Solid primitives

This chapter summarizes, completes, and compares elementary curves, elementary surfaces, offset geometric entities, solid primitives, and form features. An elementary shape exists as an individual shape and has its own type, shape characteristics, and attributes. On the other hand, it is a segment or a structural element of a more complex shape and its characteristics and attributes probably depend on other elements in the complex shape. 

A solid primitive is prepared for combination with other solid primitives or a more complex solid model under construction. It is created in its final position or repositioned after creation somewhere in the model space. Values of its dimensions are set and the solid primitive is ready for one of the element combination operations. The shapes of primitives are predefined for the modeling system or defined by engineers at application of the modeling system. Users apply one of the available solid generation rules starting from contours, sections, and curves as input entities. Primitives with predefined shape are called canonical. They are the cuboid, wedge, cylinder, cone, sphere, and torus (Figure 4-11). Inclusion of shapes other than canonical as predefined shapes is rare because application oriented shape definitions are better to define as form features. 

User-defined primitives (Figure 4-12) are created using generation rules that are applied for the generation of elementary surface models. A tabulated solid primitive or prism is created by translation of a flat contour along a vector. Rotation of a contour around a centerline produces a revolved primitive. Application of an angle... 

The basic concept of modification of a shape by form features is volume adding and removing. The shape is then adjusted by fillet and other treatment features. While solid primitives are geometric oriented shapes, form features can be application orientated. In other words, form features can be defined according to their purpose and function in the modeled part and use in a part model. At the same time, form features are often defined as pure geometry. 

The shape of a mechanical part can be divided into a well-defined set of solid primitives. A purposeful sequence of combination operations with the primitives can be applied to form the shape of the part. Constructive solid geometry (CSG) is based on this recognition. CSG was the traditional way of solid modeling. The construction method is also applied in advanced part modeling. While the traditional method applied CSG data structure, present modeling methods generate boundary representation. This difference often causes misunderstanding around CSG. 

Lines and curves are considered as initial elements in shape model construction. Higher level entities, such as wire frames, surfaces, solid primitives, and form features, are defined in the context of simple or compound lines and curves. 

Construction of simple and compound lines and curves is a starting session of shape modeling by wires, surfaces, solid primitives, and form features. Engineers communicate the design in the form of dimensional, geometric, and logical construction or design rules for the definition of line primitives and their relationships. 

The Earth s crust, mantle and core are strongly influenced by differentiation processes which could have resulted from gravitational separation ( smelting ) in an early molten phase of the planet, or from the sequence in which different chemical species condensed from the primitive solar nebula and were subsequently accreted. Seismology indicates that there is a liquid core (with a solid inner core) with radius 3500 km consisting mainly of iron (with some Ni and FeS) surrounded by a plastic (Fe, Mg silicate) mantle of thickness 2900 km. 

Figure 9.31 Some varients of allocation of PBUs fora primitive cubic packing (Pc) (a) PBU/C (b) PBU as a 3D graph and (c) as 2D planar graph (d) PBU/P black circles (b) and (c) are the sites of the lattice, that correspond to the centers of particles (or atoms), the solid lines are the bonds between them, the dotted lines are the bonds with the sites from the neighbor cells.

Their comparatively simple crystal structures may be described as a primitive packing of quasi-molecular units, and, in a way, they represent the border line between molecular and infinitely extended units in a solid (Cheetham and Day 1992). The Mo6 type core is completely surrounded by X atoms and inter-cluster bonding essentially occurs through the Mo-X interactions. The Mo—Mo bonding between clusters is very weak. 

Fig. 40 Measured (top) and simulated (bottom) XRD patterns of [Nio.7Alo.3(OH)2] (C03)o.i5-yH20 showing ordered (Vl3 x VT3)R 13.90° superlattice of carbonate anions. [The data are given as a plot, where q = 4tt sinO/X], Rhombohedral primitive cells of hydroxyl and carbonate ions are shown as solid and dashed lines respectively in the inset figure. Reprinted with permission from [263]. Copyright Elsevier Science Ltd...

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