CROSS MODEL SHAPE REUSE: COPYING AND PASTING OF ...

Proceedings of DAC’02: 2002 ASME Design Engineering Technical Conferences & Computers and Information in Engineering Conferences Montreal, Canada, September 29, 2002 - October 2, 2002

DETC’02/DAC-34064 CROSS MODEL SHAPE REUSE: COPYING AND PASTING OF FREEFORM FEATURE Chensheng Wang, Joris S.M. Vergeest, Imre Horvath Raluca Dormitrescu, Tjamme Wiegers, Yu Song Faculty of Design, Engineering and Production Delft University of Technology Landbergstraat 15, NL-2628 CE Delft, The Netherlands [email protected] ABSTRACT This paper provides a systematic approach for copying and pasting of freeform features among existing models of design. Freeform feature as complex high-level shape entity enables a fast creation and modification of a geometric model in the context of both mechanical and aesthetic design. Copying and pasting of freeform feature can enhance not only the rapid shaping of the geometric model itself, but also the inheriting of design knowledge built in existing designs. In this paper definitions of freeform feature are reviewed and consummated. An analysis of parametric and topological relevancy of freeform feature is given in terms of copying operation and an elaboration of the reconstruction of freeform feature in a new geometric model regarding to pasting operation is presented. The reuse of freeform feature is discussed, and related algorithms are presented in detail.

part models. In this strategy, shape similarity is governed by shape theory, and usually, the measure of similarity among shapes depends on human perception. One of the successful examples applying this strategy is the “Group Technology” (Gallagher 1973). The use of parameterized standard-part libraries is another example. 2.

Shape information carried by form features, which treats the shape information as a composition of form features. It analyses the shape of individual form feature from which it concludes about the whole shape. In this strategy the measurement of similarity among part’s models is hard to achieve due to feature interactions. Intensive investigations have been down to tackle this issue, but till now it still remains a challenging research field.

3.

Hybrid approach, which takes the advantages from both methods mentioned above and extends the definition of similarity of part’s shape to a higher level. It considers the modeling similarity among part’s models, which gives full attention to the affection brought by the use of CAD technology and systems. In this approach shape similarity of both global shape and individual form feature are considered, thus to speed up the design process by utilizing broad similarity among parts.

INTRODUCTION Shape reuse is one of the important means enabling design intelligence, by which preceding modeling efforts are inherited in the current design (Vergeest 2001). The most commonly known form of shape reuse is the usage of a digital part library in CAD. Especially, when the “standard parts” are parameterized models, a significant reduction of design efforts is achieved (De Martino 1994). A recent study reveals that shape reuse may happen in different ways, regarding to the intrinsic similarity built in existing design. There are three strategies in shape reuse as follows (Wang 2002): 1.

Shape information of the part as a whole, which treats the part as a single geometric model. It considers the global part shape, from which it concludes geometric similarity (or process similarity in manufacturing domain) among

Freeform feature as a complex high-level entity enables a fast creation and modification of the geometric model. In the context of both mechanical and industrial design, freeform feature has been adopted as the pivot entity for associating specific functional meaning to groups of geometric elements (such as faces, edges, vertices and so on), thus offering the advantage of treating sets of elements as a single entity (Fontana 1999).

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The study of copying and pasting of freeform feature is inspired and motivated mainly by the thoughts of design reuse across models. It is no doubt that copying and pasting of freeform feature can become an effective means to support shape reuse, thus to reach design automation. In the following sections of this paper, at first, a review of related works has been done. Then some issues concerning the possible purposes and intentions of feature reuse via copy/paste operations are addressed. As a systematic approach a complete freeform feature definition is presented for the purpose of copy/paste operations. And a couple of strategies are presented for implementing the exact copying and pasting operation on the feature's geometry. Examples of this technique are provided also and the limitations and further extensions of the present method are discussed. Finally, conclusions and future work are drawn in the last section.

freeform features. For later use in this paper, we cite some abstract fundamental definitions of freeform feature here. There are two important freeform feature categories, namely δ -feature and τ -feature which are defined as following: Definition of δ-feature: Given a primary surface S and a deformation law

δ : S a R3

with influence area AI ⊂ S ,

then the effective modified surface region Fδ = is called freeform

δ

-feature, where

n

U

{Ah }h=1,2,...,n

decomposition of disjointing surface regions n

U

h =1

h =1

δ ( Ah )

is a finite

AI , i.e.

