Patent Publication Number: US-8117145-B2

Title: Analytical model solver framework

Description:
BACKGROUND 
     Often, the most effective way to convey information to a human being is visually. Accordingly, millions of people work with a wide range of visual items in order to convey or receive information, and in order to collaborate. Such visual items might include, for example, concept sketches, engineering drawings, explosions of bills of materials, three-dimensional models depicting various structures such as buildings or molecular structures, training materials, illustrated installation instructions, planning diagrams, and so on. 
     More recently, these visual items are constructed electronically using, for example, Computer Aided Design (CAD) and solid modeling applications. Often these applications allow authors to attach data and constraints to the geometry. For instance, the application for constructing a bill of materials might allow for attributes such as part number and supplier to be associated with each part, the maximum angle between two components, or the like. An application that constructs an electronic version of an arena might have a tool for specifying a minimum clearance between seats, and so on. 
     Such applications have contributed enormously to the advancement of design and technology. However, any given application does have limits on the type as of information that can be visually conveyed, how that information is visually conveyed, or the scope of data and behavior that can be attributed to the various visual representations. If the application is to be modified to go beyond these limits, a new application would typically be authored by a computer programmer which expands the capabilities of the application, or provides an entirely new application. Also, there are limits to how much a user (other than the actual author of the model) can manipulate the model to test various scenarios. 
     BRIEF SUMMARY 
     Embodiments described herein relate to a solver framework for use with an analytical model. The analytical model includes multiple model parameters and includes definitions for analytical relationships between the model parameters. In one example, the analytical model is used to drive a view construction. 
     The solver framework coordinates the processing of multiple specialized solvers. In particular, the solver framework identifies which model parameters are known and which are unknown. The solver framework then analyzes dependencies to determine a solve order of the unknown model parameters. The specialized solvers are then charged with performing portions of the solve operation such that the specialized solvers solve for the unknown model parameters in an order which considers the dependencies. 
     In one embodiment, additional or replacement solvers may register with the solver framework to thereby make the specialized solver available for solving for unknown model parameters in the future. Accordingly, solvers that are appropriate for the particular analytical model being solved for may be designed and incorporated into the overall solver framework. This allows the solver framework to be compatible with a wide variety of analytical models since there is flexibility on the solvers used. 
     In one embodiment, the model parameters are provided to a view construction module that includes parameterized view components. The model as parameter values are then bound to the parameters of the view components. The view components may each then be executed using the provided parameter values to thereby cause a custom view composition to be formed. 
     This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In order to describe the manner in which the above-recited and other advantages and features can be obtained, a more particular description of various embodiments will be rendered by reference to the appended drawings. Understanding that these drawings depict only sample embodiments and are not therefore to be considered to be limiting of the scope of the invention, the embodiments will be described and explained with additional specificity and detail through the use of the accompanying drawings in which: 
         FIG. 1  illustrates an environment in which the principles of the present invention may be employed including a data-driven composition framework that constructs a view composition that depends on input data; 
         FIG. 2  illustrates a pipeline environment that represents one example of the environment of  FIG. 1 ; 
         FIG. 3  schematically illustrates an embodiment of the data portion of the pipeline of  FIG. 2 ; 
         FIG. 4  schematically illustrates an embodiment of the analytics portion of the pipeline of  FIG. 2 ; 
         FIG. 5  schematically illustrates an embodiment of the view portion of the pipeline of  FIG. 2 ; 
         FIG. 6  illustrates a rendering of a view composition that may be as constructed by the pipeline of  FIG. 2 ; 
         FIG. 7  illustrates a flowchart of a method for generating a view composition using the pipeline environment of  FIG. 2 ; 
         FIG. 8  illustrates a flowchart of a method for regenerating a view composition in response to user interaction with the view composition using the pipeline environment of  FIG. 2 ; 
         FIG. 9  schematically illustrates the solver of the analytics portion of  FIG. 4  in further detail including a collection of specialized solvers; 
         FIG. 10  illustrates a flowchart of the solver of  FIG. 9  solving for unknown model parameters by coordinating the actions of a collection of specialized solvers; 
         FIG. 11  illustrates a rendering of an integrated view composition that extends the example of  FIG. 6 ; 
         FIG. 12  illustrates a visualization of a shelf layout and represents just one of countless applications that the principles described herein may apply to; 
         FIG. 13  illustrates a visualization of an urban plan that the principles described herein may also apply to; 
         FIG. 14  illustrates a conventional visualization comparing children&#39;s education, that the principles of the present invention may apply to thereby creating a more dynamic learning environment; 
         FIG. 15  illustrates a conventional visualization comparing population density, that the principles of the present invention may apply to thereby creating a more dynamic learning environment; and 
         FIG. 16  illustrates a computing system that represents an environment in which the composition framework of  FIG. 1  (or portions thereof) may be implemented. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  illustrates a visual composition environment  100  that may be used to construct an interactive visual composition. The construction of the interactive visual composition is performed using data-driven analytics and visualization of the analytical results. The environment  100  includes a composition framework  110  that performs logic that is performed independent of the problem-domain of the view composition  130 . For instance, the same composition framework  110  may be used to compose interactive view compositions for city plans, molecular models, grocery shelf layouts, machine performance or assembly analysis, or other domain-specific renderings. 
     The composition framework  110  uses domain-specific data  120 , however, to construct the actual visual composition  130  that is specific to the domain. Accordingly, the same composition framework  110  may be used to construct view compositions for any number of different domains by changing the domain-specific data  120 , rather than having to recode the composition framework  110  itself. Thus, the composition framework  110  of the pipeline  100  may apply to a potentially unlimited number of problem domains, or at least to a wide variety of problem domains, by altering data, rather than recoding and recompiling. The view composition  130  may then be supplied as instructions to an appropriate 2-D or 3-D rendering module. The architecture described herein also allows for convenient incorporation of pre-existing view composition models as building blocks to new view composition models. In one embodiment, multiple view compositions may be included in an integrated view composition to allow for easy comparison between two possible solutions to a model. 
       FIG. 2  illustrates an example architecture of the composition framework  110  in the form of a pipeline environment  200 . The pipeline environment  200  includes, amongst other things, the pipeline  201  itself. The pipeline  201  includes a data portion  210 , an analytics portion  220 , and a view portion  230 , which will each be described in detail with respect to subsequent  FIGS. 3 through 5 , respectively, and the accompanying description. For now, at a general level, the data portion  210  of the pipeline  201  may accept a variety of different types of data and presents that data in a canonical form to the analytics portion  220  of the pipeline  201 . The analytics portion  220  binds the data to various model parameters, and solves for the unknowns in the model parameters using model analytics. The various parameter values are then provided to the view portion  230 , which constructs the composite view using those values of the model parameters. 
     The pipeline environment  200  also includes an authoring component  240  that allows an author or other user of the pipeline  201  to formulate and/or select data to provide to the pipeline  201 . For instance, the authoring component  240  may be used to supply data to each of data portion  210  (represented by input data  211 ), analytics portion  220  (represented by analytics data  221 ), and view portion  230  (represented by view data  231 ). The various data  211 ,  221  and  231  represent an example of the domain-specific data  120  of  FIG. 1 , and will be described in much further detail hereinafter. The authoring component  240  supports the providing of a wide variety of data including for example, data schemas, actual data to be used by the model, the location or range of possible locations of data that is to be brought in from external sources, visual (graphical or animation) objects, user interface interactions that can be performed on a visual, modeling statements (e.g., views, equations, constraints), bindings, and so forth. In one embodiment, the authoring component is but one portion of the functionality provided by an overall manager component (not shown in  FIG. 2 , but represented by the composition framework  110  of  FIG. 1 ). The manager is an overall director that controls and sequences the operation of all the other components (such as data connectors, solvers, viewers, and so forth) in response to events (such as user interaction events, external data events, and events from any of the other components such as the solvers, the operating system, and so forth). 
     Traditionally, the lifecycle of an interactive view composition application involves two key times: authoring time, and use time. At authoring time, the functionality of the interactive view composition application is coded by a programmer to provide an interactive view composition that is specific to the desired domain. For instance, the author of an interior design application (e.g., typically, a computer programmer) might code an application that permits a user to perform a finite set of actions specific to interior designing. 
