Efficient Geometry Parameterisation for Modelling and Animation

Case for Support

Part1: Previous Research and Track Record

The applicants

Principal Investigator (Bath): Professor Philip Willis, Director: Media Technology Research Centre, Department of Computer Science, University of Bath

The Media Technology Research Centre in the University of Bath (http://www.bath.ac.uk/media) was established in 1996. Based within the Department of Computer Science, it maintains strengths in digital media technology. There are several examples of MTRC influence on commercial projects. Most prominent of these is the Animo 2D computer animation package, produced by Cambridge Animation Systems and sold to Warner, Dreamworks and other major industry players.

The Principal Investigator at Bath is Professor Philip Willis. He has been active in computer graphics for 30 years. He was until 1997 one of the two Chief Editors of Computer Graphics Forum, the academic journal of the Eurographics Association. He is now Chair of the Association.

His work on facial and body animation is especially relevant to this proposal. Previous work demonstrated one of the early muscle-based facial animation systems, driven by emotion parameters. This later was extended to the first emotion-driven whole body animation. Current work combines emotion and mood models to produce realistic faces that react in a variety of ways to external stimuli, in particular in different ways according to the stimulus history and thus never the same way twice. He is also experienced in rendering for cel animation.

Some of Professor Willis’ relevant publications include: E Tanguy, P J.Willis & J Bryson, The Role of Emotions in Modular Intelligent Control, AISB Quarterly 117, Summer 2004. M Qi and P J Willis, Quasi-3D Cel-based Animation, Proceedings of Vision, Video and Graphics 2003 (Eurographics/IMA/SIGGRAPH July 2003), pp111-116, ISBN 3-905673-54-1. M. Froumentin and P J Willis, “An Efficient 2.5D Rendering and Compositing System”, Computer Graphics Forum 18 (3) 1999 Eurographics 99 Conference issue pp C385-C394 and C428 ISSN 0167-7055 D J Densley and P J Willis, Emotional Posturing: A method towards achieving emotional figure animation, Computer Animation `97, Geneva, Conference Proceedings (IEEE June 1997) pp. 8-14. ISBN 0-8186-7984-0. M Patel and P J Willis, FACES: The Facial Animation, Construction and Editing System, Proceedings of Eurographics 91 Conference, Sept 1991, pp 33-45.

Principal Investigator (Bradford): Dr Hassan Ugail, School of Informatics, University of Bradford

Hassan Ugail is a young researcher working as a lecturer at the School of Informatics at the University of Bradford. Dr Ugail has a first class BSc honours degree in Mathematics and a Post Graduate Certificate in Education (PGCE) both from King’s College London. He also has a PhD in the field of geometric modelling from the Department of Applied Mathematics at University of Leeds.

Since 1996, Dr Ugail has been working in the area of computer-aided geometric and functional design in collaboration with Professors Bloor and Wilson of the Department of Applied Mathematics at the University of Leeds. In particular, he has undertaken research work on geometric design under the EU Framework V PRIDE (Products by Rapid Integrated Detailed Engineering) project and the EPSRC funded research on “Optimal Design and Manufacture of Thin-Walled Structures” (GR/M73125/01). Dr Ugail presently holds a London Mathematical Society

1 collaborative research grant (Ref: S7-03/04-2) on “Modelling Reaction Diffusion Over Complex Three Dimensional Geometry”, in collaboration with Dr R. Satnoianu of School of Engineering and Mathematical Sciences at City University London.

Dr Ugail is an active researcher in the field of geometric modelling, design analysis and automatic optimisation. He has recently filed a patent on a novel technique for remodelling and data exchange for geometric objects (British patent no. 0410096.2). He is a reviewer for various international journals and conferences in his fields of research. He is also a member of EPSRC peer review college.

Some of Dr Ugail’s recent publications include:

J. Monterde and H. Ugail, On harmonic and biharmonic Bézier surfaces, Computer Aided Geometric Design, 21(7), 697-715, (2004). H. Ugail, Spine Based Shape Parameterisations for PDE surfaces, Journal of Computing, 72, 195-206, (2004). H. Ugail and M. Wilson, Efficient Shape Parametrisation for Automatic Design Optimisation using a Partial Differential Equation Formulation, Computers and Structures, 81(29), 2601-2609, (2003). H. Ugail, On the Spine of a PDE Surface, Mathematics of Surfaces X, M.J. Wilson and R.R. Martin (eds.), Springer, pp. 366-376, (2003a). H. Ugail, Interactive Design and Optimisation of Thin-Walled Structures for Food Packaging, Journal of Optimization and Engineering, 4(4), 291-307, (2003b). H. Ugail, M.I.G. Bloor, and M.J. Wilson, Techniques for Interactive Design Using the PDE Method, ACM Transactions on Graphics, 18(2) (1999) 195-212.

