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Annals of MTeM for 2011 & Proceedings of the 10th

International MTeM Conference

Published by MTeM 211Cluj-Napoca, Romania, Editor Cs. Gyenge

MTeM MTeM MTeM MTeM

2011201120112011

PARAMETRIZATION OF CURVES OBTAINED FROM

CLOUDS OF POINTS USING CATIA ENVIRONMENT

Pescaru, R.; [email protected]

Oancea, Gh.; [email protected]

Abstract: The parametrization of curves obtained from clouds of points is a first step towards

the materialization of customized products according to certain characteristics. This paper

presents the stages of creation of these curves starting from the objects digitizing using 3D

scanning systems, followed by the finishing and editing of the clouds of points obtained in the

previous stage, creating the curves over the finished cloud of points and their

parametrization. The parametrization involves defining lengths, choosing own coordinates

system and creating connections between the necessary points for generating curves using the

CATIA software package. A case study which will outline the possibility to obtain the

customized curves in a parametrization mode will also be presented. Key words: Reverse Engineering, scanning, parametrization, cloud points. 1. INTRODUCTION

The parametrization (xxx-a) is the process of defining a function so that all its coordinates depend on and the same variable. As already known a curve is an R to R^3 closed space function. In other words the curve is defined by three scalar functions dependable on one and the same variable. This variable is called the parameter of the point on the curve and is noted by W. As shown in figure 1 the scalar functions are the relationships between the Cartesian coordinates of the points (noted by X, Y, Z) and the W parameter.

Fig. 1. The relationship between the W parameter and the Cartesian coordinates

Often the curves representation (Lancea, 2005) cannot be realized by means of an analytical function, which implies creating it step by step, each step being defined by its own function. So each parametric curve is made up of more segments of curves. The present paper represents a follow up of the initial research previously published (Pescaru, 2010), (Pescaru & Oancea, 2011) and intends to present the different ways of curve parameterization starting from cloud of points by using the CATIA environment. 2. STAGES OF CURVES

PARAMETRIZATION

As a result of the research made by the authors, the algorithm for designing the parametric curves has been conceived for the CATIA software package from DASSAULT SYSTEMES and is described in figure 2. The Reverse Engineering Technique presupposes going trough the following important stages: 1. scanning the object to be analyzed (previously saved in a .STL format), by using a 3D scanning equipment; 2. importing the cloud of points into the CATIA environment; 3. finishing and editing the cloud of points previously obtained; 4. creating the curves onto the finished cloud of points.

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Fig. 2. Algorithm of designing the parametric curves In order to parameterize the curves into the CATIA environment one has to follow the stages presented below: 1. obtaining the curve to be parameterized, or by sectioning the finished cloud of points with the help of a working plan (we will get a section that is going to be automatically transformed into a curve by using the predefined function from CATIA), or by manually creating it; 2. defining the point of origin in considered to be the reference area, on the previously obtained curve; 3. defining a new coordinates system with the origin in the previously created point; 4. identifying, defining and initiating the necessary parameters for defining the parametric curve;

5. calculation of the base points according to the origin point and the already defined parameters; 6. calculation of the intermediate points according to the base points and the length of the initial curve; 7. generating the parametric curves through the base and intermediate points; 8. modifying the values of the initial parameters by following the update of the parametric curves. 3. CASE STUDY. CURVE FOR FOOT

SOLE

The object to be studied is presented in figure 3 and was discretized by using the LPX-1200 3D laser scanner. By using its software, Dr. PICZA, the cloud of points obtained as a result of the object scanning was saved in .PIJ extension and exported in .STL file. The result of the scanning is the one presented in figure 4.

Fig. 3. LPX-1200 scanner

Fig. 4. Cloud of points

Fig. 5. The finished cloud of points

DESIGN THE CURVES

OVER THE CLOUD OF POINTS

DEFINE

THE PARAMETERS

DEFINE

THE POINT OF ORIGIN

CALCULATION

THE BASE POINTS

ACCORDING TO THE PARAMETERS

STOP

START

DEFINE

THE CORDINATES SYSTEM

CALCULATION

THE INTERMEDIATE POINTS

ACCORDING TO THE BASE POINTS

OBTAIN CURVES

WITH DIFFERENT VALUES

OF THE PARAMETERS

GENERATE

THE PARAMETERIZED CURVES

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Once obtained, the cloud of points is imported in the CATIA environment and afterwards finished and edited, the result being presented in figure 5. The first stage of the parameterization is the process of curve creation. In order to do this we will use a predefined CATIA function that automatically intersects the finished cloud of points with the XOY plan, the result being a blue colored section (figure 6). This section is going to be automatically transformed into a white colored curve.

