Modeling the Human Ear_m2jd

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Modelling the Human Ear

Joanna Davison

Advanced Computer Science

Supervisor - Steve Maddock

16th May 2003

This report is submitted in partial fulfilment of the requirement for the degree of

MSc in Advanced Computer Science


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Declaration

All sentences or passages quoted in this dissertation from other people's work have

been specifically acknowledged by clear cross-referencing to author, work and page(s).

Any illustrations which are not the work of the author of this dissertation have been

used with the explicit permission of the originator and are specifically acknowledged. I

understand that failure to do this amounts to plagiarism and will be considered groundsfor failure in this dissertation and the degree examination as a whole.

Name:

Signature:

Date:

I


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Abstract

The ear is a very complex shaped object, a result of which is the problem of finding a

computer graphics modelling technique suitable to effectively create a realistic ear

model. Techniques applied so far consist mainly of manual methods, which generally

dont cope well with the extensive overlapping of the ear and possess minimal scope

for generating different ears from an initial model.

The aim of this project is to solve this very problem with the use of sweeping and

create not only a realistic ear, but also a model with the scope to easily produce wide

ranges of different ears to represent the diversity of ear shape of the worlds

population.

A program has been developed that, to a certain extent, satisfies the above

requirements. The level to which this has been achieved and potential improvements

are discussed at length.

II


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Acknowledgements

I would like to express thanks to my supervisor Dr. Steve Maddock, for his

suggestions and guidance in the development of the project and my tutor Marian

Gheorghe for his support. I would also like to thank Phil and my family for their love

and support over the past four years, not to mention the use of their ears.

III


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Contents

1. Introduction............................................................................................................... 1

2. Literary Review......................................................................................................... 2

2.1. The Ear................................................................................................................. 2

2.2. Modelling Techniques and Previous Attempts .................................................... 32.2.1. Manual Modelling and Editing ..................................................................... 3

2.2.2. Data Capture ................................................................................................. 5

2.3 Higher-level Description Techniques ................................................................... 6

2.2.1 Hard Primitives ........................................................................................... 6

2.2.2 Soft Primitives ............................................................................................... 7

2.2.3 Swept Primitives............................................................................................ 7

2.2.4 Procedures and Primitives.............................................................................. 8

2.3.5 Suitability to Modelling the Ear..................................................................... 9

2.4. Sweeping within Nature..................................................................................... 10

2.4.1 The Regularity of Nature ............................................................................. 10

2.4.2 Shell-shape Surface Generation................................................................... 102.4.3 Summary...................................................................................................... 12

2.5. Sweeping............................................................................................................ 12

2.5.1 A Review of the Technique and Extended Methods ................................... 12

2.5.2 Practical problems associated with sweeping.............................................. 13

3. Requirements and Analysis.................................................................................... 17

3.1 Aims and Objectives ........................................................................................... 17

3.2 Program Capabilities........................................................................................... 17

3.2.1 Ear Variation................................................................................................ 18

3.3 Sweeping the ear ................................................................................................. 19

3.3.1 Parameterisation of the Ear.......................................................................... 19

3.3.2 Sweeping Theory ......................................................................................... 20

3.3.3 Rendering the ear......................................................................................... 23

3.3.4 Summary...................................................................................................... 23

3.4 Evaluation of the Ear Model............................................................................... 24

3.4.1 Realism of ears produced............................................................................. 24

3.4.2 Comparative Evaluation With Previous Attempts....................................... 24

3.4.3 Ear Reproduction Evaluation Method ......................................................... 25

3.4.4 Summary...................................................................................................... 25

4. Design, Implementation and Testing..................................................................... 26

4.1 OpenGL............................................................................................................... 26

4.2 Program Overview.............................................................................................. 26

4.3 Generating the Ear .............................................................................................. 27

4.3.1 Surface Curve Sampling .............................................................................. 28

4.3.2 Cross Section Calculations .......................................................................... 29

4.3.3 Path Curve.................................................................................................... 35

4.3.4 Cross section curves..................................................................................... 36

4.3.5 Summary...................................................................................................... 37

4.4 Evaluation ........................................................................................................... 38

5. Results and Discussion............................................................................................ 40

5.1 Evaluation Results .............................................................................................. 40

5.2 Completion of objectives .................................................................................... 42

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5.3 Considerations for Further Development............................................................ 43

5.4 Areas of Further Investigation ............................................................................ 44

5.5 Project Progress .................................................................................................. 44

6. Conclusions.............................................................................................................. 46

References .................................................................................................................... 48

Appendix A Ear Model Example............................................................................ 50

Appendix B Ear Variations..................................................................................... 51

Appendix C Evaluation Questionnaire.................................................................. 52

Figures

Figure 2.1(a): The major features of the ear (Image adapted from [http06]).............. 2Figure 2.1(b): Depiction of cross-sectional shape of the upper helix......................... 2

Figure 2.2 (a)&(b): Ear model from [http01] (Courtesy of Steven Tubbritt) ............. 4

Figure 2.2 (c)&(d): Ear model from [http04] (Courtesy of Jon McBain)................... 4

Figure 2.2 (e)&(f): Ear model from [http05] (Courtesy of Martin Andersen)............ 4

Figure 2.2 (g)&(h): Ear model from [http02] (Courtesy of Frank Silas TBC*) ......... 4

Figure 2.3: Ear shell by Genex using a data capture method...................................... 6

Figure 2.4: CSG tree [Watt00].................................................................................... 7

Figure 2.5: Candles representing soft primtives........................................................ 7

Figure 2.6: Depth component generated using Extrusion........................................... 8

Figure 2.7: A wine glass as a solid of revolution........................................................ 8

Figure 2.8: Fractal object generated procedurally ...................................................... 8Figure 2.9: Outlining the similarity between the shell opening and the concha....... 12

Figure 2.10: An example of the problem of the curve to polygon ratio .................. 13

Figure 2.11(a): Subdivision by equal intervals......................................................... 13

Figure 2.11(b): Arc length parameterisation............................................................. 13

Figure 2.11(c): Non-uniform subdivision................................................................. 13

Figure 3.1: The right ear of each member of a family unit....................................... 18

Figure 3.2: Pinna Measurements............................................................................... 19

Figure 3.3(a): Positional continuity .......................................................................... 21

Figure 3.3(b): Tangential continuity ......................................................................... 21

Figure 4.2(a): Triangle of skeleton points................................................................. 31

Figure 4.2(b): Extended points E .............................................................................. 31

Figure 4.2(c): Distances and points .......................................................................... 31

Figure 4.2(d): Translating M,E to S,F....................................................................... 31

Figure 4.4: Computing a reference frame from the previous frame ......................... 33

Figure 4.5: QUAD_STRIP formation....................................................................... 34

Figure 4.6: Vertex normal......................................................................................... 34

Figure 4.7(a): Path curve with too high curvature .................................................... 35

Figure 4.7(b): Crimping caused by cross-section self-intersection .......................... 35

Figure 4.7(c): Path curve with increased radius of curvature around the lobe ......... 35

Figure 4.8: Convex to concave cross-sections, left to right: A, B,C......................... 36

Figure 5.1: Results of Question 1 ............................................................................. 40Figure 5.2: Results from Question 2 ......................................................................... 41

Figure 5.3: Results from Question3 .......................................................................... 42

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Figure 5.4: A selection of mammal ears ................................................................... 44

* Permission for these two images was not officially confirmed due to an expired

email address, but they were included anyway given their substantial relevance to this

work

Tables

Table 3.1: Anthropometric Statistics, %=100(2/) ................................................ 19Table 4.1: Class Responsibilities and relevant details of implementation................ 27

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1. Introduction

1. Introduction

1

There are many different techniques by which to create a computer graphics model.