Co-Investigator (Bradford): Dr Ian J. Palmer, School of Informatics, University of Bradford

Ian Palmer is a senior lecturer in digital media and is currently the Head of Department of Electronic Imaging and Media Communications at the School of Informatics. Dr Palmer’s research interests centre on computer animation and virtual environments, including the use of artificial intelligence to improve the usability and realism of interactive 3D environments. Previous work has included behavioural animation, the use of sphere-trees for collision detection and multi-processing architectures for computer animation. Recent work has been in the areas of modified A* algorithms for dynamic, multi-agent environments, action recognition for response and performance monitoring in intelligent virtual environments and the use of multi-modal interfaces for 3D computer games. He has worked on European-funded multinational projects (VISINET, MAID, VISTA and VPARK). He also gained UK HEFCE/OST funding for a Silicon Graphics Onyx Supercomputer for a three year research project into new computer animation techniques (with Professors Gardiner and Earnshaw of the University of Bradford). He is a member of Eurographics, ACM, Siggraph, IEE and the IEEE.

Some of Dr Palmer’s recent publications include:

E. Spyridou, I. J. Palmer and E. J. Williams, Speech Interaction for Networked Video Games, Proceedings of the HCI International Conference, Volume 1, ISBN: 0-8058-4930-0, pp 1046-1050, Crete, Greece, (2003). E. Spyridou, I. J. Palmer and E. J. Williams, The use of Speech in Multimodal Interfaces in Computer Games, Proceedings of the Eurographics Ireland Workshop Series, Volume 2, ISSN: 1649-1807, pp. 17-22, Coleraine, N. Ireland, (2003). E. Spyridou and I. J. Palmer, Investigation into Speech based Interaction for Video Games, Proceedings of the 3rd InternationalConference of Intelligent Games and Simulation, Game-On 2002, ISBN: 90-77039-10-4, pp. 65-72, London, (2002). A. Latiff, M. S. Cavazza, and I. J. Palmer, Co-ordination of Multi-agents Path Planning using Synchronous Near- Admissibility A* (SNA*) Algorithm”, Proceedings of GAME-ON 2001, London, (2001). A. Latiff, M. S. Cavazza, and I. J. Palmer, Action Recognition using Finite State Transition Networks (FSTN) for Synthetic Actors in Virtual Environments, A.Latiff, Sarawak, Malaysia, October 2001.

2 Part 2: Description of the proposed research

Background The modelling and animation of characters, human or otherwise, is a huge and rapidly growing field. The success of movies such as those made by Pixar and the massive computer games market has led to a need for more realistic character modelling and animation, and this realism is demanded in shorter timescales. This is apparent from the large number of computer animated TV series, such as Jimmy Neutron and Excalibur, which have short production times to satisfy the consumer demand.

The two main challenges in creating character animation are producing convincing body motion and realistic facial expressions. Depending on the type of shot and action, more time may be spent animating the face than spent on the rest of the character. In computer games it is not uncommon to use as much as 50% of the polygon budget for a character on the head, since this will generally be the focus of attention. Both body and facial animation are equally important then in creating a convincing character.

In dealing with body animations, whilst a number of techniques for this have been studied (Seo et al. 2003, Simmons et al. 2002, Yamane et al. 2004, Mohr and Gleicher 2003, Allen et al. 2003, Aubel 2002 and Aubel and Thalmann 2000), most animation systems use a form of surface (or ‘skin’) deformation based on rigid links (or ‘bones’). This has been extremely successful since it operates in a similar way to a real character (the movement of skin is related to the motion of the internal bone structure) and because it is somewhat intuitive. There are a number of problems however associated with this. Generally the artist creates the outer surface of the character and then this is passed on to a specialist in character rigging to add the structure used for deformation. These are highly skilled people who have developed many ad hoc tools to help them add the skeleton as easily as possible. There will still nearly always be some manual modification of the skin ‘weights’ to define which bone affects which part of the skin to ensure the correct effect on the skin when the bone is moved. It is also necessary, especially when using polygonal models, to make sure that there is a smooth and natural blend between areas affected by different bones. All this takes skill and time and is due to the fact that there is no inherent relationship between the skin (the visual component of the character) and the skeleton (the animation structure).

