A multi sensor approach for reverse engineering of an object

LIST OF FIGURES Figure 2.1 Realization of a product design ...4 Figure 2.2 Outline of methodology...13 Figure 3.1 Triangular mesh of cloud data...16 Figure3.2 Deviation of normal from in

A MULTIPLE-SENSOR APPROACH FOR REVERSE ENGINEERING OF AN OBJECT

BY

TAN HWEE LYNN CYRENE

(B.Eng.) DEPARTMENT OF MECHANICAL ENGINEERING

A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE

2003

ACKNOWLEDGMENTS

The author would like to express her sincere appreciation to A/Prof Zhang Yun Feng and A/Prof Loh Han Tong, from the Department of Mechanical Engineering at the National University of Singapore for their invaluable guidance, advice and discussion in the entire duration of the project It has been a rewarding experience under their supervision She would also like to express her gratitude to A/Prof Wong Yoke San for his valuable suggestions and guide in the project

She would also like to acknowledge the financial support, the research scholarship from the National University of Singapore

Special thanks are given to professional officer Mr Neo Ken Soon of the Advanced Manufacturing Laboratory for his aid in handling the equipment, fellow graduate student Wu Yi Feng for his guidance and encouragements, and final-year student Lee Lye Peng in his contribution to the project

Finally, the author would express her sincere gratitude to her family, Dominic Cheong and Lord Jesus for their constant support and love