However, realistically capturing the complex shape and concavities of the human ear is

one of the more complex objects to model and a technique capable of doing so does

not immediately present itself. There have been three-dimensional models of the

human ear created, the majority of which used manual techniques. The ears createdhave all been products of the designers artistic impression of an ear. Martin Andersen

comments:

Many people try modelling a human ear but fail in realism, because of its complex

shape. The ear is [] known as one of the most complex parts to model in 3D.

(http05)

The aim of this project is to find a solution to this complex modelling problem. In

doing so, the shape of the ear and its features are considered with particular attention to

the concavities and overlapping created by the spiral-like form of the outline shape.

Potentially suitable techniques are fully considered and an investigation is made in to

the fascinating subject of regularity in Nature and natural objects that unearths

properties of nature which would support the use of sweeping. The findings of these

areas of investigation point towards sweeping as the most promising solution.

The general concept behind sweeping is to define a three-dimensional object in terms

of a two-dimensional cross section, the generator, and a three-dimensional spine curve.

The three-dimensional object is generated by sweeping the cross-section along the path

of the three-dimensional curve.

An important factor that should be taken into consideration is the huge variancebetween individuals ears. A persons ear is in fact as unique as their fingerprint. The

size and shape of a persons ear will change as they get older and the difference

between peoples ears across race and gender are substantial. As such, it is near

impossible to define a normal ear in terms of average size and shape. Thus, in

creating a truly realistic ear, these dominating factors should be taken into

consideration. By appropriately parameterising the path and cross-sections, the scope

should be available to generate a range of different ears.

These factors shall be applied to sweeping and the potential of sweeping as an ear

modelling technique shall be deduced from the evaluation of ear models created with

the use of sweeping.

Chapter 2 presents a review of modelling techniques in general and attempts to date to

create a realistic ear model. Sweeping is also covered in detail along with potential

problems with using the technique. The factors of nature that indicate the use of a

sweeping technique are also discussed. Chapter 3 looks at the issues associated with

ear variation and addresses the process of sweeping the ear and the practical

considerations involved. Evaluation techniques to assess the realism of the ear are also

considered. Chapter 4 goes into specific detail of the theory and implementation

methods used in the program to create the final ear model. The evaluative procedure is

considered in greater depth. The findings of the evaluation process are considered in

Chapter 5, where conclusion may be drawn with respect to the initial objectives. Theproject is concluded with Chapter 6.


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This chapter begins by looking at the ear itself, and goes on to justify the use of

sweeping to model it. In doing so, previous attempts to model the ear are discussed and

evaluated, namely manual modelling and editing and a data capture technique, along

with other potential constructive modelling techniques and aspects of Nature

displaying qualities of sweeping theory. The last section of this chapter coverssweeping in detail and looks at the more practical aspects of the technique.

2.1. The Ear

The ear tends to be a somewhat unremarkable aspect of human facial appearance. This

is mainly due to the typically face-to-face nature of human interaction and the fact that

they are often covered by hair (Bruce and Young, 1998). What is commonly referred

to as the ear is in fact the pinna or earflap. Historically, the pinna is thought to have

amplified sounds, but its actual job is a little more specific than this. The pinna helps to

locate sound. Its ridges and clefts bounce a few sound waves into the ear later than the

rest, in a pattern that depends on their source which the brain then decodes (McNeill

2000). Sound location is also aided by the fact that we have two ears. The physical

separation of the ears helps localize sound sources through minute differences in the

timing of signals arriving at each ear (Bruce and Young, 1998), creating a kind of

auditory parallax.

Figure 2.1(a): The major features of the ear (Image adapted from [http06])

Figure 2.1(b): Depiction of cross-sectional shape of the upper helix

The human ear has a unique although somewhat unnoticed form, the main parts of

which can be seen in Figure 2.1(a). The outer rim is referred to as the helix, the name

reflecting its resemblance to a coil or spiral. This rim curves in over the pinna like a

breaking wave, as shown in the inset of Figure 2.1(b). Half way down the helix, a

second ridge runs alongside it, the antihelix. The arrows in Figure 2.1(a) shows the

extent of the antihelix. It swings up into a little into a little plane that splits into two

and curves round in the upper part of the ear and swings down into the lobe. The lobe

is soft and fatty in contrast to the rest of the ear, which is comprised of cartilage. Thelittle nub of flesh beside the ear is called the tragus, the job of which is to protect the


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ear canal. The hollow near the ear canal is the concha, the name being derived from the

Latin for shell(McNeill 2000).

In the same way as an individuals fingerprints are unique, so are a each persons ear

patterns, thus offering the potential by which to identify criminals. In 2001, a murder

trial in the USA and three murder trials in the UK made headlines in newspapers and

TV shows, because, in each, ear-prints had been used as evidence for the prosecutionas stated in Marks Working Group, 2001.

Features of the ear to bear in mind with respect to creating a three-dimensional model

are the spiral nature of the flow of the ear and the concavities this creates especially at

the top of the helix and around the antihelix and concha. Additionally, it should be

noted that ear shape and size can vary vastly from person to person, so a complete ear

model should be created with a view to easy reproduction of a variety of different ears

(this issue is considered in greater depth in Chapter 3).

2.2. Modelling Techniques and Previous Attempts

Previous examples of techniques used to model the human ear are relatively few and

far between. This is probably largely due to the insignificance of the ear in modelling

the human form. Most human heads are modelled with respect to a predominantly

frontal view, concentrating on the mobile features of the face involved with speech and

expression. Although some people are capable of wiggling their ears, it is rare to be

able to move the ears independently of the head. Thus, the ears are not predominately

involved in facial animation and given they are often covered by hair, not always

visible anyway. As such, the ears are considered as a secondary object with respect to

modelling and are often stuck on at a later stage if necessary. More recently there

have been attempts to model the human ear as an entity in its own right. Mostcommonly, this is in conjunction with areas of research regarding hearing aids and in-

ear headphones, for example, where the shape of the ear alone is of primary interest.

One such company is Genex Technologies, (http03), who are introducing their

modelling methods to the world of hearing aid development. Various potential

modelling techniques are considered in this section. Where attempts to model the ear

have been made using a particular technique, the success of the model is discussed.

2.2.1. Manual Modelling and Editing

Manual modelling using a three-dimensional digitiser (or equivalent manual strategy)

is one of the simplest ways in which to model an object. The designer indicates theposition of polygon vertices by placing points on an object by hand. The

threedimensional co-ordinates of these points are input to the system via athreedimensional digitiser and associated with the corresponding polygons. Thesuitability of the vertex positions on the modelled object is dependent on the

experience and decision of the designer, as such, automated strategies for ensuring

adequate representation are quite common. One of the more widely used strategies is

to draw a grid over the surface of the object and ascertain the vertex positions from the

intersections of the curved grid lines.

Most attempts so far at modelling the ear are based around a manual modelling

technique of some kind. The tinyworld website, (http01), presents a technique bySteven Tubbritt, that uses a picture of an ear with the main lines defined. Using a tool

called MAYA, polygons are fitted to the picture as closely as possible to maintain the


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essential shape of the ear. Using a side view for reference at all times, the initially

placed polygons are dragged into position, creating depth to achieve a

threedimensional model. It is a time-consuming process of extruding edges andmerging vertices to create a realistic model of the ear. The product of this particular

example creates a moderately realistic looking ear. However, on closer inspection,

where a real ear would overlap itself, such as the top of the helix, this ear model does

not. Figures 2.2(a) and 2.2(b) shows the polygon framework of the model of the earand the same ear after rendering with a shading algorithm, respectively.

essential shape of the ear. Using a side view for reference at all times, the initially

placed polygons are dragged into position, creating depth to achieve a

threedimensional model. It is a time-consuming process of extruding edges andmerging vertices to create a realistic model of the ear. The product of this particular

example creates a moderately realistic looking ear. However, on closer inspection,

where a real ear would overlap itself, such as the top of the helix, this ear model does

not. Figures 2.2(a) and 2.2(b) shows the polygon framework of the model of the earand the same ear after rendering with a shading algorithm, respectively.