     At use time, a user (e.g., perhaps a home owner or a professional interior designer) might then use the application to perform any one or more of the set of finite actions that are hard coded into the application. In the interior design application example, the user might specify the dimensions of a virtual room being displayed, add furniture and other interior design components to the room, perhaps rotate the view to get various angles on the room, set the color of each item, and so as forth. However, unless the user is a programmer that does not mind reverse-engineering and modifying the interior design application, the user is limited to the finite set of actions that were enabled by the application author. For example, unless offered by the application, the user would not be able to use the application to automatically figure out which window placement would minimize ambient noise, how the room layout performs according to Feng Shui rules, or minimize solar heat contribution. 
     However, in the pipeline environment  200  of  FIG. 2 , the authoring component  240  is used to provide data to an existing pipeline  201 , where it is the data that drives the entire process from defining the input data, to defining the analytical model, to defining how the results of the analytics are visualized in the view composition. Accordingly, one need not perform any coding in order to adapt the pipeline  201  to any one of a wide variety of domains and problems. Only the data provided to the pipeline  201  is what is to change in order to apply the pipeline  201  to visualize a different view composition either from a different problem domain altogether, or to perhaps adjust the problem solving for an existing domain. Further, since the data can be changed at use time (i.e., run time), as well as at author time, the model can be modified and/or extended at runtime. Thus, there is less, if any, distinction between authoring a model and running the model. Because all authoring involves editing data items and because the software runs all of its behavior from data, every change to data immediately affects behavior without the need for recoding and recompilation. 
     The pipeline environment  200  also includes a user interaction response module  250  that detects when a user has interacted with the displayed view composition, and then determines what to do in response. For example, some types of as interactions might require no change in the data provided to the pipeline  201  and thus require no change to the view composition. Other types of interactions may change one or more of the data  211 ,  221 , or  231 . In that case, this new or modified data may cause new input data to be provided to the data portion  210 , might require a reanalysis of the input data by the analytics portion  220 , and/or might require a re-visualization of the view composition by the view portion  230 . 
     Accordingly, the pipeline  201  may be used to extend data-driven analytical visualizations to perhaps an unlimited number of problem domains, or at least to a wide variety of problem domains. Furthermore, one need not be a programmer to alter the view composition to address a wide variety of problems. Each of the data portion  210 , the analytics portion  220  and the view portion  230  of the pipeline  201  will now be described with respect to respective data portion  300  of  FIG. 3 , the analytics portion  400  of  FIG. 4 , and the view portion  500  of  FIG. 5 , in that order. As will be apparent from  FIGS. 3 through 5 , the pipeline  201  may be constructed as a series of transformation component where they each 1) receive some appropriate input data, 2) perform some action in response to that input data (such as performing a transformation on the input data), and 3) output data which then serves as input data to the next transformation component. 
     The pipeline  201  may be implemented on the client, on the server, or may even be distributed amongst the client and the server without restriction. For instance, the pipeline  201  might be implemented on the server and provide rendering instructions as output. A browser at the client-side may then just render according to the rendering instructions received from the server. At the other end of the spectrum, the pipeline  201  may be contained on the client with authoring and/or use performed as at the client. Even if the pipeline  201  was entirely at the client, the pipeline  201  might still search data sources external to the client for appropriate information (e.g., models, connectors, canonicalizers, schemas, and others). There are also embodiments that provide a hybrid of these two approaches. For example, in one such hybrid approach, the model is hosted on a server but web browser modules are dynamically loaded on the client so that some of the model&#39;s interaction and viewing logic is made to run on the client (thus allowing richer and faster interactions and views). 
       FIG. 3  illustrates just one of many possible embodiments of a data portion  300  of the pipeline  201  of  FIG. 2 . One of the functions of the data portion  300  is to provide data in a canonical format that is consistent with schemas understood by the analytics portion  400  of the pipeline discussed with respect to  FIG. 4 . The data portion includes a data access component  310  that accesses the heterogenic data  301 . The input data  301  may be “heterogenic” in the sense that the data may (but need not) be presented to the data access component  310  in a canonical form. In fact, the data portion  300  is structured such that the heterogenic data could be of a wide variety of formats. Examples of different kinds of domain data that can be accessed and operated on by models include text and XML documents, tables, lists, hierarchies (trees), SQL database query results, BI (business intelligence) cube query results, graphical information such as 2D drawings and 3D visual models in various formats, and combinations thereof (i.e, a composite). Further, the kind of data that can be accessed can be extended declaratively, by providing a definition (e.g., a schema) for the data to be accessed. Accordingly, the data portion  300  permits a wide variety of heterogenic input into the model, and also supports runtime, declarative extension of accessible data types. 
     In one embodiment, the data access portion  300  includes a number of connectors for obtaining data from a number of different data sources. Since one of the primary functions of the connector is to place corresponding data into canonical form, such connectors will often be referred to hereinafter and in the drawings as “canonicalizers”. Each canonicalizer might have an understanding of the specific Application Program Interfaces (API&#39;s) of its corresponding data source. The canonicalizer might also include the corresponding logic for interfacing with that corresponding API to read and/or write data from and to the data source. Thus, canonicalizers bridge between external data sources and the memory image of the data. 
     The data access component  310  evaluates the input data  301 . If the input data is already canonical and thus processable by the analytics portion  400 , then the input data may be directly provided as canonical data  340  to be input to the analytics portion  400 . 
     However, if the input data  301  is not canonical, then the appropriate data canonicalization component  330  is able to convert the input data  301  into the canonical format. The data canonicalization components  330  are actually a collection of data canonicalization components  330 , each capable of converting input data having particular characteristics into canonical form. The collection of canonicalization components  330  is illustrated as including four canonicalization components  331 ,  332 ,  333  and  334 . However, the ellipses  335  represents that there may be other numbers of canonicalization components as well, perhaps even fewer that the four illustrated. 
     The input data  301  may even include a canonicalizer itself as well as an identification of correlated data characteristic(s). The data portion  300  may then register the correlated data characteristics, and provide the canonicalization component to the data canonicalization component collection  330 , where it may be added to the available canonicalization components. If input data is later received that has those correlated characteristics, the data portion  310  may then assign the input data to the correlated canonicalization component. Canonicalization components can also be found dynamically from external sources, such as from defined component libraries on the web. For example, if the schema for a given data source is known but the needed canonicalizer is not present, the canonicalizer can be located from an external component library, provided such a library can be found and contains the needed components. The pipeline might also parse data for which no schema is yet known and compare parse results versus schema information in known component libraries to attempt a dynamic determination of the type of the data, and thus to locate the needed canonicalizer components. 
     Alternatively, instead of the input data including all of the canonicalization component, the input data may instead provide a transformation definition defining canonicalization transformations. The collection  330  may then be configured to convert that transformations definition into a corresponding canonicalization component that enforces the transformations along with zero or more standard default canonicalization transformation. This represents an example of a case in which the data portion  300  consumes the input data and does not provide corresponding canonicalized data further down the pipeline. In perhaps most cases, however, the input data  301  results in corresponding canonicalized data  340  being generated. 
     In one embodiment, the data portion  310  may be configured to assign input data to the data canonicalization component on the basis of a file type and/or format type of the input data. Other characteristics might include, for example, a source of the input data. A default canonicalization component may be assigned to input data that does not have a designated corresponding canonicalization component. The default canonicalization component may apply a set of rules to attempt to canonicalize the input data. If the default canonicalization component is not able to canonicalize the data, the default canonicalization component might trigger the authoring component  240  of  FIG. 2  to prompt the user to provide a schema definition for the input data. If a schema definition does not already exist, the authoring component  240  might present a schema definition assistant to help the author generate a corresponding schema definition that may be used to transform the input data into canonical form. Once the data is in canonical form, the schema that accompanies the data provides sufficient description of the data that the rest of the pipeline  201  does not need new code to interpret the data. Instead, the pipeline  201  includes code that is able to interpret data in light of any schema that is expressible an accessible schema declaration language. 
     Regardless, canonical data  340  is provided as output data from the data portion  300  and as input data to the analytics portion  400 . The canonical data might include fields that include a variety of data types. For instance, the fields might includes simple data types such as integers, floating point numbers, strings, vectors, arrays, collections, hierarchical structures, text, XML documents, tables, lists, SQL database query results, BI (business intelligence) cube query results, graphical information such as 2D drawings and 3D visual models in various formats, or even complex combinations of these various data types. As another advantage, the canonicalization process is able to canonicalize a wide variety of input data. Furthermore, the variety of input data that the data portion  300  is able to accept is expandable. This is helpful in the case where multiple models are combined as will as be discussed later in this description. 
