Analysis of a Freeform Shape Modelling Process

Raluca DUMITRESCU, Joris S.M. VERGEEST, Tjamme WIEGERS

Delft University of Technology, Faculty of Industrial Design Engineering, Landbergstraat 15, 2628

CE Delft, The Netherlands, {r.dumitrescu, j.s.m.vergeest, t.wiegers}@io.tudelft.nl

Abstract: In this paper, we introduce and analyse a Computer-Aided Industrial Design (CAID) process. For each step

performed in the shape modelling process, durations, involved entities, concerned parameters and constraints, initial

and final states of the shapes were recorded. The modelling session consisted of three main phases and lasted 2710

seconds. The results show that transformation tools are more used than generation tools. In addition, the usage of

entities already in the scene is also preferred over the creation of new entities. Modelling activities using curves or

surfaces are equally preferred. However, curves dominated in the first part of the session, whereas surfaces are more

involved in the last part of the session.

Key words: freeform shape modelling, design experiment, curve usage, surfaces usage

1. Introduction

The increased need of freeform shapes in Computer-Aided Design / Computer-Aided Manufacturing

(CAD/CAM) technologies has lead to the development of Computer Aided Industrial Design (CAID) systems. As

freeform shapes present complex curvature, they cannot be modelled using regular geometries like spheres or

cones. Bézier, B-Splines or Non-Uniform Rational B-Spline (NURBS) representations are the commonly used

representations in current CAID. Other mathematical descriptions (e.g. implicit surfaces) exist but they are less

used in the commercial systems. The newly emerged CAID systems have gained important consideration within

the design departments in the last years due to their capabilities of modelling freeform shapes.

However, the commercial CAID systems provide low-level shape handles for the alteration of the shapes. On

the other hand, the mature CAD systems provide the designer with high-level shape handles such as radius, length,

and width. These high-level shape handles are regarded as intuitive shape handles, as the designer can easily

predict the behaviour of the shape before that shape handle is actually used. Low-level shape handles (like control

point based deformation, weight modification, or knot vector modification) are regarded as counter-intuitive. In

the case of complex freeform shapes, it is rather difficult to predict the change that occurs in the shape with a

low-level shape handle.

Moreover, up to 70% of the products' costs from 3-4% of the development costs are defined in the conceptual

design phase of the design process [3]. During this phase, CAID systems are preferred due to the possibilities they

offer to work with complex freeform shapes compared with CAD. However, designers may have difficulties in

getting the desired shapes due to above-mentioned counter-intuitiveness of the shape handles. As a result, high

amount of work around is recorded because considerable high number of modelling steps is necessary to achieve

some desired shape modifications. Therefore, designers need CAID tools that help them to get the right shape in

short time in order to have less development costs.

Different methods to support quick and intuitive freeform shape alterations or even the generation of complex

freeform shapes in CAID are presented in the literature. Among them, the freeform displacement features

approach developed by van Elsas [8] provides designers with the possibility to create and modify displaced

freeform surface features. A displaced freeform feature, DFF, represents a freeform protrusion or depression on a

freeform surface. The designer sketches a region on the global shape. This region is displaced above or below the

global surface resulting in a protrusion or a depression. After the displacement, a transition surface is generated

between the global and the displaced region preserving G1 continuity. Parameters known from the regular shape

domain, like height, slope of the transition surface, or rounding, control the resulting shape of the feature.

Industrial designers evaluated the DFF tool as useful in the conceptual design process. The method groups a set of

steps into a set of fewer steps that are more intuitive and requires less time.

Fontana et al. [4] report on tools for easy shape modification based on freeform features. Based on a B-Spline

representation of surfaces, CAD tools were developed mainly to support stylists' work. Detail modification of the

global surface to ensure aesthetical characteristics of the products is performed with deformation or elimination

laws. Consequently, border, internal or channel deformation or deformation with break, as well as sharp or

finished cuts as higher-level shape handles are defined, which preserved designers' intentions when modelling

products with freeform features.