ACKNOWLEDGMENTS i

TABLE OF CONTENTS ii

LIST OF FIGURES v

SUMMARY ix

Chapter 1 Introduction 1

1.1 Reverse Engineering……… 1

1.2 Objectives……… 3

1.3 Overview of Thesis……… 3

Chapter 2 Background and Literature Review 4

2.1 New Product Development……… 4

2.2 Reverse Engineering……… 6

2.3 Literature Review……… 7

2.4 Error from Non-contact Laser Scanner……… 9

2.5 Error from Contact Digitizer- CMM……… 10

2.6 Sensor Integration……….11

2.7 Outline of Methodology……… 13

Chapter 3 Methodology for Part Digitization 15

3.1 Processing of Measurement Data……… 15

3.2 Determination of edge segments from the triangular mesh……… 16

3.2.1 Identification of boundary……… 20

3.3 Surrounding Topology of Edge……… 25

3.4 Transformation of the Reference Systems……… 26

3.4.1 Use of Base Plate for Transformation Process……… 29

3.5 Path Planning of Digitization Process using Touch Probe……… 32

3.5.1 Determining the Direction of Digitization……… 33

3.6 Cavities……… 39

3.7 CMM Probe Path Generation……… 41

3.8 Minimization of Error by Adaptive Re-digitization……… 43

3.8.1 Determination of Error Points……… 44

3.8.2 Determination of the Position of Error Points……… 46

3.8.3 Rectification……… 49

3.9 Intersection of Edges……… 53

Chapter 4 Implementation 55

4.1 Minolta Vivid 900 Laser Scanner……… 55

4.2 Minolta Polygon Editing Software……… 57

4.3 Scanning of Object using VIVID 3D Laser Digitizer……… 58

4.4 RapidForm2000……… 60

4.5 Use of Program……… 62

4.6 Coordinate Measuring Machine CMM……… 63

Chapter 5 Case Studies .67

5.1 Case Study 1……… 67

5.1.1 Results on a Straight Edge………71

5.1.2 Results on a Curved Edge……… 75

5.1.3 Result on a Cavity……… 78

5.1.4 Rectification of Points From Manufacturing Errors……… 83

5.2 Case Study 2……… 84

Chapter 6 Conclusion and Future Work 86

Reference 87

APPENDIX A 91

APPENDIX B 93

APPENDIX C 94

APPENDIX D 100

LIST OF FIGURES

Figure 2.1 Realization of a product design 4

Figure 2.2 Outline of methodology 13

Figure 3.1 Triangular mesh of cloud data 16

Figure3.2 Deviation of normal from inaccurate edge point 17

Figure 3.3 A Pair of neighboring elements 19

Figure 3.4 Classification of edges 21

Figure 3.5 Method of reduction of edge points 23

Figure 3.6 Reduced edge points 24

Figure 3.7 Neighboring points for two regions with different curvatures 26

Figure 3.8 Model with four distinct points for transformation 27

Figure 3.9 Flow diagram of the transformation process 29

Figure 3.10 Baseplate used for transformation 30

Figure 3.11 Four chosen points for transformation 31

Figure 3.12 Characteristics of the planes for identification 31

Figure 3.13 Vertex obtained from the intersection of planes 32

Figure 3.14 Wrong probe direction 34

Figure 3.15 Approximated local surface 35

Figure 3.17 Calculation of normal vector of point 37

Figure 3.18 Determination of approach direction 38

Figure 3.19 Profile of the a cavity 40

Figure 3.20 Approach point for cavity 41

Figure 3.21 Retract and approach position 42

Figure 3.22 Touch probe movement 43

Figure 3.23 Inaccurate edge points 43

Figure 3.24 Determination of position of error point (outer plane) 47

Figure 3.25 Error points on the outside of top and bottom plane 48

Figure 3.26 Error points on the inside of top and bottom plane 49

Figure 3.27 Local accessibility range 50

Figure3.28 Angle for rectification 50

Figure 3.29 Approach direction after rectification 52

Figure 3.30 Mid-point of two skew lines 53

Figure 4.1 Minolta VIVID 900 3D laser scanner 56

Figure 4.2 Prepared object on rotating table 58

Figure 4.3 Interface for polygon editing tool 59

Figure 4.4 Surface geometry of one data set 60

Figure 4.5 Registration of two different data sets 61

Figure 4.7 Determining vertices for transformation 63

Figure 4.8 Mahr multisensor CMM 64

Figure 4.9 KMESS software 65

Figure 4.10 Flowchart of implementation process 66

Figure 5.1 Case model 67

Figure 5.2 Top and side profile of model 68

Figure 5.3 Edge points of the model 69

Figure 5.4 Accessible and non-accessible edges 70

Figure 5.5 Approach and edge points 71

Figure 5.6 Straight edge on model 71

Figure 5.7 Plot of points from first digitization 73

Figure 5.8 Plot of deviation of points from edge 73

Figure 5.9 Plot of points from second digitization 74

Figure 5.10 Plot of points of straight edge from second digitization 74

Figure 5.11 Results from the two digitization processes 75

Figure 5.12 Curved edge of model 75

Figure 5.13 Result of curved edge from first digitization process 76

Figure 5.14 Deviation plot of points of curved edge of the first digitization process 76 Figure 5.15 Result of curved edge from second digitization process 77

Figure 5.16 Deviation plot of points of curved edge of the second digitization process .78

Figure 5.18 Cavity of model 79

Figure 5.19 Result of cavity from first digitization process 79

Figure 5.20 Plane fitted through the points from first digitization 80

Figure 5.21 Deviation plot of points of cavity from the first process 80

Figure 5.22 Result of cavity from second digitization process 81

Figure 5.23 Plane fitted through the points from second digitization 82

Figure 5.24 Deviation plot of points of cavity from the second process 82

Figure 5.25 Sharp and rounded edge of triangular cavity 83

Figure 5.26 Coordinates of constructed edge points of triangular cavity 84

Figure 5.27 A freeform surface 84

Figure 5.28 Approach and edge points on surface 85

Figure 5.29 Result of the freeform surface 85

SUMMARY

This thesis describes an integrated reverse engineering approach for scanning freeform objects using a 3D scanner and a coordinate measuring machine (CMM) The aim is to achieve a more efficient digitization and obtain more accurate results by taking the advantages of both the laser and mechanical sensors with minimum human intervention The whole process is divided into four stages: the acquisition of a set of point cloud by the use of a scanner and the planning of the boundary digitization by a program, the digitization of important features of the object using a coordinate measuring machine CMM and lastly the adaptively re-digitization process of the error points The planning of the boundary digitization defines the edges of the object where two surfaces meet This approach reduces the product development lead time and obtains a set of data with good accuracy In this thesis, the combined system is described and the case studies are presented

