Module CompositeModel
Usually A CAD model cannot be represented by a single geometry entity, like the ones in the gotools-core module. The need for sets of entities, adjacency analysis and representation of adjacency arises. In addition there is a need for topological structures. The following figure shows the current topology classes in GoTools.
Topological structures for a boundary-represented solid, with corresponding GoTools shown in parentheses
Body is a boundary represented solid model. It is a virtual volume limited by one or more shells, one outer and possibly a number of inner ones. The shells are represented by the class SurfaceModel, which is also the entity used for representing a face set. In addition to being a topological entity, SurfaceModel provides an interface which views the set of surfaces as a single entity. Thus, an operation like closest point computation can be performed without caring about which surface is closest to the point, see also Section SurfaceModel.
The surface model consists of a set of faces represented by the class ftSurface. The face represents the abstract idea of a bounded surface, but it also has a pointer to the geometric representation of this surface. The geometric surface is a ParamSurface, and it may be a NURBS surface, an elementary surface or a trimmed version thereof. The face is bounded by one or more loops, one outer and possibly a number of inner ones. The inner loops represent trimming. In that case the geometric surface will be a BoundedSurface. All faces have an outer loop which either represents an outer trimming curve in the case of a BoundedSurface or the surface boundary.
A loop consists of a number of edges represented by ftEdge. The edges have a geometric representation by a ParamCurve. This is the level where adjacency information related to faces or surfaces is stored. An ftEdge is a half-edge. It knows the face to which it belongs and the geometry of the curve it corresponds to. This curve is normally a CurveOnSurface curve. Then, both parameter and geometry information are available. The ftEdge has a pointer to a twin edge. This edge belongs to the adjacent ftSurface meeting the current one along the boundary represented by the current ftEdge. This construction is a very flexible one, but it does not automatically ensure
An edge is limited by two vertices, which have a geometric representation as a point. A vertex has knowledge about all edges meeting in this point.
The CompositeModel inheritance tree
SurfaceModel represents the shell in a boundary-represented geometry model, but it is also the entity that is used to view a surface set as a single entity. In this context, it inherits the abstract superclass CompositeModel, which defines an interface for a union of geometry entities of the same type. All composite models can
- Report how many entities it consists of
- Evaluate a given entity in a given parameter or parameter pair
- Compute the closest point from a given point to the entity set
- Compute the extremal point of the entity set in a given direction
- Intersect itself with a plane
- Intersect itself with a line
- Compute the bounding box surrounding the entity set
- Check whether one specified entity is degenerate
- Reverse parameter directions corresponding to one or all entities
- Tesselate itself
- Clone itself
Tesselation is performed in the gotools-core/tesselator submodule. The methods here expect information about the tesselation resolution. For each parameter direction in the object, the number of triangles or line strips must be specified. The resolution is defined from the composite model. This can either be done setting a resolution for all entities or by a density parameter that governs the resolution. The composite model tesselation routines return a vector of shared pointers to a GeneralMesh. The type of meshes used for the concrete tesselation results are LineStrip, RegularMesh and GenericTriMesh.
The control polygon of the composite model or a selected subset of the model may be tesselated. In that case the output mesh is represented as a LineCloud, which is an entity in the gotools-core/geometry submodule.
A CompositeCurve is an ordered collection of curves. The class expects a set of curves and will order them in a sequence. The curve set should preferably be continuous, but also discontinuous sets may be represented.
A composite curve will contain a number of ParamCurves, ordering information and continuity information. The curve sequence will be parameterized as a single entity. Curve indices follow the indices for the curves given as input to the object. The class has the following type-specific functionality:
- Fetch an individual curve
- Fetch the parameter interval of the composite curve
- Given a parameter value of one individual curve, get the corresponding parameter value in the composite curve, and vice versa. Given a parameter value of the composite curve, get the index and parameter value of the individual curve.
- Evaluate the composite curve as a single entity
- Hit test. Compute the closest point in the composite curve to a given point along a given line
- Append a new curve to the composite curve
All the curves in the composite curve can be tesselated with respect to a default value, or a value given by the application. In addition a given subset of the composite curve can be tesselated with respect to the defined resolution. It is also possible to set the number of line segments for each curve relative to a given density parameter. Then the length of each line segment should roughly approximate this density. The density should be set according to the total size of the model. An upper bound of the tesselation size exists, but a large model combined with a small density will still lead to a heavy visualization model.
