Int J Adv Manuf Technol (****) **:*** ***

DOI **.1007/s00170-008-1550-1

ORIGINAL ARTICLE

Parameterization of prismatic shapes and reconstruction

of free-form shapes in reverse engineering

Kunal Soni & Daniel Chen & Terence Lerch

Received: 20 June 2007 / Accepted: 28 April 2008 / Published online: 31 May 2008

# Springer-Verlag London Limited 2008

Abstract The objective of this study is to propose a 1 Introduction

method for reverse engineering prismatic and free-form

shapes. The primary focus is on feature-based parameter- Traditionally, many manufacturers have utilized CAD/

ization of digitized geometries so that they can be further CAM/CAE (computer-aided design/computer-assisted man-

used in downstream MCAD (mechanical computer-aided ufacturing/computer-aided engineering) as their means for

design) applications. The study takes advantage of a 3D product design and development. It begins in the virtual

body scanner for rapid digitizing purpose to acquire denser environment with a goal to produce better and more

point clouds with no more than three scans. Suggested are accurate products in the physical world. However, this is

five basic steps towards successful reverse engineering not quite true due to several factors that affect the seamless

prismatic and free-form shapes. They include acquisition of transition from the virtual to the physical environment.

a raw point cloud data, processing of raw data, mesh Often concepts are modeled in solid media such as clay,

generation, surface reconstruction, and feature-based pa- wax, plaster, wood, etc., and some of the free-form shapes

rameterization. In this study, three different sample parts that they represent are difficult to replicate using CAD

that include a mechanical nozzle, a hubcap, and a bucket software due to their complex geometries. CAD inter-

seat, were reverse engineered to demonstrate the proposed operatability is another major obstacle in data exchange and

methodology. This process was proven effective toward data integrity. All of this and many more issues are

reconstruction of free-form NURBS (non-uniform rational contributing factors that cause discrepancies between the

B-spline) surfaces. It also proved efficient towards feature- CAD master model and the actual tooling or as-built part.

based parameterization of prismatic shapes. Due to the lack of accurate feedback from the prototypes,

there is a gap between the digital and production models.

Keywords Reverse engineering . Point cloud . Digitizing . On the other hand, reverse engineering starts in the

NURBS . Mesh generation . Parameterization physical environment with the goal of producing highly

accurate digital models in the virtual environment that can

be further used by CAD/CAM/CAE applications [1].

Reverse engineering software extracts geometrical and

topological information from the digitized point cloud and

describes it to the user [2]. For example, when incremental

K. Soni design modifications are made to the physical model, such

Automotive Industry Solutions, Dassault Systems Services, LLC,

as change in curvature and new fender contour etc., reverse

900 N Squirrel Road, Suite 100,

engineering becomes a feedback loop for designers to

Auburn Hills, MI 48326, USA

evaluate changes proactively during the product design

D. Chen : T. Lerch cycle. However, during product optimization, where the

Department of Engineering & Technology, ET 100,

design changes are mostly iterative and based on engineer-

Central Michigan University,

ing analysis data, it becomes essential to have a history-

Mt. Pleasant, MI 48859, USA

based parametric model.

e-mail: abpjm7@r.postjobfree.com

Int J Adv Manuf Technol (2009) 41:948 959 949

Most software packages used in reverse engineering are in ASCII format. CATIA V5 Shape workbenches were used

not yet capable of automatic feature recognition, however, to reconstruct surfaces from the point cloud, and, the Part

this study demonstrates an efficient way of parameterization Design workbench was used to create feature-based

through feature extractions. The goal is to create a history- parametric solid models. If different software is used to

based parametric model [3] from the digitized point cloud. manipulate the digitized data, the reconstructed surfaces can

Although the approach towards a parametric model of be exported in IGES or STL file format to any parametric

prismatic and free-form shapes differs slightly from each CAD software to create a history-based model.

other, the general methodology as recommended below

remains unchanged:

2 Acquisition of raw point clouds

(1) Acquisition of raw point clouds using a non-contact

laser scanner such as a 3D body scanner.

