Slicing Algorithm of VRML Model in Rapid Prototyping

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1 Slicing Algorithm of VRML Model in Rapid Prototyping Sun Yu Dept. of Computer Science & Technology, Xi an University of Science and Technology, Xi an ; China. Abstract: VRML (Virtual Reality Modeling Language) as an international standard for Virtual Reality, has already been widely adopted for graphical representation of 3D objects over the Web. Adopting VRML model in RP (Rapid Prototyping) can reduce the precision loss which is caused by triangulation in generating STL file. Hence exploring a slicing method and software for VRML model is significant to improve the accuracy of RP products, and has good expansibility and adaptability for color RP and virtual manufacturing. Slicing strategy and method for VRML model were proposed based on the analysis of VRML structure. With component-based development concept, slicing software for VRML model was developed using VC++ and OpenGL. The slicing software system has high precision and good expansibility. Keywords: Rapid Prototyping; slicing; VRML; OpenGL. 1. Introduction Rapid prototyping process is that it proceeds by first slicing the geometric model of a part into layers in the computer, and then reconstructs the physical part by producing these successive layers physically on top of each other. The CAD model has to be processed to a suitable format before downloading it to the RP system to be sliced. STL (STereoLithography) is the most commonly used interface in RP software. Disadvantages of STL file become apparent as RP systems become more widely used. First, STL file is verbose and carries a high degree of redundancy. Second, a major problem with STL inevitably causes accuracy loss. Last, by converting it to STL format, other relevant information, such as geometry, topology and material is neglected. As reported by Nourse etal. 85% of objects found in most industrial scenes can be approximated by planes, spheres, cones and cylinders [1]. As an international standard for VR, VRML contains mathematical descriptions of geometric primitives (box, cylinder, cone, or sphere) and advanced shapes (ElevationGrid, Extrusion, IndexedFaceSet, etc). Thus VRML is precise and contains less redundant data compared with STL files. Using VRML model as input of RP, the technique related to remote and virtual manufacturing and color RP can be addressed more systematically [2-3]. The key parts for slicing software in RP are intersecting model with a set of horizontal planes and generating cross-sectional contours. Hence calculating the intersections between a plane and VRML model plays an important role in the slicing software. The calculation of intersections between a plane and VRML geometric primitives was discussed in paper [6]. On the basis of analyzing and transformation the representation of VRML model, this paper proposed the slicing strategies and flowchart suitable to VRML model. With component-based development concept slicing software for VRML model was developed using VC++ and OpenGL. 2. Structure of VRML model 45

2 Journal of Modeling and Optimization Models in VRML can be created with geometry, texture and color. VRML uses a branch structure as shown in Fig.1. The header information is required in every VRML file. This header always starts with #VRML V2.0 utf8. VRML is made up of nodes, which contain mathematical descriptions of 3D points, lines, surfaces, text strings, and solids. The types of geometry nodes in VRML are Box, Cone, Sphere, Cylinder, Indexed Face Set, etc. [4] Header Group children children Shape Transform appearance geometry material Figure 1. VRML branch structure Different shapes can be grouped together by the Group node to form a more complex shape. The Group node is then divided into a number of children nodes, which contain the shapes that make up the group. Each children node is then subdivided into a number of smaller nodes like Shape node to describe the geometry and material information of the model. Nodes have fields to represent their property, their own name, and hierarchical child or parent node. Child node inherits all the properties of its parent, which makes VRML called as object-oriented language. Using Transform or Billboard nodes, VRML includes the notion of local coordinate systems (LCS), defined in terms of transformations from ancestor coordinate systems. Each Transform node is equivalent to a transformation matrix [5]. The coordinate system in which the root nodes are displayed is called the world coordinate system (WCS). All local coordinate systems are built from a series of transformations based from the WCS. Each object is defined in its own LCS. Hence each VRML object can be defined as: geometry+ appearance+ transformation from which its LCS was built. Suppose the transformation from WCS to LCS is M, coordinate of point P in WCS & LCS is ( x w, yw, z w ) & ( xl, yl, z l ) respectively, then [5] : ( x, y, z ) ( x, y, z ) M 1 l l l w w w (1) ( xw, yw, zw) ( xl, yl, zl ) M (2) Assuming n is the normal vector of a surface S, affine transformation T is applied to the surface, then the normal vector m of the new surface T (S) can be derived from Eq.(3), and normal renormalization of m is still needed. m n ( T 1) T (3) Adopting Eqs.(2) and (3) we can derive the transformation of a point and a normal vector from LCS to WCS, and where T M in Eq.(3). And adopting Eqs.(1) and (3) we can derive the transformation of a point and a normal vector from WCS to LCS, and where T M 1 in Eq.(3). Hence the polyhedrons and geometric primitives defined in its own LCS can be expressed in WCS. We can also transform the slicing plane from WCS to the LCS where the geometric primitive is defined. 46