(a) (c) (e) (g)

(b) (d) (f) (h)

Figure 2.2 (a)&(b): Ear model from [http01] (Courtesy of Steven Tubbritt)

Figure 2.2 (c)&(d): Ear model from [http04] (Courtesy of Jon McBain)

Figure 2.2 (e)&(f): Ear model from [http05] (Courtesy of Martin Andersen)

Figure 2.2 (g)&(h): Ear model from [http02] (Courtesy of Frank Silas TBC*)

The step-by-step modelling process presented by Jon McBain, (http04), again uses the

MAYA tool to generate the model. A profile of the general ear shape is created and

divided into four major areas using a split tool. Theses areas are moulded into an ear

shape by splitting and pulling out vertices to define ridges and features, adding and

deleting polygon edges as the process goes on. More vertices are used around the ear

hole to better define it and a large polygon is added at the back of the ear to close it.

Figures 2.2(c) and 2.2(d) show the product of this approach as a mesh and a rendered

view. Again, this model incorporates little of the overlapping of a real ear. This

modelling technique has a very simple but rough basis and is completely open toartistic impression since it is not generated from any specific ear image. Martin

Andersen uses a similar approach to that described on the 3d-designer website


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(http05). Andersen actually provides a video of the creation of the ear, which may be

downloaded and viewed. This considerably speeded-up recording of the continuous

steps of the ear tutorial lasts 30mins, a good indication of the time cost involved in this

type of approach to modelling the ear. However, in terms of realism and the attention

paid to the overlapping of the ear, Andersens final product, shown as a mesh and

shaded in Figures 2.2(e) and (f) respectively, is an improvement on the majority of

examples encountered.

Another slightly different manual modelling approach presented by Frank Silas,

(http02), uses a tool called Animation Master (AM). A wire frame of the ear is created,

composed of five continuous splines as shown in Figure 2.2(g). The square base spline

is a duplicate of the one on the head to which the ear will be attached. The other four

splines are created using a single spline and define a rough shape of the ear. They have

been scaled and adjusted to position, decreasing in size at different depths to look like

an ear shaped funnel. A skinning algorithm is used on the spline contours in pairs,

converting the boundary data into large numbers of triangular polygons. As with

previous attempts the final ear model is based on the impression of what the individual

modeller perceives an ear to look like. This technique is easily implemented in AM,but the correctness of the shape of the initial splines is essential and a lot of fiddling

may be required to achieve the correct end effect. Due to the technique itself, the issue

of realistic overlapping is clearly not taken into consideration. Figure 2.2(h) shows this

ear model after shading rendering, however the image quality is rather low and only

the outline is discernable.

The short falls of each attempt to model the ear using the manual methods detailed

above are consistently reoccurring. The main areas of inadequacies are the lack of

realism especially regarding the extensive overlapping of a real life ear; the lack of

scope for developing ears of varying shape through re-factoring of the initial modelproduced; excessive time cost due to the fiddly ad-hoc methods employed.

2.2.2. Data Capture

Another quite accurate modelling method for producing polygon meshes is the use of

an automated device such as a laser ranger. An example of data capture using a laser

ranger is the rotation of the laser 360 degrees around the object in question (or vice-

versa). The laser ranger returns a set of parallel contours outlining the shape of the

object which are then skinned in the same way as the manual generated splines

described above [http02]. Automated methods are typically suited to inert objects since

the process requires the object being modelled to stay in exactly the same positionthroughout the data capture process. Modelling of objects such as the head often

contain noise in the model produced due to minute unintentional movements during

the data capture stage. An additional significant drawback is the inability of laser

rangers to model concave objects. Due to the implementation of the method as

described, the incident beam will not necessarily hit certain surfaces of an object with

concavities. Both these issues, in particular the latter, imply that the automatic device

is not suited to accurate modelling of the human ear. Despite the drawbacks, attempts

have been made to apply automated processes to modelling aspects of the ear; one

such example is Genex Technologies (http03).

Genex Technologies are an electrooptical company focused on developingstateoftheart electronic imaging technologies. One of their recent developments isa revolutionary system that avoids the problems presented by the drawbacks of the


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automated process with respect to modelling the ear. The problem of noise, created by

movement, is solved using Genexs revolutionary Ear Impression 3D Digitizer with

their Rainbow 3D camera to create a 360degree model. The technology to combatnoise from automated models is clearly available with respect to the ear. However,

Genex does not overcome the limitations of modelling concave objects. Their system

only produces an impression of the ear, that is, an accurate model of the underside of

the ear. Figure 2.3 shows the ear shell created by this model, the angle is as if viewedfrom a position inside the head. Genex is currently working on creating an intraoral3D-capture tool to solve the problem of capturing data directly from inside the ear.

However, this is still at a research level. Within the boundaries of current technology,

automated systems are not suitable to model the concave shape of the human ear,

accurately or otherwise.

Figure 2.3: Ear shell by Genex using a data capture method

2.3 Higher-level Description Techniques

The drawbacks of the methods discussed above lead to the investigation of the

suitability of higher-level techniques in modelling the ear. It should be noted that this

discussion is not intended to be complete in its coverage of techniques. The techniquesselected have been chosen to display a broad view of modelling while maintaining

relevance to modelling the ear. The structure of this discussion is based around that of

work by Maddock, 1999.

In considering modelling techniques, categorisation can be made as to whether a

technique is one of refinement or construction. The constructive approach is concerned

with combining primitives to produce a whole model, while a refinement approach

takes a whole model and refines it to create another whole model. It should be noted

that the whole model products of both these types of method could themselves be

primitives.

Creating a model of the human ear is essentially concerned with constructive

modelling approaches. Thus, in discussing the relevant modelling techniques, hard

primitives, soft primitives, swept primitives and procedural primitives will be covered.

It should be noted that overlapping occurs between these primitives since the first three

types of primitives can be parameterised and treated as procedural primitives

themselves (Maddock, 1999).

2.2.1 Hard Primitives

Constructive Solid Geometry (CSG) is the classic approach to modelling solid objects,

combining simple elementary geometric solid objects or hard primitives. Traditional

examples of these 'hard' primitives (Maddock, 1999), are sphere, cylinder, cone, torus

and rectangular solids. These solids are combined using linear transformations and


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Boolean set operators, namely union, difference and intersection. The resulting model

of an object is stored as a tree representing the object's modelling history, in which the

leaves are the primitives and the nodes are the linear transforms or operators (Figure

2.4 shows a CSG tree).

Boolean set operators, namely union, difference and intersection. The resulting model

of an object is stored as a tree representing the object's modelling history, in which the

leaves are the primitives and the nodes are the linear transforms or operators (Figure

2.4 shows a CSG tree).

blend of candles

heatprofile

combined global

scalar field

Figure 2.4: CSG tree [Watt00]

Figure 2.5: Candles representing soft primtives

2.2.2 Soft Primitives

A modelling technique applicable to more organic objects is a form of implicit surface,

which creates soft or blobby objects. Implicitly defined components, most commonly

spheres, are used as primitives. These primitives are combined by summing the field

effects of the equations defining the primitives. In other words, the surface is formed

by the effect of the primitives exerting a field of influence over a local neighbourhood.