A CurveModel is an incomplete class inheriting a CompositeModel. Not all the functionality defined in CompositeModel is implemented in this class. Its main purpose is to take a set of curves, for instance read from an IGES file, compute the topology of the curve set, use the topology information to order the curves into sequences, and return these sequences as composite curves.
Nevertheless, a curve model may be evaluated, tesselated and we can fetch a particular curve in the set by index or find the associated index given a curve. The index corresponds to the order of the input curves to this class. It is also possible to compute the bounding box surrounding the curve set and the curve model may copy itself.
A surface model represents a surface set or a shell. It contains a number of parametric surfaces and topology information representing adjacency between surfaces in the set. The input surfaces to a surface model may be given as parametric surfaces or faces, i.e., of type ftSurface. In the latter case, the adjacency information may be given or not. A surface model may consist of several disjoint surface sets.
SurfaceModel has some specific functionality:
- Reset topology tolerances and recompute adjacency information, see below
- Return a specified surface or face
- Perform intersection with a line or a plane and represent the output in a surface-specific manner
- Intersect the surface set with a plane, and trim the result with respect to the orientation of the plane
- Compute the closest point in the surface set to a given point along a given line (i.e., a hit test)
- Append one or more new faces to the surface set
- Append another surface set to the current one
- Return information about the number of boundary loops in the surface set. One boundary loop will correspond to either a continuous subset of surfaces or a hole in the surface set.
- Return informations of gaps between surfaces in the set
- Return informations of kinks between surfaces in the set
- Return informations of sharp edges between surfaces in the set
- Triangulate the surface set with respect to a density parameter, and join the individual triangulations for each surface into one triangulation.
- Fetch information about neighbouring surfaces with inconsistent direction of the surface normals
- Fetch all vertices in the surface set
- Fetch vertices lying at the boundaries of the surface set
Some functionality is special for isogeometric models, where each surface is expected to be a non-trimmed spline surface and the surfaces should lie in a corner-to-corner configuration:
- Check if all surfaces are splines
- Check if the surface configuration is corner-to-corner
- Ensure a corner-to-corner configuration if this is not the case. The function applies only to spline surfaces
- Ensure that the spline surfaces in the model share the spline space at common boundaries
All the surfaces in the surface model can be tesselated with respect to a default value or a pair of values given by the application, or a given subset of the surface model can be tesselated with respect to this resolution. The application can also specify the approximate number of quads in the tesselation. Each quad is divided into two triangles. Then a long and thin surface will get more triangles in the long direction. It is also possible to set the number of triangles in each parameter direction for each surface relative to a given density parameter. Then the length of each triangle should roughly approximate this density. The density should be set according to the total size of the model. An upper bound of the tesselation size exists, but a large model combined with a small density will still lead to a heavy visualization model.
The constructor of subclasses of CompositeModel requires a set of tolerances to be defined; see Module QualityModule. With the exception of approxtol, these tolerances are used to compute adjacency between entities and to check the continuity between adjacent entities.
Intersections performed in the composite model class either return the intersection results in a format particular to the concrete composite model subclass, or the intersection results are stored in a subclass of IntResultsModel. In the latter case, intersections can be performed without caring about the composite model type.
IntResultsModel stores the intersection results and the entities involved in the intersection and has the following functionality:
- Report upon the existence and number of intersection points and intersection curve segments
- Tesselate itself
The actual geometry of the intersection results must be fetched from the subclasses IntResultsSfModel and IntResultsCompCv. The intersection results classes are very lean, but have the potential to get a rich set of functionality operating on intersection results.
SurfaceModel returns intersection results either as IntResultsSfModel or as ftCurve and a vector of ftPoints. It is also possible to fetch intersection results from IntResultSfModel as ftCurve and ftPoint.
An ftCurve is composed of a number of ftCurveSegments. An ftCurveSegment represents a piece of an intersection curve. The segment is represented by a spatial curve and a curve in the parameter domain of the parametric entities involved in the intersection, which will be one or two. Thus, the curve segments distinguish between the individual surfaces in a surface set while ftCurve itself does not. ftCurve keeps track of the continuity between the segments it is composed of. An ftCurve is able to tesselate itself.
An ftPoint relates to one face, i.e., an ftSurface, and has a geometric representation and a parameter domain representation. Each intersection point, for instance in an intersection between a surface model and a line, is represented as an ftPoint. The application has access to the position of this point, to the face with which it is associated and the parameter values in this face.