In dealing with facial animations, again it is common to create the surface of the head before adding the animation controls. Two common methods are the use of bones (as for the body described above) and the use of blend shapes or morph targets (e.g. Lavender 2003). These techniques involve creating new versions of the face that are each modelling a different expression. As long as the geometry of the new expression face has the same topology as the original, it is possible to animate the face to the new expression. Creating multiple morph targets allows the face to assume a number of expressions and additionally combinations of these expressions in different proportions. This method allows great flexibility in that any expression can be made and then combined with others. The disadvantage is that each expression has to be created by the artist separately. This is particularly time-consuming when this method is used for lip synchronisation, as each viseme must be created for the corresponding phoneme (e.g. Kundert- Gibbs and Lee 2003).

The morph target approach is often combined with a bone that moves the jaw. Whilst this gives a large number of potential expressions it introduces more problems. Since both methods deform the same surface, the order that these are applied is important. Even when this is decided, some effects may be undesirable since we are trying to distort a shape in two different ways. Whilst a bone is not always used for jaw motion, bones would usually be used in the rest of the body, including for motion of the head itself. This can still provide a number of challenges to keep the face from producing strange deformations.

The above-detailed discussion highlights the important point that existing modelling and animation techniques are time-consuming and non-intuitive in the vast majority of situations. In this research we propose to develop novel techniques to address these issues. We propose to develop a system that will offer two distinct advantages over existing techniques. Firstly, we propose to adopt a modelling technique that will allow intuitive generation and manipulation of complex geometry. Secondly, and rather more importantly, we propose to develop techniques that would allow both the modelling and animation process to be based on the same underlying model, and thus there would be no added new layer to animate the model.

3 In order to combine modelling and animation into a single framework, through which intuitive modelling and animation can be carried out, we aim to adopt a parametric design-based methodology. (e.g. King and Parent 2000 and Lee and Shin 1999). In parametric design the basic approach is to develop a generic description of an object or a class of objects in which the shape is controlled by the values of a set of design variables or parameters. A new design, created for a particular application, is obtained from this generic template by selecting particular values for the design parameters so that the item has particular properties suited to that application. If the geometry of a character concerned can be created using standard geometric constructs such as circles, ellipses, cuboids or spheres then the parameterisation of its shape is relatively straightforward. However, for realistic character modelling and animation the use of freeform surface shapes and their time-based motion is inevitable and consequently an approach that can efficiently parameterise a wide variety of geometry has to be adopted.

To this end what we propose is the use of the so-called PDE method (Bloor and Wilson 1990,Ugail et al. 1999 and You et al 2003), a novel approach to shape definition, which is capable of parameterising complex geometry in terms of a relatively small set of design variables or parameters. This particular approach adopts a boundary-value approach whereby a surface is designed by defining a number of space curves (with associated derivative information), so as to form the surface's edges, and then the surface is generated between these curves by solving an elliptic partial differential equation (PDE), rather than by using the ubiquitous polynomial surface patches of conventional approaches. The PDE method is a boundary representation scheme in that it represents a solid object by a description of its surface. Like other boundary representation schemes it describes complex surfaces by means of a collection of sub-patches joined together, but it generally does so using a small number of patches.

The PDE method and its applicability to parametric design has been the subject many research programmes in the past. Previous studies have demonstrated how the method can describe the surfaces of a variety of objects such as aircraft (e.g. Efficient Parameterisation of Aircraft Geometry, NASA grant NAGW-3198), mechanical designs (e.g. Automatic Design for Function, EPSRC grant GR/L11366/01), and thin walled structures (e.g. The Optimal Design and Manufacture of Thin-Walled Structures, EPSRC grant GR/M73125/01), although no systematic approach to shape parameterisation has been developed to date.

In broad terms the utilisation of a boundary-value approach through the use of the PDE method means that surfaces are defined by data distributed around their boundaries only, instead of data distributed over their surface area, e.g. control points. The method defines a shape in terms of a number of surface patches that collectively describe the object's shape. However, unlike spline-based approaches (e.g. Farin 2001), the method produces surface patches that exactly meet at their mutual boundaries, without the need for complicated trimming. Thus, a PDE model, when changed by altering the values of its design parameters, remains continuous; there is no need for a designer to intervene in order to close up any holes that might appear at patch boundaries. Furthermore, recent work has demonstrated that the method is capable of automatically generating the spine of the corresponding geometric models (Ugail 2004).

