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Volume Graphics

Volume Graphics978-1-4471-0737...graphics, much of which was highlighted in the first International Workshop on Volume Graphics held in March 1999 at Swansea, UK. 1 Kaufman A, Cohen

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Page 1: Volume Graphics978-1-4471-0737...graphics, much of which was highlighted in the first International Workshop on Volume Graphics held in March 1999 at Swansea, UK. 1 Kaufman A, Cohen

Volume Graphics

Page 2: Volume Graphics978-1-4471-0737...graphics, much of which was highlighted in the first International Workshop on Volume Graphics held in March 1999 at Swansea, UK. 1 Kaufman A, Cohen

Springer London Berlin Heidelberg New York Barcelona HongKong Milan Paris Singapore Tokyo

Page 3: Volume Graphics978-1-4471-0737...graphics, much of which was highlighted in the first International Workshop on Volume Graphics held in March 1999 at Swansea, UK. 1 Kaufman A, Cohen

Min Chen, Arie E. Kaufman, Roni Yagel (Eds)

Volume Graphics

Springer

Page 4: Volume Graphics978-1-4471-0737...graphics, much of which was highlighted in the first International Workshop on Volume Graphics held in March 1999 at Swansea, UK. 1 Kaufman A, Cohen

Min Chen, BSc, PhD Department of Computer Science, University of Wales Swansea, Singleton Park, Swansea, SA2 8PP, UK

Arie E. Kaufman, BSc, MSc, PhD Department of Computer Science, State University of New York at Stony Brook, Stony Brook, NY 11794, USA

Roni Yagel, BSc, MSc, PhD Insight Therapeutics, TOR Systems, Hasivim 7, PO Box 7779, Petach Tikva 49170, Israel

ISBN-13: 978-1-85233-192-4 DOl: 10.1007/978-1-4471-0737-8

British Library Cataloguing in Publication Data Volume graphics

1.Computer graphics I.Chen, Min II.Kaufman, Arie E. III. Yagel, Roni 006.6 ISBN-I3978-1-85233-192-4

Library of Congress Cataloging-in-Publication Data

e-ISBN-13: 978-1-4471-0737-8

Volume graphics / Min Chen, Arie E. Kaufman, Roni Yagel (eds.). p.cm.

Includes bibliographical references and indexes. ISBN 978-1-85233-192-4 (alk.) 1. Computer graphics. 2. Three-dimensional display systems. I. Chen, M. (Min), 1960-

II. Kaufman, Arie. III. Yagel, Roni. T385.V662000 006.6'93-dc21 99-056902

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers.

© Springer-Verlag London Limited 2000

The use of registered names, trademarks etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use.

The publisher makes no representation, express or implied, with regard to the accuracy of the informa­tion contained in this book and cannot accept any legal responsibility or liability for any errors or omis­sions that may be made.

Typesetting:: from editor's electronic ftles

34/3830-543210 Printed on acid-free paper SPIN 10738508

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Preface

Min Chen, Arie E. Kaufman and Roni Yage/

Volume graphics is concerned with graphics scenes defined in volume data types, where a model is specified by a mass of points instead of a collection of surfaces. The underlying mathematical definition of such a model is a set of scalar fields, which define the geometrical and physical properties of every point in three­dimensional space. As true 3D representations, volume data types possess more descriptive power than surface data types, and are morphologically closer to many high-level modelling schemes in traditional surface graphics such as parametric surfaces, implicit surfaces and volume sweeping.

The past decade has witnessed significant advances in volume visualisation, driven mainly by applications such as medical imaging and scientific computation. The work in this field has produced a number of volume rendering methods that enable 3D information in a volumetric dataset to be selectively rendered into 2D images. With modern computer hardware, such a process can easily be performed on an ordinary workstation. More importantly, volume-based rendering offers a consistent solution to the primary deficiencies of the traditional surface-based rendering, which include its inability to encapsulate the internal description of a model, and the difficulties in rendering amorphous phenomena.