The area of influence of a spherical primitive would clearly be a sphere where a

potential function gives a scalar value for any point, P, within the sphere (Maddock,1999). The equation below is an example of a potential function:2

2

2

1)(

=

R

rsPf for r R

where s=1 (usually), r is the distance of point, P, to the centre of the primitive and R is

the radius of influence of a primitive. At a particular value of r, a scalar field f(P), is

produced from the combined effect of each primitives potential function. One of the

simplest methods of combination is addition, where for a point, P, each contributing

potential function is evaluated and summed. The result is an object representation in

the form of an implicit surface. A naturally occurring phenomena that mirrors this

field of influence combination technique is the blending of heat profiles of multipleheat sources. Figure 2.5 shows this with two candles representing point-based field

generators. It should be noted that field functions can be coded such that they have a

positive or negative effect on the resulting surface i.e. whether they should be summed

or subtracted respectively.

2.2.3 Swept Primitives

The general concept behind swept primitives is to define a three-dimensional object in

terms of a two-dimensional cross section, the generator, and a three-dimensional spine

curve. The three-dimensional object is generated by sweeping the cross-section along

the path of the three-dimensional curve. The simplest example of this technique,referred to as extrusion, is to sweep a cross-section along a straight line creating a

depth component. An example of this is shown in Figure 2.6, where the cross section


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used is the letter F swept straight backwards to create a three-dimensional font. A

simple example of three-dimensional shape generation is a torus, where both the cross-

section and the curve are circles. A special case of sweeping is applicable to surfaces

or solids of revolution. In these cases, a curve is swept around a central axis of

revolution to produce a three-dimensional object such as the wine glass in Figure 2.7.

A more complex extension of the sweeping technique is lofting which involves using

multiple cross-sections or contours. The cross-sections can be varied by a scalingprofile curve or a finite set of cross-sections can be interpolated. Alternatively, a

combination of these two methods can be used (Maddock, 1999).

Work by Snyder in 1992, looks at sweeps and how to construct an object from a set of

procedurally defined sweeps. Qualities of the CSG process are evident in Snyders

ideas; a shape description language is used to combine (swept) primitives to create

higher-level shapes that can themselves become shape-building operators.

Figure 2.6 Figure 2.7 Figure 2.8

Figure 2.6: Depth component generated using Extrusion

Figure 2.7: A wine glass as a solid of revolution

Figure 2.8: Fractal object generated procedurally

2.2.4 Procedures and Primitives

Any parameterised modelling technique is essentially procedural. Here we split our

discussion of procedural techniques into procedural models and procedural

organisation.

Procedural models are a form of constructive modelling technique. Objects are

composed of parts, and the parameters identified, such as relationships between the

parts, can be defined to alter the object composition (Maddock, 1999). Both CSG and

Snyders shape processes (1992), are both techniques that produce objects composed

of parts and thus are included in this category.

Procedural organisation is a way of structuring a collection of simple primitives, often

by employing a shape grammar. Much of the work in this area centres on describing

the structure of plants examples of which can be found in Foleys book (1990).

Symmetry relationships can be parameterised as well as the primitives such that the

shape grammar organises a pattern of primitives into an object (Maddock, 1999). One

idea is the parameterisation of some surface attribute to create variations on a model.

Fractals employ a self-similarity attribute of objects to procedurally generate objects of

this type. The roots of this particular method lie in fractal geometry, a term used to

describe an attribute, exhibited by certain natural phenomena such as coastlines, ofstatistical self-similarity. Fractal techniques are most commonly used to generate

terrain models using, at the simplest level, recursive subdivision algorithms to divide


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the objects facets into a large number of smaller facets. A simple example of this is

uniform triangular subdivision generating a displacement in a direction normal to the

plane of the original facet (see Figure 2.8). Fractal object generation can be extended

beyond this simple example to the creation of quite complex objects.

2.3.5 Suitability to Modelling the Ear

The modelling techniques described above can all be considered effective in modelling

certain types of objects. However, in this summary section the suitability of these

methods to model the shape of human ear will be discussed. As noted in previous

sections aspects of the ear shape to note are the complexity of the shape, the spiral type

flow of the ear curves causing considerable overlapping in the general shape of the ear

and the more local overlapping of the helix and antihelix.

CSG with hard primitives is a technique that can be very effective in modelling

certain objects such as machinery parts built up in CAD as commented on by Watt,

2000, and objects modelled with a view to future editing which is easily facilitated by

the CSG tree structure (Foley 1990). CSG is perfectly suited to the application ofcreating machine parts (Maddock, 1999), however, it is not a technique well suited to

modelling biological objects like the ear. Due to the complexity of the ear shape, it

would be almost impossible to represent it using the primitives available. However, the

ideas and technique of CSG may have a value in constructing an ear shape object by

combining more complex primitives created using other types of modelling technique.

This approach to CSG is considered in Snyders work on generative modelling in

1992.

Soft Primitives clearly lend themselves to modelling more natural, organic objects.

Although this technique has not been applied to the ear before, it could potentiallyproduce a reasonably realistic model of the ear. However, given the complexity of the

ear shape and the non-blobby smooth curves of the helix, the number of primitives

required for a realistic ear could be quite substantial. Additionally, the primitives used

would have to be both positive (added) and negative (subtracted) to cope with the

overlapping of the ear shape, and whether typically spherical primitives could cope

with this substantial overlapping is uncertain. Another aspect to note is the lack of

scope for re-factoring the ear produced, to generate, with relative ease and low cost,

differently shaped ears. Taking all these factors into consideration, soft primitives

show the most potential for modelling the ear so far, but are far from an ideal solution.

In contrast to the techniques discussed above, any potential drawbacks of usingsweeping to model the ear are not immediately obvious. With the correct choice of

cross-section at the top of the helix and along the antihelix, the extensive overlapping

involved in the ear shape could be incorporated. The spiral shape of the flow of

curvature of the ear could be accommodated for by using a sweep path curve that

mirrored this shape. The available extensions of the simple sweeping technique,

involving both a scaling profile curve combined with different specified interpolated

cross-sections, is potentially capable of coping with the complexities of the ear shape.

Additionally, the use of a sweeping technique provides a reasonable scope for

producing families of different ears via relatively low labour-cost alterations to the

initial sweep curves and cross-sections.

Where procedural models are concerned, their potential for modelling the ear clearly is

directly dependant on what type of parts comprises the object. As previously


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discussed, CSG is not s suitable approach, but Snyders method [Snyd92] where the

parts are predominantly swept objects, could potentially provide an appropriate

technique by which to create an ear, providing the parts used were appropriately

realistic themselves. With respect to procedural organisation, the complex ear-shape

lacks the self-similarity and iterative shape development required to break the shape

down into a simple grammar. As a direct result of these factors, procedural

organisation cannot be applied in describing the ear.

In comparison to the other techniques considered, sweeping shows potential for

producing a realistic model of the human ear. The nature of the technique lends itself

to modelling of the overlapping cavities of the ear, the main area of the ear-shape other

techniques struggle to thoroughly accommodate. Further investigation into whether

sweeping is a suitable modelling technique leads us to consider sweeping as an

effective technique for modelling naturally occurring organic objects.

2.4. Sweeping within Nature

The aim of this section is to look at the scope of sweeping for modelling naturallyoccurring objects. In doing so, the regularities of natural objects are considered, as well

as taking a detailed look at the area of shell shapes and surface structure.

2.4.1 The Regularity of Nature

Sweeping can be effectively applied to a very wide range of man-made objects. This is

largely due to the high degree of regularity found in most man made objects with many

of these objects displaying symmetry especially around a central axis. If an object is

not symmetrical overall, it is generally comprised of balanced sub-assemblies. The

concept of regularity, especially symmetry, is one strongly promoted by sweeping. Agood example of symmetry in man-made objects can be found in objects created using

technique called woodturning. This craft involves a piece of wood being spun quickly

around its length while a lathe is used to carve groves into the surface of the wood

around its circumference, producing an object symmetrical about a central axis e.g. a

wood-turned table-leg, which clearly lends itself to being modelled using sweeping.