       FIG. 4  illustrates analytics portion  400  which represents an example of the analytics portion  220  of the pipeline  201  of  FIG. 2 . The data portion  300  provided the canonicalized data  401  to the data-model binding component  410 . While the canonicalized data  401  might have any canonicalized form, and any number of parameters, where the form and number of parameters might even differ from one piece of input data to another. For purposes of discussion, however, the canonical data  401  has fields  402 A through  402 H, which may collectively be referred to herein as “fields  402 ”. 
     On the other hand, the analytics portion  400  includes a number of model parameters  411 . The type and number of model parameters may differ according to the model. However, for purposes of discussion of a particular example, the model parameters  411  will be discussed as including model parameters  411 A,  411 B,  411 C and  411 D. In one embodiment, the identity of the model parameters, and the analytical relationships between the model parameters may be declaratively defined without using imperative coding. 
     A data-model binding component  410  intercedes between the canonicalized data fields  402  and the model parameters  411  to thereby provide bindings between the fields. In this case, the data field  402 B is bound to model parameter  411 A as represented by arrow  403 A. In other words, the value from data field  402 B is used to populate the model parameter  411 A. Also, in this example, the data field  402 E is bound to model parameter  411 B (as represented by arrow  403 B), and data field  402 H is bound to model parameter  411 C (as represented by arrow  403 C). 
     The data fields  402 A,  402 C,  402 D,  402 F and  402 G are not shown bound as to any of the model parameters. This is to emphasize that not all of the data fields from input data are always required to be used as model parameters. In one embodiment, one or more of these data fields may be used to provide instructions to the data-model binding component  410  on which fields from the canonicalized data (for this canonicalized data or perhaps any future similar canonicalized data) are to be bound to which model parameter. This represents an example of the kind of analytics data  221  that may be provided to the analytics portion  220  of  FIG. 2 . The definition of which data fields from the canonicalized data are bound to which model parameters may be formulated in a number of ways. For instance, the bindings may be 1) explicitly set by the author at authoring time, 2) explicit set by the user at use time (subject to any restrictions imposed by the author), 3) automatic binding by the authoring component  240  based on algorithmic heuristics, and/or 4) prompting by the authoring component of the author and/or user to specify a binding when it is determined that a binding cannot be made algorithmically. Thus bindings may also be resolved as part of the model logic itself. 
     The ability of an author to define which data fields are mapped to which model parameters gives the author great flexibility in being able to use symbols that the author is comfortable with to define model parameters. For instance, if one of the model parameters represents pressure, the author can name that model parameter “Pressure” or “P” or any other symbol that makes sense to the author. The author can even rename the model parameter which, in one embodiment, might cause the data model binding component  410  to automatically update to allow bindings that were previously to the model parameter of the old name to instead be bound to the model parameter of the new name, thereby preserving the desired bindings. This mechanism for binding also allows binding to be changed declaratively at runtime. 
     The model parameter  411 D is illustrated with an asterisk to emphasize that in this example, the model parameter  411 D was not assigned a value by the data-model binding component  410 . Accordingly, the model parameter  411 D remains an unknown. In other words, the model parameter  411 D is not assigned a value. 
     The modeling component  420  performs a number of functions. First, the modeling component  420  defines analytical relationships  421  between the model parameters  411 . The analytical relationships  421  are categorized into three general categories including equations  431 , rules  432  and constraints  433 . However, the list of solvers is extensible. In one embodiment, for example, one or more simulations may be incorporated as part of the analytical relationships provided a corresponding simulation engine is provided and registered as a solver. 
     The term “equation” as used herein aligns with the term as it is used in the field of mathematics. 
     The term “rules” as used herein means a conditional statement where if one or more conditions are satisfied (the conditional or “if” portion of the conditional statement), then one or more actions are to be taken (the consequence or “then” portion of the conditional statement). A rule is applied to the model parameters if one or more model parameters are expressed in the conditional statement, or one or more model parameters are expressed in the consequence statement. 
     The term “constraint” as used herein means that a restriction is applied to one or more model parameters. For instance, in a city planning model, a particular house element may be restricted to placement on a map location that has a subset of the total possible zoning designations. A bridge element may be restricted to below a certain maximum length, or a certain number of lanes. 
     An author that is familiar with the model may provide expressions of these equations, rules and constraint that apply to that model. In the case of simulations, the author might provide an appropriate simulation engine that provides the appropriate simulation relationships between model parameters. The modeling component  420  may provide a mechanism for the author to provide a natural symbolic expression for equations, rules and constraints. For example, an author of a thermodynamics related model may simply copy and paste equations from a thermodynamics textbook. The ability to bind model parameters to data fields allows the author to use whatever symbols the author is familiar with (such as the exact symbols used in the author&#39;s relied-upon textbooks) or the exact symbols that the author would like to use. 
     Prior to solving, the modeling component  420  also identifies which of the model parameters are to be solved for (i.e., hereinafter, the “output model variable” if singular, or “output model variables” if plural, or “output model variable(s)” if there could be a single or plural output model variables). The output model variables may be unknown parameters, or they might be known model parameters, where the value of the known model parameter is subject to change in the solve operation. In the example of  FIG. 4 , after the data-model binding operation, model parameters  411 A,  411 B and  411 C are known, and model parameter  411 D is unknown. Accordingly, unknown model parameter  411 D might be one of the output model variables. Alternatively or in addition, one or more of the known model parameters  411 A,  411 B and  411 C might also be output model variables. The solver  440  then solves for the output model variable(s), if possible. In one embodiment described hereinafter, the solver  440  is able to solve for a variety of output model variables, even within a single model so long as sufficient input model variables are provided to allow the solve operation to be performed. Input model variables might be, for example, known model parameters whose values are not subject to change during the solve operation. For instance, in  FIG. 4 , if the model parameters  411 A and  411 D were input model variables, the solver might instead solve for output model variables  411 B and  411 C instead. In one embodiment, the solver might output any one of a number of different data types for a single model parameter. For instance, some equation operations (such as addition, subtraction, and the like) apply regardless of the whether the operands are integers, floating point, vectors of the same, or matrices of the same. 
     In one embodiment, even when the solver  440  cannot solve for a particular output model variables, the solver  400  might still present a partial solution for that output model variable, even if a full solve to the actual numerical result (or whatever the solved-for data type) is not possible. This allows the pipeline to facilitate incremental development by prompting the author as to what information is needed to arrive at a full solve. This also helps to eliminate the distinction between author time and use time, since at least a partial solve is available throughout the various authoring stages. For an abstract example, suppose that the analytics model includes an equation a=b+c+d. Now suppose that a, c and d are output model variables, and b is an input model variable having a known value of 5 (an integer in this case). In the solving process, the solver  440  is only able to solve for one of the output model variables “d”, and assign a value of 6 (an integer) to the model parameter called “d”, but the solver  440  is not able to solve for “c”. Since “a” depends from “c”, the model parameter called “a” also remains an unknown and unsolved for. In this case, instead of assigning an integer value to “a”, the solver might do a partial solve and output the string value of “c+11” to the model parameter “a”. As previously mentioned, this might be especially helpful when a domain expert is authoring an analytics model, and will essential serve to provide partial information regarding the content of model parameter “a” and will also serve to cue the author that some further model analytics needs to be provided that allow for the “c” model parameter to be solved for. This partial solve result may be perhaps output in some fashion in the view composition to allow the domain expert to see the partial result. 
     The solver  440  is shown in simplified form in  FIG. 4 . However, the solver  440  may direct the operation of multiple constituent solvers as will be described with respect to  FIG. 9 . In  FIG. 4 , the modeling component  420  then makes the model parameters (including the now known and solved-for output model variables) available as output to be provided to the view portion  500  of  FIG. 5 . 
       FIG. 5  illustrates a view portion  500  which represents an example of the view portion  230  of  FIG. 2 . The view portion  500  receives the model parameters  411  from the analytics portion  400  of  FIG. 4 . The view portion also includes a view components repository  520  that contains a collection of view components. For example, the view components repository  520  in this example is illustrated as including view components  521  through  524 , although the view components repository  520  may contain any number of view components. The view components each may include zero or more input parameters. For example, view component  521  does not include any input parameters. However, view component  522  includes two input parameters  542 A and  542 B. View component  523  includes one input parameter  543 , and view component  524  includes one input parameter  544 . That said, this is just an example. The input parameters may, but need not necessary, affect how the visual item is rendered. The fact that the view component  521  does not include any input parameters emphasizes that there can be views that are generated without reference to any model parameters. Consider a view that comprises just fixed (built-in) data that does not change. Such a view might for example constitute reference information for the user. Alternatively, consider a view that just provides a way to browse a catalog, so that items can be selected from it for import into a model. 
