Parametric Solid Modeling

Limitations in Current CAD Systems

Overview

Current CAD systems for part modeling exhibit severe limitations as far as parametric modeling is concerned.  Not only are the  parametric definitions  inconsistent in different modeling systems, but also the algorithms for constructing and maintaining a part family are usually ill-defined and ambiguous within any single system.  Users have little (if any) control over the behaviour of a part family, once a nominal or generic part from that family has been constructed and parametrized. The following examples should help to illustrate these inconsistencies and ambiguities. These examples were constructed in the several recent versions and types of the more popular commercial CAD systems.

Inconsistencies in parametric updates

As a first example consider the behaviour of a simple part constructed in one system as shown in figure 1(a) below. It has two parameters d and t (other parameters are not shown here for the sake of clarity). Let us see how this part shape behaves for changes in the value of parameter t.  In particular  consider a simple parametric change which when executed should result in the solid shown in figure 1(b). In this system we first created the solid in figure 1(a) as a Base (rectangular block) in which a Hole (big cylinder) is made and then a Cut (small cylinder) is made. The position (controlled by the parameter t) of the hole dependent on the base and the position of the cut (controlled by the parameter d) is in turn dependent on the edge e1 which is an intersection edge of the base with the hole. When the parameter value of t is edited so that it now corresponds to that of the solid shown in figure 1(b) (essentially collapsing the face f1 and merging the edges e1 and e3), what results in this system is the solid shown in figure 1(c), with the cut jumping off the the solid.  When the solid in figure 1(a) was constructed as a Base-Cut-Hole combination and the same parametric edit executed, the resulting solid is shown in figure 1(d), with the hole jumping on the same face f2' but refering to the wrong edge. Finally when the original solid was created using a Base-Cut-Cut combination and the same parametric edit executed it resulted in an error message from the system indicating that the parametric edit could not be executed. Thus for the same solid and the same parametric edit, even though a correct update clearly exists (as shown in figure 1(b)), this one system produces three different results depending on the combination of the type of features used to construct the solid. Figure 1

Ambiguity in updates

As another example consider the following part which is constructed in another system as an union of a block and a cylinder, with the parameter t controlling the position of the cylinder with respect to the block. When the parameter value of t is changed to 0, thus translating the cylinder to the near end, the blend jumps from one side of the face f1 to the other. Should this parametric update be considered valid? If one considers this parametric edit as a continuous change then the face f3 continuously deforms taking along with it the adjacent edges and vertices. Note however there are many continuous transforms (such as a rotation about x-axis by 180 degs or a rotation about the z-axis by 90 degs) between the two solids due to the symmetry, but these transforms do not correspond to the semantics of the parametric change (which will require that the face f1 map to f1' for instance). Figure 2 Finally consider the following part shown in figure 3(a) below. It was constructed as a union of a small block over a large block. Subsequently a hole is made on the small block. This parametric solid was edited (which corresponded to changing the values of the parameters p1 and p2 to 0) in two different CAD systems. The resulting solid in the first system is shown in figure 3(b) (which is again a disconnected solid) and the result solid in the second system is shown in figure 3(c). Neither of the resulting solids  corresponds to the intuitive result that one would expect. Figure 3

Conclusion

These examples clearly demonstrate that the semantics of a parametric edit is ambiguous and inconsistent both within and also between any two systems. The inability to handle correct updates even when one exists makes this situation impalatable.