometrical operators keep and remove are used during a generalisation transition 1nn o and manipulate only the vertex index. The first one is used if vertices to keep are fewer than vertices to remove, and the second one if the number of vertices to keep is more important than those of vertices to remove (cf. sec- tion 4.4.3). We use the following notations: x insert Q for the domain of inserted vertices defined as couples   1 , n i Vinsert , x keep Q for those of kept vertices defined as couples   n i Vkeep, , x remove Q for those of removed vertices defined as couples   n i Vremove, , x and move Q for those of moved vertices defined as couples   n i Vmove, . The domain of increments points is noted inc Q , such that: 4 An Incremental Strategy for the Fast Transmission of Multi-Resolution 67 ^ ` moveremovekeepinsertinc Q Q Q Q Q ,,, For a transition nm o of an object o the expression of an increment is:        ^ ` lod ck lod bi lod a VopVopVoponmoInc ,,,,,,,, 1  o where lod=m or lod=n (manipulated vertex can belong either to o m or to o n ) and a < b < c. Refinement increments  1nnoInc o, are constituted of increments points from insert Q and move Q , and generalisation increments  1nnoInc o, are composed of vertices from keep Q , remove Q and move Q . Each increment point   j ii Vop , has an encoding cost (or size) i op C represent- ing the number of bytes used to encode a vertex and an operation. This cost de- pends on the vertex part manipulated by the geometrical operator (index only or both index and coordinates). The total encoding cost C Inc of an increment corre- sponds to the sum of costs of all its increment points. Thus it is an indicator of the time it will take to transfer the increment from a server to the client: ¦ k i opInc i CC 1 In certain situations, representation of an object is not modified between two LoD: for example, if DP algorithm is applied with a low tolerance value. Set of couples   ^ ` j ii Vop , is then replaced with an operator nop for these identical ob- jects called id O . nop operator is used for marking object o that must be kept without modifications. An increment ^` nopo, with id Oo  is used only during a generalisation transition because all objects of destination set (the more general- ised one) come from the origine set (the more detailed one). This is a consequence of the selection/elimination process (cf. section 4.2.3). Examples of increments The generalisation and refinement increments of the cases illustrated in Fig. 4.7 correspond to the following sequences: In the case A (where the number of shared vertices is greater than the number of inserted ones):      ^ ` 1 3 1 2 ,,,21, VremoveVmovePInc o      ^ ` 1 3 2 2 ,,,12, VinsertVmovePInc o In the case B (where there are more inserted vertices than shared ones):      ^ ` 1 2 1 1 ,,,21, VmoveVkeepPInc o        ^ ` 1 4 1 3 2 2 ,,,,,12, VinsertVinsertVmovePInc o 68 Jean-Michel FOLLIN, Alain BOUJU Increments act in a similar manner as EGO’s defined in Sester et al. (2004b). But geometrical operators are used in order to reduce the amount of exchanged data by reusing LoD representations of objects available in client’s cache and not to achieve a continuous generalisation like the EGO’s. Furthermore in our case, the process of increment creation is independent of the generalisation. In this way, increments can be computed from data coming from different sources. The above described different concepts are used during client-server transfer of data. Fig. 4.7. Different configurations of polylines’ LoD representations in 1-dimensional space 4.3.2 Transfer and management principles Types of multi-resolution data Different types of data implied in an embedded navigation application for visual- izing MR data have been distinguished in Follin et al. (2005a). We have consid- ered the real-time navigation of a mobile user across two LoD representations of a same thematic layer where the user requests are based on both its location and the zoom level. Only data relevant to it location are downloaded. Three types of requested data have been identified depending on locally avail- able LoD data: x already available dataset that can be reused from the same level of detail, x dataset that can only be reused from the previous level of detail, called useful objects util O , x dataset that is unavailable on the client for all LoD layers and needs to be re- trieved from the server. It can be either objects omitted during generalisation process (in the case of a refinement transition), or newly displayed objects (in all cases). Transfer models In Stockus et al. (2001), three schemes of data transfer between client and server have been defined in order to reduce the volume of exchanged data: 1. The simple communication mode where, upon a query of the client, the server will compute and send the complete answer. 