Ah = AI .

The new representation of the surface with δ-feature is then given by S = δ ( S ) = ( S − AI ) ∪ Fδ . '

RELATED WORK Shape reuse is a specific category of design reuse, which is generally appreciated as a profit factor in new product design (Duffy 1999). Intensive investigations about shape reusing technology have been carried out, not only in the domain of product design, but also of production (Eversheim 2000). Several principle objects are identified that are relevant to shape reuse methodology. They are mental model, imported model, shape model in corporate library, current CAD model, freeform feature, physical object, point cloud and geometric model (Vergeest 2001). Figure 1 shows these objects and the relationships among them. In figure 1, a freeform feature (FFF) is defined as a shape specified by a set of parameter values (multidimensional). As a powerful shaping entity, studies on freeform feature have led to a number of attempts to apply principles of feature-based design from mechanical design in the domain of freeform shape modeling and styling. For example, a grammatical feature-modeling schema has been proposed to aggregate nonregular shaped features into a sculptured object (Au 2000). Also, some technology supporting fast generating of freeform feature had been investigated to facilitate rapid forming of design concept (Van Elsas 1997).

Topological cuts (holes in solid case) are formalized as (Fontana 1999): Definition of τ-feature: Given a primary surface S and a connected surface region AT ⊂ S , the transformation

S ' = S − AT is said a sharp cut. AT is called the trimmed area and the corresponding ∂AT triming boundary. If, for example for aesthetical reasons, a deformation is applied in a surface neighborhood of AT , a finished cut is produced. Both

Imported model (www)

Mental model

Current CAD model

Shape model in corporate library

FFF

Legend:

A

B

Object B is derived from object A

A B Some fundamental studies on freeform Object A and B are Geometric feature definition had been done in (Fontana Physical mutually influencing Point cloud Physicalobject object model 1999). In this study, a classification and a group Thicker lines represent the main workflow of of detailed definitions related to freeform shape reuse features are given by means of set theory. Associating with the classification of freeform Figure 1. The eight principle objects relevant in the shape reuse methodology. feature, there are definitions about different The arrows represent dependencies among the objects

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sharp and finished cuts are called τ -features. A finished cut can be represented as S = δ d ( S − AT ) ,

1.

The shape of F is explicitly modeled with the intention to preserve it exactly.

2.

F is created as a displacement feature. Then the deformation function δ is of the type δ ( s ) = s + v for

'

where

δd

is the deformation applied in neighborhood of AT .

In fact, supposing in case that both δ -feature and τ feature exist, then a generalized freeform feature can be represented as a unified form:

s ∈ S , where v is a constant displacement vector. 3.

F is created as an offset from S with δ ( s ) = s + an , where n is a unit normal vector to S at point s and a is the offset distance.

4.

F is created by wrapping a shape G onto S, where G itself assumes deformation in the low frequency domain to adapt its consistency with S. This type of feature can also be described as an inconstant surface offset.

Inference: A unified freeform feature can be represented as: n

F = δ d ((( S − AI ) ∪ Uh=1 δ ( Ah )) − AT ) where

δ d : S a R3

When

is a deformation law.

δd ( f ) = f

equation (1) becomes represents a

δ

(1)

and AT = ∅ ( ∅ is an empty set), n

F = ( S − AI ) ∪ Uh=1 δ ( Ah ) , it

-feature; while if AI =

equation

(1)

n

U

h=1

δ ( Ah ) = ∅ , then

F = δ d (((S − ∅) ∪ ∅) − AT ) = δ d ( S − AT ) ,

becomes this

The reuse of freeform feature may also be recursive. This will produce more complicated shape entity. Figure 2 shows a schematic picture of the four categories of intention of freeform feature reuse, and the purpose-dependent result of feature reuse from source shape S to destination shape T. We emphasize that the four categories are far from exhaustive; mixtures of them and special deformation function

represents for a finished cut τ -feature. Furthermore, when δ d ( f ) = f , then F = δ d ( S − AT ) = S − AT represents for a sharp cut

τ

F explicit

Category 1 T

-feature.