Looking around, it is clear that not only man-made objects possess an element of

regularity. Living, natural objects commonly display cylindrical regularity either as a

whole or as a composition of cylindrical parts. Some simple examples include the stem

of a flower and our own limbs, fingers and toes. Marriott (1992), models a holly leaf

using sweeping, which, given the roughly cylindrical nature of the branches couldeasily be extended to a model of a holly bush. In his work, Wainwright (1988), argues

that the bodies of multi-cellular plants and animals are cylindrical in shape. He

hypothesises that this form evolved from the structural and aero-dynamical advantages

of cylinders. Thompson (1961), takes a slightly broader view, arguing that the majority

of aspects of natural growth and form are governed by underlying mathematical theory

and structure. A more detailed area of his work, namely shell-shape, is discussed in the

next section.

2.4.2 Shell-shape Surface Generation

Chapter XI of Thompsons work in 1961, looks at logarithmic spirals in which heargues that the essence of shell-shape is captured by the logarithmic spiral.

Measurements of a wide variety of shell types are presented to show their shape


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conformity. He goes on to describe a method by which to generate the surface of shell

as described in the passage below. (This particular passage is taken from Przemyslaw

and Fowler (1998), in which Thompsons observations are quoted in a slightly edited

form.)

The surface of any shell may be generated by the revolution about a fixed axis of a

closed curve, which, remaining always geometrically similar to itself, increases itsdimensions continually.[] Let us imagine some point within this closed curve, such

as its centre of gravity. Starting from a fixed origin, this characteristic point describes

an equiangular spiral in space about a fixed axis (namely the axis of the shell), with or

without a simultaneous movement of translation along the axis. The scale of the figure

increase in geometrical progression while the angle of rotation increases in

arithmetical, and the centre of similitude remains fixed. [] The form of the

generating curve is seldom open to easy mathematical expressions.

Thompsons ideas clearly display the underlying ideas of the sweeping technique using

a similar scaled cross-section. A more recent study of shell shape can be found in

Meinhardts work, which looks at biological pattern formation in shell patterning(Meinhardt, 1998), as well as the three-dimensional structure of the shell itself

(Przemyslaw and Fowler, 1998).

In Meinhardts book, a sweeping technique for modelling the surface of a shell is

presented by Przemyslaw and Fowler. The underlying ideas of which were based

Thompsons observations. The surface of the shell is defined by sweeping a generating

curve, C, along a helico-spiral, H. The size of C increases as it revolves around the

shell axis. The generating curves, C, are constructed from one or more Bezier curve

segments, which determine the shell profile and opening. The opening of the shell is

oriented using Frenet frames, which are covered in the next section.

The sweeping methods applied to generating the shell surface are of considerable

interest with respect to modelling the ear due to the rough shape similarity between

them. The general spiral form of the shell displays two properties already noted as

attributes of the ear-shape. Namely, the spiral flow of the ear curves down toward the

ear-hole and the extensive overlapping of the general ear-shape due to the spiral nature

of its form. Przemyslaw gives examples of five very different variations in shell shape

created using the same cross-section and altering only two parameter values

characterising the helico-spiral sweep path. This shell-shape variety is extended even

further by using different cross-section curves.

Given the similarities between shells and ears, the possibility of creating realistic ears

using cross-sections swept around spiral-like curves would seem to hold a lot of

potential. The vast scope for generating different shell families also supports the idea

that sweeping would enable generation of different ears by varying the sweep

parameters defining the sweep path and/or the cross-sections used.


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Figure 2.9: Outlining the similarity between the shell opening and the concha

As a side point, it is interesting to note that the name for the main concavity of the ear,the concha, is derived from the Latin word for shell (McNeill, 2000). This is due to the

resemblance of the concha to the opening of a shell. Figure 2.9 tries to capture this

resemblance outlining the similarity in shape with dotted lines. Unfortunately, the

opening of a shell only represents the shape of the cross-section used in the sweeping

method. Thus, this resemblance between ear-shape and shell-shape does not indicate a

direct relationship between sweeping the ear-shape and sweeping the surface of a shell.

2.4.3 Summary

This section has covered theories concerning the common cylindrical form of naturally

occurring objects and the more detailed work concerning shells to which ears may be

naturally linked. Both these areas of discussion have strengthened the case in favour of

using sweeping to create a potentially realistic model of the ear.

2.5. Sweeping

This section looks at the sweeping technique in greater depth, considering some of the

more practical issues associated with using this technique. We begin with a review of

the basics of sweeping as discussed briefly in Section 2.2.3.

2.5.1 A Review of the Technique and Extended Methods

The general concept behind swept primitives is to define a three-dimensional object in

terms of a two-dimensional cross section, the generator, and a three-dimensional spine

curve. The three-dimensional object is generated by sweeping the cross-section along

the path of the three-dimensional curve. The simplest example of this technique,

referred to as extrusion, is to sweep a cross-section along a straight line creating a

depth component. Cross-sections can also be swept along curves to create objects such

as the simple torus, where a circular cross-section is swept around another circle. A

special case of sweeping is applicable to surfaces or solids of revolution. In these

cases, a curve is swept around a central axis of revolution to produce a three-

dimensional object such as a wine glass.


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13


multiple cross-sections or contours. The technique was used extensively in the

shipbuilding industry to define the shape of the ships main body. Ducted solids,

generalised cylinders or tubular surfaces are terms commonly used to refer to objects

created by allowing the cross-section to vary along the length of the sweep curve. The

cross-sections can be varied by a scaling profile curve or a finite set of different cross-

sections can be interpolated. Alternatively, a combination of these two methods can beused. Snyder (1992) presents a technique that uses a shape description language to

combine (swept) primitives to create higher-level shapes that can themselves become

shape-building operators.


multiple cross-sections or contours. The technique was used extensively in the

shipbuilding industry to define the shape of the ships main body. Ducted solids,

generalised cylinders or tubular surfaces are terms commonly used to refer to objects

created by allowing the cross-section to vary along the length of the sweep curve. The

cross-sections can be varied by a scaling profile curve or a finite set of different cross-

sections can be interpolated. Alternatively, a combination of these two methods can beused. Snyder (1992) presents a technique that uses a shape description language to

combine (swept) primitives to create higher-level shapes that can themselves become

shape-building operators.

2.5.2 Practical problems associated with sweeping2.5.2 Practical problems associated with sweeping

There are certain issues that immediately arise when crosssectional sweeping is usedto model objects. There are three main difficulties associated with curved spines (Watt,

2000), which will be considered individually as follows.

There are certain issues that immediately arise when crosssectional sweeping is usedto model objects. There are three main difficulties associated with curved spines (Watt,

2000), which will be considered individually as follows.

Curve to Polygon ProcedureCurve to Polygon Procedure

The first problem is controlling the size of the polygons, an example of which is given

in Figure 2.10. In this example, the size of the polygon primitives depends on the path

of the curve. Consider the parametric position of the curve, u, in equation (1) above.

Dividing u into equal intervals does not always give the best results or cause the points

to appear at equal intervals along the curve. The latter is due to the uniform increase of

u in a straight line as opposed to along the path of the curve. Arc length

parameterisation is a procedure that does divide the curve into equal intervals.

However, this procedure is not straightforward, nor is it consistently appropriate

depending on the curvature of the curve. Figure 2.11(a) and 2.11(b) show division of acurve using equal intervals and arc length parameterisation respectively.

The first problem is controlling the size of the polygons, an example of which is given

in Figure 2.10. In this example, the size of the polygon primitives depends on the path

of the curve. Consider the parametric position of the curve, u, in equation (1) above.

Dividing u into equal intervals does not always give the best results or cause the points

to appear at equal intervals along the curve. The latter is due to the uniform increase of

u in a straight line as opposed to along the path of the curve. Arc length

parameterisation is a procedure that does divide the curve into equal intervals.