When the scanner is properly calibrated, a single scan is

(2) Processing of the raw point cloud data.

sufficient for most objects where vertical view obstruction

(3) Mesh generation (or triangulation of points) and clean-

is minimum, in order to acquire a dense point cloud. As

up

seen in Fig. 2 of the nozzle there is no vertical view

(4) Surface reconstruction from NURBS (non-uniform

obstruction, hence the optical triangulation between the

rational B-spline) curves and/or surfaces.

charged-coupled device (CCD) camera [7], laser, and the

(5) Feature-based parameterization for relational design

nozzle successfully captures all the features in a single scan.

and change management.

The acquired data, as illustrated in Fig. 3, is in the form of a

The hardware used to acquire raw point clouds is raw point cloud that needs to be processed further to filter

VITUS/Smart 3D Body Scanner by Vitronic [4] as overlapping patches of points.

illustrated Fig. 1. It is a laser-based non-contact scanner While scanning some complex free-form shapes it could

that can digitize objects in 11 s. Although the finest take two to three scans in different orientations in order to

resolution achieved is 1 mm and it is not designed for capture all the features and curvatures, if a body scanner is

scanning cavities, a 3D body scanner can quickly acquire used. Figure 4 shows the bucket seat as scanned in its

dense point clouds (Table 1) with no more than three scans normal upright orientation. Due to the vertical view

for complex objects. The purpose of utilizing a 3D body obstructions caused by the hand rests and the lower lip,

scanner in this study was primarily for rapid digitizing. the concave bucket area of the seat was not digitized as

The acquired point cloud was exported from the Human illustrated by the raw point cloud image in Fig. 5. Hence,

Solutions software provided by Vitronic to CATIA V5 [5, 6] the seat had to be scanned two more times in two different

Fig. 1 VITUS/Smart 3D body

scanner

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950

Table 1 Specification chart for 3D body scanner [4]

Overlapping points

Measurement system

in the region

Measurement principle Optical triangulation

with laser light stripe,

eye-safe

Measurement heads 8

Measurement range Height 2,040 mm

(elliptical volume) Depth 800 mm

Width 1,000 mm

Accuracy (Standard 0.1%

Deviation relative to

1,000-mm circumference)

Measurement time Adjustable, Typically

11 s

Measurement points: Horizontal 4,858 points

Vertical 550 points (11 s)

Width 2,560,800 points

Export formats Include ASCII, OBJ,

Fig. 3 Raw point cloud of nozzle

STL (ASCII and

binary), TRI, DXF,

Openinventor

3 Processing of raw point cloud data

The raw point cloud data contains as many numbers of

orientations in order to capture all the missing features and

patches as the CCD cameras involved in scanning. In this

contours.

case, the body scanner was equipped with eight CCD

Figure 6 depicts three different raw point cloud data of

cameras, hence each scan constitutes eight patches (spec-

the bucket seat, which was scanned in three different

ification chart in Table 1). Due to this fact, the acquired

orientations in order to capture all the features. Scan 1 was

data contains a great deal of noise and redundancy, which

able to digitize the back rest and the hand rests successfully,

results in enormous data sizes. For the ease of point cloud

but the bottom section was entirely missing. The seat was

re-oriented in order to digitize the front lip area, which is

represented by scan 2.A third scan was required to digitize

the concavity represented in scan 3. The file type used to

save all the digitized data was ASCII, and was later

exported to CATIA V5 Digitized Shape Editor workbench.

Fig. 2 Nozzle Fig. 4 Bucket seat

Int J Adv Manuf Technol (2009) 41:948 959 951

traps. The raw scanned data needs to be oriented about the

coordinated planes in case of multiple point clouds. This is

done in order to view the data in isometric and orthogonal

views as well as to make it easier while aligning multiple

clouds. Multiple clouds are superimposed over each other

using a cloud-to-cloud alignment tool. This technique of

aligning multiple data sets is also referred to as intelligent

registration [8, 9]. It is fully automated user-guided cloud

alignment based on curvature or volume. In order to have

an accurate alignment of the point clouds, two or more

clouds should include at least one common feature during

digitizing (Fig. 6). Some of the common features shared by

at least two raw point clouds include the seat-restraining

handle and the side handles. After a successful alignment,

all the clouds are merged to have a single unified point

cloud data set, as illustrated in Fig. 8, for the ease of

triangulation of points and other downstream processing.

