Evolution of Engineering Drawings: From 2D Hand Sketches to 3D Solids

1. Engineering Drawing Hand drawings to Solids Andrei Lozzi 2017 2 Dimensional drawing. Purported to be the earliest example of what may be called an engineering drawing: the plan of a Chaldean fortress from ~4000 BC, Scraped on a tablet. Appears to be a scaled orthogonal projection, that is a ‘plan’ in the modern sense, of a building with substantial walls. A rare and surprisingly advanced presentation.

2. 2 ½ Dimensional drawing. An Egyptian painting showing a large monument being moved. The size of the monument, number of rope handlers, water bearers, drummers and others appear to have been presented accurately. The style used in the construction of the drawing represents 2 dimensions reasonably well but depth is just implied.

6. 3 Dimensional presentation. A ‘pictorial’ presentation of the disposition of the workers and machinery used in the erection of an obelisk in 1586 (but drawn in 1743). This drawing may give the impression of being a true perspective drawing it is close but it isn't quite. It appears to present faithfully the number and location of the workers and machinery used. That is, it tries to be an objective record of what and how the work was done. Hence it may be said to be an engineering drawing.

7. Begging with Gaspar Monge in the 1800s, engineers began to use versions of orthographic projections. It was established that all true lengths and angles could be represented by this sort of Two-Dimensional drafting method. These methods allow us to draw paradoxes, which may be resolved when drawn in Three-Dimensions.

9. Perspective or Pictorial views A pictorial view, picture-like, maybe a perspective dwg or something simpler, makes the subject look realistic. The viewer can more readily comprehends the relationship of the parts to the whole. They can more quickly deduce how it may function, because it may look like similar items that the engineer is familiar with. This leads to fewer mistakes in handling. If little or no effect of perspective is shown then the parts are small. But significant perspective effect is present, then it indicates that the parts are large, like buildings. It is difficult if not impossible on such drawings to give exact information on the dimensions and method of manufacture. Pictorial drawings tend to be used to create subjective impressions not objective ones.

10. But Why SOLIDMODELLERS 3D – 2D Paradoxes It is all too easy to generate Impossible 3D items from possible 2D projections

11. Mr Escher used to mock our confidence in 2D drawings by showing that what in 2D could appear to be an impossible construction, could in fact be achievable, if thoroughly unorthodox in reality.

12. The introduction and development of CAD was initially delayed by the time that it took for code writers to understand that engineering drawings were not ‘pictures’ but some special sort of diagrams that relied extensively on symbolism. It was then slowed by the time that it took μCPU makers to go from 4 bit to 8, 16 then 32 (64 .. 128 ..) bit processors. Finally, to the present time, it has been delayed by the time it took researchers to arrive at effective solid representations in operationsand indatabases.

13. CODING SOLIDS The aim of solid modelers has been to overcome the limitations of WF (wire frame) CAD systems. WF present just lines and surfaces, requiring the reader to interpret them into real objects. WF can have many problems among these are disconnected elements and illegal (non 3D) solids. After many years of research only about 8 means to represents solid objects in software have been found to be possible and of these only about 6 of them at all practical. Of these some are simple and exact but can only describe simple solids. Others can deal with complex shapes but are almost never quite correct. The qualities that we require of solid model data bases (files) are that they be: Unique Verifiable Closed Accurate Compact & efficient

14. CSG - constructive solid geometry. Objects are arrived at by combining primitives using Boolean operations. The primitives may be many but usually include prisms, cylinders spheres and torusus. The primitives are solid shapes for which we have exact analytic expressions for their boundaries. These primitives may be merged and combined in a number of Boolean operations such that the final assembly can be completely and exactly described. Refs Computer Graphics, Foley, van Dam et al, Addison Wesley

15. Half Spaces. The existence of a solid in space may be arrived at one step at the time, by positioning a plane in space and defining on which side of that plane the solid exists. This method works well for rectangular prisms but requires an infinite number of planes for curved surfaces

16. Sweeps. An improvement on the method of Half Planes is provided by Sweeping Representation. Instead of sweeping space with straight lines to make planes as is done in Half Spaces, here curved lines are swept through curved paths. More complex objects can be defined by intersecting one sweep with another. But, it has been found difficult to close Sweeps after Boolean operations.

17. Spatial Occupancy Enumeration. An elaborate way of saying that a solid may be represented by its building blocks (crystals or molecules). Aside from the limitation with accuracy when dealing with curved surfaces, the memory requirements must be a significant limiting feature. Nevertheless this must be a most reliable way to achieve a realistic and verifiable solid. Sometimes in the future when hard RAM may be 106 larger than at present this representation method may come on its own.

18. Prismatic, Polyhedral or Euler solids. This is one of the few representations that can be ‘perfect’ by itself. The Euler equation which may be simplified to V-E+F=2 is one of the few totally general statements that can be used to guarantee a legal solid. It applies only to prismatic solids. Some early commercial polyhedral solid modellers were used by industries that had high value products. These included vehicle manufacturers

19. Boundary Representation. This method provides the only reasonable means of representing complex curved surfaces. This technique was one of the critical steps required to make solid modellers broadly acceptable. It is very demanding of computing power and memory capacity and had to wait for 32 bit operating systems to be used in PCs. Unfortunately it is inaccurate and can result in undesirable consequences. μCPU with multiple processors and greater word length will in time reduce the errors to an insignificant level.

20. Edges of a ‘cube’. Only the nearside edges are shown Edges of a 4D super-cube Here all edges are shown Projecting from higher to lower dimensions A line is a projection on 1D space of a flat 2D surface Note that this surface could actually be of any shape. A square can be the projection on 2D space of a cube. Again, the 3D object need not be a cube. Both of these projections lose a lot of information about their original object A super-cube is a projection on 3D space of a 4D cube. Just like the other projections from higher to lower spaces A super-cube in 3D is paradoxical because we cannot be sure what really it is Possible 3D interpretations of a super-cube