Thus, the utilisation of the PDE method for parametric design will have distinct advantages in that both the modelling and animation can be on the same underlying model without the need to add new layer to animate the model, i.e. the modelling can be carried out through the manipulation of the boundary conditions of the chosen PDE and the animation can be carried out by introducing a time parameter into the boundary as well as to the spine. Therefore, within a single modelling and animation environment, the use of PDEs will provide greater flexibility in model construction, improve the smoothness and therefore add greater continuity to geometric models and improve the coherence in key-framing of time-dependent geometry.

Research Programme and Methodology The main purpose of this research is to undertake a study in order to bridge the gap between modelling and animation so that both shape modelling and animation can be performed intuitively within a single layer. As mentioned earlier we will utilise the PDE method to undertake this research.

Aims and Objectives The main objectives of this research are:

 To apply the PDE method to a number of case studies in order to demonstrate that it can parameterise realistic geometries capable of modelling complex 3D geometry. We will demonstrate three substantial examples.

4  To devise efficient algorithms in order to develop a PDE-based shape parameterisation for dense surface correspondences between given sources of animation models and target models. We will measure the performance of each algorithm and its scalability.

 To devise efficient algorithms in order to develop a PDE-based shape parameterisation for transferring between existing source animation models and target models. We will measure the performance of each algorithm and its scalability.

 To develop a demonstration software environment to enable a designer, knowing nothing about the underlying algorithms, to use the methodology for realistic modelling and animation. We will deliver the software and involve a designer to deliver one of our substantial examples.

Methodology In a project of this nature, the practical application is a key test. We will therefore pursue an experimental programme, based on software implementation. We will initially use this to bring our theoretical ideas to a testable state. Thereafter, the software will become the topic of further experimentation, in regard to performance and stability of the resulting animation. In turn, we expect this to secure our theoretical understanding and to lead to publishable results.

Timeliness There is considerable expertise in animation in Europe. There is also a widely recognised economic threat from less- developed economies, where low price goes hand in hand with high artistic ability but with low access to appropriate technology. Maintaining a leading technological edge is thus vital to the UK. There is also a vast international market in computer games and the UK has a substantial reputation here. This market is technology-led and consequently needs continual innovation to succeed. This proposal offers new opportunities in both of these substantial areas.

Programme of Work The programme of work we propose in this research is a collaboration between the two identified research teams in Bath and Bradford. Each team brings in specific expertise that are paramount to undertake the proposed work. In particular, work at Bath will be mainly concentrated on animation and interaction while the Bradford research team will be working on modelling and algorithmic programming. The objectives of the research programme are, therefore, constructed with the scope to maximise the contribution through specific expertise of each research team. These objectives are to be addressed using the following methodology, a flow diagram for which is shown in Figure 1.

Stage 1: Familiarisation with parametric design and case studies (duration 10 months) The first task in the project will be to familiarise both the Research Assistants (RAs) with the basic techniques of modelling and animation. In particular the RAs will need time to get acquainted with the existing techniques of parametric design as well as the PDE method.

At this stage we will also develop a research platform to do our studies. This platform will comprise of a C++ programming environment coupled with Maya modelling and animation software. We have the support of Alias who will provide licenses for the Maya software through their research donation programme. We have chosen Maya software as part of our research platform mainly because Maya has the latest industry-standard modelling and animation tools and offers a wide user base for testing and evaluation. We also wish to utilise this since it allows us to use existing tools within Maya to import and export test models and animations rather than develop these from scratch.

Another task at this stage will be the formulation of several case studies for geometry modelling and animation. The case studies will consider the broad range of features of a complex character that a modelling and animation system must be able to capture. Examples we will consider in these case studies include PDE-based modelling of human limbs (such as hand, arm and elbow), face and facial expressions, animals, virtual characters and avatars. The Department of Electronic Imaging and Media Communications at Bradford has a large library of geometric models and animation clips through the final year student projects. Most of these geometric models and animations are of exceptional quality while some of them have been nominated for various national and international awards. Animation clips based on new software technology are available in the Department of Computer Science at Bath thorough their past projects (the recently completed EPSRC Quasi3D project is relevant here). Furthermore, if and when necessary we can utilise the Bradford-based Vicon motion capture system to further explore the suitability of the technique for this application by generating libraries of character animations.

5 Milestone 1: A research platform is built. Case studies encompassing a broad range of modelling and animation identified.