S

This inference is helpful for developing unified operation methods on freeform feature.

F displacement

Category 2

Some other methods about freeform design have also been implemented, which integrate feature-based surface design with freeform deformation (Cavendish 1995). These studies establish a good starting point for implementing the theoretical depiction of freeform feature problem. The creation of a freeform feature entity is a very timeconsuming work compared with copying and modifying of an existing freeform feature entity. This is also one of the shortcomings of current CAD system, in which the reuse of shape information built in existing design is not always concerned. In the present paper, this problem will be tackled in following section. SEMANTIC ISSUES OF FREEFORM FEATURE REUSE Copying and pasting of freeform feature can be regarded as a specific mode of the more general process of reusing precedent shape modeling effort and, as mentioned above, the knowledge associated to the designed shape. In the previous section a freeform feature F has been defined as a deformation of (and/or a removal of) a surface region. Depending on the purpose of the design, or on the design context in general, we can distinguish some obvious categories of intention of surface deformation, for example:

F′ explicit

F′ displacement

T S F offset

F′ offset

Category 3 T

S F wrap

F′ wrap

Category 4 S

T

Figure 2.

Schematic picture of the four categories of freeform feature reuse δ, possibly including intrinsic shape parameters may also lead to context-dependent types of freeform feature (Vergeest 2001b). Actually, category 4 can be regarded as a combination of explicit geometry (category 1) with the more procedurally defined offset (category 3).

Besides the different purposes of feature reuse, there are significant mathematical and numerical issues still left unsolved. For example, the feature F to be copied (or reused) may be available either procedurally (as an instance of a predefined feature class) or as a collection of low-level

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geometrical entities, or even as an unordered point-cloud set only. Also the destination surface T may appear in various representation forms. In this paper we address the reuse of features in category 1. In this case, the feature F then consists of a main part and an auxiliary part (or transition surface) that connects the main part in some way (typically smoothly) to the primary shape S. The shape of the main part of F is expected to be transferred from S to T without modification, hence a rigid body transformation should be applied to F to obtain F'. To connect the main part of F' to destination surface T, a new auxiliary part must be constructed. The shape of this new auxiliary part will in general differ from the original one. Further more, for the reason of a clear explanation, we make the following assumptions in this paper:

1. F can be described by means of projections on a plane; hence we do not yet consider features wrapped around over large angles. Also overhanging features are not considered.

As shown in Figure 3, S 0 represents primary surface, which (according to the assumptions above) can be explicitly represented as z = f 0 ( x, y ) . A secondary surface (or deformation) S1 can be written as z = f1 ( x, y ) , which can be a bump or a concave relative to S 0 . C0 is the feature '

boundary curve on S 0 , C0 is the projection of C0 on the xy plane and Ω is the area bounded by C0 . C1 is the boundary 0

'

curve on secondary surface S1 , C1 its projection and Ω its '

1 '

region. C 2 is the boundary of a cut (τ-feature) on S1 , C 2 its projection and Ω

its region, respectively. Ω

2

z

0

C2

of computational geometry; we will need this condition in the calculation of the transition surface.

S1

available.

z=f0(x,y)

C0

4. The surface S and T are available in parametric form, in

S0

particular they are represented as a collection of NURBS surfaces.

OF

THE

y

Ω x Figure 3.

1 C1’ Ω

C0’

0

ΩΤ

C2’ Ω2

United freeform feature representation

Definition 1. (Transition function) A transition function

Γ : ℜ 2 → [0,1] satisfies: 0 Γ ( x, y ) =  1

In this section we will describe the details of freeform feature representation, in which the freeform feature is explicitly defined, inspired by (Cavendish 1995). Unlike in mesh-based or animation-based modeling system, which provides flexible but inexact control over specified surface, the mechanical modeler needs precise control of the part’s geometry. Therefore the definition of freeform feature should be explicitly given. In other words, this can be achieved if the shaping of a generalized freeform feature contains at least three elements: a primary surface, a deformation surface (area) and a transitional surface. In case there is a τ-feature, then an additional boundary to indicate the cut should be included.