Other approaches that support the designer in the creation of new product forms exist in the literature. Hsiao

and Huang [5] use a neural network technique to generate new product forms from existing forms of the same

product. Firstly, the product is decomposed into its components. For each component, relations between the form

parameters and adjective image words were established and altering these parameters generates the new forms. A

similar approach is proposed by Au and Yuen [1]. Designers generate product models using grammar rules that

hold between vocabularies represented by features and the feature relationships. Other interesting approaches refer

to the shape morphing product design method reported by Hsiao and Liu [6]. The method is strongly related to the

available product's shapes. The shapes are decomposed and image words are attributed to them. The designer

selects the initial shape and a final shape and based on a morphing-ratio a new shape is generated.

Another appropriate technique that supports the generation of a new shape through reverse engineering is

presented by Hsiao and Chuang [7]. Designers select two existing products of which shapes are scanned. After

generating the characteristic curves of each scanned surface, a correspondence between the generated curves is

performed, and the combination of the two shapes generate the new shape using a blending ratio. This parameter

controls the appearance of the new shape with respect to the two existing shapes.

Whereas literature presenting new tools for designers is rich, few attempts have been made to analyse CAID

processes and see how designers model products or what tools they prefer while modelling. Bhavnani et al. [2]

introduce such observation of CAD usage. However, the results focus on the active assistance of the user from the

efficiency point of view, and discussion is on customising the interface to better fit each user or improving tool

execution.

In order to develop new intuitive CAID tools, we ran a CAID experiment to see how the modelling process is

performed. The paper presents the experiment, which had three main modelling stages. In the next section, the

experiment and the documentation of the experiment are introduced. Then, the experimental results are presented

and discussed. Finally, we draw conclusions in the last section.

2. The Design Experiment

Many design experiments presented in the literature report about aspects of human-computer interaction,

efficient usage of available tools or performance of modelling functions. However, there is no evidence of

experiments that report over the usage and generation of entities during the modelling sessions, or about the

duration needed to perform the steps during a freeform shape modelling session. These types of data are needed in

order to discover opportunities of shape modelling shortcuts. Therefore, we carried out a design experiment to

collect detailed information about the freeform shape modelling process.

In the experiment, the test person had to perform a modelling task that had three stages. Initially, a 2D image

of a physical soapbox model was shown to the test person. The test person was given the task to reproduce this

model within a CAID system. In the next two stages of the experiment, the test person had to alter the shape of the

model to fulfil two different functional requirements. For the second stage, the requirement about the

accommodation of a 20% larger soap led to a proportional modification of the model in all three directions. Later,

in the third stage, the product model had to accommodate a new soap that presented a rounded-top (as opposite of

the flat-top from the previous stages). The purpose of the last two stages was to observe how the test person copes

with unexpected situations in terms of shape modifications, preferred entities, and time spent to complete the

shape modifications. One can expect that only few steps would be necessary to complete these kinds of tasks in a

relative easy way. However, the actual shape modification processes involve more work than expected due to the

existing status of the model's shape(s) at a moment, which made later modifications difficult to accomplish. Figure

1 shows the product models generated after each stage.

The first stage consisted of creation of half of the body of the soapbox by lofting. Using an extrusion technique,

the two ridges were generated and then they were used to trim the main body. Later, with the body's profiling

curve, the second type of ridge was generated. At the end, the body and the two ridges were duplicated and rotated

into the right position and hence the whole model was ready. This stage had 175 steps and it took 2221 seconds to

complete it. The second stage was much shorter and the test person completed it using a simple scale-up technique

of the model generated in the first stage. It had five steps and took 41 seconds. However, the requirement imposed

by the new top-rounded soap and because of the geometry available in the scene, in the third stage the test person

modified the top of the model displacing its control points. This stage had 34 steps and took 448 seconds.

The complete modelling session run over a period of 2710 seconds and had 214 steps. The smallest part of a

modelling session where one activity (like selecting, extruding or the like) takes place is referred by "step".

Therefore, a step has an initial status of the shape and a final status of the shape. An activity may involve shape

modifications or entities selections as well as rotating the viewing camera that allows the user to look at the model

from different viewpoints. In addition, parameters and constraints can be assigned to each step.

