Interactive Non-Photorealistic

Home , Illustration, Technical illustration

INTERACTIVE NON-PHOTOREALISTIC

TECHNICAL ILLUSTRATION

Amy Gooch

A thesis submitted to the facultyof

The University of Utah

in partial ful llment of the requirements for the degree of

Master of Science

Department of Computer Science

The University of Utah

Decemb er 1998

THE UNIVERSITY OF UTAH GRADUATE SCHOOL

SUPERVISORY COMMITTEE APPROVAL

of a thesis submitted by

Amy Gooch

This thesis has b een read by each memb er of the following sup ervisory committee and

by ma jorityvote has b een found to b e satisfactory.

Chair: Peter Shirley

Elaine Cohen

Rich Riesenfeld

THE UNIVERSITY OF UTAH GRADUATE SCHOOL

FINAL READING APPROVAL

To the Graduate Council of the University of Utah:

Ihave read the thesis of Amy Gooch

in its nal form and have

found that 1 its format, citations, and bibliographic style are consistent and acceptable;

2 its illustrative materials including gures, tables, and charts are in place; and 3 the

nal manuscript is satisfactory to the Sup ervisory Committee and is ready for submission

to The Graduate Scho ol.

Date Peter Shirley

Chair, Sup ervisory Committee

Approved for the Ma jor Department

Rob ert Kessler

Chair/Dean

Approved for the Graduate Council

David S. Chapman

Dean of The Graduate Scho ol

ABSTRACT

Current interactive mo deling systems allow users to view mo dels in wireframe or

Phong-shaded images. However, the wireframe is based on the mo del's parameteriza-

tion, and a mo del's features may get lost in a nest of lines. Alone, a fully rendered

image may not provide enough useful information ab out the structure or mo del fea-

tures. Human technical illustrators follow certain visual conventions that are unlike

Phong-shaded or wireframe renderings, and the drawings they pro duce are sub jectively

sup erior to conventional computer renderings. This thesis explores lighting, shading,

and line illustration conventions used by technical illustrators. These conventions are

implemented in a mo deling system to create a new metho d of displaying and viewing

complex NURBS mo dels. In particular, silhouettes and edge lines are drawn in a manner

similar to p en-and-ink drawings, and a shading algorithm is used that is similar to

ink-wash or air-brush renderings for areas inside the silhouettes. This shading has a

lowintensityvariation so that the black silhouettes remain visually distinct, and it has a

co ol-to-warm hue transition to help accent surface orientation. Applying these illustration

metho ds pro duces images that are closer to human-drawn illustrations than is provided

by traditional computer graphics approaches.

To Bruce,

for all of the love and supp ort.

CONTENTS

ABSTRACT ::: :::::: ::::: :::::: :::::: ::::: :::::: :::::: :::::: ::::: iv

LIST OF FIGURES :: ::::: :::::: :::::: ::::: :::::: :::::: :::::: ::::: viii

LIST OF TABLES :::: ::::: :::::: :::::: ::::: :::::: :::::: :::::: ::::: xii

ACKNOWLEDGEMENTS : :::::: :::::: ::::: :::::: :::::: :::::: ::::: xiii

CHAPTERS

1. INTRODUCTION ::::: :::::: :::::: ::::: :::::: :::::: :::::: ::::: 1

2. BACKGROUND : ::::: :::::: :::::: ::::: :::::: :::::: :::::: ::::: 4

2.1 Paint Programs and One-Shot Images ...... 4

2.2 One-Shot Images Conveying Shap e ...... 8

2.3 InteractiveTechniques ...... 11

2.4 Perception Studies ...... 12

2.5 Background Summary ...... 13

3. ILLUSTRATION TECHNIQUES ::: ::::: :::::: :::::: :::::: ::::: 14

3.1 Lines in Technical Illustration ...... 16

3.1.1 Line Weight...... 18

3.1.2 Line Color and Shading ...... 20

3.2 Shading in Illustrations ...... 20

3.3 Illustration Summary ...... 22

4. ALGORITHMS FOR ILLUSTRATION ::: :::::: :::::: :::::: ::::: 23

4.1 Algorithms for Finding Edge Lines ...... 23

4.1.1 Algorithms for Finding Boundaries

and Discontinuities ...... 23

4.1.2 Algorithms for Finding Silhouettes for NURBS ...... 24

4.1.2.1 Some De nitions ...... 24

4.1.2.2 Mesh Metho d ...... 25

4.1.2.3 Tessellated-Mesh Metho d ...... 27

4.1.2.4 Srf-No de Metho d ...... 30

4.1.2.5 Silhouette Finding Summary ...... 34

4.1.3 Other Metho ds for Calculating Edge Lines ...... 34

4.2 Shading Algorithms ...... 35

4.2.1 Traditional Shading of Matte Ob jects ...... 35

4.2.2 Tone-based Shading of Matte Ob jects ...... 36

4.2.3 Shading of Metal Ob jects ...... 44

4.3 3D Illustration ...... 46

5. IMPLEMENTATION AND RESULTS : ::: :::::: :::::: :::::: ::::: 49

5.1 Edge Lines ...... 49

5.2 Approximation to New Shading Mo del ...... 49

6. CONCLUSION : :: ::::: :::::: :::::: ::::: :::::: :::::: :::::: ::::: 53

6.1 Future Work ...... 56

REFERENCES :::::: ::::: :::::: :::::: ::::: :::::: :::::: :::::: ::::: 57 vii

LIST OF FIGURES

1.1 An few examples of a NURBS-based mo del displayed in wireframe. The

large numb er of isolines makes distinguishing key features dicult...... 1

1.2 Hand-tuned Phong-shaded image versus technical illustration...... 2

2.1 Non-photorealistic one-shot images with a high level of abstraction...... 5

2.2 Computer-generated p en-and-ink illustrations...... 7

2.3 One-shot computer-generated p en-and-ink images conveying shap e by Winken-

2.4 Another example of one-shot image conveying shap e. Saito enhances a

Saito [29]...... 9

2.5 One-shot images conveying shap e by Do oley and Elb er...... 10

2.6 Image from a frame of Markosian et al. [24] real-time 3D interactive system

for illustrating non-self-intersecting p olygon mesh-based mo dels. Copyright

1997 Lee Markosian. Used by p ermission...... 11

ited [28]...... 15

3.2 An example of the lines an illustrator would use to convey the shap e of this

3.3 Changing which isolines are displayed can change the p erception of the

surface. The image on the right lo oks as if it has a deep er pit b ecause

the isolines go thru the maximum curvature p oint on the surface. Images

courtesy of David Johnson...... 18

3.4 Illustrators use lines to separate parts of ob jects and de ne imp ortant shap e

characteristics. This set of lines can b e imitated for NURBS mo dels by

drawing silhouettes, b oundaries, and discontinuities, shown ab ove drawn

over the wireframe representation...... 18

3.5 De nition of a silhouette: At a p oint on a surface, u; v and given E u; v

as the eyevector and nu; v as the surface normal, a silhouette p ointis

de ned as the p oint on the surface where E u; v nu; v =0ortheangle

between E u; v and nu; v is 90 degrees...... 19

3.6 Three line conventions suggested by Judy Martin [25]. Left: single line

weight used throughout the image. Middle: heavy line weight used for out

edges and parts with op en space b etween them. Right: vary line weight

Ltd. [25]...... 19

3.7 This photograph of a metal ob ject shows the anisotropic re ections and the

white edge highlights which illustrators sometimes depict...... 20

3.8 Illustrators sometimes use the convention of white interior edge lines to

pro duce a highlight [25]...... 21

3.9 Illustrators combine edge lines with a sp eci c typ e of shading. Shading

in technical illustration brings out subtle shap e attributes and provides

information ab out material prop erties. Left: Compare this shaded image of

& Co. Publishers Ltd. [25]. Right: Engine. Courtesy Macmillan Reference

USA, a Simon & Schuster Macmillan Company [28]...... 22

4.1 Interp olating silhouettes: After two neighb oring surface p oints with di erent

's are found, the p oint where E u; v nu; v = = 0 can b e found

by linearly interp olating in u or v with the two angles as calculated in

Equation 4.1. Note: = E n > 0 and = E n < 0...... 25

1 1 1 2 2 2

4.2 Calculating the mesh normals: The four mesh normals which corresp ond to

m are n , n , n , n , where for example n = vec vec , with

i;j 1;3 1;2 4;3 4;2 1;3 1 2

vec1= m m and vec2= m m ...... 26

i;j i1;j i;j 1 i;j

4.3 Envision the mesh metho d as a table of signs, where can b e +, -, or 0. .. 26

4.4 These images show the control mesh in uv-space for a surface where +,

-, or 0 denotes the sign of the dot pro duct E u; v nu; v . For the Mesh

Metho d, there are up to four dot pro ducts that need to b e calculated p er

mesh p oint, only one p er mesh p oint for Srf-No de Metho d...... 28

4.5 These images show the control mesh in uv-space for a surface, with ap-

proximations to the silhouettes. The sign of the dot pro duct E u; v nu; v

are denoted by +,-,or0...... 29

4.6 Mesh Metho d...... 30

4.7 Tessellated Mesh Metho d...... 30

4.8 Visualize the Srf-No de Metho d as a table of signs , where i; j can b e

i;j

+,-,or0...... 31

4.9 Srf-No de Metho d can result in missed silhouettes dep ending up on the no de

p oints. If for example, the no de p oints were those that corresp ond to ,

,and , there would b e three missed silhouette p oints b ecause , ,and

2 3 1 2

, are all less than 90 degrees and there would b e no sign change. However,

if the no des p oints were , ,and , then is greater than 90 degrees and

2 3

is less than 90 degrees, so the silhouette b etween the two corresp onding

no de p oints would not b e missed and could b e interp olated. The problem

of missing these silhouettes can b e remedied by re ning the control mesh. . 32

4.10 Srf-No de Metho d...... 32

4.11 Lo oking down on surface with silhouette generated with Srf-No de metho d.

Compare this image with the 2D pro jection and approximation of silhouettes

shown in Figure 4.5 using the Mesh metho d and the Srf-No de metho d. ... 33 ix

4.12 View of the same surface represented in Figure 4.5, 4.4, and 4.11 with

silhouettes generated with the Srf-No de metho d...... 33

4.13 Di use shaded image using Equation 4.1 with k = 1 and k =0. Black

shaded regions hide details, esp ecially in the small claws; edge lines could

not b e seen if added. Highlights and ne details are lost in the white shaded

regions...... 36

4.14 Image with only highlights and edges. The edge lines provide divisions

between ob ject pieces and the highlights convey the direction of the light.