The development of a commercial product progresses through several stages

of work It includes product design, analysis of performance, safety and reliability, product prototyping and design modification In some procedures, computer-aided designs are generated and analyzed; however, in other cases, a prototype of the product is first built, and its performance is verified through rigorous testing As creating a prototype of the product is important for experimental evaluation, reverse engineering plays an important role to ensure that a dimensionally accurate prototype

is created

Traditional methods of reverse engineering of free form surfaces have relied heavily on digitization techniques utilizing coordinate measurement machines (CMM) For a large range of objects with planes and simple geometric shapes, this contact digitization method is superior to non-contact techniques This is because contact

digitizers such as the CMM with touch –triggered probes are excellent in their measuring accuracy However, such systems are generally slow in acquiring points The digitization process is very time consuming and much slower than 3D optical digitizers The use of CMM is mandatory in RE when high accuracy is required in the reconstruction of functional surfaces As objects have more free form surfaces and become more complex, it becomes increasingly difficult to use the contact digitization method as it would be very time consuming and tedious for complex work pieces

For complex objects, 3D digitizers such as laser range finders, stereo image detectors, moiré interferometers and structured lighting devices can be used to obtain dense measurement data in a relatively shorter time However, the accuracy of the scanning result is not as accurate as the contact digitizer Laser range sensors tend to generate very large data files, unstructured data that is not arranged in an orderly fashion In addition, there are other disadvantages of the non-contact digitizers too For example, many redundant points on relatively flat surface would be picked up by the non-contact digitizer while critical points on the edges would be lost The large digitized errors generated from these digitizers would be very difficult to eliminate in further data processing During the scanning process, the operator must be careful in controlling the scanner to maintain a proper stand-off distance within the boundary of the operating window Furthermore, the surface reconstructed from these digitized data might lose their surface parameters.In order to solve these problems, this project proposes a digitizing strategy with an aim to combine contact and non-contact measuring devices to obtain accurate results in a shorter time

This project attempts to integrate a 3D laser scanner and a CMM to perform the reverse engineering of freeform surfaces This does not include the physical integration of the two sensors but includes their combination at the operation level

1.2 Objectives

The objectives of this project are:

a) To look into the advantages and disadvantages of the 3D laser scanner and CMM b) To propose a digitizing strategy that combines the advantages of the optical and mechanical sensors

c) To obtain a model of an object of complex geometry rapidly with high accuracy and with minimal human intervention

1.3 Overview of Thesis

Following an introduction in Chapter 1, Chapter 2 provides the background information and literature review of the previously done research Chapter 3 describes the methodology of the program for part digitization of a part while the implementation of the program is described in Chapter 4 Chapter 5 looks into the results and data derived from the program Finally, a conclusion on the project is drawn and some recommendations for future work will be put forth in Chapter 6

Chapter 2 Background and Literature Review

This chapter looks into the background work of this project and shows the literature review of the previous work done on similar areas of this work It also gives

a summary of the process out forth in this project

2.1 New Product Development

Many companies have embarked on a process of modern mechanical design so

as to design and create new products in a efficient and effective manner Figure 2.1 shows an example of a flow of work of creating a new product

Figure 2.1 Realization of a product design

Orientation and Product Conceptual Development

Visual Prototypes

Functional Prototypes

Manufacturing and Distribution Vendors

The first phase of orientation and product specification is a comprehensive orientation session that allows designers to brainstorm and determine on the specifications and objectives of the product This is useful for defining and specifying project goals and objectives, prior to entering the conceptual development phase In the conceptual development stage, the team will then generate line and thumbnail drawings while exploring different aesthetics, ergonomics and manufacturability approaches on a given project using the product specifications as a guideline Detailed design is progressed using solid and surface modeling backed up with analysis and optimization tools The client is presented with multiple conceptual designs and the break up of the parts with the preliminary manufacturing costs

In the visual prototype stage of the developmental process, the team will create full-scale prototypes of the chosen designs, which will represent actual size and proportions of the proposed design approaches These prototypes can be produced by rapid prototyping methods such as stereolithography and fused deposition These mockups will serve to assist further in the form study discussions and decision-making Reverse engineering is employed to track changes to the alterations of the dimensions are geometry of the parts during analysis After that a functional prototype would be built according to the finalized engineering assembly This functional prototype will display tolerances, clearances, and part fits and will be an accurate representation of the assembled product The functional prototype undergoes various performance testing procedures to check the capabilities of the parts and the fit between in assembly Hence, reverse engineering techniques are again employed to determine the changes of the parts during the testing process and rectification work is

Following the critical and intensive testing and analysis, the product is manufactured in large volumes and delivered to the market through distribution networks

