Knowledge Technology
New Directions for CAD (Role for FSG)
One continuing area of discussion is the role of Knowledge Technology (KT) via Knowledge Based Engineering [1] (KBE) in PLM and CAx; that KBE has demonstrated remarkable success in several design and manufacturing domains cannot be ignored; there is a lot of emphasis currently in defining the future and the look of the KT components of KBE.
This article looks at one of the various improvements that have been proposed for KBE. This improvement is titled Finite Surface Generation (FSG) and provides for a remarkable change in the computational basis for KBE.
Recap of FSG
Prior COE NewsNet articles provided a brief overview of FSG and explained the background. Here is a brief recap of those articles.
- An early article discussed the dichotomy [2] between natural ‘forms and manmade objects’ within the context of Computer Aided Tissue Engineering (CATE). Below is an example that illustrates the different types of shapes that are available only through FSG.
- The next KT article provided quick review of CATE requirements and showed that these are of a much large order of magnitude than normally seen, given CATE’s domain of the biologic [3]. Yet, some insights from CATE may very well be appropriate for the normal design situation.
- A subsequent article looked at the particulars of CATE [4]. In many cases, CATE results must integrate well with existing natural forms which results in a complicated set of requirements.
- The latest article discussed the role of archetypes in defining bio-mimetic structures [5] and suggested a new type of classification scheme related to the properties of the requirement. The properties include definition of the initial boundary conditions, the particulars of the environment, and characteristics of the related automaton.
FSG, as a method, allows design and development of natural looking forms by derivation of advanced shapes that are associated with solving minimal-energy systems. FSG has been applied in several design settings and can support all types of fabrication methods. One example designed and produced a machined part. Other designs turned out to be excellent candidates for using casting methods. FSG can support advanced material processing such as composites. Certain views consider that the real potential for FSG will be with the more advanced methods.
FSG is a non-prismatic system of geometry generation. FSG uses a more general approach to surface definition by representing a surface as a summation of small triangles, or facets. Thus a finite surface is a simplical representation of a union of triangles. The use of small triangular elements to represent surface forms is beneficial – it allows a common (albeit large) representation of most any of the varied surface forms that are traditionally formed by algebraic expression. Traditional surfaces are comprised of simple known equations for spheres, cylinders and planes; others, such as NURBS use basis polynomials. FSG is not a parameterized mapping of two variables but is instead a summation of many discrete computational events. This common format allows for the differentiation of most surface forms in terms of a varied energy state -- that is, the interplay of tension and pressure forces acting on a series of facets or nodes. For example, an FSG representation of sphere is not determined by geometry, such as radius and origin, but instead is an energy equilibrium state in the form of a sphere having uniform curvature.
In general, an initial FSG surface is a coarse set of triangles that spans a closed boundary or perhaps several boundaries. The surface moves computationally from the initial form to the final form. The initial triangular mesh is refined and moved toward a minimum energy state by an optimization method that controls motion of the surface to balance energies, of several types. The final surface form therefore meets equilibrium conditions across all facets of the mesh. This process is universally capable of representing planes, cubes, cylinders and spheres but does so computationally by creating an equivalent tessellated form.
FSG has been applied to several types of problems. For instance, FSG affords a new way to solve reverse engineering decisions related to mapping shapes to sampled data. As well, FSG has solved design problems that are not amenable to standard methods. These applications include castings and machined parts. In particular cast parts appear to be good candidates for the process because the resulting surfaces forms do not have structural discontinuities that would result in stress concentrations. The application is best suited for castings, composites, and super-plastic formed parts. There are significant benefits regardless of the manufacturing process over standard CAD modeling techniques.
Reverse Engineering by FSG
Initial studies in computer aided tissue engineering (CATE) indicate that the structure and form of bone, and other organs can be aptly simulated by this process where traditional prismatic and NURBS representation fall far short. This work allows a comparison of FSG with known Reverse Engineering [6] (RE) techniques.
All common prismatic shapes can be represented by a FSG process. Smoothness of compound surfaces has not been an issue as the scale, and number of facets can be increase to achieve the level of smoothness that is desired.
In computer tissue engineering applications, a femur (Figure 1) has been created based on MRI voxel data. This data was selectively sampled, and a complete external shape of the femur represented as a fine mesh of triangles was generated. The FSG data was several orders of magnitude less than the voxel data size; the correlation between the FSG version and the MRI data was excellent (left and middle images of Figure 1). The basis for bio-structures is not well known – we cannot create a femur from any known geometric process as we can a cylinder – computer aided tissue engineering is largely limited to reverse engineering of existing bio-forms. The right image of Figure 1 shows a solution using the normal RE approach. Not only is there a larger footprint of this NURBS solution, but it required more points thereby requiring more effort. Representational trades are discussed later in the article.
