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DQ:18.2 GEOMETRIC MODELS
Ȧã§ãX§ãThere are many ways to model a part, the major categories are,
If describing a block with a hole in it, each of the methods above will result in different descriptions
Which is best???? all of them in the right situations.
Each method has its particular advantages, and disadvantages.
The best software and hardware supports a combination of all methods.
It is assumed that other information is used to describe the geometries above, like,
The geometries can also be used to associate other information,
DQ:18.2.1 Elemental Depiction:
Depicted with the simplest of details (lines, points arcs, etc.)
Typically used in older CAD systems like AUTOCAD, CADKEY, etc.
A classic demonstration of the arbitrary nature is shown below,
DQ:18.2.2 Surface Description
The geometry is described with polygons which should represent an entire surface of an object.
Generally these polygons do not indicate which side a volume lies on, but inside/outside is defined with tricks like defining polygon vertices so that counter-clockwise is out.
STL is a good example of an engineering use of this surface representation.
This method is also used in computer games where speed is important, and the overhead of the full solid information is not desired.
Commonly used in graphics packages like HOOPS, PHIGS, CORE, etc. Also acts as the basis for the SGI computer graphics.
An example of the polygon meshes is given below.
We can also define these geometries using edge meshes.
DQ:18.2.3 Solid - Swept
A profile is created in 2D, and then swept along a path to create a volume, or to cut a volume.
The path may be straight, rotating about an axis, rotation along a helix, following a curved twisting path.
DQ:18.2.4 Solid - B-Rep (Boundary Representation)
This still bears a remote resemblance to Surface Modelling.
A BRep object is pictured below,
Each feature in a B-Rep object can be varied independently
Geometry is kept in parallel with the object topology. One example of a data structure is seen below.
A common data focus uses the edges of an object to define the shape (vertices and faces can also be used)
Euler operations can be used to build an object.
We can check to see if the solid model is valid using the basic Euler equation, or the more involved Euler-Poincare tologoical equation. These equations must be satisfied for the models to be valid.
When developing solid modelers we can use the Euler operations to ensure that the model stays topographically valid at all times.
DQ:18.2.5 Solid - CSG
Does not calculate lines/vertices/faces when storing part geometries
Uses primitive shapes such as planes, blocks, spheres, cylinders, wedges, torii, etc. to model shapes
The primitives can be rescaled to meet requirements
Uses a basic set of operators to combine or cut with the primitives,
Used in systems like PADL2, Romulus, Build, etc.
CSG designs can be stored in trees
Various types of CSG operators are possible based on closure of sets. In particular we can consider two boxes that touch, but don't overlap.
Halfspaces can be used for defining boundaries of an object.
DQ:18.2.6 Tessellated Models
Space is broken down as a regular/irregular grid.
locations in space are marked as occupied/empty/partially filled.
this method is most common when using scanners such as CAT and MRI that collect data in voxels (these are small rectangular volumes)
DQ:18.2.7 Features
The designer would simply define a part in terms of fundamental manufacturing features, such as chamfers, through slots, blind slots, etc.
Very high level, but can complicate additions of unanticipated features, like a ridge in a car hood.
- can simplify other aspects of CIM (eg. If a standard feature is used there will be a standard process plan to make that feature).
There are two levels of features commonly used in these systems,
A set of standard features for rotational parts might be,
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