2.2 Reverse Engineering

Reverse Engineering is the process whereby a replica is made of an existing physical object or part It allows designers, engineers and tooling craftsmen to leverage and gain input from physical components at every stage of the design-to-manufacturing process This approach not only allows for accurate design representation and rapid comparisons of model, but it also bridges the physical-to-digital environments throughout the product design process Geometric representation can be created in a fraction of the time of conventional CAD systems Traditionally, the initial concept of a sculptured model is realized by designers who conceptualize their ideas on clay or wood Hence, reverse engineering is very useful for generating a CAD model or drawing from physical objects with no CAD information for subsequent design and analysis within a simulation environment to ensure feasibility

at every stage of the product lifecycle

The commonly used method for reverse engineering is to the capture the geometry of an existing part by digitizers The information would then be registered

on the computer as a CAD representation At this point, alterations can be made to the CAD representation as desired by the design engineers

There are numerous reasons as to why reverse engineering is employed An example is that when a working part of a part of a system breaks or wears out and no

CAD file exists for that particular part, reverse engineering is carried out on the part assuming that the breakage or wear was not too severe The geometry of the part can

be digitized into the system and new part can be manufactured from the edited surfaces generated from the scanned data

Reverse engineering can also be used as means to archive their outdated design data to obtain a database of their products This is done to repair and maintain facilities that require replacement parts with diminishing sources of supply, or in situations where original equipment manufacturers are either unwilling or unable to supply replacement parts, or demand inflated costs for sole-source parts Reverse engineering allows for the competitive procurement of such parts

In addition, competitive advantage may be gained by companies through reverse engineering analysis for the purpose of producing and selling a similar product as their competitors

2.3 Literature Review

There have been various researches done in the area of reverse engineering of

an object for product development and modeling of massive data points obtained from digitizers Some of the work is reviewed in the following sections

Song and Kim (1997) employed the use of reverse engineering as an autonomous digitization of a free-formed surface on a CNC CMM The surface is first discretely sampled to be fitted by a polyhedron surface model of triangular plane patches The algorithm then supervises the movement of a contact type ball-tip probe

in an autonomous manner The vertices of the polyhedron are adaptively annexed as digitization proceeds so that the polyhedron approximates the surface with minimum number of data satisfying a specified geometric tolerance

Sohb and Owen (1995) came up with a sensing strategy for the reverse engineering of machined parts They proposed to reconstruct unknown machine parts

by means of stereo image detection method where feature-based CAD models are to

be first constructed from camera image information This approach constructs based CAD models from camera image information Physical objects with free-from surfaces were not discussed in their approach

feature-Another research looked into in an integrated vision touch probe system for dimensional inspection task by Nashman (1996) This process integrates a vision touch probe system which emphasizes the integration of a CMM, 3D touch probe, video camera, laser triangulation probe and a system controller The system provides sensory feedback to a CMM for dimensional tasks Experiments were then performed

on simple geometric entities Objects with 3D curves and freeform surfaces were not discussed

Chen and Grier (1997) looked into a vision-aided reverse engineering approach to reconstructing freeform surfaces by the use of a vision system to detect 3D surface boundaries by using stereo detection method The adaptively selected boundary points are then constructed into a triangular patch With this, CMM would digitize the surface points along their collision free digitizing paths It continues until the accuracy satisfies the required tolerance The use of camera as an optical sensor produces inaccurate readings and the error is added on further down the process of reconstruction

In curve and surface approximation from CMM measurement data by Menq and Chen (1996), a surface fitting method is presented A CAD directed measurement technique is employed where the part is automatically digitized The digitized data are then imported into the CAD system for smooth fitting of cross sectional curves to produce a smooth surface model All the curves with curvature continuity pass exactly through a set of ordered points generated by the CMM This approach can only be applied for smooth surface fitting Discontinuous features in part surfaces are not addressed in this research work

An approach by Milroy (1997) automates a scanning process where the next scan is determined by a previous scan An initial scan is done where the range of possible orientations of the outer edges of the scan is estimated to select subsequent gazes for the subsequent gazes for the laser scanner A disadvantage is that the first scan is made manually and each additional scan is made after calculations is made of the previous scan

2.4 Error from Non-contact Laser Scanner

Non-contact sensing systems work by projecting a laser beam onto the part surface and then inferring the location of the points through the reflected beam Multiple sets of data can be obtained by the relative motion between the specimen, the sensor, and the laser source In this way, the profile of odd shaped objects can be obtained