However, this procedure is not straightforward, nor is it consistently appropriate

depending on the curvature of the curve. Figure 2.11(a) and 2.11(b) show division of acurve using equal intervals and arc length parameterisation respectively.

a b c

Figure 2.10 Figure 2.11(a) 2.11(b) 2.11(c)

Figure 2.10: An example of the problem of the curve to polygon ratio

Figure 2.11(a): Subdivision by equal intervals

Figure 2.11(b): Arc length parameterisation

Figure 2.11(c): Non-uniform subdivision

Ideally the curve would be divided into intervals depending on the curvature of the

curve as areas of high curvature require an increased rate of polygon generation.. This

can be achieved using a curve subdivision algorithm in which the curve is subdivideduntil a linearity test is positive, i.e. the interval in question meets a flatness criterion.

Uniform subdivision is the simplest case where a user specifies a level at which


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subdivision of the curve terminates. Non-uniform subdivision means that subdivision

terminates when a curve interval meets a flatness criterion (Figure 2.11(c)). In other

words, the degree of subdivision is allocated according to curvature, so areas of high

local curvature are subject to more subdivision, as required. This second category of

subdivision is preferable but does incur extra computational cost due to the flatness

testing.

Cross-section Orientation

The second practical issue of cross-sectional sweeping is the orientation of the cross-

section with respect to a varying spine curve. In constructing ducted solids and

generalised cylinders, the object structure must be prevented from twisting, by

correctly aligning each cross-section with its neighbours. Cross-sectional alignment is

achieved by the use of reference frames that define position and orientation of a cross-

section along the central axis of the cylinder. One of the more intuitive reference

frames is the Frenet frame, discussed in considerable detail by Bloomenthal (1990), the

main points of which are presented below. A reference frame consists of three

mutually orthogonal vectors. At each set of sample points along the curve, therespective cross-section is embedded into the coordinate system formed by these

vectors.

A Frenet frame is defined on the spine curve by the sample point, P, and three

orthogonal vectors, between them defining position and orientation. Those vectors are

the tangent vector, T, the principal normal, N, and the binormal, B. Figure 2.12 shows

these vectors derived at a point, P, on the sweep curve, Q(u).

The tangent vector, T, also referred to as the unit length velocity vector, is derived

from the velocity vector or derivative of the curve:

T = V / |V| (2.1)

where, V = d/du(Q(u)) = 3au2 + 2bu + c

The normal vector, N, is often defined to be in the direction of curvature of the curve.

N is indirectly derived from the acceleration vector or second derivative of the curve,

A.

N = K / |K| (2.2)

where, K = V x A x V / |V|4

where, A = d/du(V) = 6au + 2b

The binormal vector, B, is the crossproduct of the tangent vector and the principalnormal.

B = T x N (2.3)


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Figure 2.12: Vectors B, N, T, and point, P, defining a Frenet frame

One of the main advantages of the Frenet frame is that it can be computed at arbitrary

points along the curve (Bloomenthal, 1990). The main drawback of the method is that

the Frenet frame is undefined where the curve is degenerate, i.e. at points of inflection

and along straight sections of the curve. Either side of an inflection point the curvature

vector can suddenly reverse direction causing a violent twist in the progression of

Frenet frames (Watt 2000). A term used to describe the basis of this problem is torsion,

meaning rotation around the tangent to a curve (Bloomenthal, 1990).

Bloomenthal describes a torsion minimizing solution by Shani and Ballard. The

solution is iterative using rotation minimizing frames. The basis of this solution is that

an initial reference frame is defined at the beginning of the curve. This initial reference

frame is then propagated along the curve using small local rotations. The advantage of

this method is the immunity of the reference frame to degenerative sections of the

curve. However, the result produced is not necessarily intuitive and due to the

implementation of the method, analytical computation of an arbitrary reference frame

is not permitted. A similarly based solution is that devised by Ken Sloan (http07),

which uses the orthogonal propertied of the reference frame to propagate the vectors

using cross-product computation.

Self-intersection of Cross-sections

The third practical issue of the sweeping technique is the problem of cross-sections

self-intersecting or crimping as it is sometimes referred to (Figure 2.13). Crimping

occurs in areas where the radius of curvature of the path of any points traced out by the

cross-sectional curve exceeds the radius of curvature of the sweep path (Watt, 2000).

Put another way, the curvature of the main sweep path cannot support the size of the

cross-sections at that point, creating a kink in the final object at the point of

occurrence.

A solution to this problem is presented by Roche (1989), who notes that crimping

corresponds to the intersection of two cross-sections. He suggests that in areas where

crimping occurs, it can be removed by adjusting the radius of curvature to make it

larger.


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Figure 2.13: Crimping caused by curve self-intersection


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This chapter presents an overview of the main objectives and the approaches available

to achieve them, before giving details about the implementation and mathematical

theory involved in generating an object using sweeping. The main aims with respect to

developing the ear are briefly presented, followed by a more detailed account of the

programs capabilities. The techniques to be used in generating the ear are consideredalong with available solutions to potential problems with generating swept surfaces,

and proposed parameterisation of the ear. Finally, as an important part of any

experimental project, the proposed method of evaluation is discussed.

3.1 Aims and Objectives

The central objective of this project is to investigate whether sweeping is a suitable

technique by which to model the complex shape of the human ear. In doing so, a

program which be produced which will aim to do just that. Some of the main

considerations in developing the ear are detailed as follows.

As briefly discussed in Chapter 2, there are two main areas for consideration in

generating the ear model, in which previous attempts have been lacking. The first

concerns ear shape, where capturing the extensive overlapping involved in the curves

of the ear, has not been completely effectively achieved. Secondly, given the huge

variation in peoples ears throughout the human race, the scope for generating a wide

variety of ears with relative ease would be preferable. This is again an attribute not

possessed by techniques previously used to generate the ear. With the use of sweeping,

and effective parameterisation, these are both issues that it is hoped can be solved, and

as such, are both central requirements of the generated model.

The nature of the sweeping technique, involves approximations in areas of its

implementation, such as interpolating between cross-sections. As such, attaining a high

degree of accuracy in terms of anthropometrical proportions and measurements is

unrealistic. The ear model produced will still be required to possess a certain degree of

accuracy, but this can be more visually oriented, rather than by exact measurement.

This concurs with previous examples of ear models discussed in Section 2.2.1, which

were based on creating a realistic impression of an ear, rather than a dimensionally

accurate representation.

Applications of a model of a human ear could be seen to lie in two main areas; aiding

the manufacturing of hearing aids or other acoustic devices such as in-ear headphonesand within the computer graphics fields of human facial modelling and animation.

Given the accuracy to which the ear will be produced, the latter is the most appropriate

application.

3.2 Program Capabilities

The primary requirement of the program is that it will be able to generate a model of

an ear that will be visually evaluated, as realistically resembling a human ear. It will

generate the ear as a swept surface, the details of which are covered in the next section.

A secondary requirement of the program is that it has the scope to generate multiple

ear variations based on the same framework by altering parameter values only. Thedetails of this feature are discussed below.


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3.2.1 Ear Variation

In looking at the ears of even just a handful of people, it becomes clear that the

variation in individuals ears in enormous. As with other features of the body, ear

shape and size can be inherited, for example, a well-known inherited trait is the

attachment of the lowest point of the ear lobe to the face (referred to as being lobe-

less). As a result of inheritance, family members are more likely to show similaritiesbetween their ears than unrelated people. However, Figure 3.1 demonstrates that even

between family members, the amount of variation in ear shape and size is considerable.

It is commonly known that ear size varies with age and between sexes and ear-shape is

often varied across different races as well. For example, the length of the ear increases

with age.