The emergence of volume-based techniques has not only broadened the extent of graphics applications, but also brought computer graphics closer to other scientific and engineering disciplines, including image processing, computer vision, finite element analysis and rapid prototyping.

These developments have led to beliefs that volume-based techniques have the potential to match and overtake surface-based techniques in computer graphics. In 1993, Kaufman, Cohen and Yagell first outlined a framework for volume graphics as a sub-field of computer graphics. While the primary objective of volume visualisation is to extract meaningful information from volumetric data, volume graphics is a far broader subject: it is a study of the input, storage, construction, analysis, manipulation, rendering and animation of spatial objects in a true three­dimensional form. Since 1993, considerable progress has been made in volume graphics, much of which was highlighted in the first International Workshop on Volume Graphics held in March 1999 at Swansea, UK.

1 Kaufman A, Cohen D, Yagel R. Volume graphics. IEEE Computer 1993; 26(7):51-64.

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vi Chen, Kaufman and YageJ

Structure

This book follows on from the successful Swansea Workshop. It contains a collection of works that represent the latest thinking in volume graphics, and cover a wide spectrum of the subject. All chapters were recommended by a panel of reviewers, were presented and discussed in the Swansea Workshop, and revised by the authors for this book.

The book is divided into eight parts:

• Part I (Perspectives) consists of two introductory chapters. Chapter 1 gives an overview of the current state-of-the-art, and introduces readers to a range of concepts that are central to a study of volume graphics. Chapter 2 presents the scope of volume modelling, which is a major aspect of volume graphics but whose importance was not fully recognised until recently.

• Part II (Discrete Modelling) focuses on the discrete modelling methodology. Chapter 3 presents a study of discretising triangular meshes - the most commonly-used graphical representations - with voxels, and provides a theoretical insight into the fundamentals of discrete modelling. Chapter 4 discusses different interpolation schemes for binary volume datasets, and examines the use of high-order interpolators in enhancing the smoothness of reconstructed surfaces. Chapter 5 introduces readers to the concept of isovolume, and demonstrates the importance of discrete modelling through its application in layered manufacturing.

• Part III (Complex Volumetric Objects) is concerned with advanced methods for modelling complex graphics objects using volumetric representations. Chapter 6 outlines the concept of Constructive Volume Geometry (CVG), and describes the implementation of a rendering system for CVG. Chapter 7 presents, from a software perspective, an object-oriented approach to the voxelisation of complex graphics models. Chapter 8 further examines the relationships between surface and volume representations, and describes a solution to the conversion from CSG models to offset surfaces through the use of distance volumes. Chapter 9 discusses the integration of NURBS and volume representations in creating complex volumetric objects.

• Part IV (Volume Rendering) contains work on several aspects of volume rendering, and emphasis is given to the speed of rendering algorithms, the quality of synthesised images, and the capability of creating aesthetic displays. Chapter 10 introduces readers to the two most fundamental methods for volume rendering, namely ray casting and marching cubes, and gives a qualitative and quantitative comparison between the two methods. Chapter 11 examines one of the important acceleration techniques, shear-warp factorisation, and presents an extension of the technique for multi-resolution datasets. Chapter 12 addresses two acceleration techniques, the template­based acceleration and seed filling in view lattice, and proposes a combined algorithm that is suitable for synthesising high resolution images. Chapter 13 introduces solid textures and hypertextures to the volume rendering pipeline

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Preface vii

and hence provides volume rendering with a new dimension that facilitates the creative and aesthetic aspect of volume graphics.

• Part V (Volume Animation) presents the latest developments in animating volumetric actors and objects. Chapter 14 examines the modelling of object dynamics, and focuses on the animation of amorphous phenomena, including fire, smoke and cloud. Chapter 15 addresses a range of issues in building a volumetric human model, and demonstrates the feasibility of volume animation by bringing life back to the Visible Human dataset. Chapter 16 discusses the kinematic control of volumetric actors through skeleton trees, and presents an algorithm for automated construction of a skeleton from a volume model.