     Each view component  521  through  524  includes or is associated with corresponding logic that, when executed by the view composition component  540  using the corresponding view component input parameter(s), if any, causes a corresponding view item to be placed in virtual space  550 . That virtual item may be a static image or object, or may be a dynamic animated virtual item or object For instance, each of view components  521  through  524  are associated with corresponding logic  531  through  534  that, when executed causes the corresponding virtual item  551  through  554 , respectively, to be rendered in virtual space  550 . The virtual items are illustrated as simple shapes. However, the virtual items may be quite complex in form perhaps even including animation. In this description, when a view item is rendered in virtual space, that means that the view composition component has authored sufficient instructions that, when provided to the rendering engine, the rendering engine is capable if displaying the view item on the display in the designated location and in the designated manner. 
     The view components  521  through  524  may be provided perhaps even as view data to the view portion  500  using, for example, the authoring component  240  of  FIG. 2 . For instance, the authoring component  240  might provide a selector that enables the author to select from several geometric forms, or perhaps to compose other geometric forms. The author might also specify the types of input parameters for each view component, whereas some of the input parameters may be default input parameters imposed by the view portion  500 . The logic that is associated with each view component  521  through  524  may be provided also a view data, and/or may also include some default functionality provided by the view portion  500  itself 
     The view portion  500  includes a model-view binding component  510  that is configured to bind at least some of the model parameters to corresponding input parameters of the view components  521  through  524 . For instance, model parameter  411 A is bound to the input parameter  542 A of view component  522  as represented by arrow  511 A. Model parameter  411 B is bound to the input parameter  542 B of view component  522  as represented by arrow  511 B. Also, model parameter  411 D is bound to the input parameters  543  and  544  of view components  523  and  524 , respectively, as represented by arrow  511 C. The model parameter  411 C is not shown bound to any corresponding view component parameter, emphasizing that not all model parameters need be used by the view portion of the pipeline, even if those model parameters were essential in the analytics portion. Also, the model parameter  411 D is shown bound to two different input parameters of view components representing that the model parameters may be bound to multiple view component parameters. In one embodiment, the definition of the bindings between the model parameters and the view component parameters may be formulated by 1) being explicitly set by the author at authoring time, 2) explicit set by the user at use time (subject to any restrictions imposed by the author), 3) automatic binding by the authoring component  240  based on algorithmic heuristics, and/or 4) prompting by the authoring component of the author and/or user to specify a binding when it is determined that a binding cannot be made algorithmically. 
     As previously mentioned, the view item may include an animation. To take a simple example, consider for example a bar chart that plots a company&#39;s historical and projected revenues, advertising expenses, and profits by sales region at a given point in time (such as a given calendar quarter). A bar chart could be drawn for each calendar quarter in a desired time span. Now, imagine that you draw one of these charts, say the one for the earliest time in the time span, and then every half second replace it with the chart for the next time span (e.g., the next quarter). The result will be to see the bars representing profit, sales, and advertising expense for each region change in height as the animation proceeds. In this example, the chart for each time period is a “cell” in the animation, where the cell shows an instant between movements, where the collection of cells shown in sequence simulates movement. Conventional animation models allow for animation over time using built-in hard-coded chart types. 
     However, using the pipeline  201 , by contrast, any kind of visual can be animated, and the animation can be driven by varying any one or any combination of the parameters of the visual component. To return to the bar chart example above, imagine that instead of animating by time, we animate by advertising expense. Each “cell” in this animation is a bar chart showing sales and profits over time for a given value of advertising expense. Thus, as the advertising expense is varied, the bars grow and shrink in response to the change in advertising expense. 
     The power of animated data displays is that they make very apparent to the eye what parameters are most sensitive to change in other parameters, because you immediately see how quickly and how far each parameter&#39;s values change in response to the varying of the animation parameter. 
     The pipeline  201  is also distinguished in its ability to animate due to the following characteristics: 
     First, the sequences of steps for the animation variable can be computed by the analytics of the model, versus being just a fixed sequence of steps over a predefined range. For example, in the example of varying the advertising expense as the animation variable, imagine that what is specified is to “animate by advertising expense where advertising expense is increased by 5% for each step” or “where advertising expense is 10% of total expenses for that step”. A much more sophisticated example is “animate by advertising expense where advertising expense is optimized to maximize the rate of change of sales over time”. In other words, the solver will determine a set of steps for advertising spend over time (i.e., for each successive time period such as quarter) such that the rate of growth of sales maximized. Here the user presumably wants to see not only how fast sales can be made to grow by varying advertising expense, but also wants to learn the quarterly amounts for the advertising expense that achieve this growth (the sequence of values could be plotted as part of the composite visual). 
     Second, any kind of visual can be animated, not just traditional data charts. For example, consider a Computer-Aided Design (CAD) model of a jet engine that is a) to be animated by the air speed parameter and 2) where the rotational speed of the turbine is a function of the air speed and 3) where the temperature of the turbine bearings is a function of the air speed. Jet engines have limits on how fast turbines can be rotated before either the turbine blades lose integrity or the bearing overheats. Thus, in this animation we desire that as air speed is varied the color of the turbine blades and bearing should be varied from blue (safe) to red (critical). The values for “safe” and “critical” turbine RPM and bearing temperature may well be calculated by the model based on physical characteristics of those parts. Now, as the animation varies the air speed over a defined range, we see the turbine blades and bearing each change color. What is now interesting is to notice which reaches critical first, and if either undergoes a sudden (runway) run to critical. These kinds of effects are hard to discern by looking at a chart or at a sequence of drawings, but become immediately apparent in an animation. This is but one example of animating an arbitrary visual (CAD model) by an arbitrary parameter (air speed), with the animation affecting yet other arbitrary parameters (turbine RPM and bearing temp). Any parameter(s) of any visual(s) can be animated according to any desired parameter(s) that are to serve as the animation variables. 
     Third, the pipeline  201  can be stopped mid stream so that data and parameters may be modified by the user, and the animation then restarted or resumed. Thus, for example, in the jet engine example, if runaway heating is seen to start at a given air speed, the user may stop the animation at the point the runaway beings, modify some engine design criterion, such as the kind of bearing or bearing surface material, and then continue the animation to see the effect of the change. 
     As with other of the capabilities discussed herein, animations can be defined by the author, and/or left open for the user to manipulate to test various scenarios. For example, the model may be authored to permit some visuals to be animated by the user according to parameters the user himself selects, and/or over data ranges for the animation variable that the user selects (including the ability to specify computed ranges should that be desired). Such animations can also be displayed side by side as in the other what-if comparison displays. For example, a user could compare an animation of sales and profits over time, animated by time, in two scenarios with differing prevailing interest rates in the future, or different advertising expenses ramps. In the jet engine example, the user could compare the animations of the engine for both the before and after cases of changing the bearing design. 
     At this point, a specific example of how the composition framework may be used to actually construct a view composition will be described with respect to  FIG. 6 , which illustrated 3-D renderings  600  of a view composition that includes a room layout  601  with furniture laid out within the room, and also includes a Feng Shui meter  602 . This example is provided merely to show how the principles described herein can apply to any arbitrary view composition, regardless of the domain. Accordingly, the example of  FIG. 6 , and any other example view composition described herein, should be viewed strictly as only an example that allows the abstract concept to be more fully understood by reference to non-limiting concrete examples, and not defining the broader scope of the invention. The principles described herein may apply to construct an enumerable variety of view compositions. Nevertheless, reference to a concrete example can clarify the broader abstract principles. 
       FIG. 7  illustrates a flowchart of a method  700  for generating a view construction. The method  700  may be performed by the pipeline environment  200  of  FIG. 2 , and thus will be described with frequent reference to the pipeline environment  200  of  FIG. 2 , as well as with reference to  FIGS. 3 through 5 , which each show specific portions of the pipeline of  FIG. 2 . While the method  700  may be performed to construct any view composition, the method  700  will be described with respect to the view composition  600  of  FIG. 6 . Some of the acts of the method  700  may be performed by the data portion  210  of  FIG. 2  and are listed in the left column of  FIG. 7  under the header “Data”. Other of the acts of the method  700  may be performed by the analytics portion  220  of  FIG. 2 , and are listed in the second from the left column of  FIG. 7  under the header “Analytics”. Other of the acts of the method are performed by the view portion  230  of  FIG. 2 , and are listed in the second from the right column under the header “View”. One of the acts may be performed by a rendering module and is listed in the right column under the header other. Any conventional or yet to be developed rendering module may be used to render a view composition constructed in accordance with the principles described herein. 