The accuracy of the process depends on a number of factors such as resolution where the resolution of the results is the distance between the points, the system's

optics, and the precision of the individual mechanical parts that comprise the system The object itself can also impact the accuracy of the data A more accurate result can

be obtained when the object has a white smooth matt surface A darker material tends

to absorb more of the projected laser and hence, reflects less back to the sensor while smooth materials reflect the light strongly In addition, large inclination angle between the laser beam and the part surface would also yield inferior results This is because of the shadow effect that may occur during sensing When the receiver is not at the correct angle or position, it would not be able to accurately absorb the reflected light and measure the surface In addition, as the surface becomes rougher, the reflected light would often be diffused, resulting in inaccurate data Hence, laser sensing is sensitive to the condition of the surface

Fine edges, sharp corners, and grooves on the object can also cause the laser to scatter This also reduces the accuracy of the data and results in a jagged edge in the scanned data In addition, deep openings and concavities can also be areas that are prone to error

Hence the solution to minimize the error created by inappropriate surface conditions is to coat the target object in powder or paint so that it is a light coloured diffused surface

2.5 Error from Contact Digitizer- CMM

Like any measuring system, CMMs are sensitive to ambient conditions Error arises when the temperature deviates from the "perfect" conditions of the metrology

lab Due to the thermal conditions of the machine and workpiece, the error in measurements arises

The CMM has three integrated sensors: the CCD camera, touch probe and the laser sensor The output from each individual sensor contains some level of uncertainty caused by noise in the system The precise calibration of each sensor is imperative for a consistent and precise measurement In addition, sensor degradation would also lead to errors For example, a worn out probe tip contributes to the measurement error during digitization

However, the contact digitizer is in general a more accurate mean of digitization as compared to the non-contact digitizer

2.6 Sensor Integration

Multiple sensory systems offer many advantages over single sensory systems Their primary benefits stem from the use of diverse sensors which produce logically distinct outputs In a multiple sensory system, the diversity of information is used to overcome the limitations of the individual components

In order to combine the advantages of a laser digitizer and a CMM , the strengths and the weakness of each sensor has to be compared The most obvious characteristic of the laser scanner is the fact that it is a non-contact sensor and as such,

it is able to gather a large amount of data points in a short period of time The data sets from non-contact digitizers are often noisy and cleaning process has to be done

on the data Accuracies of the non-contact systems range from 0.01 – 0.5 mm Hence,

the coordinates of the important feature points and the edges would not be accurate obtained In this thesis, the initial points obtained from the non-contact digitizer are used to drive the touch probe to conduct another round of digitization on the important features and edges The points obtained from the two resources can be combined to form a more accurate model

2.7 Outline of Methodology

The outline of the method is shown in Figure 2.2

Figure 2.2 Outline of methodology

CMM Digitization

Points Reconstruction and Merging

Program

Calculation of Deviation of Digitized Points from Edge

Re-digitization

The surface data capturing of a part is accomplished through two sensors, a Minolta Scanner and a CMM touch probe The laser scanner obtains the rough model for surface information while the touch probe obtains the feature information from the rough model obtained by the laser scanner

The first step is the acquisition of a set of point cloud of the object using the 3D laser scanner Adaptive selection of the required region of interest and reduction

of cloud data is then carried out The knowledge of the rough model is used for planning the digitizing path of the CMM probe The results are checked against a predefined tolerance For points that gives a value that deviates greatly from the profile of the edge, their position is determined and re-digitization is carried out This

is done until all the points fall within the tolerance

This proposed approach of digitization allows the surface data of the model to

be obtained at high speed using the laser scanner This information which generates the path for the touch probe reduces the computation time of the process In addition, the adaptive digitization of the important feature points and edges with the use of the touch probe enables to more accurate model to be attained as the touch probe is an accurate sensor These are the strengths of the proposed method Hence, this project explores the idea of direct digitization of the cloud points obtained from the scanner with minimal modifications The effective exploitation of these for reverse engineering based on this integrated approach could have a great impact on the industrial practice

Chapter 3 Methodology for Part Digitization

This chapter defines the main methodology taken to derive the digitization process of a model As digitization of the important features and boundaries of the model by the laser scanner is often inaccurate, this program does not rely on the edge points as the only means of reconstruction but rather using the information of the surrounding topology of the object profile

