The expanding workspace of Rapid Prototyping will draw on the new developments
in geometric modeling. Volume modeling has substantial advantages over other modeling
schemes to meet the emerging requirements of Rapid Prototyping technology. It provides us with
a new approach to design complex geometry and topology. The integration of the volume
modeling and Rapid Prototyping technology will help us to fully exploit RP's ability to fabricate
objects with complex structures. This paper addresses our research and practice in a volume
modeling system toward Rapid Prototyping. Novel techniques in volumetric data manipulation,
NURBS volume models and triangular facet generation over solid models are presented.
Computer models designed by this system and their corresponding DTM products are also
shown atthe end of this paper.Mechanical Engineerin

Chua, Chee Kai

Lin, Feng

Ma, Di

English

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Volume Modeling for Rapid PrototypingtDi Ma, Feng Lin, Chee Kai ChuaBioMedical Engineering Research CenterNanyang Technological UniversityNanyang Avenue, Singapore 639798tEmail: p144846745@ntu.edu.sgAbstract: The expanding workspace of Rapid Prototyping will draw on the new developmentsin geometric modeling. Volume modeling has substantial advantages over other modelingschemes to meet the emerging requirements of Rapid Prototyping technology. It provides us witha new approach to design complex geometry and topology. The integration of the volumemodeling and Rapid Prototyping technology will help us to fully exploit RP's ability to fabricateobjects with complex structures. This paper addresses our research and practice in a volumemodeling system toward Rapid Prototyping. Novel techniques in volumetric data manipulation,NURBS volume models and triangular facet generation over solid models are presented.Computer models designed by this system and their corresponding DTM products are alsoshown atthe end of this paper.1. IntroductionRapid prototyping (RP), otherwise known as Solid Freeform Fabrication (SFF) or LayerManufacturing Technology (LMT) , is among the latest revolutionary technologies inmanufacturing which are taking the industry by storm [1]. It represents a range of systems whichcan fabricate 3D structures from a computer-aided system in a matter of hours. A commonfeature among these RP systems is that they all apply additive methods in fabrication process,that is, to build a part, prototype, or tool in a gradual, controlled way by laying down material,point by point or layer by layer, until the part is completed. With additive methods thefabrication process is indispensable on the part's complexity. Thus complex objects witharbitrary shapes and microstructures, which, if not impossible, will be very difficult fortraditional manufacturing methods, can be fabricated through RP system with the same.manneras in fabricating simple geometry objects. The revolutionary development ofRP inmanufacturing will draw on the new development in geometric modeling.Applications of computer graphics in the area of CAD/CAM take an important role in themodern manufacturing industry. But existing CAD tools are geared towardthe design ofpartsmanufactured by traditional methods, they do not help designers exploit the expanded designspace offered by RP technology. In addition, Rapid Prototyping are encountering non-CADbased surface and volume coordinate data increasingly in commetcialdeveloping .andmanufacturing applications [2]. In some areas, such as in medicine, only non-CAD data exists.These data can not be input into current CAD/CAM systems for further modifying andmanipulation unless they are converted to geometric representation by fitting. or approximatingmethods.To overcome these problems, a new modeling scheme volume modeling is proposed totackle the emerging requirements of the RP technology. Volume modeling has the ability to77represent arbitrary geometry/topology and supports reverse engineering. The integration ofvolume modeling and RP will help us to fully exploit RP's ability to fabricate complexstructured objects.2. Volume ModelingTraditionaUy, computer graphics studies methods of modeling and rendering geometricobjects.