     Referring to  FIG. 7 , the data portion accesses input data that at least collectively affects what visual items are displayed or how a given one or more of the visual items are displayed (act  711 ). For instance, referring to  FIG. 6 , the input data might include view components for each of the items of furniture. For instance, each of the couch, the chair, the plants, the table, the flowers, and even the room itself may be represented by a corresponding view component. The view component might have input parameters that are suitable for the view component. If animation were employed, for example, some of the input parameters might affect the flow of the animation. Some of the parameters might affect the display of the visual item, and some parameters might not. 
     For instance, the room itself might be a view component. Some of the input parameters might include the dimensions of the room, the orientation of the room, the wall color, the wall texture, the floor color, the floor type, the floor texture, the position and power of the light sources in the room, and so forth. There might also be room parameters that do not necessarily get reflected in this view composition, but might get reflected in other views and uses of the room component. For instance, the room parameter might have a location of the room expressed in degrees, minutes, and seconds longitude and latitude. The room parameter might also include an identification of the author of the room component, and the average rental costs of the room. 
     The various components within the room may also be represented by a corresponding parameterized view component. For instance, each plant may be configured with an input parameter specifying a pot style, a pot color, pot dimensions, plant color, plant resiliency, plant dependencies on sunlight, plant daily water intake, plant daily oxygen production, plant position and the like. Once again, some of these parameters may affect how the display is rendered and others might not, depending on the nature of what is being displayed. 
     The Feng Shui meter  602  may also be a view component. The meter might include input parameters such as a diameter, a number of wedges to be contained in the diameter of the meter, a text color and the like. The various wedges of the Feng Shui meter may also be view components. In that case, the input parameters to the view components might be a title (e.g., water, mountain, thunder, wind, fire, earth, lake, heaven), perhaps a graphic to appear in the wedge, a color hue, or the like. 
     The analytics portion binds the input data to the model parameters (act  721 ), determines the output model variables (act  722 ), and uses the model-specific analytical relationships between the model parameters to solve for the output model variables (act  723 ). The binding operation of act  721  has been previously discussed, and essentially allows flexibility in allowing the author to define the model analytics equations, rules and constraints using symbols that the model author is comfortable with. 
     The identification or the output model variables may differ from one solving operation to the next. Even though the model parameters may stay the same, the identification of which model parameters are output model variables will depend on the availability of data to bind to particular model parameters. This has remarkable implications in terms of allowing a user to perform what-if scenarios in a given view composition. 
     For instance, in the Fung Shui room example of  FIG. 6 , suppose the user has bought a new chair to place in their living room. The user might provide the design of the room as data into the pipeline. This might be facilitated by the authoring component prompting the user to enter the room dimensions, and perhaps provide a selection tool that allows the user to select virtual furniture to drag and drop into the virtual room at appropriate locations that the actual furniture is placed in the actual room. The user might then select a piece of furniture that may be edited to have the characteristics of the new chair purchased by the user. The user might then drag and drop that chair into the room. The Feng Shui meter  602  would update automatically. In this case, the position and other attibutes of the chair would be input model variables, and the Feng Shui scores would be output model variables. As the user drags the virtual chair to various positions, the Feng Shui scores of the Feng Shui meter would update, and the user could thus test the Feng Shui consequences of placing the virtual chair in various locations. To avoid the user from having to drag the chair to every possible location to see which gives the best Feng Shui, the user can get local visual clues (such as, for example, gradient lines or arrows) that tell the user whether moving the chair in a particular direction from its current location makes things better or worse, and how much better or worse. 
     However, the user could also do something else that is unheard of in conventional view composition. The user could actually change the output model variables. For instance, the user might indicate the desired Feng Shui score in the Feng Shui meter, and leave the position of the virtual chair as the output model variable. The solver would then solve for the output model variable and provide a suggested position or positions of the chair that would achieve at least the designated Feng Shui score. The user may choose to make multiple parameters output model variables, and the system may provide multiple solutions to the output model variables. This is facilitated by a complex solver that is described in further detail with respect to  FIG. 9 . 
     Returning to  FIG. 7 , once the output model variables are solved for, the model parameters are bound to the input parameters of the parameterized view components (act  731 ). For instance, in the Feng Shui example, after the unknown Feng Shui scores are solved for, the scores are bound as input parameters to Feng Shui meter view component, or perhaps to the appropriate wedge contained in the meter. Alternatively, if the Feng Shui scores were input model variables, the position of the virtual chair may be solved for and provided as an input parameter to the chair view component. 
     A simplified example will now be presented that illustrates the principles of how the solver can rearrange equations and change the designation of input and output model variables all driven off of one analytical model. The user herself does not have to rearrange the equations. The simplified example may not accurately represent Feng Shui rules, but illustrates the principle nevertheless. Suppose the total Feng Shui (FS) of the room (FSroom) equals the FS of a chair (FSchair) and the FS of a plant (FSplant). Suppose FSchair is equal to a constant A times the distance d of the chair from the wall. Suppose FSplant is a constant, B. The total FS of the room is then: FSroom=A*d+B. If d is an input model variable, then FSroom is an output model variable and its value, displayed on the meter, changes as user repositions the chair. Now suppose the user now clicks on the meter making it an input model variable and shifting d into unknown output model variable status. In this case, the solver effectively and internally rewrites the equation above as d=(FSroom−B)/A. In that case, the view component can move the chair around, changing d, its distance from the wall, as the user changes the desired value, FSroom, on the meter. 
     The view portion then constructs a view of the visual items (act  732 ) by executing the construction logic associated with the view component using the input parameter(s), if any, to perhaps drive the construction of the view item in the view composition. The view construction may then be provided to a rendering module, which then uses the view construction as rendering instructions (act  741 ). 
     In one embodiment, the processing of constructing a view is treated as a data transformation that is performed by the solver. That is, for a given kind of view (e.g., consider a bar chart), there is a model consisting of rules, equations, and constraints that generates the view by transforming the input data into a displayable output data structure (called a scene graph) which encodes all the low level geometry and associated attributes needed by the rendering software to drive the graphics hardware. In the bar chart example, the input data would be for example the data series that is to be plotted, along with attributes for things like the chart title, axis labels, and so on. The model that generates the bar would have rules, equations, and constraints that would do things like 1) count how many entries the data series consists of in order to determine how many bars to draw, 2) calculate the range (min, max) that the data series spans in order to calculate things like the scale and starting/ending values for each axis, 3) calculate the height of the bar for each data point in the data series based on the previously calculated scale factor, 4) count how many characters are in the chart title in order to calculate a starting position and size for the title so that the title will be properly located and centered with respect to the chart, and so forth. In sum, the model that is designed to calculate a set of geometric shapes based on the input data, with those geometric shapes arranged within a hierarchical data structure of type “scene graph”. In other words, the scene graph is an output variable that the model solves for based on the input data. Thus, an author can design entirely new kinds of views, customized existing views, and compose preexisting views into composites, using the same framework that the author uses to author, customize, and compose any kind of model. Thus, authors who are not programmers can create new views without drafting new code. 
     Returning to  FIG. 2 , recall that the user interaction response module  250  detects when the user interacts with the view composition, and causes the pipeline to respond appropriately.  FIG. 8  illustrates a flowchart of a method  800  for responding to user interaction with the view composition. In particular, the user interaction response module determines which the components of the pipeline should perform further work in order to regenerate the view, and also provides data represented the user interaction, or that is at least dependent on the user interaction, to the pipeline components. In one embodiment, this is done via a transformation pipeline that runs in the reverse (upstream) view/analytics/data direction and is parallel to the (downstream) data/analytics/view pipeline. 
     Interactions are posted as events into the upstream pipeline. Each transformer in the data/analytics/view pipeline provides an upstream transformer that handles incoming interaction data. These transformers can either be null (passthroughs, which get optimized out of the path) or they can perform a transformation operation on the interaction data to be fed further upstream. This provides positive performance and responsiveness of the pipeline in that 1) interaction behaviors that would have no effect on upstream transformations, such as a view manipulation that has no effect on source data, can be handled at the most appropriate (least upstream) point in the pipeline and 2) intermediate transformers can optimize view update performance by sending heuristically-determined updates back downstream, ahead of the final updates that will eventually come from further upstream transformers. For example, upon receipt of a data edit interaction, a view-level transformer could make an immediate view update directly into the scene graph for the view (for edits it knows how to interpret), with the final complete update coming later from the upstream data transformer where the source data is actually edited. 
