3D Object Scanning to Support Computer-Aided Conceptual Design
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1 ABSTRACT 3D Object Scanning to Support Computer-Aided Conceptual Design J.S.M. Vergeest and I. Horváth Delft University of Technology Faculty of Design, Engineering and Production Jaffalaan 9, NL-2628 BX Delft, The Netherlands This paper describes a new way to support conceptual shape design based on precedent models. Technically, the method is founded on reverse engineering. The major issues to be solved are: a) Finding the optimal strategy for 3D digitizing of shape, b) Identifying those modeling entities, their nature and their parameterization, that are needed and suited for conceptual shape design, c) Representing the measured data in accordance with those entities and d) Insertion of the parametrized entities into the destination model. We present a methodology to effectively integrate the forward/reverse shape engineering activities. Furthermore, we present a practical, algorithmic solution to the free-form pattern recognition problem. REUSING PHYSICAL OBJECTS FOR SHAPE DESIGN Reverse engineering (RE) was originally motivated by the need for digitized models in downstream processes (Ingle 1994, Várady 1997, Renner 1998). Typical for conventional RE is that the input is commonly an existing, previously manufactured part (figure 1a). If RE should support conceptual shape design, then the input and output of the RE process are different to those of the conventional one. The methodology shown in figure 1b is based on the assumption that the designer is about to create and to evaluate a number of design concepts of the product. The input of RE can then be a physical artifact created manually, to serve as a starting point for shape. Also a rapidly prototyped physical model (resulting from precedent design studies) may be scanned for redesign and/or for merging with the current design, see dashed lines in figure 1. Since, in accordance with the nature of computer-aided industrial design (CAID), the design models are quickly created, rejected and/or adjusted, one requirement of RE for conceptual shape design is that the data capturing must be fast. Further, the intermediate processing of the point cloud need no longer be dedicated toward the construction of a solid model, but instead it should be enabled to impose constraints on and to apply features and parameterizations directly to the point clouds in order to enhance them. These parameters should then be made available to the designer for further shape manipulation. Presently, tools are emerging such as hand-held 3D object scanners and associated software for the fast generation and visualization of semi-ordered point clouds and triangulations. From the devices' point of view, therefore, RE for shape conceptualization seems increasingly feasible.
2 a) Conventional RE Physical object 3D scanning Point cloud Surface Surface set Model Surface model reconstruction building B-rep construction NC program FE model Rapid Prototype Downstream processes Solid model b) RE for conceptual shape design Block of clay Cardboard, paper, glue Manual claying Manual model building Concept from clay Concept from board 3D scanning Point cloud Geometric adapters Surface set Virtual clay model Enhanced point cloud Physical object Figure 1 - (a) A typical conventional Reverse Engineering process; (b) RE dedicated to the design of shape concepts. The arrows denote the transfer of objects or of data. The dashed arrows indicate the exchange of data or artifacts among the two methodologies. EXAMPLE OF A COPY AND PASTE PROCESS For shape conceptualization the application should realize the wish of a designer to "put a ridge over here, as the one you see on that part". Let us assume that a designer is at work to create a new shape, using some computer-based shape modeling system. At a particular point in time he has obtained the shape depicted in figure 2a. Then the following steps may typically occur: The designer wishes to study the inclusion of a ridge to the shape. He has a preliminary idea about the path of the ridge on the surface; he sketches the path onto the shape (figure 2b). He also has an intention concerning the characteristics of the profile of the ridge. Instead of explicitly sketching the characteristic cross-sectional profile he decides to use the shape of a ridge occurring on an existing product (figure 2c). The designer believes that the existing ridge has (almost) the same properties as the ridge he intends to create. In particular the shape of the observed cross-sectional profile matches that of the intended ridge. This could be the interpretation of "the ridge like that one" as uttered by the designer. A 3D scanning of the existing ridge is made and a digital model of the ridge is inserted into the current shape (figure 2d). The designer makes adjustments to the ridge, when needed. This copy and paste process is perceived as rather natural by practicing engineers and industrial designers (Sinha 1996). To realize this type of support, two categories of aspects need to be addressed. First, methodological issues, including finding the appropriate operation of the scanning device, the designer s acceptance of the procedure and the performance from the designer s point of view. These issues are dealt with in a different paper (Vergeest 2000). Another category of problems is related to the technical feasibility and performance of the copy and paste method. These issues are addressed in the following sections.
3 a b c d Figure 2. On the 3D CAD model (a), a contour is sketched (b). The properties of the ridge encountered in the physical part (c) are copied into the model (d). PROPOSED METHOD FOR COPY AND PASTE OF SHAPE Among the various applications of (shape) feature reuse, we focus on the explicit transfer of a feature instance from one object to another. We refer to this process as copy and paste of free-form features. Five steps can be distinguished for this process: 1) 3D scanning of the relevant portion F of the existing product S, 2) recognition of the feature from the digitized points, 3) presentation of the variables (feature parameters) to the CAID user, 4) merging the imported feature with the current CAID model D, 5) enabling the user to adapt the imported feature using the feature parameters. In this paper we present some results for step 2. MATCHING 3D SHAPES, SOME RESULTS In the following we assume that 3 3 is the ambient space of our application. However, most of the results can be generalized to 3 n, for any n > 0. A feature type (or feature, or feature class) t is specified by a mapping G t : Q t 2 3, where 2 3 is the power set (i.e. the set of all subsets) of 3 3 and Q t is the set Q t = P 1... P m, called the parameter domain of G t. Typically P i represents the domain of a continuous scalar variable q i (such as a dimension or an angle), but in general P i can be any set. For given q Q t, G t (q) specifies a subset in 3 3 referred to as feature instance, or pattern, of type t. A set of feature types G t, t= 1,...k is called a learning set.
