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− | It would be ideal to provide both analytical and numeric evaluation methods the second one being of primary importance in terms of constraint based calculations. | + | It would be ideal to provide both analytical and numeric evaluation methods the second one being of |
− | + | primary importance in terms of constraint based calculations. Considering the standard methods of | |
+ | parametrization ( see Enumeration below ) I think the implementation of an analytic solving system | ||
+ | would be easier. Though for the solution of more complex equation as well as majority of constraints, | ||
+ | libpg will have to provide support for numerical solutions. |
Proposed sytem for parametrics and constraint implementation by Dawn Thomas (homovulgaris)
Provision for Parametrics and constraints greatly improves the performance of a Computer Aided Design System both in terms of geometry generation as well as analysis. Considering the unix model of division into multiple tools and libraries for individual functions as well as the fact that parametric/constraint functionalities are not critical elements in terms of geometry generation and raytracing, a logical solution would be the implemenation of a separate library (libpg)
libpg adds the following provisions to BRL-CAD system
Part 1 would include building parametric objects based on existing non-parametric geometry objects as well as generation of purely parametric geometry. libpg acts as a library which sits above librt using the librt methods for creation and modification of geometry
A constraint system can be looked upon as a system of variables, their associated domains and set of constraints/relationships between the variables.
Fundamentally this can be visualised using a constraint network which is a 3-tuple. Further we can have a graph based visualization of the same using vertices as variables and edges connecting vertices as constraints. It would be intuitive only for networks having binary (between two variables) or unary (with self) constraints. Otherwise, one has to visualize hypergraphs which contain hyperedges which is basically a line connecting multiple vertices for example. Also note that there could arise a situation where constraints depend on constraints ( edges connected to edges in the above discussion ) and hence such hypergraphs don't fit neatly into the bipartite graph structure.
For a short review of Constraints, and Constraint Satisfaction Problems as well as links to resources on Constraints in general and geometrical constraints in particular, please see Constraint Satisfaction
LibPC is composed of two sections which are functionally implemented using 4 modules as represented in the diagram below.
The modules respectively are ( in the order of operation during a read-out solution process)
For effective integration with librt system as well as rest of existing brl-cad architecture, the Reader as well as Geometry Updater is entirely in C using standard datastructures. At the same time to make use of the functionality offered by various graph algorithms of boost as well as the power of object oriented programming model in constraint solution, the Constraint Network generator as well as solver is entirely coded in C++. Extensive use of Boost library is expected, in particular
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An object oriented method of implementation would be the creation of a mixed ( in the sense that they contain both geometric and non-geometric information ) object. The object architecture is as shown below which shows the data types as well as the public and private methods.
From an Object Oriented point of view the major advantages is in terms of the structuring of data and in particular the system of calling methods or procedures. In effect each object knows how to evaluate equations within its space. For example a line or a curve knows ( has a method to ) calculate and return the coordinates of a point with a certain parameter value in its space ( a point at 0.6 ratio of length of the curve) With this value ( coordinates) thus returned and with the existing knowledge ( parent: curveid , parameter value:0.6 ) a parametric point object has the methods to instantiate it and store it.
The above method is efficient and useful only in the generation, modification and analysis of new geometry based on existing parametric/ non-parametric geometry. The evaluation method for constraints between already existing independent geometry would require special constraint objects. The effective difference between these objects and the earlier arises from the fact that generation of the parametric geometric objects depend on parametrics whereas constraints may or may not be feasible and thus evaluation would result in multiple solutions and they represent relationship between two independently defined elements ( parametrically or not )
Two major aspects of integration with librt are
Since most of the database input-output presently is completely handled by librt, it is expedient to use the same convention for writing the new non-geometric constraint object to the database. This is achieved through the pc_constraint_export and pc_constraint_import functions which are called by such functions as wdb_export or rt_db_put_internal via a new functab entry in table.c Or in more detail the steps taken to achieve these are
Regarding the declaration or extraction of parameters, the method of approach is to use a callback function rt_functab. Associated with each existing element we add a rt_*_params function which is called via the functab. This would declare the list of parameters it is built on as well as the list of implicit constraints on these parameters if any ( for example in the case of an ellipse there are 4 parameters: 1 point - center, 3 vectors-a,b,c and associated constraints ). This data is stored as a pc_pc_set (ParameterConstraint Set) This way, after the implementation of libpc we can remove most of the code from existing rt_*_prep functions which do such implicit constraint checking handling the same via libpc
What should be the convention for naming the parameters ? Also there is a certain issue in the sense that some of the geometry are special cases of more generic geometry. So for a sphere we are concerned with only radius and center where as it is defined using ( point center) and 3 vectors (a b c). Should we name the parameter radius make 3 fastf_t * to a[0], b[1], and c[2] Or should we make 3 vectp_t to a,b,c or make 1 fast_t* to a[0], doing a further check/constraint that a[0]=b[1]=c[2] ?
The datastructures necessary for the exchange of information (pc_pc_set which itself is built using a constraint set structure and parameter set structure) are defined currently in raytrace.h (Shift to pc.h in future? )
June 10th: The idea is to implement a constraint network using graph representation of boost c++ library. From the solvers point of view the constraint network would be composed of the following ( which are class definitions in pc_solver.h file)
The action of the Solver object/method is the production of a Solution Class A Solution is basically an instantiation of parameters along with their possible values or an instantiation of the form ( param1= value, param2=value and so on) In this case the value is basically a region of the domain the parameter could occupy.
For example consider parameter set p1,p2,p3 The solution maybe
Modus operandi:
Initial draft/intent
It would be ideal to provide both analytical and numeric evaluation methods the second one being of primary importance in terms of constraint based calculations. Considering the standard methods of parametrization ( see Enumeration below ) I think the implementation of an analytic solving system would be easier. Though for the solution of more complex equation as well as majority of constraints, libpg will have to provide support for numerical solutions.