2

C1

3. The information about the construction of F is explicitly

MATHEMATICAL REPRESENTATION FREEFORM FEATURE

is the

1

z=f1(x,y)

2. Both S and T are relatively smooth and calculable in terms

This assumption will not actually hurt the adaptability of present method. For instance, to assumption 1, when needed the representation in this paper can be easily extended to parametric form. Then the projection will be measured in uv plane instead of xy -plane. At the end of the paper we will discuss the extension of the method to cases with fewer assumptions.

T

transition area, which is defined by Ω = Ω − (Ω ∪ Ω ) . Then a definition of a freeform feature with regard to copy/paste operation can be given as follows. T

( x, y ) ⊂ Ω 0 ( x, y ) ⊂ Ω 1

(2)

There is a family of functions that can satisfy Equation (2), called transition function family, in which each of them possesses a definite degree of continuity. For example the Hermite interpolating function is the most commonly used transition function. Parametrically, the continuity of transition function Γ( x, y ) defines the continuity of the transitional n

surface. Different degrees of continuity are denoted by G and

C n . G n represents for geometric continuity, for instance, G1 continuity implies tangents have common direction at the

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common points. In contrast to geometric continuity, parametric continuity C

n

is defined in terms of derivates of parameters, 2

for instance, to curves c1 : c1 (t ) and c2 : c2 (t ) , C continuity implies the second derivative of position with respect to t is the same for both curves at the common point,

∂ c1 (t ) ∂ c2 (t ) , where c1 (t1 ) = c2 (t 2 ) . = 2 ∂t t =t ∂t 2 t=t ''

i.e.,

''

1

and restriction on r , a detailed discussion can be found in (Cavendish 1992). Definition 4. (δ-feature) A freeform δ-feature is a compound surface, which can be explicitly defined as:

 f 1 ( x , y ), (x, y) ∈ Ω 1 T  g ( x , y ), (x, y) ∈ Ω

δ ( x, y ) = 

2

Given Γ( x, y ) , the transitional surface between S 0 and

S1 can be constructed as: Definition 2. (Transitional surface) A transitional surface z = g (x, y ) between S0 and S1 is a convex combination of

S 0 : z = f 0 ( x, y ) and S1 : z = f1 ( x, y ) : g(x, y) = (1− Γ(x, y)) f0 (x, y) + Γ(x, y) f1(x, y)

g ( x, y ) = (1 − t ) f 0 ( x, y ) + tf1 ( x, y ) [0 ≤ t ≤ 1] defines a ruled transitional surface between S 0 and S1 , which equation:

0

is C ( G ) continuous. Generally, the feature boundary C0 is an offset of secondary boundary C1 , then a relationship between C0 and

Definition 5. (τ-feature) A freeform τ-feature is a compound surface, which can be explicitly defined as:

δ (x, y ), ( x, y ) ∈ Ω 0 − Ω 2 τ ( x, y ) =  2 ∅,

where set.

δ ( x, y ) is defined by Equation (5), and ∅

T

When Ω ≡ ∅ , then f ( x, y ) defines a freeform 2

then the feature boundary C0 is a constant radial offset of the

feature; when

secondary boundary curve C1 :

compound feature (both

'

Figure 4.

'

Feature boundary

T

is the outward-pointing unit normal vector to curve C1 , and r is an input offset distance. The engineering meaning of feature boundary is that supposing that feature height is h , and then r/h represents the slope of freeform feature. Figure 4

is an empty

1 2  f1 ( x, y ), ( x, y ) ∈ Ω − Ω  f ( x, y ) =  g ( x, y ), ( x, y ) ∈ ΩT ∅, ( x, y ) ∈ Ω 2 

parametric curve of arc length s, i.e., C1 ( s ) : ( x1 ( s ), y1 ( s )) ,

where n( s) = ( − y1 ( s ), x1 ( s ))

( 6)

Inference 1. (Generalized freeform feature representation) A generalized freeform feature is a compound surface, which can be explicitly defined as:

Definition 3. (Feature boundary) Supposing that the secondary boundary curve can be expressed by any sufficiently smooth

(4)

( x, y ) ∈ Ω

As mentioned in the previous section, a definition of a unified representation of freeform feature can then be derived from Equation (5) and (6).