In order to include all types of data mentioned above into the same representation, we developed a model of

data representation that allows easy access and

visualisation of the modelling session. Table 1

shows how the durations of the modelling steps,

involved entities, and the initial and final shape(s)

of the steps, and the set of parameters and

constraints in use during a modelling step were

recorded for further analysis.

Fig.1 Models generated at the end of the three modellingstages: (a) initial model; (b) scaled-up model; (c)top-rounded model.

One important advantage of documenting the data from the modelling session into such format (Table 1) is that

it allows for easy aggregation of the modelling steps into set of steps that led to a specific shape creation or

modification. Secondly, it can also incorporate data from other types of shape modelling processes, like clay

modelling [9].

For this experiment, the CAID software used was Maya 3.0 from Alias|Wavefront. During the experiment, we

video captured the screen window with a rate of one frame per second. The platform was a PC Pentium III with

256 MB RAM and the operating system Windows 2000. The necessary data collected from the experiment was

based on both the video file and the log file (i.e., file that contains the tools / actions and their settings as used

during the modelling session).

3. Experimental Results and Discussion

In this section, we present and discuss the results from the design experiment. Quantitative content analysis

has been performed based on the documented data (as shown in Table 1). Figure 2 shows how many times and

which type of tools (functions) were involved throughout the modelling session. As can be seen, tool involvement

varies between 1 and 48, with an average value of 20. Exceptions refer to the Selection and Co-Selection of

entities, which rank on a higher value and Unselecting ranks at a lower value. The relative high value of the

Delete function shows that during the session, a significant number of entities were used to help the test person in

getting the desired result and then these entities were deleted after this achievement. The shape transformation

tools are grouped together above the average value, whereas the shape generation tools are grouped together

below the average value. This grouping indicates that much work-around has to be done to accomplish the desired

results.

Figure 3(a) shows the duration, D, of each modelling step. As can be seen, the mean value for the duration of

the modelling steps is 12.6 seconds and most steps were actually completed within a limit of 5 to 20 seconds.

Steps involving modification tools that required the

set-up of their parameters ranked above this time

limit. In addition, steps involving transformation

tools required only few seconds. When the test

person knows what should be the resulting shape,

this shape can be reached relatively easy and fast,

although many steps may be necessary for this.

However, the three extreme values recorded

represent the computational time required to

perform projections and trimmings and, therefore,

they cannot be taken into discussion.

Table1. Representational example of the data from the modelling session.

Step

No

Duration [sec]

Activity + Entities Initial Shape, Si Parameters Constraints Final shape, Sf

New Shape(s)

65 10 Rotate surface, S2

Pivot point at (0,0,0) 180º around Y

-

Fig.2 Types of tools used during the modelling session

Figure 3(b) shows the time evolution throughout the modelling session. As could be expected, the slopes of the

first and third stage are nearly equal with the slope of the whole modelling session, and the slope of the second

stage is 2 times steeper than are the others. This is because the second stage was relatively easy and fast to

accomplish given the symmetry of the product model and, hence, the low number of steps involved. The steep

slope in the beginning part of the modelling session indicates a high frequency of modelling step completion; in

other words, many shorter steps were performed and the shorter the steps, the steeper the slope. In that part,

simple geometry was in the scene and the surfaces were easy to cope with. However, for more complex

geometries and different types of surface's involvement, as it was the case for the second part of the first stage, the

steps' completion rose difficulties to the test person and require high computational time. This resulted in a less

sharp slope.

In the case of freeform shape modelling, it is important to analyse how entities are generated and used over the

modelling session. From the Table 1, two different types of entities were distinguished: curves and surfaces.

However, some entities are used in the beginning and during a modelling step, whereas others are just generated at

the end of the modelling step. Therefore, we can further distinguish between existing entities, EE, and new entities,

NE. Existing entities include existing curves, EC, and existing surfaces, ES, i.e. ESECEE += . They are used

to modify existing entities or to generate new entities. The new entities represent those new curves, NC, and new

surfaces, NS that are generated at the end of a modelling step, i.e. NSNCNE += .