     When the semantics of a given view interaction have a nontrivial mapping to the needed underlying data edits, intermediate transformers can provide the needed upstream mapping. For example, dragging a point on a graph of a computed result could require a backwards solve that would calculate new values for multiple source data items that feed the computed value on the graph. The solver-level upstream transformer would be able to invoke the needed solve and to propagate upstream the needed data edits. 
       FIG. 8  illustrates a flowchart of a method  800  for responding to user interaction with the view construction. Upon detecting that the user has interacted with the rendering of a view composition on the display (act  801 ), it is first determined whether or not the user interaction requires regeneration of the view (decision block  802 ). This may be performed by the rendering engine raising an event that is interpreted by the user interaction response component  250  of  FIG. 2 . If the user interaction does not require regeneration of the view (No in decision block  802 ), then the pipeline does not perform any further action to reconstruct the view (act  803 ), although the rendering engine itself may perform some transformation on the view. An example of such a user interaction might be if the user were to increase the contrast of the rendering of the view construction, or rotate the view construction. Since those actions might be undertaken by the rendering engine itself, the pipeline need perform no work to reconstruct the view in response to the user interaction. 
     If, on the other hand, it is determined that the type of user interaction does require regeneration of the view construction (Yes in decision block  802 ), the view is reconstructed by the pipeline (act  804 ). This may involve some altering of the data provided to the pipeline. For instance, in the Feng Shui example, suppose the user were to move the position of the virtual chair within the virtual room, the position parameter of the virtual chair component would thus change. An event would be fired informing the analytics portion that the corresponding model parameter representing the position of the virtual chair should be altered as well. The analytics component would then resolve for the Feng Shui scores, repopulate the corresponding input parameters of the Feng Shui meter or wedges, causing the Feng Shui meter to update with current Feng Shui scores suitable for the new position of the chair. 
     The user interaction might require that model parameters that were previously known are now unknown, and that previously unknown parameters are now known. That is one of several possible examples that might require a change in designation of input and output model variables such that previously designated input model variables might become output model variables, and vice versa. In that case, the analytics portion would solve for the new output model variable(s) thereby driving the reconstruction of the view composition. 
     Solver Framework 
       FIG. 9  illustrates a solver environment  900  that may represent an example of the solver  440  of  FIG. 4 . The solver environment  900  may be implemented in software, hardware, or a combination. The solver environment  900  includes a solver framework  901  that manages and coordinates the operations of a collection  910  of specialized solvers. The collection  910  is illustrated as including three specialized solvers  911 ,  912  and  913 , but the ellipses  914  represents that there could be other numbers (i.e., more than three or less than three) of specialized solvers as well. Furthermore, the ellipsis  914  also represents that the collection  910  of specialized solves is extensible. As new specialized solvers are discovered and/or developed that can help with the model analytics, those new specialized solvers may be incorporated into the collection  910  to supplement the existing specialized solvers, or perhaps to replace one or more of the existing solvers. For example,  FIG. 9  illustrates that a new solver  915  is being registered into the collection  910  using the solver registration module  921 . As one example, a new solver might be perhaps a simulation solver which accepts one or more known values, and solves for one or more unknown values. Other examples include solvers for systems of linear equations, differential equations, polynomials, integrals, root-finders, factorizers, optimizers, and so forth. Every solver can work in numerical mode or in symbolic mode or in mixed numeric-symbolic mode. The numeric portions of solutions can drive the parameterized rendering downstream. The symbolic portions of the solution can drive partial solution rendering. 
     The collection of specialized solvers may include any solver that is suitable for solving for the output model variables. If, for example, the model is to determine drag of a bicycle, the solving of complex calculus equations might be warranted. In that case, a specialized complex calculus solver may be incorporated into the collection  910  to perhaps supplement or replace an existing equations solver. In one embodiment, each solver is designed to solve for one or more output model variables in a particular kind of analytics relationship. For example, there might be one or more equation solvers configured to solve for unknowns in an equation. There might be one or more rules solvers configured to apply rules to solve for unknowns. There might be one or more constraints solvers configured to apply constraints to thereby solve for unknowns. Other types of solves might be, for example, a simulation solver which performs simulations using input data to thereby construct corresponding output data. 
     The solver framework  901  is configured to coordinate processing of one or more or all of the specialized solvers in the collection  910  to thereby cause one or more output model variables to be solved for. The solver framework  901  is then configured to provide the solved for values to one or more other external components. For instance, referring to  FIG. 2 , the solver framework  901  may provide the model parameter values to the view portion  230  of the pipeline, so that the solving operation thereby affects how the view components execute to render a view item, or thereby affect other data that is associated with the view item. As another potential effect of solving, the model analytics themselves might be altered. For instance, as just one of many examples in which this might be implemented, the model might be authored with modifiable rules set so that, during a given solve, some rule(s) and/or constraint(s) that are initially inactive become activated, and some that are initially activated become inactivated. Equations can be modified this way as well. 
       FIG. 10  illustrates a flowchart of a method  1000  for the solver framework  901  to coordinate processing amongst the specialized solvers in the collection  910 . The method  1000  of  FIG. 10  will now be described with frequent reference to the solver environment  900  of  FIG. 9 . 
     The solver framework begins a solve operation by identifying which of the model parameters are input model variables (act  1001 ), and which of the model parameters are output model variables (act  1002 ), and by identifying the model analytics that define the relationship between the model parameters (act  1003 ). Given this information, the solver framework analyzes dependencies in the model parameters (act  1004 ). Even given a fixed set of model parameters, and given a fixed set of model analytics, the dependencies may change depending on which of the model parameters are input model variables and which are output model variables. Accordingly, the system can infer a dependency graph each time a solve operation is performed using the identity of which model parameters are input, and based on the model analytics. The user need not specify the dependency graph for each solve. By evaluating dependencies for every solve operation, the solver framework has the flexibility to solve for one set of one or more model variables during one solve operation, and solve for another set of one or more model variables for the next solve operation. In the context of  FIGS. 2 through 5 , that means greater flexibility for a user to specify what is input and what is output by interfacing with the view composition. 
     In some solve operations, the model may not have any output model variables at all. In that case, the solve will verify that all of the known model parameter values, taken together, satisfy all the relationships expressed by the analytics for that model. In other words, if you were to erase any one data value, turning it into an unknown, and then solve, the value that was erased would be recomputed by the model and would be the same as it was before. Thus, a model that is loaded can already exist in solved form, and of course a model that has unknowns and gets solves now also exists in solved form. What is significant is that a user interacting with a view of a solved model is nevertheless able to edit the view, which may have the effect of changing a data value or values, and thus cause a re-solve that will attempt to recompute data values for output model variables so that the new set of data values is consistent with the analytics. Which data values a user can edit (whether or not a model starts with output model variables) is controlled by the author; in fact, this is controlled by the author defining which variables represented permitted unknowns. 
     If there are expressions that have one or more unknowns that may be independently solved without first solving for other unknowns in other expressions (Yes in decision block  1005 ), then those expressions may be solved at any time (act  1006 ), even perhaps in parallel with other solving steps. On the other hand, if there are expressions that have unknowns that cannot be solved without first solving for an unknown in another expression, then a solve dependency has been found. In that case, the expression becomes part of a relational structure (such as a dependency tree) that defines a specific order of operation with respect to another expression. 
     In the case of expressions that have interconnected solve dependencies from other expressions, an order of execution of the specialized solvers is determined based on the analyzed dependencies (act  1007 ). The solvers are then executed in the determined order (act  1008 ). In one example, in the case where the model analytics are expressed as equations, constraints, and rules, the order of execution may be as follows 1) equations with dependencies or that are not fully solvable as an independent expression are rewritten as constraints 2) the constraints are solved, 3) the equations are solved, and 4) the rules are solved. The rules solving may cause the data to be updated. 