C1 can be defined.

C 0 ( s ) = C 1 ( s ) + rn (s)

(5 )

where g ( x, y ) is a transition surface as defined by Equation (3).

(3)

For example, let Γ( x, y ) be substituted by t , then

0

shows the relationship between secondary and primary feature boundary. For smoothness constraints on C1 ( s ) and C0 ( s ) ,

Ω ≠∅, 2

δ

(7 )

δ

-

f ( x, y ) defines a freeform and

τ

feature included). This is

τ -feature. Specifically, when Ω 0 = Ω1 , T then Ω = ∅ , f (x, y ) = ∅ defines a sharp cut τ -feature. also called finished

Inference 2. (Main freeform feature element) Freeform feature as a characterized shape entity is mainly represented by secondary surface in (7), associating with transition surface. So in a freeform feature definition, the secondary surface is called main freeform feature element. Inference 3. (Auxiliary freeform feature element) In a freeform feature definition, the transition surface is served as an associating shape element, which helps to connect the main feature element with primary surface under certain continuity conditions. Therefore, the transition surface is called auxiliary freeform feature element. An auxiliary freeform feature element may vary according to the primary surface, but the main freeform feature element

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preserves its shape within the scope of this paper. Of course this is not an essential condition. However, since the shape character of a freeform feature is mainly carried by the main freeform feature element, its behavior must be explicitly predictable during the copy/paste operation.

l = p r + tn p with primary surface S0 , where n

pc ( xc , yc , zc ) . Obviously, pr is an interpolation of S0 inside the trimmed area bounded by C0 . In other words, here we need that the system can support interpolation beyond the definition area of S0 (In fact, the definition of

pr is unnecessarily precise, because after pasting of the freeform feature, some other technique can be employed to allocate the feature freely and exactly. This remains for future work.). The z ' axis is pointing into the same direction as does n p .[*]

COPYING OF FREEFORM FEATURE

1.

Select the freeform feature in existing geometric model. According to the definition above, in this case the secondary surface f1 ( x, y ) should be explicitly indicated.

is

the surface normal of S0 that passes through point

In terms of this unified freeform feature representation in (7), it is feasible to implement a set of explicit operating methods for freeform features in an integrated framework, in particular, for instance copying and pasting operations.

According to inference 2 and 3, in fact, copying of an existing freeform feature means that the secondary surface f1 ( x, y ) is copied and the boundary condition of the transition surface is gathered and stored, and will be used to reconstruct the freeform feature later in the new geometric model. It is carried out by several steps as follow:

p

8.

Transform the secondary surface

f1 ( x, y ) to local

coordinate system o'− x ' y ' z ' defined in step 7, i.e.,

f1 ( x, y ) ⇒ f1T ( x, y ) . f1T ( x, y ) to the T T T system's clipboard, together with C0 and C1 ( G0 and

9.

Copy all geometric parameters of

f1 ( x, y ) is a compound surface, then all its subsurfaces that composes f1 ( x, y ) should be selected. If

2.

Start Select FFF

Analyze the secondary surface(s) to find out its outmost boundary C1 based on both its geometric and parametric

Find out C1

representation. If f1 ( x, y ) is a compound surface, then

Find out transition surface along C1

C1 should be constructed as a compound curve while keeping its continuity at each end unchanged. 3.

Identify the transitional surface along C1 .

4.

Identify the primary boundary curve C0 by means of

TT C1T C(G GetGet 1 1 )

Find out C0 TT C0T C (G GetGet 00 )

Construct local coord. System at p Pr(xr,yr,zr)

analyzing the transition surface connected with C1 . 5.

Analyze the transitional continuity along boundary curve C1 , both G and C continuity are examined in this case.

T Do Dotransf. transform: ⇒f1T(x,y) T(xr,yfr,1z(x,y) r)f1(x,y)=f 1 (x,y)

Copy f1T(x,y), C0T and C1T to clipboard

The continuity of transition surface along C1 will be T

Abnormal handling

T

written as G1 and C1 respectively. 6.