4 An Incremental Strategy for the Fast Transmission of Multi-Resolution 69 2. The two-step communication schema where all queries are still executed on the server but the client maintains data cache and can reuse already received objects ; 3. The pre-computed answer mode where the client can execute some queries locally without connection to the server. In Follin et al. (2005a) we have proposed a general transfer model of MR data based on the communication with a pre-computed answer. MR data transfer is per- formed in order to reuse data already locally available at a LoD different from re- quested one. Thus, local processing of LoD objects can be made as answer to a client request of transition between a LoD m to a LoD n representation (zoom in or out), i.e. from a source layer to a destination one. It can also be made each time that required data are covered by data available at a different LoD (during a pan operation or as a consequence of the user’s displacement). This data transfer model is decomposed in four steps: 1. Local computing of the identifiers of objects reusable at the destination and source layers, 2. Sending of a request to the server including identifiers of the destination and source layers, completed by two sets of identifiers: objects available at que- ried level n and objects m util O exclusively available at source level m, 3. Sending by the server of an answer which mainly includes (if there is no data update) missing objects at both LoDs and increments set   nmOInc m util o, allowing reuse of objects m util O only available in level m and required for level n, 4. Rebuilding of missing LoD n objects from same objects m util O available at level m and   nmOInc m util o, . Comparison between mono-resolution and multi-resolution strategy This transfer strategy can be called multi-resolution strategy because it is based on incremental reconstruction of data: not only available object at level n but also useful objects of level m (i.e. data only available in l m and reusable for l n ) are con- sidered on the client side. This strategy can be compared with a mono-resolution one for which only objects available at required level n are taken into account. Ef- ficiency of our model for reducing the amount of transferred data can be evaluated with such a comparison (section 4.5.4). 70 Jean-Michel FOLLIN, Alain BOUJU 4.4 Incremental strategy: conditions and interest 4.4.1 Discussion about increment creation and reconstruction Two types of functions are distinguished in incremental strategy: those for cre- ating increments from two LoD representations of the same object and those for reconstructing the LoD representation of an object from another LoD of the same object and the corresponding increment. The first are performed on the server side and the second on the client side. More details on formal functions and algorithms are given in Follin et al. (2005b). The reconstruction algorithms present a linear complexity because only one browsing of increment is necessary for reconstructing a polyline. So it can be per- formed rapidly on the client side where computing resources are limited. By con- sequent, it will be supposed that the gain in transmission remains interesting in spite of the client side process of increment reconstruction. 4.4.2 Required conditions If LoD n objects set O n is required on the client-side then transfer from the server and use of an increment set   nmOInc m o, rather than transfer of O n depends on the following conditions described in Follin et al. (2005b): x existence of a set app O of objects matched between O m and O n , x for each matched object of app O , existence of a set of shared vertices, x ratio on the sizes of the different LoD representations geometries (more detailed object must contain more vertices than more generalised one) x from the transfer point of view, a significant reduction of the size of   nmOInc m o, compared with the size of O n . The first three conditions are “structural”: data have to verify them. The fourth one is linked to the modeling and encoding of increments and objects. By comput- ing the costs C Inc of increments, we can consider the cases where transfer and use of an increment is more interesting than transfer of the corresponding LoD object. 