Figure 1 - FSG Femur example
RE application of FSG are not limited to bio-mimetic forms. Tessellated surfaces can be created from solid models or laser surveys of existing objects. The data files are then translated to an FSG form. Generally, the RE situation involves a large number of points, where the count can be in the millions, that must be fit with geometric shapes. One step of the process may be to determine if a region or subset of the points represents a known shape such as a tube or plane. Normally, a subset is determined by some type of rule; this subset is then matched against alternative parametric shapes.
FSG can interrogate point cloud data and determine the discontinuities such as boundaries of planes cylinders and spheres; then, these objects can be identified and isolated. Since the boundaries of such features are of singular importance to the recreation of the feature, then, the interior points can be eliminate or reduced to compress the dataset size.
In this type of RE context, FSG can help filter large datasets and can discover underlying prismatic shapes. The normal RE approach uses all the points, filters points, and then does trial-and-error searches. The FSG approach is different is that FSG identifies alternative boundary conditions using only a small subset of the points. In one case, FSG required only a few hundred of 10s of 1000s of points; not only did the FSG approach converge to an acceptable solution, it allowed faster convergence. In this type of approach, the larger point set is mainly used for checking results.
Design by FSG
An example of how FSG can improve results produced by CAx is shown in Figure 2 as differences in appearance for the three alternatives. The two on the left are examples of approaches that use traditional shapes: I-Bean and Cylinder. The FSG form is shown on the right.
Figure 2 - Alternatives
The FSG solution has an ‘organic’ look that might be considered more aesthetic than the other two; also upon comparative analysis, it weighs considerably less and is stronger than the other two designs. The analysis results are shown in Figure 2. The FSG Form has no structural discontinuities and can meet the torsional stiffness requirement.
As covered in the above-referenced articles, FSG uses a sparse initial form that is manipulated via an automaton within an environment. The specification of the initial boundary conditions is a major control factor for FSG. In this case (FSG Form), the mess was an empty shell. A solid can be formed using a variable offset on the mesh. The FSG solution is then essentially a shell with an open interior. The thickness for the variable offset can be controlled by a design constraint. Another option is to have the interior shell follow the external contour during the numeric solution of minimal-energy system.
Internally, FSG uses a basic representation that is an annotated mesh; this mesh supports numeric processing and convergence. As such, FSG is b-rep (boundary representation) in nature. One discussion looks at how close the b-rep of a constructive (CSG) method can approximate the FSG. On the other hand, there is the question of whether it is necessary to have a solid representation. Methods based upon CSG require meshing to support analysis. FSG can support analysis natively.
An option might be to use FSG to perturb a mesh in order to effect change to a CSG model. Mapping the b-rep results back to the necessary parametric deltas is an open problem of CAx and is of much interest. A subsequent article will discuss issues and trades related to such transformation and analysis approaches.
The design by FSG (FSG Form) is both lighter and stronger. This type of design suggests several new methods for solving problems related to CAx which will be discussed in a future paper.
The FSG convergence process is controlled by parameters, constraint fields, and rules. There are other decisions that concern trades between alternatives produced by the FSG method. These decisions are heavily influenced by KBE and multi-disciplinary optimization techniques.
Conclusion
This article looks at FSG in terms of what it entails as well as its potential use in KBE. One example looks at FSG in the context of Computer Aid Tissue Engineering and demonstrates a novel approach to reverse engineering. Another example shows how a FSG design compared to two traditional approaches in terms of appeal of the design and of physical properties. This example demonstrates some of the benefits that can result from applying the FSG approach.
In the design example, there is a single part. FSG can be applied to a collection of parts for which the overall energy system is minimized. Subsequent articles will provide discussion of FSG, look at other types of applications of FSG, consider modeling trades that are still open, and describe continuing efforts at bringing FSG into CAx and PLM.
References
[1] Switlik, John “Knowledge Based Engineering: Update”, COE NewsNet, October/November 2005
[2] Swanson, Kurt “New Directions For CAD #1”, COE NewsNet – October/November 2004
[3] Swanson, Kurt “New Directions For CAD #2”, COE NewsNet – April 2005
[4] Switlik, John “New Directions for CAD (Bio-CAD as an example)” COE Newsnet – July 2005
[5] Swanson, Kurt “New Directions For CAD #3”, COE NewsNet – October/November 2005
[6] Switlik, John M. and Macy, B. “Reverse Engineering – Support for An Empirical Process”, COE NewsNet – September 2003
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