Figure 4 shows the involvement of new and existing curves over the modelling session. For the modelling

steps where existing curves occurred, they scored two on average. Also, the modelling steps where new curves

were generated present an average of one new curve per step. However, for the whole modelling session a mean

of one existing curve and 0.2 new curves were recorded. That is, curves were more used within modification tasks

and less used for generation tasks. Curves' involvement is predominately in the first half of the modelling session

and decreases gradually towards the end of the session.

Surfaces' occurrence is shown in Figure 5. As opposite to curves' occurrence, which appears mostly in the first

half of the session, surfaces' occurrence is recorded in the second half of the session. For existing surfaces, there is

Fig.3 (a) Plot of the duration of each modelling stepversus its corresponding step index; (b) Plot of the timeevolution over the modelling session. The three stages ofthe design experiments are indicated.

Fig.4 (a) The number of existing curves used during each modelling step; (b) The number of new curves generated at the end of each modelling step.

a fluctuating usage through the modelling session, and a mean value of 1.14 surfaces per step was recorded.

However, new surfaces' occurrence proves to have a constant rate of 0.1 over the session. Therefore, compared to

the mean of the new curves, fewer new surfaces are generated per step, and that is probably because there is a

preference for manipulating curves instead of surfaces.

Figure 6(a) shows the involvement of the existing entities, EE, per step and the new entities, NE, are shown in

Figure 6(b). With a mean value of 2.1, existing entities are more likely to be involved during the session compared

to the generation of new entities, which present a mean value of 0.3 over the session. The same can also be

concluded from Figure 4 and Figure 5. Still, the slope of the existing entities increases and the slope of the new

entities decreases over the session. It means that existing surfaces have more influence than existing curves, and

new curves have more influence over new surfaces.

Further, we present how the evolution of entities was recorded over the session. Figure 7(a) presents the sum

of the existing curves, SEC, and the sum of all existing surfaces, SES. They represent the accumulation of all

existing curves or surfaces involved over the modelling session, SEC=∑N

i

ECi and SES=∑N

i

ESi. Figure 7(b)

presents the accumulation of the new curves, SNC, and of the new surfaces, SNS. These are the sum of the new

curves or surfaces generated over the modelling session, SNC=∑N

i

NCi and respectively, SNS=∑N

i

NSi. Although

curves dominate on a large part of the session, there were still more existing surfaces recorded at the end of the

session. This is probably because towards the end of a modelling task the focus is more on surfaces and become

less or none on curves. However, the sum of all curves (i.e. SEC +SNC) and the sum of all surfaces (SES + SNS)

over the whole modelling session is almost equal, 261 vs. 268.

Finally, Figure 8 shows the sum of the existing and new entities, SEE and SNE, involved as a cumulative

function over the modelling session, i.e. SEE=∑N

i

EEi and SNE=∑N

i

NEi. As can be seen, existing entity

involvement is nearly ten times higher than the new entity involvement. This indicates that a large quantity of

work-around it is performed before the desired result it is obtained.

Fig.6 (a) Plot of the number of existing entities usedduring each modelling step; (b) Plot of the number of newentities generated at the end of each modelling step.

Fig.5 (a) Plot of the number of existing surfaces usedduring each modelling step; (b) Plot of the number of newsurfaces generated at the end of each modelling step.

4. Conclusions

In this paper, a computer-aided industrial design experiment was presented and analysed. It was found that

transformation tools group together and ranked higher that the other group of generation tools. The existence of

many short steps over the modelling session and the frequent usage of the Selection and Delete functions was also

noted in this session, which suggests that the experimental results confirmed the hypothesis of the high amount of

work-around that has to be performed by the CAID user until she/he gets the desired shape. The dominance of the

existing entities over the new entities may also indicate the same amount of work-around.

In addition, the analysis revealed that curves are equally used compared with surfaces in a freeform shape

modelling, and curves' involvement is predominately in the first half of the modelling session and decreases

gradually towards the end of the session as opposite to surfaces' involvement. That is because to the focus towards

the end surface-model that is the result of the modelling session. The development of new freeform modelling

tools should consider these findings. Tools intended for idea generation should give the designer the possibility to

model using alterable parameters, thus, reducing the number of steps currently performed in modelling sessions.

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