Some shap e information is lost, esp ecially in the regions of high curvature of

the ob ject pieces. However, these highlights and edges could not b e added

to Figure 4.13 b ecause the highlights would b e invisible in the light regions

and the silhouettes would b e invisible in the dark regions...... 37

4.15 Phong-shaded image with edge lines and k =0:5 and k =0:1. Like

Figure 4.13, details are lost in the dark gray regions, esp ecially in the small

claws, where they are colored the constant shade of k k regardless of surface

orientation. However, edge lines and highlights provide shap e information

that was gained in Figure 4.14, but could not b e added to Figure 4.13. ... 38

4.16 Approximately constant luminance tone rendering. Edge lines and high-

lights are clearly noticeable. Unlike Figures 4.13 and 4.15 some details in

shaded regions, like the small claws, are visible. The lack of luminance shift

makes these changes subtle...... 39

4.17 How the tone is created for a pure red ob ject by summing a blue-to-yellow

and a dark-red-to-red tone...... 40

4.18 Luminance/hue tone rendering. This image combines the luminance shift

of Figure 4.13 and the hue shift of Figure 4.16. Edge lines, highlights, ne

details in the dark shaded regions such as the small claws, as well as details

in the high luminance regions are all visible. In addition, shap e details are

apparent unlike Figure 4.14 where the ob ject app ears at. In this gure, the

variables of Equation 4.1 and Equation 4.1 are: b =0:4, y =0:4, =0:2,

=0:6...... 41

4.19 Luminance/hue tone rendering, similar to Figure 4.18 except b = 0:55,

y =0:3, =0:25, =0:5. The di erentvalues of b and y determine the

strength of the overall temp erature shift, where as and determine the

prominence of the ob ject color, and the strength of the luminance shift. .. 42

4.20 Comparing shaded, colored spheres. Top: Colored Phong-shaded spheres

with edge lines and highlights. Bottom: Colored spheres shaded with hue

and luminance shift, including edge lines and highlights. Note: In the rst

Phong-shaded sphere violet, the edge lines disapp ear, but are visible in

the corresp onding hue and luminance shaded violet sphere. In the last

Phong-shaded sphere white, the highlightvanishes, but is noticed in the

corresp onding hue and luminance shaded white sphere b elow it. The spheres

in the second row also retain their \color name." ...... 43

4.21 Tone and undertone shaded spheres with backgrounds getting darker...... 43 x

4.22 Shaded spheres without edgelines. Top: Colored Phong-shaded spheres

without edge lines. Bottom: Colored spheres shaded with hue and lumi-

nance shift, without edge lines...... 43

4.23 An anisotropic re ection can b e seen in the metal ob jects in this photograph. 44

4.24 Representing metallic material prop erties...... 45

4.25 Comparing this gure to Figure 1.1, the edge lines displayed provide shap e

information without cluttering the screen...... 46

4.26 Frames from the NPR JOT Program, to which I used Markosian et al.'s

silhouette nding technique [24] and added the Op enGL approximation to

the new shading mo del. This will b e discussed further in Chapter 5...... 47

5.1 An Alpha

1 mo del that was tessellated and imp orted into the JOT NPR

Program...... 50

5.2 Comparison of traditional computer graphics techniques and techniques for

creating technical illustrations...... 52

6.1 Phong shading versus edge lines...... 54

6.2 Edge lines...... 54

6.3 These computer generated images were pro duced by using the illustration

convention of alternating dark and light bands, to convey the metallic

material prop erty of the two images. The convention is rather e ective,

even for an ob ject that may not naturally b e metal...... 55 xi

LIST OF TABLES

2.1 Summary of non-photorealistic and other computer graphics pap ers...... 5

ACKNOWLEDGEMENTS

Thanks to Bruce Go o ch, Peter Shirley, Elaine Cohen, Rich Riesenfeld, Susan and

Tice Ashurst, Georgette Zub eck, David Johnson, Bill Martin, Richard Co ey, Colette

Mullenho , Brian Loss, Matt Kaplan, Tom Thompson, Russ Fish, Mark Blo omenthal,

and the rest of the Alpha1 and SCI research groups, past and present. Thanks to Lee

Markosian, Loring Holden, Rob ert Zeleznik, and Andrew Forsb erg, from Brown Univer-

sity, for letting me collab orate on the JOT Pro ject. Also, thanks to Jason Herschaft for the

dinosaur claw mo del. This work was supp orted in part byDARPA F33615-96-C-5621

and/or the NSF Science and Technology Center for Computer Graphics and Scienti c

Visualization ASC-89-20219. All opinions, ndings, conclusions, or recommendations

expressed in this do cument are mine and do not necessarily re ect the views of the sp onsoring agencies.

CHAPTER 1

INTRODUCTION

The advent of photography and computer graphics has not replaced artists. Imagery

generated by artists provides information ab out ob jects that may not b e readily apparent

in photographs or real life. The same goal should apply to computer-generated images.

This is the driving force b ehind non-photorealistic rendering. The term non-photorealistic

rendering NPR is applied to imagery that lo oks as though it was made by artists, such

as p en-and-ink or watercolor. Many computer graphics researchers are exploring NPR

techniques as an alternative to realistic rendering. More imp ortantly, non-photorealistic

rendering is now b eing acknowledged for its ability to communicate the shap e and struc-

ture of complex mo dels. Techniques whichhave long b een used by artists can emphasize

sp eci c features, exp ose subtle shap e attributes, omit extraneous information, and convey

material prop erties. These artistic techniques are the result of an evolutionary pro cess,

conceived and re ned over several centuries. Therefore, imitating some of these techniques

and exploring the p erceptual psychology b ehind technical illustration are go o d rst steps

in going b eyond realistic rendering.

In this thesis I explore technical illustrations for a NURBS-based mo deling system.

A driving force for exploring technical illustration comes from viewing the wireframe

representation of complex NURBS-based mo dels, usually a mess of lines, as shown in

Figure 1.1. More motivation for exploring illustration techniques is provided by comparing

the two mechanical part images in Figure 1.2. The rst image is a hand-tuned, computer

Figure 1.1. An few examples of a NURBS-based mo del displayed in wireframe. The

large numb er of isolines makes distinguishing key features dicult.

a Hand-tuned Phong-rendered image of me- b Illustration of a mechanical part using

chanical part by Dr. Sam Drake. It to ok him lines to separate parts and shading to con-

approximately six hours to hand tune this image. vey material prop erties. Courtesy Macmil-

lan Reference USA, a Simon & Schuster

Macmillan Company [28].

Figure 1.2. Hand-tuned Phong-shaded image versus technical illustration.

generated, Phong-shaded part, which to ok ab out six hours for Professor Sam Draketo

complete. The second image is an illustration from the b o ok The Way Science Works

by Macmillian [28]. The illustration uses lines to separate parts and shading to convey

material prop erties. I would like to b e able to automatically generate images with many

of the characteristics of the illustration in Figure 1.2b for NURBS-based mo dels.

Examining technical manuals, illustrated textb o oks, and encyclop edias reveals shading

and line illustration conventions which are quite di erent than traditional computer

graphics conventions. The use of these artistic conventions pro duces technical il lustra-

tions, a subset of non-photorealistic rendering. In order to create illustration rules for

technical illustration, I reviewed several b o oks, e.g., [28, 25], and concluded that in addi-

tion to using color to di erentiate parts [40], technical illustrators use black lines, as well

as a sp eci c typ e of shading which rarely includes shadows. These two-dimensional 2D

line illustration conventions can b e imitated by drawing lines consisting of silhouettes,

surface b oundaries, and discontinuities. Adding shading completes the image and can b e

used to convey imp ortant nongeometric qualities of an ob ject such as material prop erties.

Line, shading, and lighting techniques used by illustrators can convey a more accurate

representation of shap e and material prop erties of mechanical parts than traditional com-

puter graphics metho ds. These illustration techniques can improve or replace traditional

representation of mo dels such as wireframe or Phong-shaded. In Chapter 2, I review what

has b een done in computer graphics as well as some of the researchonhuman recognition

in p erception studies. In Chapter 3, I describ e the illustration conventions used for lines

and shading. In Chapter 4, I discuss algorithms to imitate lines and shading of technical

illustration. I will also discuss how these mayormay not change for three-dimensional

3D interactive illustrations. In Chapter 5, I will discuss the implementation details for

3D illustration, and in Chapter 6 I will draw some conclusions and prop ose some future

research goals.

CHAPTER 2

BACKGROUND

Non-photorealistic rendering NPR techniques vary greatly in their level of abstrac-

tion. In technical illustrations, shap e information is valued ab ove realism and aesthetics.

Therefore a high level of abstraction, like the images in Figure 2.1, would b e inappropriate.

As summarized in Table 2.1, no work has b een done which uses the ideas and techniques

of technical illustrators to generate not only 2D technical illustrations but also to provide

an interactiveenvironment for viewing 3D mo dels as 3D technical illustrations. A review

of the pap ers involving NPR or other illustration techniques used in computer graphics

reveals that most pap ers can b e partitioned into two categories: those which generate

only aesthetic images and those whose purp ose is to convey shap e and structure. The

images in the latter category may themselves b e aesthetically pleasing, but this is a

side e ect rather than a primary goal. These pap ers can also b e further divided into

those that generate a single image and those that are part of an interactive or animation

system. Human p erception and recognition studies [2, 4, 7] are another valuable source

of information. These p erception studies suggest an explanation of why line drawings,

like technical illustrations, are enough for ob ject recognition and provide a hintastowhy

they may also provide shap e information.

2.1 Paint Programs and One-Shot Images

Creating sophisticated paint programs which generate single images and emulate

techniques used by artists for centuries was the fo cus of research done by Meier [27],

Haeb erli [17], Curtis [10], Salisbury et al. [30, 31, 32], and Winkenbach et al. [38].

However, conveying shap e and structure is not the goal of these images.

Meier [27] presents a technique for rendering animations in whichevery frame lo oks

as though it were painted by an artist. She mo dels the surfaces of 3D ob jects as 3D

particle sets. The surface area of each triangle is computed, and particles are randomly

distributed. The numb er of particles p er triangle is equal to a ratio of the surface area

Meier [27]. Used by p ermission. Paul Haeb erli [17]. Curtis [10]. Used by p ermis-

Used by p ermission. sion.

Figure 2.1. Non-photorealistic one-shot images with a high level of abstraction.

Table 2.1. Summary of non-photorealistic and other computer graphics pap ers.

Author Line Shading Automatic 3D Applicable Additional

Drawing Not user- Interactive to Il lustration

driven Technical Rules*

Il lustration

p p p p

Markosian [24]

p p p p

Do oley [11]

p p p p

Saito [29]

p p

Driskill [12]

p p p

Elb er [13]

p p p p

Seligmann [34]

p p p

Land [22]

p p p p

Gooch [15]

p p p

Zeleznik [42]

p p

Salisbury [32, 31]

p p p

Salisbury [30]

p p p

Winkenbach [38]

p p p

Winkenbach [39]

p p

Meier [27]

Haeb erli [17]

Litwinowicz [23]

Curtis [10]

p p p p p

This Thesis

Note: \Line drawing" and \shading" categories are checked if the work uses shading

and line drawing conventions similar to traditional illustration techniques. \Automatic"

means that user intervention is not required and it is not a user-driven program; i.e.,

it is not like a paint program.