4.4.3 Cost of increments and efficient objects The theoretic costs of different increments points can be established by taking into consideration a specific encoding of data used by different geometrical operators. We consider sizes of Java primitive types to evaluate the cases where it is more in- teresting to use increment rather than “entire” objects: 4 An Incremental Strategy for the Fast Transmission of Multi-Resolution 71 x Each couple of coordinates (x, y) are encoded by two double on 2 u 8 bytes, x Each index i is encoded by an integer on 4 bytes Geometrical operators can work with the same vertices parts: move and insert use both coordinates and index, keep and remove use an index. In order to deter- mine the operator to apply, from the implementation point of view, a variable op encoded by one byte is used. This encoding is not “perfect” but can be considered as a way to implement our concepts in a simple data structure and to measure its efficiency. In addition to increment points of inc Q we can define the “entire” vertices of Q : they correspond to couples   n i Vdownload , where operator download ma- nipulates coordinates x and y of each vertex V composing an object o n . This opera- tor is used to measure efficiency of multi-resolution strategy in comparison with a mono-resolution one (Fig. 4.8). From the transfer point of view, we can measure interest of downloading in- crements points rather than LoD representation by taking into account proportion between different categories of points. We consider two LoD polylines P 1 and P 2 : vertices composing them can be inserted, shared or moved. Vertices’ numbers of polylines P 2 and P 1 are respectively noted S2 and S1: o P 2 is composed of n shared shared vertices and n moved moved ones: S2 = n shared + n moved , o P 1 is composed of n shared shared vertices, n moved moved ones, and n in- serted inserted ones: S1 = n shared + n moved + n inserted . These notations of points numbers are used in association with cost notations in order to evaluate interest of our strategy during a generalisation transition, and during a refinement one. Increments points Cost notation Cost (used data) Cost (estimated in bytes) insert Q insert C opiy x ,,, 21 move Q move C opiyx ,,, '' 21 keep Q keep C opi, 5 remove Q remove C opi, 5 Q (“entire” vertex) dwnld C y x , 16 Fig. 4.8. Costs of operators used in transformation between different LoD representations of a polyline For a generalisation transition from P 1 to P 2 (i.e. for decreasing resolution) two strategies are possible: 72 Jean-Michel FOLLIN, Alain BOUJU x Download and use increments points V keep of keep Q or V remove of remove Q (con- servation of shared vertices or removal of additional ones) and of V move of move Q (displacement) in order to reuse P 1 . x Download S2 vertices from Q of P 2 . Keep operator is used if number of additional vertices is greater than those of shared ones, i.e. if n inserted > n shared . At the opposite, remove operator is more inter- esting if n shared > n inserted . Furthermore cost of different incremental operations must be smaller than those of downloading “entire” vertices. If n shared < n inserted , the following equation needs to be respected:  sharedkeepmovedmovemovedshareddwnld nCnCnnC ! It means we must have the following proportion between the polyline’s vertices: 2,2 u n shared < n moved If n inserted < n shared , the following equation needs to be solved:  insertedremovemovedmovemovedshareddwnld nCnCnnC ! It means that we must observe the following repartition of the polyline’s vertices: 3,2 u n shared < n moved + n inserted For a refinement transition from P 2 to P 1 (i.e. for increasing resolution) two strategies are considered: x Download and use increments points V insert of insert Q and V move of move Q in or- der to reuse P 2 . x Download S1 vertices V of P 1 . Incremental operations of insertion and displacement are more interesting if their global cost    movedmoveinsertedinsert nCnC  is smaller than those of downloading polyline P 1 , that is noted  insertedmovedshareddwnld nnnC   . It im- plies the respect of the same repartition between polyline’s vertices than in the case of generalisation transition with suppression (when n inserted < n shared ), i.e. 3,2 u n shared < n moved + n inserted These equations are used during increment creation on the server side: incre- ments are only computed for objects for which points proportions between n shared , n moved and n inserted respect the conditions of efficiency given by them. These objects are noted eff O . Increment sets are computed between two datasets at consecutive levels of detail in a generalisation direction and in a refinement one. They are stored on the server side, recomputed if data are updated and transferred to a client for reusing data available in its cache. The reconstruction is finally performed on the client side to create the instances of objects by reusing the available LoD representations. [...]