4 The problem of freeform pattern fitting to a digitized shape can be stated as follows. For given shape S 3 3, for given shape F S and for given t, find q Q t such that d(g t (q), S) is minimal, i.e. search for min q Qt d(g t (q), F), (1) where d is a difference criterion (or similarity measure) for two subsets of 3 3. Equation (1) should deliver the feature instance of type t that matches F optimally. In this paper we make the following assumptions. a) Shape S approximates (part of) the boundary of a 3D object; typically S is a discrete point set originating from 3D surface scanning. b) Feature instance G t (q) represents (part of) the boundary of a 3D solid. It can be represented as a collection of surfaces. However, degenerate cases such as the collapsing of the feature instance into a curve or a point are not excluded. Figure 3. Point cloud from the part in figure 2c obtained by 3D digitizing (left). A detail view of the region of interest is shown (right). We need to make a distinction between two types among the parameters q i of equation (1). The first type of parameters are those that are critical to the designer; the designer uses them to deform the shape once it has been inserted into the current model D. We refer to these parameters as feature parameters, denoted q F i and the remaining ones are the circumstantial parameters denoted q C i. The circumstantial parameters are needed for the correct positioning of F relative to D and for the smooth connection between F and D. Although this positioning and smoothness are important factors, they may not be perceived as critical design parameters by the designer. Therefore it can be expected that the q F i need and the q C i need not to be controlled by the designer. Details about the origin of these requirements can be found in (Vergeest 2000). Equation (1) has been implemented by a variant of the directed Hausdorff distance d(g t (q), S) that measures the dissimilarity d between the proposed feature geometry G t (q) and point data S (Hagedoorn 1999, Vergeest 2000a). d is defined as the mean Eucledian distance to the data over all points in the pattern. The latter points are obtained by a sampling procedure over the pattern. We have conducted matching computations for a "ridge in freeform surface" feature (figure 4). The data points originated from scanning of the physical object shown in figure 2c. The distance d as a function of two of the set of variables (q) are shown in figure 5.
5 c 3 c 2 c 1 z w h a x y Figure 4. Picture to the left: Freeform ridge feature G(q) and its parameters (q). Picture to the right: To prepare for the distance computation, points have been sampled from the ridge pattern (thick points); these are shown adjacent to the digitized sample F (thin points) Distance (mm) Distance (mm) z (mm) Height (mm) Figure 5. The directed Hausdorff distance d between the data sample and the ridge pattern as a function of the z-coordinate of the template (left) and d as a function of the height h of the ridge (right). The ridge pattern matched the data with d = 0.31 mm, where the scale of the problem, i.e. the size of the matching pattern, was approximately mm. CONCLUSIONS We have presented the results of an algorithm to match parametrized shape templates to digitized points. The algorithm is to become a part of an envisaged design tool for the explicit reuse of freeform shape patterns. We have demonstrated that fitting of freeform shape patterns to scanned 3D objects is feasible. Pose parameters can be determined, but also feature parameters can be obtained, which have relevance for a designer. The presented method is relatively robust, even if the scanning is sparse and/or if the data contains noise. The technique can be applied to any freeform shape, but it can be used for prismatic objects as well. We have proposed a
6 number of improvements to the fitting algorithm, to increase its effectiveness and efficiency. The method will be applied to different types of patterns of freeform features, including those containing holes. Methodological research is needed to place the matching technique in a context familiar to the designer and stylist. ACKNOWLEDGMENTS The authors thank Sander Spanjaard and Jos Jelier for their very important contributions to this work. REFERENCES M. Hagedoorn and R.C. Veltkamp (1999), "Reliable and efficient pattern matching using an affine invariant metric". Int. Journal of Computer Vision, 31(2/3): K.A. Ingle (1994), Reverse Engineering. McGraw-Hill, New York. G. Renner, T. Váradi and V. Weiss (1998), "Reverse engineering of freeform features". Proc. PROLAMAT 98, IFIP. S.S. Sinha and P. Seneviratne (1996), "Part to Art". Proc. ASME Computers in Engineering Conf., 96-DETC/DFM-1293, ASME, New York, pp 1-7. T. Várady, R.R. Martin and J. Cox (1997), Reverse engineering of geometrical models - an introduction. Computer-Aided Design, Vol. 29, No. 4, pp J.S.M. Vergeest, I. Horváth, J. Jelier and Z. Rusák (2000), "Freeform surface copy and paste techniques for shape synthesis". I. Horváth, A.J. Medland and J.S.M. Vergeest (Eds.), Proc. 3d Int. Symp. of Competitive Engineering, Delft University Press, Delft (in press). J.S.M. Vergeest and I. Horváth (2000a), " fitting Freeform shape patterns to scanned 3D objects". Proceedings of ASME2000 DETC/ICIE, Computers and Information in Engineering Conference, September 10-13, 2000, Baltimore, Maryland, ASME, New York (in review).
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