*Layout, cut-a-ways and ob ject transparency, line style, etc.

of triangle to the surface area of the whole ob ject. To maintain coherence from one

shot of the ob ject to the next, the random seed is stored for each particle. Particles are

transformed into screen space and sorted with regard to the distance from viewer. The

particles are then painted with 2D paint strokes, starting farthest from viewer, moving

forwards, until everything is painted. The user determines artistic decisions like light,

color, and brush stroke, similar to most paint programs. The geometric lighting prop erties

of the surface control the app earance of the brush strokes.

Haeb erli [17] created a paint program which allows the user to manipulate an image

using to ols that can change the color and size of a brush, as well as the direction and shap e

of the stroke. The goal of his program is to allow the user to communicate surface color,

surface curvature, center of fo cus, and lo cation of edges, as well as eliminate distracting

detail, to provide cues ab out surface orientation and to in uence viewer's p erception

of the sub ject. Haeb erli studied the techniques of several artists. He observed that

traditional artists exaggerate imp ortant edges. Where dark areas meet light areas, the

dark region is drawn darker and light region is drawn lighter. This causes the depth

relationship b etween ob jects in a scene to b e more explicit where they overlap. Haeb erli

also notes that artists use color to provide depth cues b ecause, p erceptually, green, cyan,

blue co ol-colored shap es recede, whereas red, orange, yellow, magenta warm-colored

ob jects advance. He commented in his pap er that he used these color depth cues and

other techniques to enhance digital images b efore the paint b egins, but he never provided

any details on how these could b e used algorithmically.

The computer-generated watercolor work by Curtis et al. [10] created a high-end

paint program which generates pictures by interactive painting, or automatic image

\watercolorization" or 3D non-photorealistic rendering. Given a 3D geometric scene,

they generate mattes isolating each ob ject and then use the photorealistic rendering of the

scene as the target image. The authors studied the techniques and physics of watercolor

painting to develop ed algorithms, which dep end on the b ehavior of the paint, water,

and pap er. They provide information on watercolor materials and e ects of dry-brush,

edge darkening, backruns, granulation and separation of pigments, ow patterns, glazing,

washes.

Salisbury et al. [32, 30, 31] designed an interactive system which allows users to paint

with stroke textures to create p en-and-ink style illustrations, as shown in Figure 2.2a.

Using \stroke textures," the user can interactively create images similar to p en-and-

ink drawings of an illustrator by placing the stroke textures. Their system supp orts

scanned or rendered images which the user can reference as guides for outline and tone

intensity [32]. In their pap er, \Scale-Dep endent Repro duction of Pen-and-Ink Illustra-

tions" [30], they gave a new reconstruction algorithm that magni es the low-resolution

image while keeping the resulting image sharp along discontinuities. Scalability makes it

really easy to incorp orate p en-and-ink style image in printed media. Their \Orientable

Textures for Image-Based Pen-and-Ink Illustration" [31] pap er added high-level to ols so

the user could sp ecify the texture orientation as well as new stroke textures. The end

result is a comp elling 2D p en-and-ink illustration.

Winkenbach et al. [38] itemized rules and traditions of hand-drawn black-and-white

illustrations and incorp orated a large number of those principles into an automated

rendering system. To render a scene, visible surfaces and shadow p olygons are computed.

The p olygons are pro jected to normalized device co ordinate space and then used to build

a 2D BSP binary space partition tree and planar map. Visible surfaces are rendered,

and textures and strokes applied to surfaces using set op erations on the 2D BSP tree.

Afterwards, outline strokes are added. Their system allows the user to sp ecify where the

detail lies. They also takeinto consideration the viewing direction of user, in addition to

the light source. They are limited by a library of \stroke textures." Their pro cess takes

ab out 30 minutes to compute and print out the resulting image, as shown in Figure 2.2b.

bury [30 ]. Used by p ermission.

Figure 2.2. Computer-generated p en-and-ink illustrations.

2.2 One-Shot Images Conveying Shap e

The research reviewed in the previous section concentrated on generating aesthetically

pleasing images. The work done by Seligmann and Feiner [34], Winkenbach et al. [39],

Saito et al. [29], Land et al. [22], Elb er [13], and Do oley et al. [11] generated images

in which the primary goal is to convey shap e information. However, these techniques

generate single images and do not allow user interaction.

Seligmann and Feiner [34] created a system based on the idea that an illustration is

a picture that is designed to ful ll communicativeintent. They assert that the purp ose

of illustration is to show an ob ject's material, size, orientation, and, p erhaps, howto

use it. The purp ose is not only to display geometric and material information but to

also provide the viewer information ab out the ob ject's features, physical prop erties, and

abstract prop erties. \Illustration ob jects are generated based on b oth the representation

of the physical ob ject as well as the communicativeintent"p. 131, i.e., the images must

convey the geometric characteristics as well as the purp ose of each of the ob jects, such

as whichway to turn a dial on an image of a radio. Their \Intent-Based Illustration

System" IBIS uses a generate-and-test approach to consider how the nal illustration

will lo ok. For each illustration, there are several metho ds and several evaluators. By

p erforming the p ermutations of the metho ds and then evaluating them by the \rules,"

IBIS automatically generates the image that would lo ok \b est."

Winkenbach et al. [39] renders a single p en-and-ink style image for parametric free-

form surfaces, using \controlled-density hatching" in order to convey tone intensity,

texture and shap e, as shown in Figure 2.3. Their pap er provides a highly detailed

algorithm on drawing lines strokes which gradually disapp ear in light areas of the surface

or where to o many lines converge. They use a planar map constructed from the parametric

surfaces to clip strokes and generate outlines. The planar map is not constructed from 3D

Figure 2.3. One-shot computer-generated p en-and-ink images conveying shap e by

BSP Trees, but by the following metho d. They tessellate every ob ject and then compute

the higher-resolution piecewise linear approximations for all silhouette curves of meshed

ob jects, similar to Elb er and Cohen [13], whose work is discussed in Section 2.3. The

planar map is created by determining which mesh faces are closest to the view. They

then use 2D BSP trees to implement shadows [6].

Saito and Takahashi [29] o er convincing pictures to showhow 3D mo dels enhanced

with discontinuity lines, contour lines, and curved hatching can generate images which

convey shap e and structure, as shown in Figure 2.4. They prop ose \new rendering

techniques to pro duce 3D images with enhanced visual comprehensibility," realized with

2D image pro cessing. They construct a data structure called G-bu er, which preserves a

set of geometric prop erties. If shap es and camera parameters are xed, any combination

of enhancement can b e examined without changing the contents of the G-bu er.

Land and Alferness [22] present a metho d for rendering 3D geometric mo dels as black

and white drawings. They compute Gaussian and mean surface curvatures of ob jects

and allow the user to threshold, combine, and mo dify these curvatures. They pro duce

images that contain shap e information that is indep endent of orientation or illumination.

They state that, p erceptually,humans are go o d at inferring shap e from line drawings,

\Lines which approximate lines of curvature may b e particularly e ective indicators for

humans"p. 2.

Elb er [13] provides surface information with four typ es of curves: the surface b oundary

curves, curves along C discontinuities in the surface, isoparametric curves, and silhouette

curves, as shown in Figure 2.5a. All of the ab ove curves except silhouette curves are

Figure 2.4. Another example of one-shot image conveying shap e. Saito enhances a

view-indep endent and only need to b e calculated once p er mo del. Silhouette curves are

calculated by normalizing the view orientation so that the view is on the p ositive z-axis

at in nity and the image is pro jected onto the plane z=0. Elb er de nes a silhouette p oint

as a p oint on the surface whose normal has a zero z-comp onent. The silhouette curve

of the surface b ecomes the set of silhouette p oints forming a continuous curve. When

a C discontinuity is found in a surface, Elb er divides the surface into two surfaces.

Elb er's metho ds cannot b e applied directly in an interactive system, b ecause the metho d

uses costly ray-surface intersection calculations to determine visibility. I build up on

his observations, using a di erent metho d to calculate silhouettes in order to achieve

interactive rates.

Do oley and Cohen [11] created an illustration system which used display primitives,

such as transparency, lines with variable width, and b oundary/end p oint conditions, as

shown in Figure 2.5b. Visibility information is gathered byray tracing, which helps to

communicate structure and illuminate unnecessary details and clutter. By establishing

a user-de ned hierarchy of comp onents, users can de ne not only what they want to see

but how they want to see it. However, in their implementation the camera mo del is then

generated and for the rest of the pro cess remains xed. Most of time is sp entray tracing

to gather visibility information, which is done separately for lines and surfaces. After

the information on lines and surfaces is put together, illustration primitives are created,

sion. Do oley [11]. Used by p ermis-

sion.

Figure 2.5. One-shot images conveying shap e by Do oley and Elb er.

placed in an image bu er, and read by a scan-line renderer. No measurements of the

time it to ok to generate the illustrations were given. The result is a 2D illustrated image

which cannot b e manipulated like a 3D mo del.

2.3 InteractiveTechniques

The batch-oriented systems presented previously lack the ability for the user to in-

teractively change the viewp oint. There are only a few systems which allow the user to

manipulate the viewp oint and the environment.

The Sketch system develop ed by Zeleznik et al. [42] uses gestures to create and ma-

nipulate p olygonal shap es, \bridging the gap b etween hand sketches and computer-based

mo deling programs." The emphasis of their system is creating and editing p olygonal

ob jects.

Driskill [12] explored illustrating explo ded views of assembly with minimal user inter-

vention through a 3D, interactive display. She listed some basic illustration rules as they

apply to explo ded views; however, she was less concerned with how the mo del app eared,

since her emphasis was conveying relationships b etween parts.

Markosian et al. [24] develop ed a real-time 3D interactive system for illustrating non-

self-intersecting p olygon mesh-based mo dels, as seen in Figure 2.6. Their basic scheme is

to use probabilistic identi cation of silhouette edges, interframe coherence of silhouette

edges, and improvements and simpli cations in App el's hidden-line algorithm [1], a

metho d based on the notion of quantitativeinvisibility whichkeeps track of front facing

Figure 2.6. Image from a frame of Markosian et al. [24] real-time 3D interactive system

Markosian. Used by p ermission.

p olygons dep endent up on the camera's p osition. However, using randomized checks for

silhouettes causes problems with frame-to-frame coherence as well as intro ducing the

risk of missing new silhouettes. They also had to add some extra tests to deal with

silhouettes that cusp. They view these p ossible silhouette misses as less imp ortantina

real-time system. Using techniques based on economy of line, they convey information

with few strokes, displaying silhouette edges and certain user-chosen key features, such

as creases. In addition, they added options for sketchy lines or hatched shading strokes.

The end result is a 3D interactiveenvironment, where a single frame lo oks like an artist's

sketch. They achieved their real-time interaction by using the silhouette calculated in

the previous frame to guess at which lines are to b e shown in the next. Their metho ds

are only applicable for p olygonal mo dels and do not convey material prop erties.

2.4 Perception Studies

In computer graphics there has b een very little work on quantifying claims like \Image

1 conveys more shap e information than Image 2." However, p erceptual psychologists have

p erformed numerous studies and exp eriments, trying to learn ab out human recognition

and the waywe visually pro cess information. Perception studies can help to provide a

quantitative analysis instead of merely giving an educated hyp othesis on the e ectiveness

of an image to convey shap e information. Studies by Christou et al. [7], Bra je et al. [4],

and Biederman et al. [2] supp ort the use of line drawings as an e ective metho d for

providing substantial shap e information.