• Part VI (Parallel and Distributed Environments) reports the developments of high performance hardware and software for volume graphics. Chapter 17 considers the problem of isosurface extraction from tetrahedral datasets, and presents a parallel solution to multi-resolutional isosurfacing. Chapter 18 discusses the design of special purpose hardware for direct volume rendering, and proposes a pipelined architecture based on look-up tables and crossbar switches. Chapter 19 further examines the problems in the design of volume rendering hardware, and presents an architecture facilitating algorithmic optimisation. Chapter 20 looks at the acceleration of the voxelisation processes with high performance hardware, and offers support to a range of graphics objects. Chapter 21 takes volume graphics to the Internet, and discusses the issues in managing collaborative activities in a distributed rendering environment.

• Part VII (Applications) illustrates the potentials of volume graphics by giving several example applications of volume techniques. Chapter 22 describes the use of volume-based techniques in radiotherapy - a typical application area of volume graphics. Chapter 23 presents a solution to facial reconstruction for forensic identification using volume deformation. Chapter 24 examines the modelling of weathering effect on a class of volumetric objects (i.e. stones), and provides an example of effective use of volume models in simulating real life phenomena. Chapter 25 discusses the generation of 3D artistic text using volume-based techniques.

• Part VIII (Glossary and Indices) contains a glossary of terms commonly used in volume graphics, an author index and a subject index.

In addition, the book contains a 16 page colour section that illustrates the main features of volume graphics with images synthesised using a variety of volume-based techniques. There is also a world wide web site set up specially for readers of this book by providing additional resources (e.g. images, animations and links to authors' home pages) and up-to-date information on volume graphics (e.g. regularly maintained glossary and bibliography pages). The URL (Uniform Resource Locator) of this web site is http://vg.swan.ac.uk!.

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viii Chen, Kaufman and Yagel

Objectives

This book is intended for students who are studying an advanced course on computer graphics, visualisation or medical imaging. It is suitable as a reference book for researchers and software developers who are working or wish to work in areas of volume graphics. The book draws on an extensive range of sources and materials, with the following aims:

To provide a framework in a structured manner for established concepts and existing knowledge in volume graphics; To present up-to-date developments which will likely form a basis for further investigation and exploration.

While this book marks the adolescence of volume graphics, it also presents us with many technical problems for which solutions are yet to be found. Here we reiterate the following nine questions2, originally proposed by the Programme Committee of the First International Workshop on Volume Graphics, to challenge readers in pursuing further research and development in areas of volume graphics.

1. Is storage requirement for volume representations really more expensive than polygonal representations? What would be the merits and demerits of having volume datasets, instead of triangle meshes, as the primary graphics representation? Should one consider curvilinear and irregular grids as the fundamental representation, and develop more general modelling and rendering techniques based on it?

2. How should reflection, refraction and shadow be specified and rendered in volume graphics, especially, when it involves amorphous volume objects?

3. Since a raster image is a 2D "volume" dataset, an animation sequence is a volume dataset, and some image-based modelling methods employ higher­dimensional volume datasets, what are the mathematical concepts which may unify various volume-based modelling and rendering techniques, and assist in the development of homogeneous graphics hardware and Application Programming Interfaces (APIs)?

4. Is voxel-based radiosity computationally feasible? Do volume representations offer any advantages for the calculation of global illumination?

5. Can the "Visible Human" walk? Motion capture and computational physics can naturally operate on connected solid/surface objects. How should physical properties be defined and attached to discrete volume representations, and how can motion and deformation of volume objects be specified and animated? How would one implement "force and touch" feedback with volume data?

2 Some of the questions have been addressed by the contributions included in this book and some pioneering work in the literature. However, substantial research is required to provide adequate or definite answers to these questions. We also recognise that there may be some other important questions which could be included in the list.