The remaining noise and redundancy can be eliminated

by filtering or data-thinning tools. The raw point cloud can

be filtered in two ways, homogeneously or adaptively.

Homogeneous point removal thins the point cloud evenly,

Fig. 5 Partial point cloud of seat

whereas the adaptive option reduces the data points

according to curvature sampling based on chordal height

triangulation and further processing towards a parametric deviation analysis and voxel bining, i.e., removes points

model, the raw point cloud needs to be processed, while from planar regions but retains data in proximity of edges

keeping true to the original shape of the digitized object. and areas of high curvature, to maintain original accuracy

The flow chart in Fig. 7 represents the steps towards and detail [10].

successful processing of the raw point cloud data. Figure 9 illustrates the master model of the hubcap

Most reverse-engineering software have tools that can (Fig. 9a) that was scanned, its corresponding raw point

automatically detect and remove any outliers from the raw cloud, and the processed cloud data. Initially, the imported

point cloud. However, any unwanted cloud area such as the raw cloud had a total number of 78,714 points with an

podium or any support needs to be removed using selection ASCII file size of 1.65 megabytes; refer to Fig. 9b.

Fig. 6 Three raw point clouds

Scan 3: Concave detail

representing all the missing

features

Seat restraining handle

common in 2 & 3

Scan 2: Front lip

Scan 1: Back rest

and arm rests

Side handles

common in 1 & 2

Int J Adv Manuf Technol (2009) 41:948 959

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Fig. 7 Raw point cloud

Raw data

processing

Removal of unwanted points

Planar Orientation

Single Cloud Orientation Multiple Clouds Orientation

Cloud Alignments

Cloud Union

Data Thinning

Homogeneous Filtering Adaptive Filtering

However, after clean up, the scan data was reduced to processed point cloud is most likely to have inconsistencies

15,061 with a file size of 500 kilobytes as illustrated in such as, non-manifold vertices and edges, redundant and

Fig. 9c. acute angled triangles, and triangles with inconsistent

orientation, etc. The noise over a mesh surface depends

on how clean the point cloud was prior to triangulation.

Similar to the raw point cloud data, the mesh needs to be

4 Mesh generation

cleaned up and refined. The flow chart in Fig. 10 illustrates

Mesh generation or triangulation of points is also referred the suggested steps towards mesh processing.

to as tessellation, and it is an automated process of The freshly generated raw mesh has a very high density

connecting the closest three points to form a triangle. This of triangles, as shown in Fig. 11a, which results in high data

is repeated until the entire point cloud is networked to form volume. Most software programs provide automated tools

an unambiguous, coherent, and consistent triangulated for mesh clean-up. Upon analysis, inconsistencies are

surface [11 13]. The initial mesh generated from the detected and removed automatically. Any remaining un-

wanted triangles can be interactively removed prior to gaps/

holes filling. Usually, after clean-up, the mesh will have

small gaps and holes as depicted in Fig. 11b that can be

filled either interactively or automatically depending on the

size of hole and curvature of the surface. Using surface

information or volumetric algorithms, holes are filled

automatically. There maybe some user input required such

as specifying hole-size and shape control parameters,

especially while filling holes over a curved surface as

shown in Fig. 11c. Sometimes re-meshing the existing

mesh also helps in closing large gaps.

Smoothing is the next step in refining the mesh as

illustrated in Fig. 12a. The reason for smoothing the mesh

is to be able to reconstruct surfaces of better quality and

higher accuracy. One method is by using automatic tools

that need user input and its effect is global. The second

method is by using a brush tool for interactively smoothing

local regions of the mesh. If the smoothing effect is too

strong, then there is the possibility of losing features with

sharp corners or smaller radii. Once smoothing is done, the

mesh needs to be refined by reducing the number of

Fig. 8 Point cloud union

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Fig. 9 Hubcap in wood and its

corresponding point cloud data

(a) Hubcap master model (b) Point cloud at 1.65 MB (c) Point cloud at 500 KB

triangles, also called decimation, and, re-configuring the A preferable neutral file format for exporting the mesh is