A study by Christou et al. [7] showed four scenes to sub jects. Each scene was comp osed

of a numb er of planar, cylindrical, and ellipsoidal surfaces. One scene contained shaded

surfaces similar to Phong shading; another scene with textured ob jects; a scene which

only included contours, the line-drawn edges of the ob jects; and a scene with contours and

textured ob jects. The sub jects were asked to sp ecify the surface attitude, the orientation

of the lo cal tangent plane at a p oint on a surface with resp ect to the viewing direction,

at random p oints on in the scene. These tests showed that the sub jects had improved

p erformance in the scenes containing contours. They concluded, \a few simple lines

de ning the outline of an ob ject suce to determine its 3-D structure. The ecological

signi cance of contours is clear. They delineate the di erent comp onents of complex

ob jects and the di erent parts of a scene"p. 712.

Another recognition study by Bra je et al. [4] found that humans fail to use much

of the information available to an ideal observer. Their conclusion was that human

vision is designed to extract image features, suchascontours, that enhance recognition,

disregarding most of the other information available.

Biederman et al. [2] concluded that simple line drawings can b e identi ed ab out as

quickly and as accurately as fully detailed, textured, colored photos of the same ob ject

with the same viewp oint. The question they tried to answer was whether the presence

of gradients made it easier to determine an ob ject's 3D structure over that which can

b e derived solely by the depiction of an ob ject's edges. They concluded, for example,

that one could determine the curvature of a cylinder, planarity of a square, or volumetric

characteristics of a nonsense ob ject from a line drawing, without the presence of surface

gradients. They noted that instruction materials for assembling equipment are more

easily followed when the parts are drawn instead of photographed. Their opinion is that

repro duced photographic images typically have insucient contrast for determining the

contours of comp onents. Although it seems that one could mo dify a photograph to get

the necessary contrast, there are other techniques, like cut-a-ways, that cannot b e easily

accomplished, if at all, with photography.

2.5 Background Summary

Non-photorealistic rendering techniques used in computer graphics vary greatly in

their level of abstraction. Those that pro duce images suchaswatercolor or p en-and-ink

are at a high level of abstraction whichwould b e inappropriate for technical illustration.

Using a medium level of abstraction like technical illustration helps to reduce the viewer's

confusion by exp osing subtle shap e attributes and reducing distracting details. Adding

interaction gives the user motion cues to help deal with visual complexity, cues that are

missing in 2D images. A review of past research reveals that no one has created a 3D

interactiveenvironment that takes advantage of shap e information given by line drawings

and artistic shading, presenting the shap e information without the confusion pro duced by

the many lines in a wireframe representation or the limitations of Phong-shaded images.

CHAPTER 3

ILLUSTRATION TECHNIQUES

The illustrations in several b o oks, e.g., [25, 28], imply that illustrators use fairly

algorithmic principles. Although there are a wide varietyofstyles and techniques found

in technical illustration, there are some common themes. This is particularly true when

examining color illustrations done with air-brush and p en. The following characteristics

are present in many illustrations, as shown in Figure 3.1:

edge lines are drawn with black curves.

matte ob jects are shaded with intensities far from black or white with warmth or

co olness of color indicative of surface normal.

a single light source provides white highlights.

shadows are rarely included, but if they are used, they are placed where they do not

o cclude details or imp ortant features.

metal ob jects are shaded as if very anisotropic.

These form only a subset of the conventions used by illustrators. I have concentrated

only on the material prop erty and shading asp ects of illustration. Work done in com-

puter graphics by Seligmann and Feiner [34] and Do oley and Cohen [11] concentrate on

additional asp ects of technical illustration likelayout, ob ject transparency, and line style.

These characteristics result from a hierarchy of priorities. The edge lines and high-

lights are black and white, resp ectively, and provide a great deal of shap e information

themselves. Several studies in the eld of p erception [2, 4, 8, 35]have concluded that

sub jects can recognize 3D ob jects at least as well, if not b etter, when the edge lines

contours are drawn versus shaded or textured images. Christou et al. [7] concluded in

a p erceptual study that \a few simple lines de ning the outline of an ob ject suce to

determine its 3-D structure"p. 712. As seen in children's coloring b o oks, humans are 15

Does not Cast Shadows

Metal Shadows do not Shaded

obsure detail a

White Highlight Line Cool Shading

Black Edge lines

Warm

Shading

go o d at inferring shap e from line drawings. Lines can help distinguish di erent parts and

features of an ob ject and draw attention to details whichmay b e lost in shading. As

demonstrated by Figure 3.1a, many illustrators use black edge lines to separate parts.

Sometimes an illustrator mightcho ose to use a white highlight line instead of a black

edge line for interior silhouettes or discontinuities. Deciding which lines to draw and how

to draw them is essential in imitating the conventions used in technical illustration. In

Section 3.1, I will discuss the rules, prop erties, and typ es of lines needed to convey shap e

information like the line drawings of technical illustrators. In the next chapter I will

discuss implementation details.

When shading is added, in addition to edge lines, shap e information can b e maximized

if the shading uses colors and intensities that are visually distinct from b oth the black

edge lines and the white highlights. This means the dynamic range available for shading

may b e limited. Figure 3.1a provides a go o d example of how an illustrator uses lights

and artistic shading. In the gure, the light is up and to the right of the ob ject and

pro duces highlights as you would exp ect in a computer-generated Phong-shaded image.

However, the illustrator also used co ol shading for the upp er part of the ob ject with

warm shading on the lower, b ottom half of the ob ject. This co ol and warm shading is

not dep endent up on the light and mayhave b een used to pull the eye from the cut-a-

way to the b ottom of the image. Illustrators rarely use shadows in an illustration. As

shown in Figure 3.1b, shadows are used only when they do not obscure details in other

parts. Another imp ortantcharacteristic used in technical illustration is the conveyance

of material prop erty. Figure 3.1b shows how an illustrator alternates bands of light

and dark to represent a metallic ob ject, similar to the real anisotropic re ections seen

on real milled metal parts. These shading conventions will b e investigated in detail in

Section 3.2.

3.1 Lines in Technical Illustration

To decide which lines to draw, I started by analyzing some examples from hand drawn

technical illustrations. The illustration in Figure 3.2 consists of just enough lines to

separate individual parts and to suggest imp ortant features in the shap e of each ob ject.

Most NURBS mo deling systems display only a wireframe or a shaded image. A

wireframe display is common b ecause it can give a lot of information which is o ccluded

by shading. However, a wireframe display of a complex mo del can b e confusing due

Figure 3.2. An example of the lines an illustrator would use to convey the shap e of this

to the numb er of lines b eing displayed. The wireframe of a NURBS surface consists of

isolines, which are parameterization dep endent. Figure 3.3 demonstrates that changing

which isolines are displayed can change the p erception of the surface.

By drawing silhouettes, surface b oundaries, and discontinuities for a NURBS-based

mo del instead of isolines, one can imitate the lines drawn in technical illustrations without

b eing parameterization dep endent. An example of these three di erent line typ es is

provided in Figure 3.4. Silhouettes contain the set of p oints on a surface where E u; v

nu; v =0orthe angle b etween E u; v and nu; v is 90 degrees, given a p ointona

surface, u; v , with E u; v as the vector from the eyeto u; v , and nu; v asthe

surface normal Figure 3.5. Regions where the surface normal changes abruptly, C

discontinuities, are also imp ortant in de ning the shap e of an ob ject. Sometimes surface

Figure 3.3. Changing which isolines are displayed can change the p erception of the

surface. The image on the right lo oks as if it has a deep er pit b ecause the isolines go thru

the maximum curvature p oint on the surface. Images courtesy of David Johnson.

Silhouettes Boundaries Discontinuities

Figure 3.4. Illustrators use lines to separate parts of ob jects and de ne imp ortant

shap e characteristics. This set of lines can b e imitated for NURBS mo dels by drawing

silhouettes, b oundaries, and discontinuities, shown ab ove drawn over the wireframe

representation.

b oundaries also need to b e drawn, but only in the case where there is not a surface

connecting another surface or where the jointbetween surfaces changes abruptly. For

example, the vertical b oundary drawn in a dotted line in Figure 3.4 should not b e drawn,

since it is a shared surface b oundary [18]. The calculations and implementation details

necessary to create these line drawings will b e addressed in Chapter 4.

3.1.1 Line Weight

There are many line weight conventions and an illustrator cho oses a sp eci c line weight

convention dep endent up on the intent of the 2D image. In the b o ok Technical Il lustration, 19

E silhouette point

silhouette point

Figure 3.5. De nition of a silhouette: At a p oint on a surface, u; v and given E u; v

as the eyevector and nu; v as the surface normal, a silhouette p oint is de ned as the

p oint on the surface where E u; v nu; v = 0 or the angle b etween E u; v and nu; v

is 90 degrees.

Martin [25] discusses three common conventions, as shown in Figure 3.6:

Single line weight used throughout the image

Two line weights used, with the heavier describing the outer edges and parts with

op en space b ehind them

Variation of line weight along a single line, emphasizing the p ersp ective of the

drawing, with heavy lines in the foreground, tap ering towards the farthest part

of the ob ject.

Figure 3.6. Three line conventions suggested by Judy Martin [25]. Left: single line

weight used throughout the image. Middle: heavy line weight used for out edges and

parts with op en space b etween them. Right: vary line weight to emphasize p ersp ective.

Other less often used conventions include varying the line weight dep endent up on the

direction of the light source, giving a shadowed e ect or varying the line due to abrupt

changes in the geometry curvature based. However, most illustrators use b old external

lines, with thinner interior lines.

3.1.2 Line Color and Shading

In almost all illustrations, lines are drawn in black. Occasionally, if the illustration

incorp orates shading, another convention may apply in which some interior lines are

drawn in white, like a highlight. This technique may b e the representation of the real

white highlights as can b e seen on edges of the mechanical part in Figure 3.7. By using

this convention, lines drawn in black and white suggest a light source, and denote the

mo del's orientation. For example, Figure 3.8 shows how an artist may use white for

interior lines, pro ducing a highlight.

3.2 Shading in Illustrations

Shading in technical illustration brings out subtle shap e attributes and provides in-

formation ab out material prop erties, as shown in Figure 3.9. Most illustrators use a

single light source and technical illustrations rarely include shadows. In most technical

illustrations, hue changes are used to indicate surface orientation rather than re ectance

Figure 3.7. This photograph of a metal ob ject shows the anisotropic re ections and the

white edge highlights which illustrators sometimes depict.

Figure 3.8. Illustrators sometimes use the convention of white interior edge lines to

pro duce a highlight [25].

b ecause shap e information is valued ab ove precise re ectance information. Adding a hue

shift to the shading mo del allows a reduction in the dynamic range of the shading, to

ensure that highlights and edge lines remain distinct. A simple low dynamic-range shading

mo del is consistent with several of the principles from Tufte's recent b o ok [36]. He has a

case study of improving a computer graphics animation bylowering the contrast of the

shading and adding black lines to indicate direction. He states that this is an example of

the strategy of the smal lest e ective di erence :

Make al l visual distinctions as subtle as possible, but stil l clear and e ective.