Figure 3.1: The right ear of each member of a family unit

Given the huge range of ear measurements possible, a very useful feature of the

program, would be to have a predefined set of default parameter values which generate

a typical ear according to higher level parameters of age race and sex. However,

anthropometric measurements of ears are quite limited and hard to find especially in

relation to a persons age, gender or race. Three main sources of measurement datawere found ((Algazi et al, 2001),(Differient et al, 1981),(Tilley et al, 1993)). The

second two of these were aimed at design and engineering applications and although

the measurements were presented as averages for certain age groups and specified

race, the data given was measurements of ear length only. The most substantial survey

of ear size available is from a study in connection with Head-related Transfer

Functions (HRTFs). HRTFs capture the sound localization cues created by the

scattering of incident sound waves by the body and are defined by head, shoulder and

ear shape (Algazi et al, 2001), thus anthropometric measurements of these features

have been recorded. Algazi et al. (2001) present measurements for ten different aspects

of the pinna (external ear), as shown in Figure 3.2 Due to the area of application in

which the measurements are taken, the choice of anthropometry is relevant to theunderstanding or estimation of HRTFs. Thus, for example, no measurements are made

of the lobe area of the ear since this bears no influence over sound localisation. The

data for each of the ten pinna measurements was obtained from 43 subjects (27 men

and 16 women) from the CIPIC Interface Laboratory, California, where the studies

were being conducted. The results of the measurements (in cm) are listed in Table 3.1.


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Var Measurement

d1 cavum conchaheight

1.91 0.18 19

d2 cymba conchaheight

0.68 0.12 35

d3 cavum conchawidth

1.58 0.28 35

d4 fossa height 1.51 0.33 44d5 pinna height 6.41 0.51 16

d6 pinna width 2.92 0.27 18

d7 intertragal incisurewidth

0.53 0.14 51

d8 cavum conchadepth

1.02 0.16 32

1 pinna rotationangle

24.01 6.59 55

2 pinna flare angle 28.53 6.70 47

Figure 3.2: Pinna Measurements

Table 3.1: Anthropometric Statistics, =100(2 / )

Given the data is not presented according to the type of person (age, race, gender)

measured, the only value of this data in terms of modelling the ear, is in ascertaining

conceivable ear measurements i.e. what dimension values comprise a normal ear,

rather than defining a higher level of control.

Due to the lack of data available, defining a higher level of control is not a feasible

option, i.e. it will not be possible to enable the program to automatically generate ear

variations according to age, race and sex input parameters, and a lower level of control

must be used. Different ears will be created by manually altering more specific

parameters, such that visually pleasing ears are generated. Parameters are discussed in

more detail in Section 3.3.1..

3.3 Sweeping the ear

The ear will be treated as a generalised cylinder. The cross-sections will be varied

along the sweep curve using interpolation. This section sets out the parameterisation of

the ear, and theory of the sweeping process intended to model it. Any additional

information about most of the techniques discussed here can be found in Chapter 3 of

Watts book, 3D Computer Graphics (2000).

3.3.1 Parameterisation of the Ear

The ear will be parameterised by a path curve defining the outline shape of the ear and

the cross sectional curves and their position along the path curve, defining local ear

shape at that point and the surrounding local area. The parameters will be the control

point coordinates for the path curve, and for the cross sections, the control point

coordinates and the position along the path curves at which they will be placed. This

position will be represented as an integer indicating the path curve segment and a

floating-point value between 0 and 1 indicating the parametric position along the

segment in question.

This approach will result in there being a large number of specific parameters, which isnot a particularly useable or efficient parameterisation. However, for the purpose of


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this investigation, it is appropriate, and provides the level of detail and flexibility in

defining the ear, that is required to generate the desired result.

An ideal method of parameter input are a Bezier Curve Editor. This would entail

default initial ear curves being generated and displayed on the screen, then by selecting

the relevant cross section or path curve their shape or position could be edited.

Guidelines would indicate the bounds of the curve of a normal ear for the path andeach cross section when they were selected. Once editing was completed, the curve

would be submitted and the control points for that curve automatically stored, and

inputted to create the desired swept surface.

Other methods of input would be more manual approaches such as an input file

containing control points and cross section positions in a format readable by the

program or an input class containing similar data, which could be obtained by calling

get methods for that class.

While a Bezier Curve Editor would make generating different ears very quick and

efficient, time constraints for this project may mean that one of the manual inputmethods would have to be adopted. However this option could be made more efficient

by accompanying it with the use of an existing Bezier curve drawing tool, where

points must be read off manually for each control point.

3.3.2 Sweeping Theory

The cross-sections will be formed by two-dimensional closed curves placed onto the

sweep path curve at specific points. The position of a cross-section on each segment of

the curve will have a value between 0 and 1, where position 0 is the start of the curve

segment and position 1 is the end. The sweep path curve is a three-dimensional opencurve onto which the cross-sections are placed. It should be noted that if a curve editor

were incorporated into the final program, it would be advisable to use a two-

dimensional curve editor, and apply a technique discussed by Marriot (1991), to

compose the two-dimensional path together, to form three-dimensional objects.

Both cross-sectional curves and sweep curves will be constructed using cubic Bezier

curves segments. This segmented curve representation will be used, as it is a relatively

simple method by which to create a complex curve of almost any shape. The curve

segments used are cubic because lower degree curves do not provide enough flexibility

in shape control, while curves with degree higher than three, require more computation

and are less intuitive to use.

Bezier Curves

A Bezier curve is a space curve Q(u), defined in terms of a parameter u (0 u 1). Itsfour control points determine the shape of the curve, Pi (i = 0,1,2,3), where P0 and P3

are the endpoints of the curve, and P1 and P2 control its shape. A Bezier curve is then

given by:

=

=3

0

)()(i

ii uBPuQ (2.1)

where Pi are the control points and Bi(u) are the Berstein blending functions which

sum to 1 for 0 u 1:


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21

B0(u) = (1-u)3

, B1(u) = 3u(1-u)2 , B2(u) = 3u2(1-u) , B3(u) = u3

B (u) = (1-u)03

, B (u) = 3u(1-u) , B (u) = 3u (1-u) , B (u) = u1 2 2 2 33

The control point definition of of Bezier curve segments means that joining curve

segments together and sweeping are simplified, since operations can involve the

control points of the curve, rather than the curve itself.

The control point definition of of Bezier curve segments means that joining curve

segments together and sweeping are simplified, since operations can involve the

control points of the curve, rather than the curve itself.

Joining Bezier Curve SegmentsJoining Bezier Curve Segments

Connecting curve segments to make up curves that are more complex implies that

constraints must apply at the joins (Watt, 2000). The default constraint is positional

continuity, which means that the end-point of the first curve segment is co-incident

with the start point of the next curve segment. This is shown in Figure 3.3(a) where

control points S3 and R0 are equal. If however, a smooth join is required between

segments then first order (or tangential) continuity should be used. First order

continuity means that the tangent vectors at the start of one curve and the end of the

adjacent curve, match to within a constant. This type of continuity is shown between

two curves in Figure 3.3(b) where control points S3 and R0 are equal and therelationship, (S3 S2) = k(R1 R0), exists such that S2 and R1 are collinear (Maddock,

2003).

Connecting curve segments to make up curves that are more complex implies that

constraints must apply at the joins (Watt, 2000). The default constraint is positional

continuity, which means that the end-point of the first curve segment is co-incident

with the start point of the next curve segment. This is shown in Figure 3.3(a) where

control points S

3 and R0 are equal. If however, a smooth join is required between

segments then first order (or tangential) continuity should be used. First order

continuity means that the tangent vectors at the start of one curve and the end of the

adjacent curve, match to within a constant. This type of continuity is shown between

two curves in Figure 3.3(b) where control points S3 and R0 are equal and therelationship, (S3 S2) = k(R1 R0), exists such that S2 and R1 are collinear (Maddock,

2003).