STL . Depending on the quality and accuracy of the mesh,

orientation of the triangular fan depending on the edge

length of adjacent triangles which, is also referred to as the exported STL file can be used directly towards rapid

optimization [8, 13]. prototyping, CAM, and CAE that include finite element

Decimation is a process that works on curvature-based analysis and computer fluid dynamics analysis.

sampling, number of triangles over flat regions, or low

curvatures are reduced drastically while maintaining a high

triangular count over high curvature areas such as fillet 5 Surface reconstruction

radii illustrated in Fig. 12b. Optimizing the mesh usually

follows after decimating. It is a process of reorienting the Surfaces can be reconstructed from the mesh using three

adjacent edges of a triangular fan about a point to a user- distinct techniques: feature extraction, surface fitting, and

specified angle, also increasing or decreasing the edge networking of curves. These techniques can be used in

length of the triangles to a user-specified range. In doing so, combination or individually in reconstructing the surfaces

the triangular count may increase by a small percentage, of any sample part. When dealing with free-form shapes,

hence, optimizing and decimating the mesh can be used fitting NURBS surface patches to the segmented mesh is

iteratively by the user to achieve the desired accuracy and used primarily. Wherever applicable, a network of curves

add sharpness to the mesh as shown in Fig. 12c. and feature extraction are also used in combination towards a

complete surface reconstruction. For prismatic shapes,

feature extraction usually works the best. From mesh to a

fully reconstructed surface remains mostly a semi-automated

to somewhat interactive process, depending on the complex-

Mesh from Processed Point Cloud

ity of the part. However, there are very few software

programs that claim to have fully automated the process of

Mesh Clean-up (automatic removal of inconsistencies)

reverse engineering sample parts from their refined point

cloud through surface reconstruction.

Feature extraction works by intersecting planes with the

Filling Holes

mesh to create section curves which is later converted to

NURBS curves of degree 6 or above to give it a smoothing

Adaptive Hole Fill Interactive Triangles

effect. Mathematically, a NURBS curve [14] is represented

as

Smoothing

P

n

Ni;p u wi Pi

Global (automatic)/Local (interactive brush smoothing)

i 0

C u a u b

Pn

Ni;p u wi

Decimation

i 0

where C(u) is a vector-valued function of the independent

Optimization

variable u, the subscript p is the degree, Pi (i=0 n) are

the control points (forming control polygon), wi are the

Clean Mesh

weights on NURBS curve, and Ni,p(u) is the pth - degree

Fig. 10 Mesh processing

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Fig. 11 Mesh generation

(a) Raw mesh in wire frame (b) After mesh clean-up (c) Hole filling

B-spline basis functions defined on the non-uniform knot method is a discreet algorithm based on the number of

vector sample points from the original curve and tries to minimize

8 9 the difference between these sample points and the

> >

U a; . . . ; a; u p 1 u m p 1 ; b; . . . ; b

> {z } {z } > a set of sample points, a set of pre-computed parameters are

: ;

p 1 p 1 chosen. Evaluating the curve at these parameters yields

control points Qi = C(ti) on the curve C(ti) [15, 16]. Then

Unless otherwise stated, it assumes a =0, b =1, and wi > 0

the algorithm works by determining the approximating

for all i.

curve C (ti) such that the following sum is minimized.

Re-positioning control point has a transitional effect on

the NURBS curve while, weight modification has a

X

m

Q'i Qi 2

perspective effect, where curve points in the affected

domain are pulled (or pushed) along a straight line that i 0

meets the control point corresponding to the weight being

where Q i represents control points on the approximating

modified.

curve C (ti). However, the user can assume the quality of

Usually, the NURBS curve deviates slightly from the

section curve in order to accommodate for the smoothing the NURBS curve and control the deviation within an input

effect. This is also referred to as curve approximation or tolerance. Every extracted curve represents a profile for a

curve fitting. NURBS curves are converted to NUBS (non- feature creation. Figure 13 illustrates a few steps towards

uniform B-spline) curves by setting the weights to 1, so the surface reconstruction of a hubcap that has a radial

curve can be represented as symmetry. Figure 13a shows a NURBS curve extracted

from the planar section that is used as a profile to create the

X

n

C u Ni;p u Pi revolved base feature shown in Fig. 13b. Likewise, other

i 0 feature curves are extracted and formed into a circular

pattern towards a finished hubcap in Fig. 13c.