Tufte feels that this principle is so imp ortant that he devotes an entire chapter to it

in his b o ok Visual Explanations.Tufte's principle provides a p ossible explanation of why

cross-hatching is common in black and white drawings and rare in colored drawings: col-

ored shading provides a more subtle, but adequately e ective, di erence to communicate

surface orientation. Based on observing several illustrations, surfaces with little or no

curvature are generally at or Phong-shaded in technical illustrations. Surfaces which

have high curvature are shaded similar to the Phong shading mo del or are co ol-to-warm

shaded as in Go o ch et al. [15], unless the surface has a material prop erty such as metal.

Illustrators apply di erent conventions to convey metallic surface prop erties, esp ecially

if the ob ject has regions of high curvature like an ellipsoid. In the next chapter I will

discuss the algorithms used for shading in computer graphics and why it is inadequate

for technical illustration. I will also discuss the shading algorithms used by Goochetal.

Figure 3.9. Illustrators combine edge lines with a sp eci c typ e of shading. Shading

in technical illustration brings out subtle shap e attributes and provides information

ab out material prop erties. Left: Compare this shaded image of airplane p edal to the

Right: Engine. Courtesy Macmillan Reference USA, a Simon & Schuster Macmillan

Company [28].

for matte and metal ob jects.

3.3 Illustration Summary

Technical illustration can b e imitated in computer graphics by using black edge lines,

a single light source, tone and undertone shading with highlights as presented in Go o ch

et al., and no shadows. For a NURBS-based mo del, displaying silhouettes, surface

b oundaries, and discontinuities provides shap e information similar to that of traditional

technical illustrations. In the next chapter, I will discuss some algorithms for nding

these silhouettes, b oundaries, and discontinuities using geometric information of NURBS

surfaces. I will also mention some of the other p ossibilities for generating edge lines for

p olygonal ob jects, like the work of Markosian et al., as well as some image pro cessing

techniques.

CHAPTER 4

ALGORITHMS FOR ILLUSTRATION

One of the most imp ortant issues to address when trying to create illustrations is

how to calculate the edge lines. Edge lines for p olygonal ob jects can b e generated

interactively using the techniques of Markosian et al. [24]. In order to calculate edge

lines for higher-order geometric mo dels, like NURBS, the surfaces would havetobe

tessellated to apply Markosian's technique. On high-end systems, image-pro cessing tech-

niques [29] could b e made interactive. In Section 4.1, I will discuss how silhouettes,

surface b oundaries, and discontinuities can b e calculated for NURBS surface, as well as

suggest some other techniques for calculating edge lines. After calculating edge lines, the

illustrations are completed by considering a new shading mo del and material prop erties

presented by Gooch et al. [15], summarized in Section 4.2. In Section 4.3, I will discuss

the considerations that need to b e made to create 3D technical illustrations.

4.1 Algorithms for Finding Edge Lines

Using the geometric information intrinsic to NURBS allows some precalculations.

Surface normals are view-indep endent and can b e precalculated, given that it is known

which normals one will need. As stated in Section 3.1, in order to imitate the edge lines

used in technical illustration for a NURBS mo del, surface b oundaries and discontinuities,

as well as silhouettes, need to b e drawn. In Section 4.1.1, I will discuss how to nd

b oundaries and discontinuities for NURBS surfaces. In Section 4.1.2, I will de ne some

algorithms for nding silhouettes on NURBS surfaces.

4.1.1 Algorithms for Finding Boundaries

and Discontinuities

Surface b oundaries and discontinuities are view-indep endent and only need to b e cal-

culated once p er mo del. Boundaries can b e found easily from the surface implementation.

As discussed in Section 3.1 and Figure 3.4, not all b oundaries should b e drawn. I de ne

unshared b oundaries to mean those surface b oundaries which are not shared byany

other surface [18]. Only \unshared" b oundaries should b e drawn, or in the cases where

the jointbetween two surface b oundaries changes abruptly. Discontinuities are due to

knot multiplicities and are very simple to extract since they fall along isolines.

4.1.2 Algorithms for Finding Silhouettes for NURBS

Silhouettes are the only view-dep endent part. A brute force metho d will be at

interactive so long as the numb er of surfaces and the amount of silhouette testing are

kept reasonable. De ning the b ounds on reasonable dep ends on machine and program

sp eed as well as the numb er of control p oints for the NURBS mo del.

Ihave explored three metho ds for nding silhouettes for a given viewp oint. I will

de ne the metho ds as Mesh Metho d, Tessellated-Mesh Metho d, and Srf-No de Metho d.

4.1.2.1 Some De nitions

Let:

the surface

u; v a p oint on the surface at parametrics valuesu; v

E u; v vector from the eye p ointto u; v

nu; v the normal at u; v

the angle b etween the vectors E u; v and nu; v

m control p oint of the mesh indexed by i; j

i;j

Given E u; v and nu; v , a silhouette p oint is de ned as the p oint on the surface where

E u; v nu; v = 0 or the angle b etween E u; v and nu; v is 90 degrees, as shown in

Figure 3.5.

Linear interp olation is done only in one parametric dimension, u or v, keeping the other

constant. Given two surface p oints at parametric values t and t , such that t =t ;v

1 2 1 1 o

and t =t ;v , can b e de ned by nt , the normal at t , and E t , the eyevector,

2 2 o i i i i

as seen in Equation 4.1.

E t nt

i i

= arccos

kE t nt k

i i

Given and and the corresp onding parametric values, t and t , linear interp olation

1 2 1 2

will give an approximate t where the angle is 90 degrees or

t = t t t

2 2 1

2 1

Linear interp olation is further explained by Figure 4.1

4.1.2.2 Mesh Metho d

The Mesh Metho d relies up on the control mesh of a surface, , to supply information

on where a silhouette could and could not b e. Due to the variation diminishing prop erties

of the control mesh, one can rule out where there cannot b e a silhouette p oint on the

surface. If there is a silhouette in the control mesh, then there may b e a silhouette

p oint on the surface of the ob ject. However, nding silhouettes is not easy and requires

maintaining some large data structures. For every mesh p oint, m , one needs a control

i;j

p oint data structure which contains u, v , surface p oint u; v , normal nu; v , mesh

indices i and j, and the sign, ,ofE u; v nu; v . A 2D marching-cub e data structure

is necessary for holding the silhouette p oints and assembling them into silhouette curves.

The 2D marching-cub e data structure contains four control p oints and their u,v values,

as well as a list of p ossible silhouette p oints four are p ossible b etween the mesh p oints

with four additional p oints p ossible at the mesh p oints.

N N θ = 90ο θ1 N E

θ 2

Figure 4.1.Interp olating silhouettes: After two neighb oring surface p oints with di erent

's are found, the p oint where E u; v nu; v = = 0 can b e found by linearly interp o-

lating in u or v with the two angles as calculated in Equation 4.1. Note: = E n > 0

1 1 1

and = E n < 0.

2 2 2

The algorithm is as follows. First nd the normals at each of the control mesh p oints.

For every mesh p oint, there are up to four p ossible normals that need to b e calculated,

n , n , n , n as can b e seen in Figure 4.2. This calculation only needs to b e done

1;3 1;2 4;3 4;2

once p er surface; the rest of the calculations needs to b e made every time the viewp oint

changes.

Next, classify each mesh normal based on the sign, ,ofE u; v nu,v. There are four

signs p er mesh p oint. For example, a 4x3 control mesh can b e visually represented and

stored in a table like Figure 4.3.

To de ne which set of signs signal a p ossible silhouette, I lo oked at the combinations of

's stored in the table. The trick is in determining what constitutes a p ossible silhouette.

This metho d creates a large numb er of sign group variations which can indicate p ossible

silhouettes, as can b e seen by lo oking at the combinations of pluses and minuses around

each mesh p oint in Figure 4.4a. The implementation of this metho d involves a large

set of case statements, lo oking at the mesh and the relative signs to determine where

silhouettes maybe.

u v m i , j−1

vec2

vec1 vec4 m i −1, j m i , j m i +1, j

vec3

Four Normals: n = vec vec m i , j+1 1 , 2 1 x 2 n 4 , 2 = vec4 x vec2 n 4 , 3 = vec4 x vec3

n 1 , 3 = vec1 x vec3

Figure 4.2. Calculating the mesh normals: The four mesh normals which corre-

sp ond to m are n , n , n , n , where for example n = vec vec , with

i;j 1;3 1;2 4;3 4;2 1;3 1 2

vec1= m m and vec2= m m .

i;j i1;j i;j 1 i;j

0;0 0;1 0;2 0;3 0;4 0;5

1;0 1;1 1;2 1;3 1;4 1;5

2;0 2;1 2;2 2;3 2;4 2;5

3;0 3;1 3;2 3;3 3;4 3;5

Figure 4.3.Envision the mesh metho d as a table of signs, where can b e +, -, or 0.

Comparisons need to b e made in b oth the u m and m and in the v m and

i;j i+1;j i;j

m directions.

i;j +1

First check for =0. If = 0 then interp olate based on the parametric values

i;j i;j

asso ciated with m and m to get the silhouette p oint on the surface, if there is

i1;j i+1;j

one.

Next, check for changes b etween the mesh p oints in the u and v directions, i.e., m

i;j

and m ,aswell as m and m .For example, this would mean lo oking at the two

i+1;j i;j i;j +1

groups: m , , , and m , , , in Figure 4.3.

1;1 1;1 1;2 2;1 2;2 2;1 1;3 1;4 2;3 2;4

There are four sign comparisons made p er b ox in the 2D marching cub e data structure:

for example, and , and , and , and .

0;2 0;3 1;2 1;3 0;2 1;2 0;3 1;3

If a sign change is found, then the linear interp olation describ ed in Section 4.1.2.1 will

provide a silhouette p oint at u,v. The silhouette p oints are stored in the 2D marching-

cub e structure. Silhouette p oints are turned into silhouette curves by traveling though

the marching cub e data structure, connecting p oints to form edges. The top image in

Figure 4.4 provides a visualization of the and Figure 4.5 the approximate silhouette

i;j

lines for the Mesh Metho d and the Srf-No de Metho d. Figure 4.6 shows the results of the

Mesh Metho d on a surface. Using the Secant Metho d or Newton's Metho d, these edges

can b e re ned.

