Alpha_l is a nonuniform rational B-spline (NURBs) based solid modeling system that
has been developed at the University of Utah over the past 10 years. In addition to being
useful in modeling objects that are described by simple rotation and extrusion operations,
the real power of Alpha_l is demonstrated in the modeling of complex parts with sculptured
surfaces. For the past several years, a major research thrust has been to use Alpha_l to
semi-automatically generate process plan information and numerical control code to manufacture
mechanical parts directly from the models. A long term goal is to support an on-line
remote manufacturing facility for producing prototype parts. Recently, a 3D Systems stereo
lithography machine has been added to the advanced manufacturing laboratory. The stereo
lithography process and other SFF techniques are of particular interest for supporting a
remote manufacturing facility in that these processes are inherently much safer than numerically
controlled machining. Special Alpha_l interfaces including a new slicing algorithm
are being developed for the SFF machine use. By generating a SFF part directly from
its NURBs description, Alpha_l should facilitate the manufacture of complex parts while
providing smoother surfaces.Mechanical Engineerin

Drake, Samuel H.

English

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ALPHA_I, REMOTE MANUFACTURING, ANDSOLID FREEFORM FABRICATION *Samuel H. DrakeUniversity of UtahMay 1990work was supported in part by DARPA (N00014-88-K-0689). All opinions, findings, conclusions orrecommendations expressed in this document are those of the author and do not necessarily reflect the views ofthe sponsoring agencies.114ALPHA_I, REMOTE MANUFACTURING, ANDSOLID FREEFORM FABRICATION *Samuel H. DrakeUniversity of UtahMay 1990AbstractAlpha_l is a nonuniform rational B-spline (NURBs) based solid modeling system thathas been developed at the University of Utah over the past 10 years. In addition to beinguseful in modeling objects that are described by simple rotation and extrusion operations,the real power of Alpha_l is demonstrated in the modeling of complex parts with sculpturedsurfaces. For the past several years, a major research thrust has been to use Alpha_l tosemi-automatically generate process plan information and numerical control code to manu-facture mechanical parts directly from the models. A long term goal is to support an on-lineremote manufacturing facility for producing prototype parts. Recently, a 3D Systems stereolithography machine has been added to the advanced manufacturing laboratory. The stereolithography process and other SFF techniques are of particular interest for supporting aremote manufacturing facility in that these processes are inherently much safer than nu-merically controlled machining. Special Alpha_l interfaces including a new slicing algorithmare being developed for the SFF machine use. By generating a SFF part directly fromits NURBs description, Alpha_l should facilitate the manufacture of complex parts whileproviding smoother surfaces.1 IntroductionAlpha_1 is a nonuniform rational B-spline (NURBs) based solid modeling system that has beendeveloped at the University of Utah over the past 10 years. While Alpha_1 is quite useful inmodeling objects that are described by simple rotation and extrusion operations, the real powerof Alpha_1 is in modeling complex parts that include sculptured surfaces.For the past several years, a major research thrust has been to use Alpha_1 to semi-automatically generate process plan information and numerical control code to manufacturemechanical parts directly from the models. A long term goal is to support an on-line remotemanufacturing facility for producing prototype parts. Ultimately, it should be possible to design"'This work was supported in part by DARPA (N00014-88-K-0689). All opinions, findings, conclusions orrecommendations expressed in this document are those of the author and do not necessarily reflect the views ofthe sponsoring agencies.115parts or complete assemblies of parts in one location and have them manufactured in one ormore remote locations and then shipped to where they are needed. This system would be amechanical analog to the MOSIS (Metal Oxide on Silicon Implementation Service) that is nowavailable. for vtsI.designers.Currently, the University of Utah advanced manufacturing laboratory has several state-of-the-art CNC machines including a 5-.axis vertical machining center (milling machine) and a turn-ing center (lathe) with a servo spindle and powered rotary tools. A direct computer controlledcoordinate measuring machine is being acquired to both automatically inspect manufacturedparts and to input data from existing parts and physical models.Recently, a 3D Systems stereo lithography machine has been