... Computers & Geosciences 31 , pp 179– 188 Follin, J.-M., Bouju, A., Bertrand, F and A Stockus (2005): An Increment Based Model for Multi-resolution Geodata Management in a Mobile System Proceedings of the 5th International Workshop W2GIS 2005, Lausanne (Switzerland), December 15-16, Lecture Notes in Computer Science, Vol 38 33, Springler Verlag, pp.42- 53 Hampe, M., Anders, K.-H and M Sester (20 03) : MRDB applications... Cecconi, A and Galanda, M (2002): Adaptive Zooming in Web Cartography Proceedings of SVG Open 2002 Zurich (Switzerland), pp 78- 83 Cecconi, A (20 03) : Integration of cartographic generalization and multi-scale databases for enhanced web mapping PhD Thesis, University of Zurich Follin, J.M., A Bouju, Bertrand, F and P Boursier, (2005): Multi-resolution extension for transmission of geodata in a mobile context... (Switzerland), December 15-16, Lecture Notes in Computer Science, Vol 38 33, , Springler Verlag, pp.54-65 5 Evaluating the Effectiveness of Non-Realistic 3D Maps for Navigation with Mobile Devices Malisa Ana PLESA, William CARTWRIGHT School of Mathematical and Geospatial Science, RMIT University, Melbourne, Victoria, Australia Abstract Small mobile computer platforms are being employed to deliver maps and. .. di Genova Bertolotto, M and Egenhofer, M J (2001): Progressive transmission of vector map data over the World Wild Web GeoInformatica, Vol 5, No 4, pp 34 5 -37 3 78 Jean-Michel FOLLIN, Alain BOUJU Brenner, C and M Sester (20 03) : Continuous Generalization for Small Mobile Displays International Conference on Next Generation Geospatial Information, Boston (USA), October 19-21, 20 03 Buttenfield, B (2002):... cartography has employed 3D and provides historical and contemporary examples to illustrate this section The focus then moves to mobile maps and the design considerations for maps on small, mobile devices The next section outlines the concept of expressive city models for small-screen delivery It then outlines a research project 5 Evaluating the Effectiveness of Non-Realistic 3D Maps for Navigation 81... part of the landscape character, and can serve for identification purposes This instigates partiality towards 3D representations of urban areas, despite the difficulties involved in their production (Keates, 1989) There has also been some evidence suggesting that users are able to recognise landmarks and find route easier with a 3D model rather than a symbolic 2D map (Kray et al., 20 03) 5 Evaluating... features exaggerated street widths, and is presented in an isometric projection to conserve visibility and scale These maps are functional, providing an adequate amount of information to be used for many purposes 88 Malisa Ana PLESA, William CARTWRIGHT Fig 5.4 The original London Underground map (right) compared to Beck’s 1 933 map (Source: Black, 20 03, p. 134 -5) 5.4 Mobile maps The computer revolution... usefulness (Graham et al., 20 03) Field trials and usability studies have identified advantages associated with the use of 3D graphics for navigation in urban areas (Rakkolainen and Vainio, 2001) To date, three-dimensional maps on small screens have also tended towards realistic representations High-quality 3D maps on small devices face similar inconveniences relating to time and cost as those witnessed... real-world situations The use of mobile devices for navigation is becoming increasingly popular, and it brings with it an interest in the portrayal of 3D spatial information Current research has focused on realistic representations (Rakkolainen and Vainio, 2001; Vainio et al., 2002; Kray et al., 20 03) , with little interest in alternative methods of display If Döllner and Walther’s (20 03) technique is to become... university students and rated their map reading, computer, and handheld device skills as average to good It was deemed important to include individuals possessing the above criteria as the map design was of utmost interest to this study, rather than the individuals’ proficiency with map-related products and interacting with technology Participants were aged between 18 and 25 years, with 3 females and 7 males . Lec- ture Notes in Computer Science, Vol. 38 33, Springler Verlag, pp.42- 53. Hampe, M., Anders, K H. and M. Sester (20 03) : MRDB applications for data revision and real-time generalisation. Proceedings. A. and Galanda, M. (2002): Adaptive Zooming in Web Cartography. Proceedings of SVG Open 2002. Zurich (Switzerland), pp. 78- 83. Cecconi, A. (20 03) : Integration of cartographic generalization and. has employed 3D and provides historical and contemporary examples to illustrate this section. The focus then moves to mobile maps and the design consid- erations for maps on small, mobile devices.