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Preface ix

6. Many digitisation devices generate volume datasets, but not many graphics objects are available in volume representations (e.g. a teapot containing some tea). Is surface-based digitisation technologically or economically superior to volume-based digitisation? What are the obstacles to the extensive use of volume-based digitisation?

7. In volume graphics, what is the role of the techniques developed for image processing and computer vision? Can the use of frequency-domain representations of volume data be extended to a wider range of volume graphics applications in addition to data processing? Can wavelets or other methods be used to compress large volume datasets and still produce reasonably accurate images efficiently?

8. How will real-time volume rendering be made generally available? When will a single CPU be powerful enough to support interactive volume graphics? What is the future of parallel volume rendering hardware and software? Would network bandwidth become a bottleneck for Internet-based volume graphics?

9. Is volume graphics ready to exert any impact upon a wider range of graphics applications, i.e. CAD, games, films and digital art? What are the necessary technological developments in both volume-based hardware and software in order to raise the impact of volume graphics and its applications, including medical imaging and scientific visualisation?

Acknowledgements

We wish to thank all authors for their contributions, and their collaborative effort in producing an up-to-date book in such a dynamic field. We thank all referees and sub­referees who reviewed the submissions for this book. We are particularly grateful for their highly professional recommendations and helpful comments. They include Nicholas Ayache, Ken Brodlie, Daniel Cohen-Or, Michael Doggett, David Duce, Jose L. Encarnajao, Henry Fuchs, Issei Fujishiro, Sara Gibson, Michael E. Goss, Andrew Grant, Sven Giirke, Pat Hanrahan, Chuck Hansen, Karl H. Hahne, Roger Hubbold, Nigel John, Mark W. Jones, Gunter Knittel, Adrian Leu, Bill Lorensen, Martin Maidhof, Tom Malzbender, Nelson Max, Michael Meiftner, Greg Nielson, Nao Ozawa, Frits Post, Georgios Sakas, Richard Satherley, Hans-Peter Seidel, Norsert Schiffne, Wolfgang Strafter, Jean-Philippe Thirion, Stephen Treavett, Philip J. Willis, Craig M. Wittenbrink and Brian Wyvill. We would like to thank Rona Chen who compiled the author and subject indices of this book.

We also take this opportunity to express our appreciation all those who gave generous support to the Swansea Workshop, and a special thank you to the sponsors and local organisers of the Workshop.

Last, but not least, we thank Karen Barker and Rosie Kemp at Springer-Verlag who have been a source of enthusiasm, understanding and support in the process of producing this book.

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Contents

Colour Plates xv

Part I: Perspectives

1. State-of-the-Art in Volume Graphics Arie E. Kaufman .................................................................................................. 3

2. Volume Modelling Gregory M. Nielson ............................................................................................ 29

Part II: Discrete Modelling

3. Minimally Thin Discrete Triangulation Valentin E. Brimkov, Reneta P. Barneva and Philippe Nehlig ........................... 51

4. Smooth Boundary Surfaces from Binary 3D Datasets Daniel Cohen-Or, Arie Kadash, David Levin and Rani Yagel ........................... 71

5. Manufacturing Isovolumes Michael Bailey ................................................................................................... 79

Part III: Complex Volumetric Objects

6. Constructive Representations of Volumetric Environments Min Chen, John V. Tucker and Adrian Leu ........................................................ 97

7. vxt: A Class Library for Object Voxelisation Milos Sramek andArie E. Kaufman ................................................................ 119

8. 3D Scan-Conversion of CSG Models into Distance, Closest-Point and Colour Volumes David E. Breen, Sean Mauch and Ross T. Whitaker ........................................ 135

9. NURBS Volume for Modelling Complex Objects Zhongke Wu, Hock Soon Seah and Feng Lin ................................................... 159

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xii

Part IV: Volume Rendering

10. Voxels versus Polygons: A Comparative Approach for Volume Graphics

Contents

Dirk Bartz and Michael M eij3ner .. ................................................................... 171