•Volumegraphics [3], as a sub~discipline of computer graphics, focuses on specialmethoclSiiiof modeling. and rendering complex objects/phenomena with inhomogeneous materialsandarbitrarystructuresina discrete 3~dimensional space. In volume modeling, objects are storedin. a.cliscretevolurnetricdataset,which is defined by a grid of voxels, figure 1. A voxel isaspatial element which is defined by a unit cube centered at (x, y, z). Each voxel is associatedwith its properties such as density, color, opacity, physical size and other user~definedparameters.Figure 1: A 3 X 3 X 3 volumetric data set, each solidcircle represents a voxelA volume model is a discrete representation of 3D objects. It has a close correspondencewith RP process (layer by layer). The access to a given point in a volume data set is easy. In alinear list, the address of an individual voxel with coordinate (x, y, z) is:Addr =zxxmax x Ymax + yxxmax + Xwhere Xmax X Ymax X Zmax is the resolution of the 3D data set. This formula can be easilyextended to address a layer of voxels. On the other hand, RP process is a "discretized"fabrication process. RP technology decreases the 3~dimensional fabrication process into a 2~dimensional one. In a specific layer, small fabrication primitives, such as drops or layers, areapplied over former layer. A volume model is ready to provide corresponding point or layerinformation with each case.Compared with the other modeling schemes, volume modeling has the following distinctproperties:• model complex geometry / topology object78As there is no constraints put on the voxel description, complex structures can be achievedjust by defining voxels either within or outside the modeled object. In addition, Booleanoperations can be easily applied on the volume models. CAD tools built using volumemodels allow arbitrary shape manipulation and sculpting.l1li design inhomogeneous objectBy defining the property of each voxel within it, a volume model can representinhomogeneous objects (composites), flexible objects and objects that are made of solid,liquid and amorphous materials. Conventional design tools are not oriented to the design ofcomposite objects.l1li easy 3D data acquisition3D medical image data obtained from CT/MRI scanners are natural volume models. It is easyto obtain the volume models from these 3D image data set. This is of great value in reverseengineering.3. Modeling TechnologyDue to its discrete property, the control and manipulation over the volume models are noteasy. To overcome the drawback of the lack of structural information within a volume model,NURBS-based volume modeling is proposed [4]. NURBS has become the de facto standard forthe representation, design and data exchange of geometric information processed by computers[5]. An NURBS-based volume modeler will have advantages from both NURBS modeling andvolume modeling.NURBS volume is proposed to represent 3D solid objects. Its Cartesian coordinate form is asfollows:",m ",n ",I "( )_ k=o £..Jj=O £...ik=l.)Ni,p(u)Nj,q(v)Nk,r(t)Wi,j,k~,j,kV U, v, t - ",m "C'n "C'Ik=l.) £..Jj=l.) £..Jk=l.)Ni,p(u)Nj,c/v)Nk,r(t)Wi,j,kwhere Pi,j,k =(Xi,j,k' Yi,j,k' Zi,j,k) are the Cartesian coordinates of the volume control points. Wi,j,kis the weight on the control point ~,j,k' p, q, r are the order of the volume in the parametric u-direction, v-direction and t-direction respectively. U ={uo,Ul' ...... ,U j }, V ={vo' Vl' ...... ,vg } andT={to,tl' ......'th } are knot vectors in the respective directions, f= m ± p, g = n ±q, h =1 ± r.Ni,p(u), Nj,q(v), Nk,,(t) are pth-order, qth-order, rth-order B-spline basis functions defined on theknot vectors U, V, T respectively.A NURBS volume is a continuous model while a volume model is a discrete representation.A NURBS volume can be turned into its corresponding volume model through the process ofvoxelization [6]. As Boolean operations are difficult to be applied on high order NURBSvolumes, the key idea of NURBS based volume modeling is to exploit the flexibility of NURBSmodeling and use the voxelized objects as components to construct complex objects.4. Interfacing Volume Modeling with Rapid Prototyping79The general method tp interface 3Ddi~crete data ~et with Rapid Prototyping is to use contourinformation as input [7]. It reqlJiresthe~xtractionofthecontourinformation from a 3D discretedata set. This step is straightforward. But tl1emajor drawback inthis approach is the need forinterpolation when processing c011tollr.datA.sets [;2].As STL is the de facto standard input format for RP, it is logical to generate STL filesd.irectlyJrom avolume model. Generatic.m of STL files through volume modeling and i~o-surfaceextractioni$ proposed. A modified MarchingCubes algorithm is used to generate triangle facetsAndgetthe~radientinformation of each vertex from a volume model. Marching Cubes algorithmis a classic iso-surface extraction algorithm [8]. It is performed 011 a volumetric data set andgenerates triangle facets within each unit cube using a divide-and-conquer approach. It retainsinter-slice connectivity from the original 3D data. After verifying the consistence of facetnormals, then write them into aSTLJormatfile.:Figure+show~anearSTL model.Figure 2: ear