4.1.2.3 Tessellated-Mesh Metho d

Avariation on the Mesh Metho d is the Tessellated Mesh Metho d. In order to simplify

the numb er of p ossible sign combinations, I tessellated the control mesh. The control

mesh of a surface is a set of bilinear patches. I split each of those bilinear patches into

triangles bycho osing the diagonals to b e in the direction of minimum curvature across

each bilinear patch. Then there is only one normal p er triangle or two normals p er

bilinear patch. However, checking for silhouettes with these normals only tells one where

a silhouette may b e. After cho osing the area that mayhave silhouettes, you then haveto

nd the corresp onding p oint on the surface and nd the nearby silhouette p oint and curve

if it exists. A winged-edge data structure can keep track of all of these data and is useful

for turning silhouette p oints into silhouette curves. The only part left is to re ne these

jaggy lines as seen in Figure 4.7 into silhouette curves. I did not pro ceed past nding the

approximate silhouette curves b ecause this metho d was to o slow. 28

u 0,0 ++++ ++++++++++++++++++++ v ++++ +++++++++++++++----- ++++ +++++++++++++++------+++++++++++++++++--+ ---- +++++++++++++++----- ++++ +++++++++++++------++++ +++++++------

++++ +------+++++ a Mesh Metho d

u 0,0 + + + + + + + + + + + + +

v + + + + + + + + + + + - -

- - + + + + + + + + - - -

+ + + + + + ------

+ + + ------+ + +

b Srf-No de Metho d

Figure 4.4. These images show the control mesh in uv-space for a surface where +,

-, or 0 denotes the sign of the dot pro duct E u; v nu; v . For the Mesh Metho d, there

are up to four dot pro ducts that need to b e calculated p er mesh p oint, only one p er mesh

p oint for Srf-No de Metho d. 29

u 0,0 ++++ ++++++++++++++++++++ v ++++ +++++++++++++++----- ++++ +++++++++++++++------+++++++++++++++++--+ ---- +++++++++++++++----- ++++ +++++++++++++------++++ +++++++------

++++ +------+++++ a Mesh Metho d

u 0,0 + + + + + + + + + + + + +

v + + + + + + + + + + + - -

- - + + + + + + + + - - -

+ + + + + + ------

+ + + ------+ + +

b Srf-No de Metho d

Figure 4.5. These images show the control mesh in uv-space for a surface, with

approximations to the silhouettes. The sign of the dot pro duct E u; v nu; v are

denoted by +,-,or0.

a View of surface with silhouettes generated with mesh b Lo oking down on sur-

metho d. face with silhouettes.

Figure 4.6. Mesh Metho d.

a View of surface with approximate silhouettes generated b Lo oking down on sur-

with the tessellated mesh metho d. face with approximate sil-

houettes.

Figure 4.7.Tessellated Mesh Metho d.

4.1.2.4 Srf-No de Metho d

The Srf-No de Metho d is the most concise. No des corresp ond to parameter values

which are the average of consecutive sets of or der 1 knots from the knot vector,

ignoring the rst and last ones. There are exactly the same numb er of no des as there are

control p oints. It is often convenient to use the no des when a parameter value or p oint

on the curve needs to b e asso ciated with a control p oint [19].

A normal is calculated for every no de p oint on a surface, as shown in Figure 4.4b.

This calculation can b e done as a prepro cess and only has to b e done once p er surface.

Then, E u; v nu; v is calculated for every view and every no de p oint, where nu; v

is the surface normal at the no de p oint and E u; v is the vector from the eye to the p oint

on the surface. The resulting signs of the dot pro ducts, , are stored in a table, one p er

i;j

no de p oint, as shown in Figure 4.8. If is zero then there is a silhouette at that no de

i;j

p oint on the surface. By searching the table in the u direction and then in the v direction,

a silhouette can b e found by comparing to and to , resp ectively. If

i;j i+1;j i;j i;j +1

a sign changes from + to - or from - to +, then there is a silhouette b etween those two

p oints on the surface, as shown in Figure 4.4b.

When a region containing a silhouette p oint is found b etween twonodepoints, it is

linearly interp olated, as shown in Figure 4.1. The interp olation is based on two surface

p oints and the resp ective angles formed by the normal and the eyevector, calculated as

in Equation 4.1 and 4.1 and as discussed in Section 4.1.2.1.

In order for this metho d to work, the surface has to b e suciently re ned or it may

miss silhouettes, as discussed in Figure 4.9. Surface re nement only needs to b e done

once and can b e done as a prepro cess over the whole surface. However, the re nement

increases the numb er of control p oints and thus the number of checks necessary to lo cate

the silhouette p oints. It may b e b etter to re ne the area where a silhouette may b e, based

on testing the control mesh.

Using a 2D marching-cub e data structure makes it easy to connect the silhouette

p oints to form linear silhouette curves. Figure 4.5b provides a visualization of the

i;j

and the approximate silhouette lines. This metho d results in edge lines as displayed in

Figure 4.10. Another exaple is shown in the top down view shown in Figure 4.11 and the

view from the eye p oint in Figure 4.12.

0;0 0;1 0;2 0;3

1;0 1;1 1;2 1;3

2;0

2;1 2;2 2;3

Figure 4.8. Visualize the Srf-No de Metho d as a table of signs , where i; j can b e

i;j +, -, or 0. 32

N N N α θ 3 θ1 N

θ 2

Figure 4.9. Srf-No de Metho d can result in missed silhouettes dep ending up on the no de

p oints. If for example, the no de p oints were those that corresp ond to , ,and , there

1 2 3

would b e three missed silhouette p oints b ecause , ,and , are all less than 90 degrees

1 2 3

and there would b e no sign change. However, if the no des p oints were , ,and , then

2 3

is greater than 90 degrees and is less than 90 degrees, so the silhouette b etween

the two corresp onding no de p oints would not b e missed and could b e interp olated. The

problem of missing these silhouettes can b e remedied by re ning the control mesh.

a View of surface with silhouettes and surface b oundaries b Lo oking down on sur-

generated with Srf-No de Metho d. face with silhouettes and

surface b oundaries.

Figure 4.10. Srf-No de Metho d.

Figure 4.11. Lo oking down on surface with silhouette generated with Srf-No de metho d.

Compare this image with the 2D pro jection and approximation of silhouettes shown in

Figure 4.5 using the Mesh metho d and the Srf-No de metho d.

Figure 4.12. View of the same surface represented in Figure 4.5, 4.4, and 4.11 with silhouettes generated with the Srf-No de metho d.

4.1.2.5 Silhouette Finding Summary

The Mesh Metho d and the Tessellated-Mesh Metho d are counter-intuitive and do not

have the elegant algorithmic nature that the Srf-No de metho d has. There app ears to b e

far to o many combinations of the signs of the dot pro duct, signE u; v nu; v = 's,

that could signal a p ossible silhouette in the Mesh Metho d and Tessellated-Mesh Metho d.

Once it is determined that there is a silhouette on the control mesh and hence a p ossible

silhouette on the surface, there would need to b e a check to determine whether or not

there is a silhouette on the surface.

The Srf-No de metho d is the most concise and do es not require the maintenance of

large data structures whichmay b og down the desired interactive rates. However, the

Srf-No de metho d has the restriction that all of the surfaces must b e suciently re ned.

Although this increases the numb er of dot pro ducts that need to b e calculated, most of

op erations can b e done as a prepro cess.

In order to achieve real-time geometric silhouette calculations, one could take advan-

tage of previously calculated silhouettes and the movement of the view to approximate

the next set of silhouettes. As in Markosian's algorithm, there would have to b e some

way of determining where silhouettes may suddenly app ear, i.e., a region that suddenly

has silhouettes that were not in the previous frame. Normal or visibility cones [33, 20]

could also b e used to rule out where silhouettes could not b e; then a test of the whole

surface may not b e necessary. If the mo del can b e suciently tessellated, Markosian's

algorithm may b e preferred. However, for a highly trimmed NURBS mo del, tessellation

may not b e the b est choice.

4.1.3 Other Metho ds for Calculating Edge Lines

Trying to nd these silhouettes based on geometry may b e to o slow for very large

mo dels. The Srf-No de metho d requires suciently re ned surfaces and b ogs down on

large mo dels like the Bezier teap ot mo del which has 23 surfaces.

At SIGGRAPH 1998, Cassidy Curtis presented a technical sketchentitled \Lo ose and

Sketchy" [9]. Based on 3D geometry he calculated edge lines using a depth map. The

depth map is converted into a \template image," which approximates the edge lines in

the image. In the template image, each pixel represents the amount of ink needed in its

immediate neighborhood. The template image is created by calculating the magnitude

of the gradient of the depth map, thresholding it to give binary values, and then blurring

the result. This technique may b e faster than using the geometric information to get edge

lines. Curtis then uses this template image and another image called the \force eld," also

created from the depth map, along with a sto chastic, physically-based particle system to

create sketchy lines. This metho d is not interactive, and his algorithm takes ab out 10-60

seconds to generate \lo ose and sketchy" images, but maybeinteractive if used only to

calculate the template image.

Other metho ds for implementing interactive/real-time edge line should b e explored,

esp ecially using Op enGL, b oth in software and hardware. For example there is a sample

program called \silhouette" which uses the Op enGL API's stencil bu er [26], but this

metho d misses interior silhouettes.

4.2 Shading Algorithms

4.2.1 Traditional Shading of Matte Ob jects

Traditional di use shading sets luminance prop ortional to the cosine of the angle

between light direction and surface normal:

I = k k + k max 0; l n^ ;

d d

where I is the RGB color to b e displayed for a given p oint on the surface, k is the

RGB di use re ectance at the p oint, k is the RGB ambient illumination, l is the unit

vector in the direction of the light source, and n^ is the unit surface normal vector at the

p oint. This mo del is shown for k = 1 and k = 0 in Figure 4.13. This unsatisfactory

image hides shap e and material information in the dark regions. Both highlights and

edge lines can provide additional information ab out the ob ject. These are shown alone

in Figure 4.14 with no shading. Edge lines and highlights could not b e e ectively added

to Figure 4.13 b ecause the highlights would b e lost in the light regions and the edge lines

would b e lost in the dark regions.

To add edge lines to the shading in Equation 4.1, either of two standard heuristics

could b e used. First k could b e raised until it is large enough that the dim shading is

visually distinct from the black edge lines, but this would result in loss of ne details.

Alternatively, a second light source could b e added, whichwould add con icting highlights

and shading. To make the highlights visible on top of the shading, k could b e lowered

until it is visually distinct from white. An image with hand-tuned k and k is shown

a d

in Figure 4.15. This is the b est achromatic image using one light source and traditional

shading. This image is p o or at communicating shap e information, such as details in

the claw nearest the b ottom of the image, where it is colored the constant shade k k

regardless of surface orientation.

4.2.2 Tone-based Shading of Matte Ob jects

In a colored medium such as air-brush and p en, artists often use b oth hue and

luminance grayscale intensity shifts. Adding black and white to a given color results in

what artists call shades in the case of black and tints in the case of white. When color

scales are created by adding gray to a certain color they are called tones [3]. Such tones

vary in hue but do not typically vary much in luminance. Adding the complementofa

color can also create tones. Tones are considered a crucial concept to illustrators and

are esp ecially useful when the illustrator is restricted to a small luminance range [21].