11. Fast Multi-Resolution Volume Rendering Yuting Yang, Feng Lin and Hock Soon Seah .................................................... 185

12. High-Quality Volume Rendering Using Seed Filling in View Lattice Jarkko Oikarinen, Rami Hietala and Lasse Jyrkinen ...................................... 199

13. Extending Hypertextures to Non-Geometrically Definable Volume Data Richard Satherley and Mark W. Jones ............................................................. 211

Part V: Volume Animation

14. Fast Volume Rendering and Animation of Amorphous Phenomena Scott A. King, Roger A. Crawfis and Wayland Reid ........................................ 229

15. Visible Human Animation Zhongke Wu and Edmond C. Prakash ............................................................. 243

16. Realistic Volume Animation with Alias Nikhil Gagvani and Deborah Silver ................................................................ 253

Part VI: Parallel and Distributed Environments

17. Multi-Resolutional Parallel Isosurface Extraction based on Tetrahedral Bisection Thomas Gerstner and Martin Rumpf. .............................................................. 267

18. A Volume Rendering Crossbar and SRAM-Based Hardware Miron Deyssenroth, Martijn de Boer, Alexander Gropl, 1iirgen Hesser and Reinhard Manner ............................................................... 279

19. Algorithmically Optimised Real-Time Volume Rendering Bernd Vettermann, 1iirgen Hesser and Reinhard Manner ................................ 287

20. Hardware Accelerated Voxelisation Shiaofen Fang and Hongsheng Chen ............................................................... 301

21. Volume Graphics and the Internet Ken Brodlie and Jason Wood ........................................................................... 317

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Contents

Part VII: Applications

22. InViVo-IORT - A System for Qnality Control in Intra-Operative Radiotherapy

Xlll

Stefan Walter, Gerd Straf3mann and Marco Schmitt ........................................ 335

23. Computer Aided Facial Reconstruction for Forensic Identification Simon D. Michael. ............. ............................................................................... 345

24. A Morphological Approach to Volume Synthesis of Weathered Stones Nao Ozawa and Issei Fujishiro .............................................. .......................... 367

25. Volumetric Modelling of 3D Text Zhongke Wu and Edmond C. Prakash ............................................................. 379

Part VIII: Glossaries and Indices

Glossary Mark W. Jones, Adrian Leu, Richard Satherley and Steve Treavett ........................ 391

Author Index ......................................................................................................... 407 SUbject Index ......................................................................................................... 413

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Colour Plates xv

A Plate I. Volume data types can be used to represent geometric models as well as digital samples. In particular, volume representations can effectively and efficiently support the modelling and rendering of the interiors of objects and amorphous phenomena such as fire, clouds and smoke (Chapter 1). This is one of the most important features of volume graphics and it is illustrated in the above image which shows a volume-sampled plane together with a volumetric cloud over a volumetric model of terrain enhanced with satellite images.

V Plate II. The image below is from a real-time animation of smoke emanating from a locomotive (Chapter 14), demonstrating the descriptive power of volume graphics.

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xvi

A}> Plate III. Volume graphi enable animation of amorphou phenomena (e.g. cloud, du t fire, etc.) to be rendered in real­time on graphics hardware with dedicated tcxturc memory (Chapter 14). The image above how a herd of cattle kicking up a cloud of real -time dust created using a textured plats algorithm. The images on the right are

several till from an animation of a cow moving thr ugh real- time fire, demonstrating the interaction between an effect and other objects in the environment.

Colour Plates

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Colour Plates

}> Plate V. The most fundamental data structure in volume graphics is a volume buffer where sampled or simulated datasets can be intermixed with geometric objects in a true 3D manner (Chapter 1).

v Plate VI. The internal structure of a volume object can sometimes be used to control the motion and deformation of the object. This image shows the walking of the Visible Male dataset controlled by a skeleton tree (Chapter 16).

xvii

'" Plate IV. Medical imaging is one of the main applications and driving forces of volume visualisation (Chapter 22). The ability to digitise and visualise internal structures of real-life objects has laid the foundation for volume graphics.

