Topology Topological entities

The analysis of the effect of the change of a geometric entity on other geometric entities needs information about the geometric entities adjoining it. In other words, the model must include information about connecting curves and surfaces. This information is carried by topological entities of the boundary representation. 

Individually described point, curve, and surface geometrical entities are mapped to vertex, edge, and face topological entities, respectively. In Figure 2-4, lines enclosing the surface Sj,... 

Different shapes can be described by the same topology if they have the same number of surfaces and intersection curves. As an example, Figure 3-12 shows three different shapes with the same topology. Modification of a surface or curve often requires modification of curves and surfaces that are mapped to entities in the neighborhood of the topological entity to which the modified geometric entity is mapped. In Figure 3-13, four different... 

The primary application of lumps is the description of segments. Figure 3-19 shows two typical examples of the creation of lumps by the intersection of two solids. In Figure 3-19a, a cylinder is cut by a prism. When the diameter of the cylinder is larger than the dimension of the base rectangle of the prism, the result is four separated solids. In Figure 3-19b, lumps are created by the intersection of two prisms the body topological entity includes four lumps. 

Entities in a curve network (Figure 3-45) are the curve (Cy), vertex (vj), edge (ej), and boundary (B]). Vertex and edge entities act as topological entities. The intersection points of curves are mapped to vertices. Part of a curve between two intersection... 

Fig. 5.17. Two different topologies for a finite area surface without edge, (a) A sphere, the simplest possible topology, nh = 0 and the integral of the Gaussian curvature is 47t. (b) More complex topological entity, the sphere with two handles, nh = 2 and the integral of the Gaussian curvature is — 47t...

The idea is to create two models or topology entities one is an instance of the MainReactor model where mass transfer and reaction take place, and the other... 

A Topologicalindividual is a subclass of TopologicalThing and is the superclass of the classes used for modeling topological entities and relationships. 

A B REP is an entity that has a scope. A B REP may have a material property associated with it. The B REP is a self-contained entity in the sense that no entity in the B REP may refer to an entity outside the scope of the B REP. All referenced entities must be within the B REP scope itself. The scope of a B REP contains both topological and geometrical entities. Geometry is represented by lists of the entities POINT, DIRECTION, EDGE CURVE and FACE SURFACE which are referenced by the topological entities defined subsequently. Topology is represented by lists of the entities, VERTEX, EDGE, LOOP, FACE and SHELL in that order so that no entity is referenced before it is defined. 

A shell is a topological entity defined within the scope of a B REP. It is defined by a list of references to its bounding faces. The order of the list is arbitrary but the faces must be connected and form a continuous surface which divides the three-dimensional space into two distinct regions. 

The entity FACE.SURFACE consists of a class of surfaces that may be referenced by the topological entity FACE in a B REP. 

An EDGE is a topological entity defined within the scope of a B REP. It... 

Mixtures containing up to several thousand distinct chemical entities are often synthesized and tested in mix-and-split combinatorial chemistry. The descriptor representation of a mixture may be approximated as the descriptor average of its individual component molecules, e.g., using atom-pair and topological torsion descriptors. 

---