Analyze the transitional continuity along curve C0 , T

T

denoted as G0 and C0 respectively. 7.

computed as follows: let the center of the bounding box of picked freeform feature be pc ( xc , yc , z c ) , then pr is defined

by

the

intersection

of

the

normal

line

FFF Geometry data

Stop

Figure 5. Procedure of copying a freeform feature

Construct a local coordinate system o'− x ' y ' z ' at point

pr ( xr , yr , z r ) . pr is a reference point, which is

Clipboard:

[*]

definition

is:

y = np × x '

x'

In this case the

x'

keeping '

. If

and

y'

axes are left undefined. A possible

unchanged,

np × x = 0 , '

i.e.,

x ' = (1,0,0) ,

then

then an alternative can be: let

y = (0,1,0) , then x = y × n p . '

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'

'

Copyright © 2002 by ASME

merge this local geometry to the global model by

G1T ). To do this, a template to hold these data should be Step 8 uses the characteristic that computational attributes of geometry are invariant under affine transformations. This has been usually adopted as a theorem. The procedure of copying of freeform feature is shown in figure 5. An abnormal handling routine is invoked when an unexpected error occurs, and the clipboard is served as a data carrier to transfer geometry among different process (within or across models). If there exists a τ-feature on the secondary surface S1 , it should also be explicitly indicated. Then its boundary should be copied. In this paper we mainly focus on the operation of δfeature, so the operation of τ-feature is not discussed in detail here.

'

transforming f1 ( x, y ) ⇒ f1 ( x, y ) . T

pre-defined and registered to the windows system. 5.

'

Get C 0 according to C1 , which is the feature boundary in global coordinate system. This is implemented by '

projecting C1 onto a plane P and computing Equation (4). Plane P is perpendicular to n . 6.

'

Project C 0 along n onto the primary surface S0 of the new model to get C 0 .

Figure 6 demonstrates step 5 and 6. The computation of C 0 should be within the limitation of system precision as described in next section. In Figure 6 P is a temporary plane, P1 is a point on C1 and P0 is the point on primary surface S0 relative to P1 .

PASTING OF FREEFORM FEATURE As an effective manner to support cross-model design reuse, copy/paste operation of freeform feature provides an easy way for the designer to capture interested shape characters depicted by form features in an existing model. A series of preliminary actions have been described in the previous section, which collects all of the necessary geometry information about a freeform feature. The pasting operation of freeform feature can then be implemented by following steps: 1. 2.

n C1 ’

P1 P1

P

S0

Giving a pivot point p ( x p , y p , z p ) , either by selecting a

7.

4.

Allocate the freeform feature

f1T ( x, y ) in this local

coordinate system or − xr y y z r by pasting the geometry data from clipboard into the new geometric model. Then

P0

Calculation of C0 T

Construct the transition surface according to C 0 , C1 , C0 T

T

T

constructed by two boundary curves ( C 0 and C1 ), and several section curves with cross boundary tangent vectors at each corresponding pair of end points. This surface can then be converted to a shell body or a solid body by skinning the shell body, if the data is compatible with a solid modeling supporting system.

at

previous section.

r

and C1 ( G0 and G1 implied). The transition surface is

called projection vector.

pr ( xr , yr , z r ) with zr axis pointing the same direction as n . The definition of xr and yr is the same as in

n(s)

C0

Figure 6.

line: l = p + tn with primary surface S0 . n is also Construct a local coordinate system or − xr yr z r

C0’

S1

pr

point pr ( xr , yr , z r ) is defined by the intersection of

3.

C1 Ω1

Check whether the data format in the clipboard is correct according to the internal definition of operation, including.

previously defined point into a pick-table or just by indicating the geometric part model, referencing to that the freeform feature will be pasted. In each case the new part’s geometric model should be aware by the application properly and a surface normal vector n passing through p( x p , y p , z p ) should be computed. Then a reference

Projection line that is parallel to n

8.

Clear the geometry data in the clipboard.