added to the advanced manu-facturing laboratory. The stereo lithography process and other solid freeform fabrication (SFF)techniques have several major advantages for initial experiments in supporting a remote manu-facturing facility. It is an inherently safe process in that errors can not cause a crash that coulddamage the machine or even injure the operator. Also, considerably less information is requiredto manufacture a part using SFF. With conventional machining, it is necessary to have com-plete process planning information including information on sequence of operations, fixturing,cutting tools, and material properties. Conversely, with SFF there is no material information,no cutting tool information, and almost no fixturing information required.In many cases, the SFF process should allow prototype parts to be made without machining.This will be especially true if parts can be made from engineering materials either directly orindirectly. Even if more conventional manufactuing techniques are ultimately required, SFFprocesses can be used to prove out the model before using the conventional techniques.2 The Alpha_l Modeling SystemAlpha_l is a spline based, boundary representation solid modeler that is used to model a largeclass of sculptured and non-sculptured mechanical parts. Objects which fall into this categoryinclude turbine blades, airplanes, helicopters, automobiles and automobile parts, sewing machineparts, robots and robot parts, molded plastic parts and the molds to produce them, etc. Evenparts that have, at first glance, a simple geometry sometimes cannot be accurately modeledwithout sculptured surfaces.AlphaJ also demonstrates the utility of high quality graphics in the mechanical designprocess, particularly when dealing with sculptured surfaces. Proper perception of a complexshape is not possible from a line drawing or rough shaded rendering. Much of the perceivedinformation about the shape of a sculptured object comes from the highlights caused by specularreflections from the surface. Without an accurate lighting model and a high resolution image,the highlights, and thus the perceived shape, will be distorted. Surface ripples that might beinvisible in a line drawing show up immediately in a shaded raster image.AlphaJ also serves as an experimental testbed on which new modeling ideas and techniquescan be easily mounted and evaluated.1162.1 B·Splines in Alpha_1The tensor product parametric NURBs surface representation is the single representation thatoccurs throughout the Alpha.l system, and is supported by the entire system. Much of thesystem has been extended to support the "trimmed" surfaces, which are the results of Booleanoperations derived. from the eSG design paradigm.B-splines have a nu.mber of desirable properties for use in computer-aided geometric design.A B-spline curve/surface is a piecewise rational function and exhibits specified degrees of con-tinuity along specified isoparametric values, called "knot lines". For example, cubic B-splinecurves can be C 3 , C 2 , C 1 , Co, or discontinuous at such a knot value, as specified. This ensuresthat a curve which should be smooth is indeed smooth, but by properly manipulating the knotvector, discontinuities of specified derivatives may be inserted in the curve.B-splines have the convex hull property; that is, the curve always lies within the convex hullof the control points. It is therefore easy to bound the curve/surface, simplifying the calculationssuch as those required for producing an image or calculating errors in NC paths. Another featureof B-splines that is useful in a design system is that they provide "local control". Changing thelocation of a single control point modifies the shape of only a portion of the surface; the rest ofthe surface remains unchanged. This allows, for example, a designer to shape one region of asurface without affecting other regions that may be already complete.The use of rational B-splines allows the exact representation of a large class of shapes,including the common quadric surfaces such as spheres, cylinders and cones. A polynomialB-spline, since it is a piecewise parametric polynomial curve or surface, can only approximatea circular or elliptical shape. By adding a weight or homogeneous component at each controlpoint, it is possible to model these shapes exactly. Since many common mechanical parts havecircular cross sections, it is critical that a design system be able to reproduce such shapes exactly.A B-spline may be evaluated by computing the value at any given point. Often, however, anapproximation to the entire curve or surface is desired. This may be found via a "subdivision"or "refinement" process. The Oslo Algorithm provides a method for taking a B-spline andcomputing a new B-spline, point for point identical to the original, but