Fig. 6. The section obtained by intersect the cloud of points with the XOY plan The second stage implies defining a point by using the specific function that presupposes the selection of the curve and the position of the point. This point will become the origin of the new coordinates system (P1 in figure 7). By means of the Axis Systems command from the main menu of the CATIA environment we pass on to the third stage that defines the coordinates system and the working plan. The forth stage begins with the identification of the main parameters that define the humans sole foot, respectively: A the length for the cut of the foot; LP the length of the foot; Z the length for the width of the foot; L the length from the top of the foot to the width of it. All these parameters are defined in CATIA by means of the Formula command that requests entering their initial value as follows: A = 31mm; LP = 70mm; Z = 34,7mm; L = 22,4mm. The fifth and the most important stage imply defining the base points according to the systems origin and the parameters previously defined. Figure 7 outlines the base points, their description being presented below:

P1 the utmost point corresponding to the narrow part of the foot. This point will become the origin of the new coordinates system;

P2 the opposite of the P1 point, is defined according to P1 and the A parameter;

P3 the utmost point of the heel, defined as half the distance between P1 and P2;

P4 the utmost point from P3, defined according to the LP parameter;

P5 utmost point specific for the wide part of the foot, defined according to P4 and L and Z parameters;

P6 the opposite of P5, defined according to P4 and L and Z parameters.

Fig. 7. The base points of the curve The sixth stage consists of defining the intermediate points, colored in figure 8 in green, necessary for keeping the shape of the curve. These intermediate points are defined by using the specific function, selecting the base curve and introducing a length formula between the base points from the area they need to be defined into.

Fig.8. The intermediate points of the curve

P4

P3

P5

P1

P6

P2

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The seventh stage is the one in which the parametric curves are generated. These curves are spline curves and interpolate between the selected points. The result of this stage is presented in figure 9.

Fig.9. Parametric curves The algorithm of curves parameterization obtained on the cloud of points closes by the eight stage that allows parameters value modification. For an easier entering of these values the use of parameterized tables is recommended. This parameterized table (Ghionea, 2009) is an essential tool in CATIA, where each parameter has a column allocated and each value configuration a row. In figure 10 in presented the parameterized table with the initial values of the parameters. The result of this stage is described in figure 11, where the modified curve is colored in magenta and the initial one in white.

Fig.10. Parameterized table in CATIA

Fig.11. Initial vs. modified parameterized curve

4. CONCLUSION

The theoretical notions and the case study presented in this work have outlined the utility of the Reverse Engineering technique onto the curves parameterization obtained on clouds of points. The proposed algorithm has outlined the stages to be followed in order to obtain parameterized curves and has demonstrated its integration process within any Reverse Engineering project. Future research will concentrate on the parameterization of shoe type objects according to the characteristics of the clients foot in order to personalize the product. 5. ACKNOWLEDGEMENT

This paper is supported by the Sectoral Operational Programme Human Resources Development (SOP HRD), financed from the European Social Fund and by the Romanian Government under the project number POSDRU/89/1.5/S/59323. 6. REFERENCES Ghionea, I.G. (2009). CATIA v5. Aplicaii n inginerie mecanic, Editura BREN, ISBN 978-973-648-843-6, Bucureti. Lancea, C. (2005). Concepie i fabricaie asistate de calculator, Editura Universitii Transilvania, ISBN 973-635-442-3, Braov. Pescaru, R. (2010). Product customization using Reverse Engineering technique, Annals of Daaam for 2010 & Proceedings of the 21st International Daaam Symposium Intelligent manufacturing & automation: focus on interdisciplinary solutions, Katalinic, B. (Ed.), pp. 1405-1406, ISSN 1726-9679, Zadar, October, 2010, Croatia. Pescaru, R. & Oancea, Gh. (2011). Objects Digitizing with High Level of Customization

Using Reverse Engineering Technique, Proceedings of the 15th International Conference Modern Technologies, Quality and Innovation Volume II, Nedelcu, D., Slatineanu, L., Mazuru, S., Milosevic, O.(Ed.), pp. 849-852, ISSN 2069-6736, Vadul lui Vod Chiinu, Mai, 2011, Republic of Moldova. xxx-a. Technical article: The Curves of CATIA Geometric Modeler, available from: http://www.maruf.ca/files/caadoc/CAAGobTechArticles/Curves.htm, Accesed: 04/2011

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