A composite curve represents its intersection results as an instance of IntResultsCompCv. Intersection points, which are the expected result in this case, are represented as PointOnCurve. Intersection curve segments are represented as pairs of PointOnCurves. The two points limit the extension of the intersection curve segment. The class PointOnCurve lies in the gotools-core/geometry submodule and holds a parametric curve, a parameter value and the geometric representation of the point. This content is accessible from the public user interface.
Composite models of any type are created in the composite model factory. To open this factory, the tolerances described in Module QualityModule are required. These tolerances are distributed to the composite models created in the factory.
The factory creates models from two sources. Either the data of a model is read from an IGES file or g2 file, or the model is created specifically from user input. The various possibilities are:
- Create one or more models from an IGES file. In the first case, either a composite model or a surface model is made, depending on which entity dominates the file. In the second case, both composite curves and a surface models may be generated.
- Create one or more models from a g2 file.
- Create a composite model from SISL curves or surfaces.
- Create a surface model representing a box.
- Create a sphere or a sphere segment. The output is a surface model consisting of one surface.
- Create a surface model representing a cylinder. The model consists of one surface.
- Create a surface model by interpolating a set of curves. The model consists of one surface.
- Create a composite curve with one segment from a circular arc, an elliptic arc or a line segment.
The topological face (ftSurface) has access to the geometric representation of this face and information about neighbouring faces. In addition, it has knowledge about the solid (Body) it belongs to, if any.
The geometric surface is of type ParamSurface and described in the documentation of the gotools-core/geometry submodule.
The face is limited by a number of Loops. The geometric surface corresponding to a face corresponds to the trimmed face, so the information present in the boundary loops of the face does also exist in the surface description.
ftSurface has a rich set of functionality of different types:
-
Access functionality
- Fetch the corresponding surface
- Fetch boundary loops
- Fetch edges belonging to the boundary loops
- Fetch neighbouring faces
- Fetch all vertices or subsets of vertices
- Fetch the body owning this face
- Fetch all bodies meeting in this face, maximum 2
- Fetch the coincident face in a volume model
-
Quality checking
- Check for discontinuities in the surface
- Check the distance between a face and corresponding edges and vertices
- Check the orientation of loops belonging to the face
- Check if the face has a narrow region
- Check for acute angles in the boundary loops
-
Functionality related to an isogeometric model
- Check if the corresponding surface is a spline
- Check if this face and the neighbouring face have corresponding spline spaces
- Ensure that this face and the neighbouring face have corresponding spline spaces
- Check if this face and the neighbouring face satisfy a corner-to-corner condition
- Ensure that this face and the neighbouring face satisfy a corner-to-corner condition
- Fetch adjacency information between this face and a neighbouring face
- Fetch information about boundaries where the face has no neighbouring face
- Fetch information about coefficient enumerations for spline surface belonging to adjacent faces and free boundaries
-
Other queries
- Evaluations
- Closest point computations
- Perform smoothing on the current face
- Compute bounding box
The topological edge is implemented in the class ftEdge and it is a half-edge. Thus, it contains information related to one face only. However, it has access to the corresponding half-edge when the edge represents a boundary between two adjacent faces. The topological edge has a geometric representation as a ParamCurve. The edge may represent a restriction of the curve. This restriction is implemented using limiting parameters in the parameter interval of the curve.
The main functionality is:
- Fetch the curve representing the geometry description of the edge
- Fetch the parameters limiting the edge compared to the corresponding curve
- Fetch the face to which the edge belongs
- Given an edge parameter, compute the corresponding face parameter
- Access to geometry information like bounding box, results of evaluation, closest point computations and an estimate of the curve length
- Information about the vertices limiting the edge, i.e., access to vertices and the edge parameter corresponding to a vertex
- Access to the radial edge if this entity exist. A radial edge is defined in volume model and the entity is described in the [[documentation of the
trivariatemodelmodule|Module TrivariateModel]]. - Get all surfaces meeting in this edge, with a maximum of two
This module depends on the following GoTools modules:
- GoTools Core
- Implicitization
- Intersections
- Parametrization
- Igeslib
- Topology
In addition it depends on the following modules external to GoTools:
- SISL: SINTEF's spline library, available with GPL license.
- TTL: SINTEF's a generic triangulation library, available with GPL license.
- newmat: Robert Davies' library for matrix operations, available with a permissive license.
- Vibeke Skytt, Gang Xu, Bernard Mourrain, First version of isogeometric analysis framework library