with more knots, andtherefore more control points and more polynomial spans. It can be used to split, or subdivide, aB-spline into two pieces that, together, make tip the original. The new control polygon, formedby joining the control points in order, more closely approximates the curve than did the original.Thus, by adding enough new knots, the control polygon itself may be used as an approximationto the curve.2.2 A Short Description of the Alpha_l SystemThe Alpha.J.. system provides a number of capabilities. A short listing of the features of Alpha_lincludes:• an interactive, extensible geometric editor,• drafting style geometric construction operators,• high-level shape modification and design operators,117• automatic creation of primitive objects,• support. for parametric design,• feature based" design,• the ability to perform set operations to combine objects into more complex assemblies,• high quality graphical renderings of object models,• computation of simple mass properties of modeled objects,• direct interface to 3D systems stereo lithography machine, and• model driven CNC code generation2.3 Set OperationsThe ability to perform set operations, usually union, intersection, and difference, on models isrecognized as one of the characteristics of a true solid modeling system. Set operations performa number of useful functions in the modeling process. They can be used to combine simplerobjects into more complex ones. It is not necessary to design an entire object in one piece;it may be broken down into simpler components that can be designed independently. Theregions where the different parts meet are not explicitly designed, but arise from the interactionbetween the independently designed pieces. Using set operations to combine the parts producesthe interface region automatically. A good example of this interaction occurs in a turbineblade, where the airfoil portion of the blade must be designed to meet certain aerodynamic orhydrodynamic constraints. The root of the blade is designed to hold the blade into the turbineduring operation, and must meet an entirely different set of mechanical constraints. The airfoilmust, however, be attached to the root, and a set operation is an ideal way to model the mergerof the two.The Alpha_l system has the ability to perform set operations on "partially bounded sets". Aslong as they satisfy certain loose criteria, boundaries of objects to be combined by set operationsneed not be closed. This is a nice feature for the designer, who is not arbitrarily forced to closeobject boundaries just so that set operations may be performed. A good example of this is seenin the design of a turbine blade root, where none of the boundaries of the subpieces completelyenclose a volume, but the final model does have a closed boundary.2.4 GraphicsA key concept put forth by the Alpha_l project is that design of mechanical parts and, inparticular, of sculptured mechanical parts, is greatly aided by high quality graphic rendering ofthe model. Towards this end, the AlphaJ system incorporates both a scanline rendering programand a ray tracing program that can produce images of B-spline surfaces. This process canadaptively subdivide surfaces until the pieces are flat, to a given resolution, produce polyhedralapproximations, and either ray trace or scanline render the resulting polygons. The progranlhas many options to control the rendering process, the lighting model, surface characteristics,118and output form. It is possible to specify transparent or semi-transparent surfaces, allowing thedesigner to see interior details as well. Control over lighting is also provided, to allow carefulplacement of highlights to give maximum shape information. Images created with the ray tracingprogram may also include shadows, reflections, and texture mapping.Geometric EditorThe geometric editors for Alpha_I, shape_edit and model-server, are implemented in PortableStandard Lisp (PSL). Lisp provides a rich interpretive environment in which arbitrary andextensible data structures may be easily created. The embedding of the editor in a languageleads easily to the concept of the program as the model, rather than the output created by theprogram. It is also easy, therefore, to create a parametric model, one that can represent a familyof parts by changing a set of parameters. Many tools and operations are provided for shapedefinition. These include drafting operations, sweep operations, shape modification operations. and primitive objects.The drafting paradigm of design is supported by providing a number of drafting type opera-tions that deal with points, lines, and arcs in the plane. Arcs and line segments may be chainedtogether into a B-spline curve. Curves can be used to construct surfaces in many ways. Alpha_lalso has a particularly rich