The above NUBS curve is later approximated using least A network of curves works in a similar way as feature

squares curve approximation algorithm. The least-squares extraction except there are several planes parallel to each

Fig. 12 Smoothing, decimating,

and optimizing

(a) Smoothing (b) Decimated and optimized (c) Decimated and optimized

wire-frame view shaded view

Int J Adv Manuf Technol (2009) 41:948 959 955

Fig. 13 Reconstruction of a

hubcap using feature extraction

(a) Extracted NURBS curve (b) Revolved base feature (c) Created circular pattern

A B-spline surface of degree (p,q) [14] can be represented

other, in two directions, and intersecting a segment of the

mesh to form a network of several NURBS curves as as

depicted in Fig. 14a. These overlapping NURBS curves can XX

n m

S u; v Ni;p u Nj;q v Pi;j

be converted to a network of curves that act as a single unit.

i 0 j 0

Or, each of these curves can be treated as guides and

profiles to form a surface patch. For simple shapes, a single

network of curves over the entire mesh could be sufficient

Where the points Pi,,j form a control net and the B-splines

to reconstruct the surface geometry as shown in Fig. 14b.

However, more complex shapes may take several surface are defined over

8 9

patches from a network of curves, feature extraction and/or

> >

{z } {z } >

: ;

over a segmented mesh area as shown in Fig. 15a. NURBS p 1 p 1

8 9

> >

surface can be considered as a product of two NURBS {z } {z }>

: ;

and the basis function are the product of the basis functions

p 1 p 1

of the respective curves [15]. This leads to an isoparametric

curve in the v-direction for a fixed u, and in the u-direction The mesh has to be segmented either interactively or

for a fixed v. Implementing the least-squares method, automatically, depending on the capability of the software

NURBS surface can be approximated using NUBS surface. program used prior to surface fitting [17]. Interactive

Fig. 14 Network of curves

(a) Planar intersections (b) Networked NURBS surface patch

Int J Adv Manuf Technol (2009) 41:948 959

956

Fig. 15 Surface fitting

(a) NURBS surface fitting on a (b) G2 blend between two NURBS patches

segmented mesh area to maintain curvature continuity

segmentation essentially involves splitting the desired mesh the segmented mesh area. The edges of all the adjacent

area using selection traps. Once again, the user assumes patches must be kept consistent with their geometric

control over the quality of the surface patch by specifying continuities. Typically for free-form shapes, all the patches

the tolerance and degree of quadratic patch (order six or are continuous in curvature - G2 continuity, as illustrated in

above). Distance analysis can be performed on the fly to Fig. 15b, also concurrently is both positional and tangential

determine the range of deviation of the surface patch from continuous [14, 18]. Once the surface reconstruction is

Fig. 16 Parametric solid model

(a) Reference wire frame (b) Sketches-profiles, guides

(c) Lofted trunk d) Boolean add e) Boolean remove f) Final nozzle

Int J Adv Manuf Technol (2009) 41:948 959 957

process is described effectively. After the initial surface

reconstruction is accomplished, a wire frame is created by

intersecting orthogonal planes with the initial surfaces as

illustrated in Fig. 16a. This wire frame serves as a point of

reference to establish key dimensions and geometric

constraints for the sketches, Fig. 16b, of guide curves and

cross-section profiles of the lofted feature as illustrated in

Fig. 16c, and, the circular sketches for the Boolean add and

material removal operations for the main body as portrayed

in Figs. 16d, e. Finally, the dress-up features such as draft

angle, fillets, and shell are applied as shown in Fig. 16f.

The specification tree represented in Fig. 17 shows the

complete feature-based parameterization of the nozzle.