3 3. Slicing strategies and flowchart In the selection of fabrication orientation, relocation of a model is realized by modifying the transformation matrix of the model meanwhile the representation form of the model is still invariable. The key parts for slicing in RP are intersecting model with a set of horizontal planes and generating cross-sectional contours. The approach for slicing polyhedrons is similar to existing STL-based slicing algorithms, and the key point is to calculate plane-polygon intersection. To achieve high intersection precision, we calculate plane sections of the geometric primitives (sphere, cylinder and cone) using solid geometry. An algorithm for calculating the intersection of a plane and VRML geometric primitives has been proposed by LI Zhanli [6]. Figure 2. Slicing procedure of VRML model When there is non-uniform scaling or scaling with a specified axis, the geometric primitive may be irregular when described in WCS. If they are still regular in WCS, then the intersection will be achieved in WCS. Otherwise we transform the slicing plane from WCS to the LCS defined the geometric primitive, and calculate the intersection curves in the LCS, and then transform the intersection from LCS to WCS. Most of layer-based model can only support straight lines, which can be directly inputted to RPM. In terms of above discussion, intersections obtained may consist of quadratic curves and lines. With discretization and union operations, by analyzing and rearranging intersections, cross-sectional data can be finally obtained, and then the system final output is CLI slice file. Based on above slicing strategies, the slicing procedure is proposed and described in the flowchart shown in 47

4 Journal of Modeling and Optimization Fig CBD Slicing software development The concept of component-based development (CBD) is widely used in software development. CBD facilitates reuse of the existing components with the new ones. Reuse concept of software development components has been taken from manufacturing industry and civil engineering field. The best example in this case is: a component is an independent part of the system having complete functionalities [7]. A component is designed to serve a particular purpose, for example displaying VRML model. Component is like a pattern that forces developers to use the predefined procedures. It meets the specifications to plug it into new software development components. In the process of designing and developing this slicing software, component technique was taken into use. The whole software was divided into three modules, or three component modules: VRML model loading and browsing, model slicing module, and contour data generation module. CLI, as the slice data file, is the output of this slicing software. The VRML model loading and browsing component was discussed and implemented in paper [8]. Based on above slicing strategy and procedure, with COM the well known architectures of CBD, the other two components were developed using Visual C++ and OpenGL. 5. Application example and Conclusion Based on above research results, software for slicing VRML model into CLI file was developed using VC++ and OpenGL. An application example is illustrated in Fig.4. Practical applications show that the slicing method based on VRML is reliable, precise and applicable in RP software. In aspect of polyhedron, one of the advantages of VRML files is that they contain less redundant data compared with STL files. In VRML files, it is not necessary to include the normal vectors as the vertices of all faces are taken in only counter-clockwise direction. STL files may use the same X, Y and Z coordinates many times over while VRML files used the coordinate index instead of the coordinates, which can save a lot of space. In aspect of geometric primitives, VRML can represent models accurately while only needs a few of data. Taking a sphere for example, VRML uses a radius value while STL uses about triangles to represent a radius 500 mm with error 0.2 mm. Fig.4 briefly illustrates a comparison of slicing cone in VRML with that in STL. Figure 3. An application example 48

5 Besides, VRML files are very convenient in storing the color information of a model. It is meaningful to color RP and virtual prototyping and virtual manufacturing using VRML as RP input. Figure 4. Comparison of slicing for cone in VRML & STL References [1] Petitjean, S. A survey of methods for recovering quadrics in triangle meshes. ACM Comput. Surv., 2002, 34(2): [2] Korean Society of Precision Engineering. A Study on Rapid Prototyping using VRML Model[J]. International Journal of the Korean Society of Precision Engineering, 2002,3(02): [3] Ling Wai Ming, Ian Gibson. Specification of VRML in Color Rapid Prototyping[J]. International Journal of CAD/CAM,2002,(1): 1-9. [4] VRML. The Virtual Reality Modeling Language, International Standard ISO/IEC :1997. [5] Li Zhanli, Sun Xiuying. Realization method of coordinate transform in VRML[J]. Journal of Xi an University of Science & Technology, 2006,26(02): [6] Li Zhanli, Sun Xiuying. Computing the intersection of a plane and geometric primitives in VRML model for rapid prototyping software[j]. Wuhan Ligong Daxue Xuebao,2006,28(suppl.1): [7] M.R.J. Qureshi, S.A. Hussain. A reusable software component-based development process model[j]. Advances in Engineering Software,2007, (01): [8]Li Zhanli, Sun Xiuying. Visualization of VRML model in RP software[j]. Computer Engineering and Design, 2007,28(05):