set of sweep operators that can be used to generate sculpted surfacesin a predictable manner.To simplify the task of working with B-spline surfaces, high level shape modification anddesign operators have been created. For example, the bend operator takes a previously definedsurface and bends it. A thickening operation starts with a single surface, computes a surfacethat is offset from it by a given amount, and joins the edges of the two to form an object shapedlike the original surface.To accommodate models created by CSG systems, or for those cases when primitive shapesare desired, routines are included for automatically creating some basic objects. These includeboxes, spheres and ellipsoids, cylinders and cones, and tori. The surfaces of the primitives arerepresented as B-splines, so any of the shape modification operators can be applied to them.Real objects often have rounded corners, instead of the sharp corners on the primitive shapes.Therefore, provision has been made to create versions of some of the primitives with roundedcorners. In particular, cuboidal shapes with rounded edges and corners are supported. The radiineed not be identical on all edges, and the faces need not be at right angles.Finally, special purpose routines can be written to model any desired family of shapes. Anexample of this are the manufacturing features which can be optionally loaded into the geometriceditor. Features including counterbores, countersinks, slotted holes, and rounded pockets havebeen defined in terms of built-in objects in the geometric editor. Linear and radial patterns ofthose features can also be constructed.3 Using Alpha_l for Solid Freeform FabricationSFF machines will be accessible to a potentially much larger user community than milling andturning machines. Therefore it is important to be able to drive them as automatically and asdirectly from the model as possible.119Special Alpha_l interfaces are being developed to drive the 3D SFF directly from the model.To implement this interface, it is necessary to generate a complete solid polyhedron whose facetsare properly triangulated. This means that the process .requires triangles arranged so that anedge of one triangle cannotcontainave:rt~xofan.adjacent triangle.Fortunately, the scanline rendering algorithm produces polygonal approximations for bothtrimmed and regular NURBs surfaces. Using that form, it is relatively easy to generate properlytriangulated surfaces for models that have only a single surface or a collection of surfaces withcorrectly declared adjacencies. As most real models contain many surfaces, it becomes relativedifficult for the designer to design surfaces· that exactly meet the other adjacent surfaces andprovide the correct adjacency information. For complex parts it is generally easier to designsimple overlapping surfaces and trim them using boolean or set operations. It should be notedthat it is sometimes possible to generate the effect of combining surfaces by using the Systems" merge" operator.A more complex algorithm has been developed to properly triangulate models with thetrimmed surface boundaries that result from using the boolean or set operators. Several recentparts represent the output from this algorithm. One potential problem with the current methodof treating trimmed surfaces is that the current slicing .routine used by 3D Systems tends tocollapse long thin triangles into degenerate lines.Anticipating potential future interfaces for SFF machines, we have also investigated therequirements and algorithms that would provide the necessary slice and layer information di-rectly from the NURBs model and have demonstrated the ability to directly generate orientedslice curves from complex AlphaJ NURBs models. By generating a SFF part directly fromits Alpha_l NURBs description, the manufacture of complex parts would be facilitated whileproviding more accurate surfaces.ReferencesDrake, S. and S. Sela, A Foundation for Features, Mechanical Engineering, Volume 111, No.1,January 1989.Riesenfeld, R.F., E. Cohen, and S. H. Drake, Computer Graphics Techniques Applied to Man-ufacturing Problems, , Third Annual Computer Graphics Synposium, Hewlett Parkard, FortCollins, Colorado, June 1989.Riesenfeld, R. F., A View Of Spline-Based Solid Modelling, Proceedings of AutoFact-5, 1983.Riesenfeld, R. F. Modeling with NURBS Curves and Surfaces, to appear in t'lcmeers in CAD (L. Piegl, ed).Riesenfeld, R. F. Design Tools for Shaping Spline Models, in Mathematical Methods in ComputerAided Geometric Design, (Edited by T. Lyche and L. Schumaker), Academic 1989.120

ALPHA_I, Remote Manufacturing, and Solid Freeform Fabrication

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ALPHA_I, Remote Manufacturing, and Solid Freeform Fabrication

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