     Once the solvers are executed in the designated order, it is then determined whether or not solving should stop (decision block  1009 ). The solving process should stop if, for example, all of the output model variables are solved for, or if it is determined that even though not all of the output model variables are solved for, the specialized solvers can do nothing further to solve for any more of the output model variables. If the solving process should not end (No in decision block  1009 ), the process returns back to the analyzing of dependencies (act  1004 ). This time, however, the identity of the input and output model variables may have changed due to one or more output model variables being solved for. On the other hand, if the solving process should end (Yes in decision block  1009 ) the solve ends (act  1010 ). However, if a model cannot be fully solved because there are too many output model variables, the model nevertheless may succeed in generating a partial solution where the output model variable have been assigned symbolic values reflective of how far the solve was able to proceed. For example, if a model has an equation A=B+C, and B is known to be “2” and is an input model variable but C is an output model variable and A is also an output model variable and needs to be solved for, the model solver cannot product a numerical value for A since while B is known C is unknown; so instead of a full solve, the solver returns “2+C” as the value for A. It is thus clear to the author what additional variable needs to become known, either by supplying it a value or by adding further rules/equations/constraints or simulations that can successfully produce the needed value from other input data. 
     This method  1000  may repeat each time the solver framework detects that there has been a change in the value of any of the known model parameters, and/or each time the solver framework determines that the identity of the known and unknown model parameters has changed. Solving can proceed in at least two ways. First, if a model can be fully solved symbolically (that is, if all equations, rules, and constraints can be algorithmically rewritten so that a computable expression exists for each unknown) then that is done, and then the model is computed. In other words, data values are generated for each unknown, and/or data values that are permitted to be adjusted are adjusted. As a second possible way, if a model cannot be fully solved symbolically, it is partially solved symbolically, and then it is determined if one or more numerical methods can be used to effect the needed solution. Further, an optimization step occurs such that even in the first case, it is determined whether use of numerical methods may be the faster way to compute the needed values versus performing the symbolic solve method. Although the symbolic method can be faster, there are cases where a symbolic solve may perform so many term rewrites and/or so many rewriting rules searches that it would be faster to abandon this and solve using numeric methods. 
     Composite View Composition 
     The pipeline  201  also includes a model importation mechanism  241  that is perhaps included as part of the authoring mechanism  240 . The model importation mechanism  241  provides a user interface or other assistance to the author to allow the author to import at least a portion of a pre-existing analytics-driven model into the current analytics-driven model that the user is constructing. Accordingly, the author need not always begin from scratch when authoring a new analytics model. The importation may be of an entire analytics-driven model, or perhaps a portion of the model. For instance, the importation may cause one or more or all of the following six potential effects. 
     As a first potential effect of the importation, additional model input data may be added to the pipeline. For instance, referring to  FIG. 2 , additional data might be added to the input data  211 , the analytics data  221  and/or the view data  231 . The additional model input data might also include additional connectors being added to the data access component  310  of  FIG. 3 , or perhaps different canonicalization components  330 . 
     As a second potential effect of the importation, there may be additional or modified bindings between the model input data and the model parameters. For instance, referring to  FIG. 4 , the data-model binder  410  may cause additional bindings to occur between the canonicalized data  401  and the model parameters  411 . This may cause an increase in the number of known model parameters. 
     As a third potential effect of the importation, there may be additional model parameters to generate a supplemental set of model parameters. For instance, referring to  FIG. 4 , the model parameters  411  may be augmented due to the importation of the analytical behaviors of the imported model. 
     As a fourth potential effect of the importation, there may be additional analytical relationships (such as equations, rules and constraints) added to the model. The additional input data resulting from the first potential effect, the additional bindings resulting for the second potential effect, the additional model parameters resulting from the third potential effect, and the additional analytical relationships resulting from the fourth effect. Any one of more of these additional items may be viewed as additional data that affects the view composition. Furthermore, any one or more of these effects could change the behavior of the solver  440  of  FIG. 4 . 
     As a fifth potential effect of the importation, there may be additional or different bindings between the model parameters and the input parameters of the view. For instance, referring to  FIG. 5 , the model-view binding component  510  binds a potentially augmented set of model parameters  411  to a potentially augmented set of view components in the view component repository  520 . 
     As a sixth potential effect of the importation, there may be additional parameterized view components added to the view component repository  520  of  FIG. 5 , resulting in perhaps new view items being added to the view composition. 
     Accordingly, by importing all or a portion of another model, the data associated with that model is imported. Since the view composition is data-driven, this means that the imported portions of the model are incorporated immediately into the current view composition. 
     When the portion of the pre-existing analytics-driven analytics model is imported, a change in data supplied to the pipeline  201  occurs, thereby causing the pipeline  201  to immediately, or in response to some other event, cause a regeneration of the view composition. Thus, upon what is essentially a copy and paste operation from an existing model, that resulting composite model might be immediately viewable on the display due to a resolve operation. 
     As an example of how useful this feature might be, consider the Feng Shui room view composition of  FIG. 6 . The author of this application may be a Feng Shui expert, and might want to just start from a standard room layout view composition model. Accordingly, by importing a pre-existing room layout model, the Feng Shui expert is now relatively quickly, if not instantly, able to see the room layout  601  show up on the display shown in  FIG. 6 . Not only that, but now the furniture and room item catalog that normally might come with the standard room layout view composition model, has now become available to the Feng Shui application of  FIG. 6 . 
     Now, the Feng Shui expert might want to import a basic pie chart element as a foundation for building the Feng Shui chart element  602 . Now, however, the Feng Shui expert might specify specific fixed input parameters for the chart element including perhaps that there are 8 wedges total, and perhaps a background image and a title for each wedge. Now the Fung Shui expert need only specify the analytical relationships specifying how the model parameters are interrelated. Specifically, the color, position, and type of furniture or other room item might have an effect on a particular Feng Shui score. The expert can simply write down those relationships, to thereby analytically interconnect the room layout  601  and the Feng Shui score. This type of collaborative ability to build on the work of others may generate a tremendous wave of creativity in creating applications that solve problems and permit visual analysis. This especially contrasts with systems that might allow a user to visually program a one-way data flow using a fixed dependency graph. Those systems can do one-way solves, the way originally programmed from input to output. The principles described herein allow solves in multiple ways, depending on what is known and what is unknown at any time given the interactive session with the user. 
     Visual Interaction 
     The view composition process has been described until this point as being a single view composition being rendered at a time. For instance,  FIG. 6  illustrates a single view composition generated from a set of input data However, the principles described herein can be extended to an example in which there is an integrated view composition that includes multiple constituent view compositions. This might be helpful in a number of different circumstances. 
     For example, given a single set of input data, when the solver mechanism is solving for output model variables, there might be multiple possible solutions. The constituent view compositions might each represents one of multiple possible solutions, where another constituent view composition might represented another possible solution. 
     In another example, a user simply might want to retain a previous view composition that was generated using a particular set of input data, and then modify the input data to try a new scenario to thereby generate a new view composition. The user might then want to retain also that second view composition, and try a third possible scenario by altering the input data once again. The user could then view the three scenarios at the same time, perhaps through a side-by-side comparison, to obtain information that might otherwise be difficult to obtain by just looking at one view composition at a time. 
       FIG. 11  illustrates an integrated view composition  1100  that extends from the Feng Shui example of  FIG. 6 . In the integrated view composition, the first view composition  600  of  FIG. 6  is represented once again using elements  601  and  602 , exactly as shown in  FIG. 6 . However, here, there is a second view composition that is emphasized represented. The second view composition is similar to the first view composition in the there are two elements, a room display and a Feng Shui score meter. However, the input data for the second view composition was different than the input data for the first view composition. For instance, in this case, the position data for several of the items of furniture would be different thereby causing their position in the room layout  1101  of the second view composition to be different than that of the room layout  601  of the first view composition. However, the different position of the various furniture items correlates to different Fung Shui scores in the Fung Shui meter  1102  of the second view composition as compared to the Fung Shui meter  602  of the first view composition. 
     The integrated view composition may also include a comparison element that visually represents a comparison of a value of at least one parameter across some of all of the previously created and presently displayed view composition. For instance, in  FIG. 11 , there might be a bar graph showing perhaps the cost and delivery time for each of the displayed view compositions. Such a comparison element might be an additional view component in the view component repository  520 . Perhaps that comparison view element might only be rendered if there are multiple view compositions being displayed. In that case, the comparison view composition input parameters may be mapped to the model parameters for different solving iterations of the model. For instance, the comparison view composition input parameters might be mapped to the cost parameter that was generated for both of the generations of the first and second view compositions of  FIG. 11 , and mapped to the delivery parameter that was generated for both of the generations of the first and second view compositions. 