In the procedure of pasting of freeform feature the transition surface is not constructed as it was in the original model, but according to the new model geometry. However, the boundary continuity conditions are carried on. These steps will establish a hard copy of original freeform feature. In other words, the original shape of the freeform

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feature (main freeform feature element) is kept unchanged. But, we should mention here that it is possible to modify the original feature shape to obtain special effects, such as melt down, stretching and twisting, etc., as described in Section 3, while the original shape character of freeform feature still inherited. This remains for future work. Figure 7 shows the whole process of operation of freeform feature pasting.

where r = u

rv =

1 ∂ '' S 0

1 ∂ "S 0

∂u

is main curvature of S 0 at P0 , and 2

is secondary curvature of S 0 at P0 . Then the

∂v 2 '

maximum interpolation step at P1 along C 0 is decided by the following equation:

CONTROL OF COMPUTATIONAL PRECISION

∆ s = Minimum ( ∆ s1 , ∆ s u , ∆ s v )

There are two aspects related to the precision control of computation, which should be take into consideration, one is ' 0

(8 )

After calculation of each Pi on S 0 , a re-parameterization

the precision at point P1 along C , the other at P0 on primary

should be done if the parametric point numbers on C1 and C 0

surface S 0 .

do not match.

According to Equation (4), supposing that the tolerance is

ε , then the biggest step of interpolation at P1

'

along C 0 will

be:

∆s1 = 2ε (2r1 − ε ) , where r1 =

1 ∂ "C0'

'

is the curvature radius of C 0 at P1 .

∆s u = 2ε (2r u − ε ) , ∆s v = 2ε (2r v − ε )

Start Correct data format in clipboard? Y Pivot p Pr , n Vp and current model Def. local coord. system Allocate Allocate f1’T(x,y) Calculate Calculate C1C ,C 00 Construct transition surf. Clear clipboard Abnormal handling

Figure 7.

Stop

Process of freeform feature pasting

An application platform has been implemented to validate the algorithm proposed in the presented paper, and here are some examples to demonstrate the result of applying the tools of copy/paste freeform feature across models. This platform is developed with the support of ACIS kernel. Figure 8 shows the interface of cross model feature reuse. As shown, there is one model, in which an interested feature exists (picture (a)), by copy/paste operation, the feature is then easily constructed in another model (picture (b)). This demonstration employs a multi-document interface so that the system can open several parts’ models at the same time. This multi-documents interface facilitates the transfer of features from one model to another significantly. By the support of this tool, freeform features cannot only be copied/pasted cross models, but also within the same model.

∂s 2

At point P0 on surface S 0 , we have:

N

EXAMPLES

Clipboard: FFF geometry data

Another example is given by Figure 9, where in model (a), a freeform feature is of interest to the designer, and is intended to be reused. The freeform feature should be explicitly according the definition given in this paper. Otherwise a feature matching method should be invoked first to reform the feature geometry to be compliant to the formal definition in case that the feature is arbitrarily defined (Vergeest 2001b). The following operation sequence is exactly the same as what was depicted in the former section correspondingly. In picture (b) the red color indicated that a feature is picked, and its bounding box and the reference coordinate system are shown. Some analysis will be performed by the system to determine the feature boundary and the continuity of the transitional surface. In this example a ruled surface is detected. These boundary conditions together with the feature geometry (which were transformed into reference coordinate system) are stored into the clipboard for later use. Picture (c) shows the picked freeform feature geometry in the clipboard. The paste operation of the freeform feature into a new model (or within the same model) is rather simple. Just

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Positioning and scaling of freeform features while pasting are also important issues that should be considered, for example in case that the freeform feature is bigger than the target model. This is not yet considered in the above example and remains for future work. CONCLUSIONS AND FUTURE WORK In this paper we have introduced a systematic method to implement the reuse of a freeform feature entity. This technology is a powerful tool to enhance freeform modeling Furthermore it may provide higher-level support to conceptual modeling.

Figure 8. Interface of cross-model feature reuse pick the face that the freeform feature will be pasted, and then the system will construct the copied feature according to the process proposed. Here are some basic requirements as discussed to ensure that the computation is carried out correctly. But these assumptions are not the necessary conditions. They depend strongly on the implementation environment. A much more looser computation restriction can also be expected. In Figure 9, picture (d) shows a model with one freeform feature pasted, and the local reference coordinate system and surface normal are also shown. Picture (e) shows a model with two freeform featured imbedded. Theoretically, there is no limitation of the number of times to paste a feature into the new model once copied.