3.1 Processing of Measurement Data

The use of the laser scanner results in a very high density point cloud Copious points are present when merging of multiple sets of data Noise, uneven point distributions, discontinuities, holes and disjoint parts are often present Hence, the point cloud has to undergo cleaning up processes to prevent long computational times, exceeding of memory storage limits and generation of computational stability problems The data is thinned based on the voxel binning method where the cloud data is subdivided by the bin size into small cubes that are called voxels Each voxel retains only a single point closest to the center of the bin All other points are then removed In this manner, the data set is reduced A triangular-based modeling scheme

is then applied to the point cloud to determine the surface, neighborhoods and connectivity of the data points

In this edge-based growing approach, the triangulation algorithm starts with an initial triangular seed defined by the user Shi (2001) This forms the initial edge boundary list Following a counter-clockwise direction, the triangular mesh grows by means of interrogating the geometric and topological information in the neighborhood

of the seed triangle Hence, a complex free form surface with holes can be triangulated in one computing session without manually dividing it into several simple patches The process is repeated until all the points in the set are meshed ( See Figure 3.1)

Figure 3.1 Triangular mesh of cloud data

3.2 Determination of edge segments from the triangular

In the event where an inaccurate edge point is selected, the tool path planning process would be affected as the direction of approach of the touch probe is dependent

on the edge points If the edge point selected is slightly off the true edge of the model,

it would result in a great deviation in the computation of the normal of the planes used for determining the direction of touch probe As seen in Figure 3.2, a wrongly extract edge point would result in a different direction of the normal, which leads to inaccuracy in the approach direction of the touch probe

Figure3.2 Deviation of normal from inaccurate edge point

In addition, the edge points extracted by the segmentation process do not truly reflect the true edge points of the edges of the physical object This is due to the digitization error of the laser scanner as profiles of sharp edges on the object are the least accurately captured by the laser scanner The solution to this problem is to automatically determine the edge points from the cloud data

The edge detection methods attempts to detect discontinuities of components

in the point data Fan et al (1987) used local surface curvature properties to identify significant boundaries in the data range Chen and Liu (1997) segmented the CMM data by slicing and fitting them by two-dimensional NURBS spline curves where the

Correct edge point1

Neighbor point Normal 1

Normal 2

boundary points were determined by the calculation of the maximum curvature of the BURBS spline Milroy et al.(1997) used a semi-automatic edge-based approach for orthogonal cross-section models where the surface differential properties were estimated at each point in the model The curvature extremes were flagged as edge points and an energy-minimization active contour technique was employed to link the edge points

The proposed edge segmentation done in this thesis is to first establish the relationship of the vertices of the triangular mesh as seen in section 3.1 The relevant data is placed in a structure so that the information of the vertices and the neighboring elements can be attained for the path planning process of the edges and feature points The external and internal loops can be distinguished through this method of triangulation (Shi, 2001)

For a given surface composed of triangular elements, each triangle has three adjacent elements If two elements have a common edge then they are neighbors to each other In Figure 3.3, the edge formed by vertices and is a common edge

between two triangles Hence, triangle T i and T k are a pair of elements with neighborhood relationship

k

v1 v2k

Figure 3.3 A Pair of neighboring elements

A data structure is adopted to store the topological information of the triangular elements, and only the vertices of each triangle are needed and stored Structure { T k; //kth triangle on the list

n3; //the neighboring vertex about point v3k and v1k

N k; //normal vector of triangle

(1) Initialize S(i) as null set

(2) For each triangle T k for k= 1 ≤ k ≤ N t , add the triangle Tk to the sets S( v1k ),

S( v2k ) and S( v3k ) respectively where v1k , v2k , v3k are nodes of the triangle Tk.

(3) For each triangle Tk , determine and record the neighbors of the triangle Tk A

neighbor of the triangle Tk is another element present in both sets S( v1k ), S( v2k ) in which v1kand v2kare vertices of the triangle T k