Another quality of color used by artists is the temperature of the color. The temp erature

Figure 4.13. Di use shaded image using Equation 4.1 with k = 1 and k =0. Black

shaded regions hide details, esp ecially in the small claws; edge lines could not b e seen if

added. Highlights and ne details are lost in the white shaded regions.

of a color is de ned as b eing warm red, orange, and yellow, co ol blue, violet, and green,

or temp erate red-violets and yellow-greens. The depth cue comes from the p erception

that co ol colors recede whereas warm colors advance. In addition, ob ject colors change

temp erature in sunlit scenes b ecause co ol skylight and warm sunlightvary in relative

contribution across the surface, so there may b e ecological reasons to exp ect humans

to b e sensitive to color temp erature variation. Not only is the temp erature of a hue

dep endent up on the hue itself, but this advancing and receding relationship is e ected by

proximity [5]. Gooch et al. used these techniques and their psychophysical relationship

as the basis for their shading mo del.

The classic computer graphics shading mo del can b e generalized to exp eriment with

tones by using the cosine term l n^ of Equation 4.1 to blend b etween twoRGB colors,

Figure 4.14. Image with only highlights and edges. The edge lines provide divisions

between ob ject pieces and the highlights convey the direction of the light. Some shap e

information is lost, esp ecially in the regions of high curvature of the ob ject pieces.

However, these highlights and edges could not b e added to Figure 4.13 b ecause the

highlights would b e invisible in the light regions and the silhouettes would b e invisible in the dark regions.

k and k :

warm

cool

! !

1+ l n^

1+l n^

I =

k + 1 k :

warm

cool

2 2

Note that the quantity l n^ varies over the interval [1; 1]. To ensure the image

shows this full variation, the lightvector l should b e p erp endicular to the gaze direction.

Because the human vision system assumes illumination comes from ab ove [14], it is b est

to p osition the light up and to the right and to keep this p osition constant.

An image that uses a color scale with little luminance variation is shown in Figure 4.16.

This image shows that a sense of depth can b e communicated at least partially byahue

shift. However, the lack of a strong co ol-to-warm hue shift and the lack of a luminance

Figure 4.15. Phong-shaded image with edge lines and k =0:5 and k =0:1. Like

Figure 4.13, details are lost in the dark gray regions, esp ecially in the small claws, where

they are colored the constant shade of k k regardless of surface orientation. However,

edge lines and highlights provide shap e information that was gained in Figure 4.14, but could not b e added to Figure 4.13.

shift makes the shap e information subtle. The unnatural colors may also b e problematic.

The colors chosen for this hue shift must b e picked with care. A red-green hue shift

would b e undesirable b ecause of red-green color blindness. A blue-yellowhue shift is

most common in many art forms and may b e most natural b ecause of yellow sun-light

and shadows lit by the ambient blue sky. Blue and yellow, having a very large intensity

shift, will also provide the desired luminance shift.

In order to automate this hue shift technique and to add some luminance variation

to the use of tones, Gooch et al. examined two extreme p ossibilities for color scale

generation: blue to yellow tones and scaled ob ject-color shades. The nal mo del is a

linear combination of these techniques. Blue and yellow tones are chosen to insure a co ol

to warm color transition regardless of the di use color of the ob ject.

The blue-to-yellow tones range from a fully saturated blue: k =0; 0;b;b 2 [0; 1]

bl ue

in RGB space to a fully saturated yellow: k =y; y; 0;y 2 [0; 1]. This pro duces a

y ellow

Figure 4.16. Approximately constant luminance tone rendering. Edge lines and

highlights are clearly noticeable. Unlike Figures 4.13 and 4.15 some details in shaded

regions, like the small claws, are visible. The lack of luminance shift makes these changes subtle.

very sculpted but unnatural image and is indep endent of the ob ject's di use re ectance

k . The extreme tone related to k is a variation of di use shading where k is pure

d d cool

black and k = k . This would lo ok much like traditional di use shading, but the

warm

entire ob ject would vary in luminance, including where l n^ < 0. A compromise b etween

these strategies will result in a combination of tone scaled ob ject-color and a co ol-to-warm

undertone, an e ect which artists achieveby combining pigments. The undertones can

b e simulated by a linear blend b etween the blue/yellow and black/ob ject-color tones:

k = k + k ;

cool bl ue d

k = k + k : 4.1

warm

y ellow d

Plugging these values into Equation 4.1 leaves four free parameters: b, y , , and .

The values for b and y will determine the strength of the overall temp erature shift, and

the values of and will determine the prominence of the ob ject color and the strength

of the luminance shift. In order to stayaway from shading which will visually interfere

with black and white, intermediate values should b e supplied for these constants. An

example of a resulting tone for a pure red ob ject is shown in Figure 4.17.

Substituting the values for k and k from Equation 4.1 into the tone Equa-

warm

cool

tion 4.1 results in shading with values within the middle luminance range as desired.

Figure 4.18 is shown with b =0:4, y =0:4, =0:2, and =0:6. To show that the exact

values are not crucial to appropriate app earance, the same mo del is shown in Figure 4.19

darken pure blue to yellow +

select pure black to object color =

final tone

Figure 4.17.How the tone is created for a pure red ob ject by summing a blue-to-yellow and a dark-red-to-red tone.

with b =0:55, y =0:3, =0:25, and =0:5. Unlike Figure 4.15, subtleties of shap e in

the claws are visible in Figures 4.18 and 4.19.

The mo del is appropriate for a range of ob ject colors. Both traditional shading and

the new tone-based shading are applied to a set of spheres in Figure 4.20. Note that

with the new shading metho d ob jects retain their \color name" so colors can still b e used

to di erentiate ob jects like countries on a p olitical map, but the intensities used do not

interfere with the clear p erception of black edge lines and white highlights. One issue

that is mentioned as p eople study these sphere comparisons is that the spheres lo ok more

like buttons or app ear attened. Ihyp othesize a few reasons why this maybeso. The

linear ramp of the shading may b e to o uniform and cause the spheres to atten. The

shading presented here is just a rst pass approximation to the shading artists use and

Figure 4.18. Luminance/hue tone rendering. This image combines the luminance shift

of Figure 4.13 and the hue shift of Figure 4.16. Edge lines, highlights, ne details in

the dark shaded regions such as the small claws, as well as details in the high luminance

regions are all visible. In addition, shap e details are apparent unlike Figure 4.14 where

the ob ject app ears at. In this gure, the variables of Equation 4.1 and Equation 4.1 are:

b =0:4, y =0:4, =0:2, =0:6.

much improvement could b e made. Another problem may b e that the dark silhouettes

around to the ob ject may tie the spheres to the background. Figure 4.21 shows three

sets of spheres, shaded the same but put against di erent gradations of background. The

edge lines of the spheres on the darkest background fade a little bit and even seem to thin

towards the light, due to the gradation of the background. In my opinion, the spheres

set against the darkest background, where the edge lines lo ose some emphasis, seem to

b e a little more three dimension than the spheres with edge lines.

Figure 4.22 shows b oth the Phong-shaded spheres and the spheres with new shading

without edge lines. Without the edge lines, the spheres stand out more. Spheres are not

really the b est mo del to test this new shading and edge lines. Edge lines are not really

necessary on a sphere, since edge lines are used by illustrators to di erentiate parts and

discontinuities in a mo del, something that is not really necessary in a simple mo del like

Figure 4.19. Luminance/hue tone rendering, similar to Figure 4.18 except b =0:55,

y =0:3, =0:25, =0:5. The di erentvalues of b and y determine the strength of

the overall temp erature shift, where as and determine the prominence of the ob ject color, and the strength of the luminance shift.

Figure 4.20. Comparing shaded, colored spheres. Top: Colored Phong-shaded spheres

with edge lines and highlights. Bottom: Colored spheres shaded with hue and luminance

shift, including edge lines and highlights. Note: In the rst Phong-shaded sphere violet,

the edge lines disapp ear, but are visible in the corresp onding hue and luminance shaded

violet sphere. In the last Phong-shaded sphere white, the highlightvanishes, but is

noticed in the corresp onding hue and luminance shaded white sphere b elow it. The

spheres in the second row also retain their \color name."

Figure 4.21.Tone and undertone shaded spheres with backgrounds getting darker.

Figure 4.22. Shaded spheres without edgelines. Top: Colored Phong-shaded spheres

without edge lines. Bottom: Colored spheres shaded with hue and luminance shift, without edge lines.

a sphere. However, it is a computer graphics tradition to test a shading mo del on the

spheres.

4.2.3 Shading of Metal Ob jects

Illustrators use a di erent technique to communicate the surface prop erties of metallic

ob jects, as shown in the photograph in Figure 4.23. In practice illustrators represent

a metallic surface by alternating dark and light bands. This technique is the artistic

representation of real e ects that can b e seen on milled metal parts, such as those found

on cars or appliances. Milling creates what is known as \anisotropic re ection." Lines

are streaked in the direction of the axis of minimum curvature, parallel to the milling

axis. Interestingly, this visual convention is used even for smo oth metal ob jects [25, 28].

This convention emphasizes that realism is not the primary goal of technical illustration.

To simulate a milled ob ject, Go o ch et al. [15] maps a set of 20 strip es of varying

intensity along the parametric axis of maximum curvature. The strip es are random

intensities between 0.0 and 0.5 with the strip e closest to the light source direction

overwritten with white. Between the strip e centers the colors are linearly interp olated.

An ob ject is shown Phong-shaded, metal-shaded without and with edge lines, and

metal-shaded with a co ol-warm hue shift in Figure 4.24. The metal-shaded ob ject is

more obviously metal than the Phong-shaded image and the metal-shaded ob ject with

edge lines provides more shap e information. The co ol-warm hue metal-shaded ob ject is

not quite as convincing as the achromatic image, but it is more visually consistent with

the co ol-warm matte-shaded mo del of Section 4.2.2, so it is useful when b oth metal and

Figure 4.23. An anisotropic re ection can be seen in the metal ob jects in this photograph.

a Phong-shaded ob ject. b New metal-shaded ob ject

without edge lines.

c New metal-shaded ob ject d Metal-shaded ob ject with a

with edge lines. co ol-to-warm shift.

Figure 4.24. Representing metallic material prop erties.

matte ob jects are shown together.

4.3 3D Illustration

Imitating 2D technical illustrations is fairly straightforward. However, there are

several new issues to address when creating 3D illustrations. Three-dimensional technical

illustrations involveaninteractive display of the mo del while preserving the characteristics

of technical illustrations. By allowing the user to move the ob jects in space, more

shap e information maybeavailable than can b e conveyed by 2D images. Interaction

provides the user with motion cues to help deal with visual complexity, cues that are

missing in 2D images. Also, removing the distracting wireframe lines and displaying

just silhouettes, b oundaries and discontinuities will provide shap e information without

cluttering the screen, as shown in Figure 4.25.

The question remains, \how do the 2D illustration rules change for a 3D interactive

technical illustration?" Adapting the shading and line conventions presented in Chap-

ter 3 is fairly straightforward as long as the line width conventions have frame-to-frame

coherence. The more interesting issues dep end up on changing the viewer's p osition versus

moving the ob ject. Since there are no proto cols in traditional illustration, it maybebest

to mo del these 3D illustration conventions based on how one would move real ob ject.