STLmodelVolume modelers have;qdvantages oVer surface and solid modelersin the goal of achievingvalidity of STL file generation.. The seamless r~presentationof a volume model avoids theproblems caused byinternalwaUsandstructures. The process of Marching Cubes algorithm toproduce triangle facet guarantees .the final. model's shell-closure property. The coherenc.emechanism makes the final>STLJree of leaks and overlapping facet. Correct facet-orientationcan be obtained by normal verificatiOn.5. Software System DevelopmentAn experimental system has been developed for volume modeling and STL generation.Figure 3 gives an overview of/the architecture of this geometric modeling system. The systemconsists three layers: input layer, internal layer and output layer, each layer includes both dataand operations.Research has been started with the fundamental issues such as 3D data acquisition,volumetric data segmentation, voxelization of parametric surface and volume, volume rendering,surface boundary reconstruction, and interface with CAD/CAM systems.80InputInternalModeling operations f--~VisualizationOutputFigure 3: System Architecture6. Experimental Result3D measurementSTL models generated from the experimental system were fabricated by DTM Corporation'sSinterstation 2000 system. The SLS (Selective Laser Sintering) process creates three-dimensional objects, layer by layer, from CAD data files in the industry-standard STL file formatusing powdered materials with heat generated by C02 laser within the Sinterstation 2000System. The interaction of the laser beam with the powder raises the temperature to the glasstransition temperature which is below the point of melting, resulting in particle bonding, fusingthe particles to themselves and the previous layer to form a solid [9].Figure 4,5 show the STL models and their corresponding DTM's products respectively. STLfiles are displayed by Materialise's Magics View.Part Por (Figure 4) is a porosity model created by a computer simulation process. Thearbitrary shape and inner microstructure of part Por illustrate the ability of volume modelingcomplex topOlogy and geometry design.The original image data of part Halfbrain. (figure 5) is obtained· from a 128 X 128 X 84resolution version ofUNC chapeFHillbrain data, anMRI scan of human head. We only use halfpart ofthe brainnlOdel.81(a) STL modelFigure 4: Part Por(b) DTM product7. Conclusion(a) STL modelFigure 5: Part Halfbrain(b) DTM productThis paper addressed the research and practice in a volume modeling system toward RP. Byits close resemblance with the process of RP and its ability to represent natural objects/scenes,volume modeling is proposed as the modeling scheme to tackle the challenges posed by RPtechnology. A.s the lack of structural information in a volume model causes the manipulation andcontrol over a volume model difficult, NURBS-based volume modeling is proposed to handlethis problem. NURBS-based volume modeling possesses advantages from both NURBSmodeling and volume modeling. The issue of interfacing between volume modeling and RP isalso addressed. A. novel approach is proposed for generating STL file format through volumemodeling and iso-surface extraction. This approach guarantees the validity of the final STL files.82References:1. Chua Chee Kai and Leong Kah Fai, Rapid Prototyping: Principles and Applications inManufacturing, John Wiley. & Sons, Inc.,. 19972. Vail, N.K., et aI, "Interfacing Reverse Engineering Data to Rapid Prototyping", SolidFreeform Fabrication Proceedings 1996, Austin, TX, August, 19963. Kaufman, A., Cohen, D., Yagel, R., "Volume Graphics", IEEE Computer, pp. 51-64, Vo1.26,No.7, 19934. Zhongke Wu, Hock Song Seah and Feng Lin, "NURES-based volume modeling", Workshopon Volume Graphics '99, Swansea, UK, March, 19995. Piegl and W. Tiller, The NURBS book. New York: Springer-Verlag, 19976. Zhongke Wu, Hock Song Seah and Feng Lin, "Voxelization of NURES curve, surface andvolume", submitted to IEEE transaction on Visualization and Computer Graphics.7. Richard H. Crawford, "Computer Aspects of Solid Free Form Fabrication: Geometry,Process Control, and Design", Solid Freeform Fabrication Proceedings 1993, Austin,TX,August, 19938. Lorence, W.E. and Cline, H.E., "Marching cubes: a high resolution 3D surface constructionalgorithm", Computer Graphics, pp.163-169, Vo1.21, No.4, 19879. Chua Chee Kai, et aI, "A Study of the State-of-the-Art Rapid Prototyping Technologies", TheInternational Journal ofAdvanced Manufacturing Technology, pp.146-152, Vol. 14, 199883

Volume Modeling for Rapid Prototyping

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Volume Modeling for Rapid Prototyping

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