We emphasize that: (1). Although copying and pasting of freeform feature discussed in this paper deals mainly with geometric issues, its idea is useful to the development of a next generation of intelligent CAD systems, in which the reuse of existing design knowledge should be considered. (2). Inference 1 (Equation (7)) gives a generalized freeform feature definition. This makes it possible for us to manipulate freeform feature under a unified schema. The present method introduced in this paper, of course, has some limitations. For example, it seems that, geometrically if the feature is bigger than the destination object, then the method will not work. But this is not the actual limitation, because when pasted the feature should be allowed to be scaled, rotated or shifted by the user arbitrarily. These facilities will be provided in the future. Another limitation is that, in the present representation of '

freeform feature, we suppose that the cut boundary C 2 is '

within main feature boundary C 0 . This is of '

'

course unnecessary. When C 2 is out of C 0 , then a new feature boundary region should be given by Ω = Ω ∪ Ω . Then the presented definition is simply extended to cover this case. 0

1

The projection plan shown in Figure 3 is not necessarily on xy -plane. For some special case, the projection of freeform feature on xy -plane may be not sufficient to explain the geometric relationship among feature ingredients, for instance, the projection may be a line. But this problem can be solved by considering the feature projection on the plane that is perpendicular to the surface normal of S 0 at a proper point. Then all the other definitions remain unchanged. Figure 9.

Examples of cross model copy/paste of a freeform feature

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Overall control over freeform features is possible and it is a challenging research field in

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freeform modeling, too. We believe that it is feasible to construct a complex geometric part model based only on freeform features. Of course automatic generation of information for downstream use, for example, in process planning, NC programming, etc., which relate to a particular feature or feature set, is also practically feasible according to this study.

Wang, C., Horvath, I., Vergeest, J. S. M., (2002), “Towards the reuse of shape information in design”, TMCE’02, Feb 24-28, Wuhan, P.R.China

REFERENCES Au, C. K., Yuen, M. M. F., (2000), “A semantic feature language for sculptured object modeling”, Computer-Aided Design, Vol. 32, pp63-74. Cavendish, J. C., (1995), “Integrating feature-based surface design with freeform deformation”, Computer-Aided Design, Vol.27, No.9, pp703-711. Cavendish, J .C., Marin, S. P., (1992), “A procedural featurebased approach for designing functional surfaces”, in Hagen, H (Ed.), Topics in surface modeling SIAM, USA, pp145-168. De Martino, T., Falcidieno, B., Giannini, F., Hassinger, S. and Ovtcharova, J., (1994), “Feature-based modelling by integrating design and recognition approaches”, ComputerAided Design, vol. 26, No. 8, pp646-652. Duffy, A. H. B., Ferns, A. F., (1999), “An analysis of design reuse benefits”, Proceedings of ICED’99 Conference, Technische Universitat Munchen, pp 799-804. Eversheim, W., Deckert, C., Westekemper, M., (2000), “Increasing efficiency through integration of freeform features into CAD/CAM-chain”, Proceedings of the 9th symposium on product data technology, Europe 2000, Quality marketing services, Sandhurst, pp355-362. Fontana, M., Giannini, F., Meirana, M., (1999), “A freeform feature taxonomy”, EUROGRAPHICS’99, vol. 18, No. 3 Gallagher, C. C., Knight, W. A., (1973), “Group Technology ”, Butterworth & Co. (Publishers) Ltd., England. Van Elsas, P. A., (1997), “Freeform displacement features in conceptual design”, PhD thesis, Delft university press. Vergeest, J. S. M., Horvath, I., Spanjaard, S., (2001), “A methodology for reusing of freeform shape content”, Proceedings of DETC’01, 2001 ASME Design Engineering Technical Conferences and Computers and information in Engineering Conference, Pittsburgh, Pennsylvania, Sep. 9-12, 2001 Vergeest J.S.M. (2001b), "Shape context - informal description and formal definition". Technical Report, Faculty of Design, Engineering and Production, Delft University of Technology, Delft, 19 December 2001, http://dutoa36.io.tudelft.nl/docs/dynash002.pdf.

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