This has an e ect on how the lightchanges with resp ect to the ob ject. The light p osition

can b e relative to the ob ject or to the viewer. When one lo oks at a small ob ject in

one's hand, one turns the ob ject and do es not move one's head, so the light stays in the

same p osition relative to the eye. However when one moves an ob ject in an mo deling

program or when one is lo oking at a large part, ones is actually moving the eye p oint,

not the ob ject. As shown in Figure 4.26, the shading mo del presented in Section 3.2 is

used to its full advantage if the surface varies completely from co ol to warm, as shown in

comparing Figure 4.26b and Figure 4.26c. This would mean moving the ob ject, not

Figure 4.25. Comparing this gure to Figure 1.1, the edge lines displayed provide shap e information without cluttering the screen.

the viewp oint.

When illustrators lightmultiple ob jects, they may use a di erent shading across

di erent ob jects, inferring that each ob ject has its own light, which do es not a ect the

other ob jects in the environment, similar to the \virtual lights" byWalter et al. [37]. For

example, two ob jects in a scene may b e lit di erently to draw attention to di erent at-

tributes of each ob ject. If this was accomplished by adding two lights to the environment,

the multiple highlights would b e confusing.

Most material prop erties are semiconstant as the view direction or lighting changes.

However the metal shading presented in Section 4.2.3 is the replication of the anisotropic

re ection due to the surface of the ob ject and the re ection of the environment. When a

real metal part is rotated in one's hand, the banding do es not stick to the ob ject, but re-

mains constant since the environment is not changing. However, in an non-photorealistic

a Frame of mo del with b Frame after the cam- c Frame after moving the

new shading in an interac- era p osition is moved to view ob ject instead of the cam-

tiveenvironment with lights the side of the mo del. era, allowing the surface to

p ositioned up and to the vary completely from co ol to

right. warm.

Figure 4.26. Frames from the NPR JOT Program, to which I used Markosian et

al.'s silhouette nding technique [24] and added the Op enGL approximation to the new shading mo del. This will b e discussed further in Chapter 5.

interactiveenvironmentitmay b e to o jarring to have the metal shading changing abruptly.

Using a metal texture would b e more appropriate and a metal texture in an interactive

environmentwould still convey the material prop erty.

Another notion is to allow the relative size of the ob ject to control the motion of the

viewer, the ob ject, and the light source in an interactive 3D illustration. In the end,

allowing the user to cho ose whether the ob ject moves or the eye p ointchanges, as well

as having control over the lights, may help the viewer gain the most shap e information.

CHAPTER 5

IMPLEMENTATION AND RESULTS

5.1 Edge Lines

The algorithms for the Srf-No de Metho d, the Mesh Metho d, and the Tessellated-Mesh

Metho d were all integrated into the Alpha

1 system, using the existing NURBS surface

evaluators and functions when p ossible. Alpha 1 is a B-spline research system which

integrates computer graphics, mo deling geometric, simulation, and physically based,

rendering realistic and non-realistic, virtual prototyping, mechanical design, visualiza-

tion, animation, teleconferencing, and human-computer interaction. In the viewer called

\motif3d," one can load a NURBS mo del and toggle display options such as isolines, the

control mesh, and Phong shading. I added the option to display silhouettes as well as

the new shading, as explained in the next section.

Using the JOT program, a Utah-Brown collab oration, I was able to use the Op enGL

shading mo del approximation presented in the next section along with the silhouette

nding technique of Markosian et al. to pro duce interactive illustrations for p olygonal

mo dels, as shown in Figure 5.1. The original Sketch [42] system was deeply intertwined

with the Brown UGA [41] system, which prevented easy distribution of Sketch. To

overcome this problem, Sketchwas rewritten as part of the JOT framework. JOT allows

Sketchtowork with di erent underlying graphics kernels that provide basic services

such as CSGs, intersection, creation of geometric primitives, etc. Currently JOT works

with various graphics kernels including Alpha

1, the Amo deler package from Auto desk,

ARCADE from Fraunhofer IGD, and a partial implementation on top of Op en Inventor.

In addition, JOT can b e used on various di erent UNIX platforms and Windows NT.

5.2 Approximation to New Shading Mo del

The new shading mo del presented in Section 4.2.2 cannot b e implemented directly in

high-level graphics packages that use Phong shading. However, the Phong lighting mo del

a Image of with edge lines only. b Image with new shading and edge lines.

Figure 5.1. An Alpha

1 mo del that was tessellated and imp orted into the JOT NPR

Program.

can b e used as a basis for approximating our mo del. This is in the spirit of the nonlinear

approximation to global illumination used byWalter et al. [37]. In most graphics systems

e.g., Op enGL negative colors for the lights can b e used. Then Equation 4.1 can b e

^ ^

approximated bytwo lights in directions l and l with intensities k k =2 and

warm

cool

k k =2 resp ectively, and an ambient term of k + k =2. This assumes

warm warm

cool cool

the ob ject color is set to white. The Phong highlight should b e turned o to remove the

jarring artifacts caused by the negative blue light. Highlights could b e added on systems

with accumulation bu ers [16].

C++ Co de fragment for generating the two lights, using the Op enGL API:

GLfloat R_warm, G_warm, B_warm,R_cool, G_cool, B_cool;

R_warm=207/255.0; G_warm=207/255. 0; B_warm=145/255 .0;

R_cool=80/255.0; G_cool=80/255.0 ; B_cool=145/255 .0;

GLfloat hi_diffuse[] = { R_warm-R_cool /2.0 ,

G_warm-G_cool /2.0 ,

B_warm-B_cool /2.0 };

GLfloat lo_diffuse[] = { R_cool-R_warm /2.0 ,

G_cool-G_warm /2.0 ,

B_cool-B_warm /2.0 };

GLfloat hi_position[] = { 1, 1, EYE, 1 };

GLfloat lo_position[] = { -1, -1, EYE, 1 };

GLfloat ambient[] = { 0.5, 0.5, 0.5 };

glLightModelfvGL _LI GHT _MOD EL_ AMB IENT , ambient;

glLightfvGL_LIGH T0, GL_DIFFUSE, hi_diffuse;

glLightfvGL_LIGH T0, GL_POSITION, hi_position;

glEnable GL_LIGHT0 ;

glLightfvGL_LIGH T1, GL_DIFFUSE, lo_diffuse;

glLightfvGL_LIGH T1, GL_POSITION, lo_position;

glEnable GL_LIGHT1 ;

This approximation is shown compared to traditional Phong shading and the exact

mo del in Figure 5.2. Using this approximation, I was able to add the new shading to the

Alpha

1 system as well.

A light source cannot b e used for metals on a conventional API. However, either

environment maps or texture maps can b e used to pro duce alternating light and dark strip es.

a Phong shading mo del for b New shading mo del without

colored ob ject. edge lines.

c New shading mo del: edge d Approximation: Phong

lines, highlights, and co ol-to- shading, two colored lights,

warm hue shift. and edge lines.

Figure 5.2. Comparison of traditional computer graphics techniques and techniques for

creating technical illustrations.

CHAPTER 6

CONCLUSION

One of the largest goals in computer graphics has b een realistic image synthesis.

However, in a numb er of situations, an image which highlights particular information

is valued ab ove realism. For example, an automobile repair manual uses illustrations to

remove unnecessary details and to draw attention to sp eci c features.

Many computer-generated images have to b e hand-tuned and they still convey shap e

p o orly. The goal of my researchwas to use the techniques explored by illustrators for

centuries to automatically generate images like technical illustrations and to b e able to

interact with these illustrations in three dimensions.

As seen in Figure 6.1a, Phong-shaded 3D imagery do es not provide geometric in-

formation of the same richness as human-drawn technical illustrations. In this thesis,

Ihave reviewed some conventions to create computer-generated images and interaction

which imitates colored technical illustrations. One of the most imp ortantcharacteristics

of illustration is the use of lines to separate parts and to strengthen shap e information,

as seen in Figure 6.1b.

The shading used in computer-generated illustrations should use a low dynamic range

which do es not interfere with black edge lines and white highlights. By combining the

tone and undertone techniques of the shading presented in Section 4.2.2, the shading may

strengthen the shap e information, while maintaining the low dynamic range. It is easy

to see how imp ortant the role is that edge lines play in distinguishing parts or surface

discontinuities, as shown in Figure 6.2a. This new shading is tailored not to interfere

with edge lines and highlights. Shading without edge lines results in a subtle image, from

which it is harder to distinguish key b oundaries of the mo del.

As shown in Figure 6.2b, putting together a low dynamic range shading which

uses tones and undertones with edge lines results in an image that may convey more

shap e information than the traditional Phong-shaded approach, Figure 6.1a. Using the

illustration mo del presented in this thesis, one is no longer required to guess the b est

a Phong-shaded image. b Image with edge lines

only.

Figure 6.1. Phong shading versus edge lines.

a Image with new shading b New Shading with Edge

without edge lines. Lines.

Figure 6.2. Edge lines.

p osition for lights or to tweak the co ecients of the lighting mo del. In this thesis, I have

also explored representing metal material prop erties, using a convention similar to that

of most illustrators, as discussed in Section 4.2.3 and shown in Figure 6.3.

Since there are few examples of interactive 3D illustrations, there are not any conven-

tions one has to follow. Adapting the shading and line conventions presented in Chapter 3

is straightforward as long as the line width conventions have frame-to-frame coherence.

However, when interacting with 3D illustration one has to address the issue of whether

to move the ob ject or just change the viewer's p osition in mo del space. There are cases

when one would wanttomove around a large ob ject changing the view, and conversely

one maywanttomove a small ob ject as if holding it moving the ob ject. This is

directly related to whether the lightmoves or sticks to an ob ject. It may b e disorienting

for the shading to change on a part as orientation of the part changes. However, the

shading mo del presented in Section 3.2 is used to its full advantage if the surface varies

completely from warm to co ol. This would mean moving the ob ject, not the viewp oint.

However, when a manufacturer designs the ho o d of a car, they want to lo ok at the way

the app earance of the car changes as the lightchanges. Therefore, an interactive3D

illustration environment should consider the relative size of the ob ject in order to control

Figure 6.3. These computer generated images were pro duced by using the illustration

convention of alternating dark and light bands, to convey the metallic material prop erty

of the two images. The convention is rather e ective, even for an ob ject that may not naturally b e metal.

the motion of the viewer and the ob ject, as well as the illumination source and allowing

the user to control these options to maximize the amountofavailable shap e information.

6.1 Future Work

The work presented here is exploratory and shows the advantages of non-photorealism

in its ability to convey shap e information. There are many p ossible improvements and

additions to this work including incorp orating other illustration techniques such as auto-

matic layout, di erent line styles, cut-a-ways, explo ded views, and ob ject transparency.

Exploring a nonlinear shading mo del or a p erceptually uniform gradation from co ol to

warm may tap into more shap e information.

Ihave prop osed a new metho d of displaying and interacting with 3D mo dels; however

it has not b een proven that these illustration metho ds are b etter than a photograph. It

has b een observed that in some images, the new shading may atten an ob ject, but I

could only get opinions or makemyown hyp othesis. Scienti cally analyzing whether

or not the techniques presented here provide more shap e information than traditional

approaches in computer graphics may lead to more e ective metho ds for conveying the

imp ortant geometric prop erties of 3D mo dels.

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