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xviii

» Plate VII. Voxelisation is a process that converts surface data types to volume data types. Special purpose hardware has been developed to accelerate such a process (Chapter 20). The image below is a voxelised teapot rendered with a "knot" dataset.

Colour Plates

<. Plate VIII. Complex objects can be constructed through voxelisation. This image shows a voxelised tree trunk that is generated by sweeping a 2D image along a path with both twisting and scaling operations (Chapter 9).

» Plate IX. Volume graphics can be used to synthesise graphical images with voxelised representations at a quality comparable to surface graphics with geometric representations. The top image shows a 4-level sphereflake composed of 7381 spheres, and the bottom image shows an equivalent volume object with a 5123 grid, which is obtained using vxt -a voxelisation library (Chapter 7). There is hardly any noticeable difference between these two images.

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Colour Plates

,. Plate X. Constructive volume geometry (CVG) facilitates constructive representation of volume objects, including both discrete volume datasets and scalar fields. These operations are normally defined in the real domain, and enable the construction of complex volume objects through the combination of the geometrical and physical properties of simple (solid and amorphous) volume objects (Chapter 6). The top image shows the application of a union operation to a solid cube and an amorphous cube. The bottom image shows a sphere defined by a set of scalar fields, from which an oval object is subtracted to reveal its interior.

,. Plate XII. CVG also allows discrete volume datasets to be intermixed with mathematical objects defined by scalar fields (Chapter 6). The image on the right includes both volume datasets (i.e. the cr skull and water texture) and mathematical objects (i.e. the sphere and rob).

4: Plate XI. With CVG, images can be integrated naturally into graphics scenes as volume objects. In this scene, an image of a cloud is used to define the solid sky background as well as the amorphous cloud volume (Chapter 6).

xix

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xx Colour Plates

A Plate Xlll. Texture mapping can be u ed in volume graphics to add details to objects in a true 3D manner. The images in thi plate are rendered with different olid texture con tmcted from primitive nonlinear basi function (Chapter 13).

» Plate Xv. 3D texture mapping can also be achieved using the real-domain inter­section operation in Constructive Volume Geometry (Chapter 6).

0( Plate XIV. In volume graphics texture can be generated during voxeli ati n a well a rendering. For in tance, to ynthe i e the image on the left, a olid texture i first mapped, during voxelisation, onto the bolt and nut that is defined by a sequence of sa operation . The volume- ampled dataset i then ray traced ( hapter 1).

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Colour Plates

)0- Plate XVI. Hypertextures enable the production of complex textures u ing v lume rendering paradigm ( hapter 13). They can be used to model phenomena, of which the surface structures are not well defined. The images on the right show the application of two hypertextures - a fire texture and a fur hypertexture wi th bias controlling the curl -to a cr skull.

xxi

<{ V Plate XVII. Hypertextures can al 0 be u. ed to imulate the geometrical change of an object. The image on the left how a melting function applied to a cr skull, while the image below shows a voxeli cd tank with a hypertextured barrel using a imilar melting function (the

tank data i courtesy of Arie Kaufman).

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xxii Colour Plates

v Plate XVIIJ. A distance volume ( hapter 8) is a volume dataset where the value at each voxel repre ents the shortest distance to the urface of an object. Additional information, such as the close t point on the surface and its colour can al 0

be generated during voxelisation. From a di tance volume, different offset surfaces can ea ily be constructed through i osurfacing. The image below shows a set of anti-aliased colour-shaded offset surfaces obtained from a distance, colour and closest­point volume of an X-29 jet fighter.

imilarly, the image on the left displays a et of offset surfaces constructed from a dart volume.