     Referring to  FIG. 11 , there is also a selection mechanism that allows the user to visually emphasize a selected subset of the total available previously constructed view compositions. The selection mechanism is illustrated as including three possible view constructions  1111 ,  1112  and  1113 , that are illustrated in thumbnail form, or are illustrated in some other deemphasized manner. Each thumbnail view composition  1111  through  1113  includes a corresponding checkbox  1121  through  1123 . The user might check the checkbox corresponding to any view composition that is to be visually emphasized. In this case, the checkboxes  1121  and  1123  are checked, thereby causing larger forms of the corresponding view constructions to be displayed. 
     The integrated view composition, or even any single view composition for that matter, may have a mechanism for a user to interact with the view composition to designate what model parameters should be treated as an unknown thereby triggering another solve by the analytical solver mechanism. For instance, in the room display  1101  of  FIG. 11 , one might right click on a particular item of furniture, right click on a particular parameter (e.g., position), and a drop down menu might appear allowing the user to designate that the parameter should be treated as unknown. The user might then right click on the harmony percentage (e.g., 95% in the Fung Shui score meter  1102 ), whereupon a slider might appear (or a text box of other user input mechanism) that allows the user to designate a different harmony percentage. Since this would result in the identity of the known and unknown parameters being changed, a re-solve would result, and the item of furniture whose position was designated as an unknown might appear in a new location. 
     In one embodiment, the integrated view composition might also include a visual prompt for an adjustment that could be made that might trend a value of a model parameter in a particular direction. For example, in the Feng Shui example, if a particular harmony score is designated as a known input parameter, various positions of the furniture might be suggested for that item of furniture whose position was designated as an unknown. For instance, perhaps several arrows might emanate from the furniture suggesting a direction to move the furniture in order to obtain a higher harmony percentage, a different direction to move to maximize the water score, a different direction to move to maximum the water score, and so forth. The view component might also show shadows where the chair could be moved to increase a particular score. Thus, a user might user those visual prompts in order to improve the design around a particular parameter desired to be optimized. In another example, perhaps the user wants to reduce costs. The user might then designate the cost as an unknown to be minimized resulting in a different set of suggested furniture selections. 
     Additional Example Applications 
     The architecture of  FIGS. 1 and 2  may allow countless data-driven analytics model to be constructed, regardless of the domain. There is nothing at all the need be similar about these domains. Wherever there is a problem to be solved where it might be helpful to apply analytics to visuals, the principles described herein may be beneficial. Upon until now, only a few example applications have been described including a Feng Shui room layout application. To demonstrate the wide-ranging applicability of the principles described herein, several additional wide-ranging example applications will now be described. 
     Additional Example #1—Retailer Shelf Arrangements 
     Product salespersons often use 3-D visualizations to sell retailers on shelf arrangements, end displays and new promotions. With the pipeline  201 , the salesperson will be able to do what-ifs on the spot. Given some product placements and given a minimum daily sales/linear foot threshold, the salesperson may calculate and visualize the minimum required stock at hand. Conversely, given some stock at hand and given a bi-weekly replenishment cycle, the salesperson might calculate product placements that will give the desired sales/linear foot. The retailer will be able to visualize the impact, compare scenarios, and compare profits.  FIG. 12  illustrates an example retailer shelf arrangement visualization. The input data might include visual images of the product, a number of the product, a linear square footage allocated for each product, and shelf number for each product, and so forth. 
     Additional Example #2—Urban Planning 
     Urban planning mash ups are becoming prominent. Using the principles described herein, analytics can get integrated into such solutions. A city planner will open a traffic model created by experts, and drag a bridge in from a gallery of road improvements. The bridge will bring with it analytical behavior like length constraints and high-wind operating limits. Via appropriate visualizations, the planner will see and compare the effect on traffic of different bridge types and placements. The principles described herein may be applied to any map scenarios where the map might be for a wide variety of purposes. The map might be for understanding the features of a terrain and finding directions to some location. The map might also be a visual backdrop for comparing regionalized data. More recently, maps are being used to create virtual worlds in which buildings, interiors and arbitrary 2-D or 3-D objects can be overlaid or positioned in the map.  FIG. 13  illustrates an example visualized urban plan. 
     Additional Example #3—Visual Education 
     In domains like science, medicine, and demographics where complex data needs to be understood not just by domain practitioners but also the public, authors can used the principles described herein to create data visualizations that intrigue and engage the mass audience. They will use domain-specific metaphors, and impart the authors&#39; sense of style.  FIG. 14  is an illustration about children&#39;s education.  FIG. 15  is a conventional illustration about population density. Conventionally, such visualizations are just static illustrations. With the principles described herein, these can become live, interactive experiences. For instance, by inputting a geographically distributed growth pattern as input data, a user might see the population peaks change. Some visualizations, where the authored model supports this, will let users do what-ifs. That is, the author may change some values and see the effect on that change on other values. 
     Accordingly, the principles described herein provide a major paradigm shift in the world of visualized problem solving and analysis. The paradigm shift applies across all domains as the principles described herein may apply to any 
     Having described the embodiments in some detail, as a side-note, the various operations and structures described herein may, but need, not be implemented by way of a computing system. Accordingly, to conclude this description, an example computing system will be described with respect to  FIG. 16 . 
       FIG. 16  illustrates a computing system  1600 . Computing systems are now increasingly taking a wide variety of forms. Computing systems may, for example, be handheld devices, appliances, laptop computers, desktop computers, mainframes, distributed computing systems, or even devices that have not conventionally considered a computing system. In this description and in the claims, the term “computing system” is defined broadly as including any device or system (or combination thereof) that includes at least one processor, and a memory capable of having thereon computer-executable instructions that may be executed by the processor. The memory may take any form and may depend on the nature and form of the computing system. A computing system may be distributed over a network environment and may include multiple constituent computing systems. 
     As illustrated in  FIG. 16 , in its most basic configuration, a computing system  1600  typically includes at least one processing unit  1602  and memory  1604 . The memory  1604  may be physical system memory, which may be volatile, non-volatile, or some combination of the two. The term “memory” may also be used herein to refer to non-volatile mass storage such as physical storage media. If the computing system is distributed, the processing, memory and/or storage capability may be distributed as well. As used herein, the term “module” or “component” can refer to software objects or routines that execute on the computing system. The different components, modules, engines, and services described herein may be implemented as objects or processes that execute on the computing system (e.g., as separate threads). 
     In the description that follows, embodiments are described with reference to acts that are performed by one or more computing systems. If such acts are implemented in software, one or more processors of the associated computing system that performs the act direct the operation of the computing system in response to having executed computer-executable instructions. An example of such an operation involves the manipulation of data. The computer-executable instructions (and the manipulated data) may be stored in the memory  1604  of the computing system  1600 . 
     Computing system  1600  may also contain communication channels  1608  that allow the computing system  1600  to communicate with other message processors over, for example, network  1610 . Communication channels  1608  are examples of communications media. Communications media typically embody computer-readable instructions, data structures, program modules, or other data in a modulated data signal such as a carrier wave or other transport mechanism and include any information-delivery media. By way of example, and not limitation, communications media include wired media, such as wired networks and direct-wired connections, and wireless media such as acoustic, radio, infrared, and other wireless media. The term computer-readable media as used herein includes both storage media and communications media. 
     Embodiments within the scope of the present invention also include computer-readable media for carrying or having computer-executable instructions or data structures stored thereon. Such computer-readable media can be any available media that can be accessed by a general purpose or special purpose computer. By way of example, and not limitation, such computer-readable media can comprise physical storage and/or memory media such as RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to carry or store desired program code means in the form of computer-executable instructions or data structures and which can be accessed by a general purpose or special purpose computer. When information is transferred or provided over a network or another communications connection (either hardwired, wireless, or a combination of hardwired or wireless) to a computer, the computer properly views the connection as a computer-readable medium. Thus, any such connection is properly termed a computer-readable medium. Combinations of the above should also be included within the scope of computer-readable media. 
     Computer-executable instructions comprise, for example, instructions and data which cause a general purpose computer, special purpose computer, or special purpose processing device to perform a certain function or group of functions. Although the subject matter has been described in language specific to structural features and/or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described herein. Rather, the specific features and acts described herein are disclosed as example forms of implementing the claims. 
     The present invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. The scope of the invention is, therefore, indicated by the appended claims rather than by the foregoing description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope.