Fig. 8.2 shows the five basic RP system elements that affect shape: (1) data creation, (2) common data exchange format, (3) model validity and repair, (4) compensation, and (5) support structures.

Fig. 8.2. RP elements affecting shape.

Data Creation

The first step in the overall RP process is the creation of geometric data, either as a 3D solid using a CAD workstation, or as 2D slices using a scanning device. In either case, the data must represent a valid geometric model; namely, one whose boundary surfaces enclose a finite volume, contain no holes exposing the interior, and do not fold back on themselves. In other words, the object must have an "inside." Nonmanifold conditions such as zero-thickness dangling surfaces or more than two surfaces meeting along a common edge, among others, are not allowed (Weiler 1986).1 Even thin shells have finite volumes. The model is valid if for each point in 3D space the computer can determine uniquely whether that point lies inside, on, or outside the boundary surface of the model, and if the region around the point (neighborhood) is "well behaved." This fundamental property makes possible the automatic geometric manipulation operations that give SFF its appeal as an automated process.

If 2D contour data are sent directly to the SFF machine, the information implicit in the description must be sufficient to stitch together a valid 3D volume.

Common Data Exchange Format

For reasons of competitiveness, targeted markets, and performance, CAD systems utilize a variety of geometric mathematical forms and data formats. SFF machine vendors accommodate this variety by requiring that all external input geometric models be expressed in a neutral format. CAD vendors are responsible for providing CAD post-processors that translate their internal CAD representations to this common format.

Model Validity and Repair

To be more precise, CAD post-processors actually approximate the vendors' internal CAD geometric forms (e.g., B-splines) with a simplified mathematical form (triangles), which in turn is expressed in a specified data format: STL. Unfortunately, this approximating operation, if not done precisely, sometimes introduces undesirable geometric anomalies, such as holes or overlapping portions in the boundary surface. Consequently, most SFF machines have software to check the input model to ensure it is a valid solid, that is, it is a well-behaved, closed, and bounded model with a finite interior. If this is not the case, then capabilities are needed to repair the model.

Given a valid model, a series of geometric operations must be performed on the model (model preparation) to ensure that the physical part will meet the input specifications. For example, the model needs to be oriented and scaled for the SFF machine workspace. The orientation depends on factors relating to surface quality, build time, support structures, downstream processing characteristics (shrinkage, curling, distortion, resin flow), and part tolerance, among others (Frank and Fadel 1994; Thompson and Crawford 1995). The nesting (Beascoechea 1995, 1996) of many parts in a single build chamber and the building of assemblies concurrently are also considerations.


The model shape may need to be altered to compensate for anticipated downstream physical anomalies introduced during fabrication, such as shrinkage, warpage, curl, and deformation. Most compensation today is coarse and usually left to an operator's intuition, gained by trial and error. The status of predictive analytic models is discussed later.

Support Structures

Support structures are needed in liquid-based processes to prop up overhanging portions of the 3D part, to attach the part to the workspace platform, and to internally buttress hollow parts. Parts and supports may need drain holes. Support locations for overhangs can be determined by checking the direction of surface normals and by z-axis projections of the model. Software exists to automatically generate support structures that attempt to use the least possible amount of material. Powder- and sheet-based processes use the surrounding unprocessed material for support. Even in these latter processes, the Japanese would like to shorten the time required to remove unprocessed support material and clean the part to high surface quality. The cost of data preparation and post-processing can amount to two-thirds of the total cost of building a part (Dolenc and Mäkelä 1995).

For very precise parts with many thin protrusions, the compensation and support structure generation operations may need to be iterated, because the support may distort the previously compensated part.

To obtain the necessary motion control trajectories to drive the actual solidification mechanism, the prepared geometric model is sliced into layers of possible different thicknesses, and the slices are scanned into lines (if required), mimicking in reverse the layer-to-layer physical building process (Rock 1991; Dolenc and Mäkelä 1994; Suh and Wozny 1994). The scanned lines determine when a laser beam or some other solidifying agent is turned on or off. The layer thickness determines the amount to raise or lower the part and/or the container for recoating.

Using a manufacturing interpretation, Otto et al. (1995) categorize SFF software as the following types: (1) design (original part); (2) computer-aided process planning (part orientation, scaling, nesting, support design, compensation); and (3) computer-aided manufacturing programming (slicing, commands, and controls).

Ultimately, more sophisticated control strategies based on process sensor feedback loops are desirable, but this is still a topic of research.

1 Weiler 1986 is the original reference. Papers on the subject have appeared in the IFIP WG5.2 series of volumes on geometric modeling in Wozny et al. 1988, Wozny et al. 1990, Turner et al. 1991, and Wilson et al. 1992.
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Published: March 1997; WTEC Hyper-Librarian