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Colour Plates xxiii

A Plate XIX. This is a morphing sequence where a distance volume of a dart (top left) is transformed into a volume model of an X-29 jet fighter (bottom right). The intermediate volumes are generated using level set methods. The intermediate surface colours are obtained by interpolating the information derived from the colours of the dart and jet fighter, and their closest-volumes (Chapter 8).

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xxiv Colour Plates

Plate xx. he two mo t

fundamental methods for

rendering volume data types are ray

ca ting and urface extraction ( hapter 10).

For in tance, consider a volume repre entation of a lobster, whieh was digiti ed using a computed tomography scanner, and eoloured according to a classification of resin, shell, and meat data in the volume (above). We can ynthesi an image by ca ting ray from the

image plane into the volume (top left), or by extracting a et of i urface u ing the marching cube algorithm (left).

> Plate XXI. Special purpose hardware architec­tures have been developed for direct volume rendering (Chapters 18 and 19). This image was rendered on a simulated architecture based on look­up tables and crossbar switches (Chapter 18).

V Plate XXII. Parallel processing is another common approach for speeding up computation in volume graphics (Chapter 17). The images below are isosurfaces extracted using a parallel multi­resolutional algorithm with varying number of processes. Colours indicate the portions extracted by different processes.

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Colour Plates

» Plate XXIII. There are a number of acceleration techniques for direct volume rendering, including template-based ray casting and seed filling in view lattice. The image on the right was rendered using a combination of both acceleration techniques (Chapter 12).

xxv

<{v Plate XXIV. A multi-resolution approach is often used in volume graphics to upport interactive activitie on computer

hardware that i not powerful enough to upport reaJ-time rendering. The three

images on the left resulted from a multi­resolution algorithm based on shear-warp factori alion which i one of the major acceleration techniques for direct volume rendering by ray casting ( hapter 11). Three different error tolerance values (from a high tolerance value on the left to a zero tolerance value on the boltom-right) were applied to the rendering of the " ngine" data et.

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xxvi

A~ Plate XXV. Reali tic animation of voxel-ba ed actors object can be achieved in volume graphics ( bapter 15). The image on the left are several till frame of an

actor who change from a Iccping po ture to a tanding

po ition. The image below how an animation equence of

the walking of the actor.

Colour Plates

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Colour Plates

» Plate XXVII. An isovolume is first constructed from a kull dataset (in the Vi ualization Toolkit), and it i then manufactured into a bardcopy (Chapter 5).

XXVII

Plate XXVI. Isovolume (also called interval volume) is a volumetric repre entation of a et of i osurface . It i a fundamental data typ u ed in rapid prototyping, and in particular, the layered manufacturing process. An example of such machinery is the Z Corporation Z402 y tern ( hapter 5).

« Plate XXVIII. lWo manufactured foetal isovolumes ( hapter 5).

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xxviii Colour Plates

..,. ... , ~ .

-( /I.. Plate XXIX. The ultimate aim of a facial reconstruction technique is to produce a likene f the face from skeletali ed remains so that it bear ufficient resemblance to the individual prior to death. Volume def rmati n techniques can be u ed to construct faces by di torting a reference head (left) under the control of feature on keletalised remains ( hapter 23).

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Colour Plates

A> Plate XXX. 3D artistic text (Chapter 25) can be created [rom 20 bitmap by a erie of operation including weeping, tran formation deformation and volume texturc mapping.

Plate XXXJ. A European old ca lie synlhesi ed by u ing a morphological operator called weathering ( hapler 24).

xxix

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xxx Colour Plates

AV Plate XXXII. The Internet is becoming a medium for volume graphics (Chapter 21). It offers new opportunities to a range of volume graphics applications, while challenging volume graphics in a number of aspects including its efficiency, data management, and multi-user interaction. The image above shows a user interface where Dr Bone is collaborating with Dr Blood at a remote site to look at CT and SPECT data together. The image below shows Drs. Blood and Bone pointing out features to each other (with different coloured cursors).