This process determines the relationship of the vertices in the generated mesh

3.2.1 Identification of boundary

There has been much research done in the area of segmentation of triangulated mesh for boundary detection A common local characteristic quantity used in segmentation process is the curvature Curvature is usually selected as a mathematical basis for region separation Hamman (1994) presented a method for the approximation of principal curvatures at 3-surface points where the normal vectors of each 3-surface point is used for the approximation process Based on the triangulation and the normal vectors, the local least square approximants were then constructed After differentiation, the curvatures are plotted on a graph and the curvatures were used as the curvature estimates at the 3-surface points Woo (2002) proposed octree-based 3D grid method to handle a large amount of unordered sets of point data where the final 3D grids are constructed through a refinement process and iterative subdivision of cells using the normal values of points Hence, boundary regions are obtained Razdan et al (1994) used the watershed segmentation scheme to determine

hard boundaries of the triangular elements The edge detection method used by Hamman (1994) is used in this project as the method is efficient and robust for most applications Based on the change of curvature in the normals of each of the triangular elements, the boundary points are determined The boundary points are then classified into groups of the same curvature so that boundary points on the same edge line are grouped together The boundary points are placed in sets of point data, E1, E2, E3,…….,

En In each set of point data are the edge points on the same edge where point set E= {e1 , e2, e3, e4,……, en } Figure 3.4 shows an example of the classification of the edges

Figure 3.4 Classification of edges

In each point set E, the edge points obtained are in an unsorted manner and hence they have to be linked up to form a sequence of points using the sequencing unsorted edge point algorithm given below The sequenced edge points are then

placed in point sets S where each set contains the sequenced edge points s1 , s2, s3,

s4,……, sn Sequencing of the points is done so that the path of the touch probe can be

Edge Group 4

Edge Group 8Edge Group 9

Edge Group 2

Edge Group 5

Edge Group 6

Edge Group 7 Edge Group 10 Edge Group 11 Edge Group 12 Edge Group 13

Edge Group 3Edge Group 1

Edge Group 14

determined The unsorted edge points are determined using the algorithm in Section 3.2.1.1

3.2.1.1 Sequencing unsorted edge points algorithm

Input: Sets of unsorted boundary points Ek, E2,E3,… En

Output: Set of sequenced boundary points Sk,S2,S3,… Sn

Steps:

From each of the point set E i = { e1i , e2i, e3i, e4i,……, eni }, where e1i , e2i, e3i, e4i,……, eni

are the coordinates of the edge points in the set E i

(a) randomly select a point as the initial seed point, estart

(b) Determine the nearest point eni from the point set Ei that is the nearest to

the initial seed point, estart that is found in step (a)

(c) Flag the point determined in (b) as s1i and continue to find the next closet

point to s1i and name it s2i

(d) Continue until all the points in the point set Ei are flagged and recorded in the sequenced point set Si

The digitization process by the laser scanner of the object generates a very dense set of data points Hence, it results in many redundant edge points In order to increase the efficiency and manageability of the data, the dense edge points are further reduced to decrease the computation time In addition, there would also be fewer points for the touch probe to digitize A representative edge is derived from the dense edge points This is done by the shape tolerance method where there will be lesser edge points would be used to represent the edge on the parts of the edge with smooth continuity and more edge points to represent the curved parts of the edge Figure 3.5 illustrates this method

Figure 3.5 Method of reduction of edge points

Edge reduction algorithm

Input: Sets of sequenced edge points Sk,S2,S3,… Sn

User-defined shape tolerance parameter δ0

Output: Sets of reduced edge points Rk,R2,R3,… Rn

For each set of sequenced edge points

(a) Select the first and last points and draw a line joining them

(b) Determine the distance of each of the edge points to the line drawn in (a)

(c) Determine the point A with the largest distance δ1 from the line (Refer to Figure 3.5)

Else stop

(e) Join the start point to the point A and join another line from point A to the end point

(f) For each line connected determine the point B that forms the largest distance δ2

to the line segment formed by the starting point to point A and determine point

C that forms the largest distance δ3 to the line joining point A to the end point (g) If δ2, δ3 > δ0, continue to next step

Else stop

(h) Forms lines with all the points determined earlier i.e start point to point B, point

B to point A, point A to point C and point C to the end point Find the largest distance and compare to δ0 The process stop when the largest distance determine is lesser or equals to the user defined shape tolerance parameter δ0

(i) Record all the determined points and save them in set R

In this way, the dense edge points are reduced so that it is manageable and increasing efficiency in the digitization of the object by the touch probe The resultant profile of the edge is shown in Figure 3.6