The tree structure of this parametric model is based on the

relationship between isolated bodies (Trunk, Base, etc.)

interacting through Boolean operations to produce an

intermediate result. These results are grouped under a

parent body (Main Body) to which dress-up features (fillets

and shell) are applied. Later, the Main Body interacts with

its parent body to produce the final part body (Nozzle).

This approach facilitates towards stable and robust design.

If changes are made to operations or features, only those

elements affected will be updated [19].

7 Discussions and recommendations

The recommendation towards the proposed methodology of

reverse-engineering process concerning the accuracy and

quality of the re-modeled part is: Once the point cloud

undergoes meshing, it is important for the user to perform a

distance analysis using software tools. The purpose is to

Fig. 17 Parametric history tree [19]

determine the deviation of the mesh from the digitized point

cloud as depicted in Fig. 18 that shows a statistical distribution

accomplished, it can be thickened to form a solid or in percentage deviation of mesh from point cloud. This will

exported as an IGES or STL file to other MCAD packages help the user in setting a target tolerance while refining the

for downstream applications.

6 Feature-based parameterization

This phase of the reverse-engineering process is suitable for

prismatic shapes where the extracted feature can be

parameterized. Having MCAD data can be useful towards

quick change management, creating formal 2D drawings

with GD&T information or, used further in design

optimization based on engineering analysis. All the

extracted curves are constrained geometrically and dimen-

sionally to be used as profile sketches for parametric feature

creations such as sweep, loft, extrude, revolve, etc. and

perform Boolean operations as well. In doing so, we re

building a history of creation that can be later used for

modifications. In the following images of the nozzle, this Fig. 18 Distance analysis of the mesh from the point cloud

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Fig. 19 Distance analysis of

NURBS patch from the seg- NURBS patch

mented mesh

Mesh Segment

mesh. Similarly, when surfaces are being reconstructed, thermore, a methodology to re-create a history-based para-

distance analysis is recommended, as is shown in Fig. 19, metric model of prismatic shapes has been successfully

which shows a statistical distribution in percentage deviation established. This approach towards parameterization also has

of NURBS patch from mesh. However, setting a tolerance important advantages such as a relational design with

may not be as critical as the quality of the surface, especially associative geometry that would respond to changes quickly

in the case of free-form shapes. This is illustrated in Fig. 20, and, portability of the wire frame and sketches to any

which shows inflections on the NURBS patch represented in parametric CAD package. This can be a crucial step towards

Fig. 19. Hence, it is important to perform a surface-quality overcoming CAD inter-operatability issues especially when

check along with distance analysis in order to determine a CAD translators do not deliver a complete result.

good trade-off between surface quality and accuracy. Above The parameterization demonstrated in this study is

all, the goal is to maintain the integrity of the original shape. limited to prismatic shapes only. Further research is

required to overcome the challenge of parameterization of

free-form shapes. This is due to the fact that if almost all

free-form surface reconstruction constitutes of NURBS

8 Conclusions

curves and surfaces, it becomes very difficult to manipulate

This study successfully demonstrates the methodology imple- them through quick and precise dimensional changes.

mented towards reverse engineering prismatic and free-form Conceptually it could be possible to have a history-based

shapes from digitizing through surface reconstruction. Fur- parametric model of free-form shapes if the wire frame

Fig. 20 Surface curvature

analysis of the NURBS patch

NURBS Patch

in Fig. 19

Inflected region

Int J Adv Manuf Technol (2009) 41:948 959 959

consists of B-spline curves interpolated through coordinate 8. Rapidform, http://www.rapidform.com/57

9. Grimm T (2005) Reverse engineering: magic, mystique, and

points, instead of being manipulated by control points. This

myth. Deskt Eng 10(12):32 37

could lead to the creation of a relational design with an 10. Weir D, Milroy D, Bradley C, Vickers G (2000) Wrap-around

associative geometry that quickly responds to changes B-spline surface fitting to digitized data with applications to

reverse engineering. J Manuf Sci Eng 122(2):323 330 DOI

throughout its engineering lifecycle.

10.1115/1.538922

11. Gibson D (2004) Thesis: Parametric feature recognition and

surface construction from digital point cloud scans of mechanical

parts, University of Oklahoma, Norman, Oklahoma

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