Figure 3.3(a) Figure 3.3(b)

Figure 3.3(a): Positional continuity

Figure 3.3(b): Tangential continuity

Due to the smooth curved form of the ear, first order continuity will be used to join the

Bezier curve segments of both the cross-section curves and the sweep path curves.

Practical Considerations

Solutions to the practical problems behind sweeping, discussed in Section 2.5.2, must

also be incorporated into the process of generating the swept ear surface. The problem

of crimping due to cross section self-intersection will be solved using the method

suggested by Roche (1989), which essentially involves increasing the radius of

curvature. This means that the path should be defined such that it does not involve

areas where the direction of the curve changes particularly sharply. Areas of the ear

that do involve high curvature can be modelled by altering the cross section shape

rather than the path to reflect the ear shape. Doing this will indirectly help solve the

curve to polygon procedure problem. Eliminating high areas of curvature from the path

will mean that less computationally expensive subdivision mat be applied and non-uniform curve subdivision may not be necessary in evaluating the curves. Subdivision


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can be achieved using the less computationally expensive arc length parameterisation

method or regular intervals.

The third practical problem is that of correctly orienting the cross sections along the

path curve. The Frenet frame is an effective solution as long as there are no degenerate

areas along the path curve. Areas of high curvature (and therefore points of inflection)

along the path should be able to be avoided as described above, but it is probable thatthere will be straight sections of the curve and it is at these points that a violent twist

can occur in the progression of Frenet frames. As such the initial reference frame will

be calculated as a Frenet frame, and then propagated along the path curve using the

method by Bloomenthal or Sloan described in Section 2.5.2.

Cross-sectional Interpolation

Cross-sectional interpolation will be used to define cross-sections between those

initially specified. The finite set of initial cross-sections will be defined using Bezier

curve segments. It is possible that these cross-sections will not all have the same

number of segments. To interpolate between cross-sections it is essential that all cross-sections have the same number of segments. A method can be used to achieve this by

redefining the cross-sections so they all have the same number of segments as the

cross-section with the most segments (Marriott, 1992). Once all cross-sections have an

equal number of segments, one of two interpolation techniques may be applied; linear

interpolation or non-linear interpolation.

Given two cross-sectional curves, A and B, linear interpolation finds the cross-

sectional curve, C, at the required position. Only two curves are required for the linear

calculation that uses evenly spaced points between the two curves. This method

produces inaccuracies causing jerkiness in the final model especially when usingpolygonal representation when joining curve segments together. This jerky effect is

illustrated in Figure 3.5(a) where the sudden change in surface direction can be clearly

seen at the cross-sections.

Figure 3.5(a): Liner Interpolation Figure 3.5(b): Non-linear Interpolation

Non-linear interpolation overcomes the jerkiness of linear interpolation by using a

curve-fitting scheme. This method requires four initial cross-sections, two either side

of the required position for the interpolated cross-section. These four cross-sections are

used to fit a curve between them all, from which a set of Bezier Curves are calculated,

and form the new cross-section. The smooth effect of non-linear interpolation is

illustrated in Figure 3.5(b).


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Summary

Using the techniques described above, the sweeping method produces a series of bi-

cubic Bezier patches representing the surface of the ear.

3.3.3 Rendering the ear

For the purpose of this project the ear only needs to be displayed so that it can be

visually evaluated. As such, it will not be necessary to display it as a polygon mesh,

but only as a shaded surface. This simplifies the rendering procedure, as polygon

intersection algorithms will not be required. The surface will be evaluated at regular

intervals and displayed as a series of shaded polygons. The evaluation interval size will

be directly dependant on how frequent it needs to be to make the surface appear

smooth.

To render the parametrically represented surface of the ear one of two types of

algorithm are available. Algorithms that render directly from the parametric

description, or those that approximate the surface by a polygon mesh (Watt, 2000).The second option is easier to implement, and computationally less expensive, and a

variation of this method will be used for the ear model.

To create a series of polygons, the patches must be subdivided. Uniform subdivision

can be achieved by either applying a subdivision algorithm, which recursively divides

patches into quarters terminating after n subdivisions, or by evaluating the surface at

set intervals. Alternatively, non-uniform subdivision is achieved in a similar way to

uniform subdivision, except that each subdivision product is tested for flatness so that

subdivision terminates when a predefined flatness is reached.

Given uniform subdivision is applied regardless of curvature, depending on the

number of subdivisions (or frequency of sampling) it may not cope well with high

areas of curvature i.e. the resulting surface would not appear smooth. Non-uniform

subdivision aims to combat this problem, but there are disadvantages to this technique.

Patch tearing can occur, where holes can appear between patches. This is due to a

patch boundary being approximated by a different number of straight lines than a

neighbouring patch. A solution is to test the polygon normals and if the tear is visible

to the eye, an extra polygon must be added. Non-uniform subdivision is also

considerably more computationally expensive due to the flatness test, which must be

applied after every subdivision.

Since the ear does not have a particularly shiny surface, it can be relatively realistically

shaded using a basic Gouraud shading option.Additionally, the use of polygons makesshading relatively quick and easy using the polygon vertex normals.

3.3.4 Summary

The sweeping method presented uses both patches and polygons to get the most out of

the advantages of both representations. For example, the smoothness of patches is

employed, as is the ease of shading when using a polygon mesh. The advantages of

both representations are presented in Maddocks comparison between polygons and

parametric patches, which considers a wide range of aspects of modelling, (Maddock,2002).


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3.4 Evaluation of the Ear Model

Evaluation is a key area of any experimental work. In this case, it is especially

important as there needs to be some method by which to determine whether a realistic

model of a human ear has been achieved. There are essentially two angles from which

this issue may be approached, evaluation by visual appearance and evaluation by

actual measurement. Evaluation by appearance is the most relevant method, given thenature of the final ear models as discussed in Section 3.1. The visual appearance of the

ear is the most obviously an important factor when considering the reality of the

model. However, given the position of the ear on the head, we are accustomed to

seeing the ear from a face-to-face perspective or from the side. Thus, factors such as

the depth of the ear (z component) or distance from the head will be less visually

detectable as being incorrect or abnormal by the average person.

Peoples opinions on the visual appearance of the ear model produced will be

invaluable in determining whether a realistic looking ear shape has been produced.

Ideally, the evaluation would consist of a group of volunteers comparing a set of ears

comprised of both real and computer generated ears. For the purpose of the rest of thischapter, the group of people evaluating the ears will be referred to as the testers. As

explained in Section 3.1, ear shape and size varies dependant on the age, race and

gender of a person. As such, it seems logical to assume that a persons perception of

what a normal or realistic ear would look like may vary dependant of their age, race

or gender. As such, the testers will comprise a cross-section of people of mixed age,

race and gender. The ears will be evaluated in the form of images from various angles

either on the screen. The details of three proposed evaluation methods are detailed in

the next few sections.

The evaluation of the ear models produced will be solely shape oriented, discountingfactors such as texture. The evaluation will investigate the following issues: realism of

the ear shapes produced; whether any improvement has been achieved compared to

previous attempts; the scope for generating a variety of realistic ears; intuitiveness of

the technique; potential for producing a specific ear.

3.4.1 Realism of ears produced

The realism of the shape of the ear is one of the main aspects to be assessed. The

proposed method of evaluation is to present the tester with a group of ears, composed

of both computer-generated ears and photographic images of an ear and ask them to

select those, which they believe are most realistic in shape. The main obstacleassociated with this evaluation method is the difference in rendering of the computer-

generated ear and the photographic image. The testers would instantly spot the real

ear due to the photographic quality of the picture thus nullifying the test. The proposed

solution to the problem is to destroy the rendering of both images to the same level

such that the shape of the two ears can be compared fairly. An example of this would

be to apply edge effects and noise to an image in PaintShop Pro thus destroying the

rendering such that the photogr

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Modeling the Human Ear_m2jd