Figure 3.6 Reduced edge points

3.3 Surrounding Topology of Edge

With the boundary points extracted and sequenced from the process described above, the surrounding topology of the edge can be determined from the information

of the data structure shown in Section 3.2 The neighboring points are points n3k, n3k

and n3k from the data structure These points are connected directly to the vertices of the boundary edge points deduced from the earlier section This is done to create an approximate local surface to the surrounding area of the edge for the computation of the direction of approach in the digitization process A small local surface is approximated instead of using the normal of a large plane This is done so that edges which have high curvature and freeform characteristics can also be automatically digitized

However, the position of the neighborhood points has to be further classified to the side of the edge in which they lie on In order to differentiate the two sides of the edge, it is simply defined as the top plane and the bottom plane (Figure 3.7) The normal vector is used to characterize the planarity of the point neighborhood

Figure 3.7 Neighboring points for two regions with different curvatures

A search is done through the data structure to determine the edge segments and the two neighboring points on the two regions with different curvature The coordinates of the neighboring points and the corresponding edge segments are recorded

3.4 Transformation of the Reference Systems

With the necessary information obtained from the point cloud of the scanned object, transformation is required to be done on the coordinates This is because the proposed strategy integrates the use of a laser 3D digitizer and a CMM These are two different work stations and hence, they are different working reference systems A transformation is required to be done on the data obtained from the scanner so that the transformed points can be used to drive the touch probe when the object is placed on the CMM Four corner points or distinct feature points of the object are selected from the set of points obtained from the laser scanner This is to determine the

Boundary Line Top neighbor point

Bottom neighbor point

,

(

),

31 3 3

3 3 3

z y x

z y x

s s

c c c

transformation matrix of the two working systems, the scanner and the CMM The same 4 corner points or distinct feature points are manually digitized on the CMM Figure 3.8 shows an example of the object with its four corner points

Figure 3.8 Model with four distinct points for transformation

A transformation matrix is used to convert all the coordinates points obtained from the scanner to the corresponding coordinate points on the CMM The flow of the program is described below

Step 1: Determine the transformation matrix

0

0

34 33

32

31

24 23

22

21

14 13

12

11

a a

a

a

a a

a

a

a a

4 4 4

3 3 3

2 2 2

1 1 1

c c c

c c c

c c c

c c c

z y x

z y x

z y x

z y x

4 4 4

3 3 3

2 2 2

1 1 1

s s s

s s s

s s s

s s s

z y x

z y x

z y y

z y x

,

(

),

,

(

2 2

2

2 2

),,(

4 4 4

4 4 4

s s s

c c c

z y x

z y x

34 33 32 31

24 23 22 21

14 13 12 11

a a a

a

a a a

a

a a a

4 4 4

3 3 3

2 2 2

1 1 1

c c c

c c c

c c c

c c c

z y

x

z y

x

z y

x

z y

4 4 4

3 3 3

2 2 2

1 1 1

s s s

s s s

s s s

s s s

z y

x

z y

x

z y

y

z y

x

is the 4 coordinate points from Laser Scanner

Step 2: Transforming data set from laser scanner to the corresponding CMM data

1

34 33 32 31

24 23 22 21

14 13 12 11

s s s

c

c

c

z y x a a a a

a a a a

a a a a

A flow diagram is illustrated in Figure 3.9

Figure 3.9 Flow diagram of the transformation process

3.4.1 Use of Base Plate for Transformation Process

In order to obtain the transformation matrix between the two different

reference systems, four distinct points have to be extracted from the cloud data set of

the laser scanner first Following that, the object has to be placed on the CMM to

digitize exactly the same four points However, the four coordinate points obtained

from the CMM would not perfectly coincide with the four points extracted from the

cloud data set of the laser scanner This is due to the human error in selecting the

points from the cloud data Hence, the transformation matrix obtained would not truly

reflect the real transformation of the two systems This greatly affects the digitization

process as the transformation matrix would be used to transform all the data points

initially obtained from the laser digitizer to the working reference datum of the CMM

Output Step 1

This problem is being rectified by the use of a dimensionally known baseplate The workpiece is first placed on the baseplate (Figure 3.10 )

Figure 3.10 Baseplate used for transformation The object is then scanned together with its baseplate by the laser digitizer The baseplate has its known planes and it is designed such that three exclusive planes would intersect to give only one unique vertex (Figure 3.11) The characteristics of the planes are determined (Figure 3.12) and used to obtain the intersection of the coordinates of the four distinct vertices to be used for deriving the transformation matrix This is done by the geometric calculation of the intersection of the six planes