Stage 2: PDE-based shape parameterisation for efficient modelling and manipulation of complex geometry (duration 7 months) The essential aim of this part of the research is to develop PDE-based parametric models for defining a given geometry model. Thus, the aim here is to define the shape of a character using a small set of smoothly connected PDE surfaces. Building from the previous work (e.g. GR/M73125/01 on “The Optimal Design and Manufacture of Thin-Walled Structures” and Ugail and Wilson 2003), research will be directed to develop a generic parametric model for the geometry models so that changes in their shape can be carried out via a set of variables or parameters. Since the PDE surfaces are characterised by the boundaries or the character lines defining the shape, the design parameters can be built around them to ensure intuitive shape manipulation. A hierarchical approach for shape parameterisation will be adopted to capture both the large-scale and small-scale features of the geometry model in question.

One of the aims of this part of the research will be to look into ways by which the number of design parameters defining the complete shape of the virtual character can be kept as low as possible and yet to allow the designer the flexibility of changing the shape to bring about prominent variations in the shape and size of various parts of the geometry model.

Milestone 2: Efficient modelling and manipulation of complex geometry through PDE-based parametric approach achieved.

Stage 3: Development of techniques for Dense Shape Correspondence (duration 8 months) The aim here will be to develop a methodology based on shape parameterisation in order to map a given set of expressions from a source model onto a target model. Assuming we have two geometric models with a shared topological structure, we will require a set of correspondences between the two models to be determined. No assumption will be made about the polygon count and the connectivity structures between the models. This should find particular application in facial animation where it is common practice to create a new set of visemes as morph targets for a new character by manipulating the base model into a number of new, distorted versions. Reusing visemes by mapping the PDE parameters from a previous character will greatly accelerate this process whilst still allowing for alterations to the final shape.

At the initial stage of this part of the investigation we will manually identify areas of interest between the models in order to identify an initial set of parameters to map features between two given models. These initial investigations will provide us with future directions in order to choose an optimal number of PDE surface patches parameterised by the corresponding boundary curves. This will further enable us to provide an insight into the sort of shape parameters to be accommodated.

The next step at this stage would be to automate the process of dense surface correspondence. In order to do this we will investigate harmonic mapping techniques using the corresponding PDE boundary conditions between the source and the target model. These techniques will be further refined by means of using heuristic search techniques. For example, in the case of facial models one could use the tip of the nose, relative positions of the eye sockets, and position and size of the ears as possible heuristic search rules. The techniques developed here will be tested on case studies identified in Stage 1.

Milestone 3: Semi-automatic feature mapping procedures achieved. Automatic procedures for dense surface correspondence achieved.

Stage 4: Development of techniques for transferring animations (duration 9 months) The aim here will be to develop a methodology in order to successfully transfer the animations from a source model onto a target model. Following the work of the previous stage, given two geometric models, we will be in a position to automatically obtain the corresponding PDE models that are efficiently parameterised. Moreover, the two PDE models will have their parameters identified according the features that are to be mapped.

Work will be carried out in order to extend the previous static shape parameterisation so that time dependency can be introduced. The aim here is to recreate a wide variety of animations, identified in the case studies by means of

6 introducing time-dependent shape parameterisation into PDE models. If we consider again the previous example of facial animation, we can use the new visemes of the PDE model and then create animations based on these models, either by reusing existing animations from other models or by creating new animations from the visemes. Hence, we can now transfer the geometric deformations from particular models to new PDE-based models (achieved in stage 3) and copy the animation information that uses these.

In order to conduct this, a set of motion vectors will be identified in the source animation model. When the animation is based on deformation from the skeletal model, the PDE-based spine will be utilised to play the role of the skeleton. In the case of facial animations, some kind of muscle model is often then utilised to create animations. In this case we will look into the possibilities of using higher order PDEs, where the higher orders of the PDE will play the roles of muscles.

Milestone 4: Animation transfer system implemented where time-dependent geometric deformations from a given source model onto a target model can be successfully transferred.

Stage 5: Development of an intuitive demonstration environment (duration 2 months) The final stage of this research programme will centre around the creation of a user interface that will enable a designer to carry out typical modelling and animation in an intuitive fashion. The user interface will be a standalone environment independent of Maya and will be programmed using C++. The interface, at this stage, is not necessarily a software package but an environment, which will enable us to demonstrate the new technology to interested parties.

Milestone 5: An intuitive demonstration environment for modelling and animation achieved.

Relevance to Beneficiaries The beneficiaries of this research would be both academic and industrial workers. In particular, the computer graphics and digital media industry will benefit from this research.

The methodology and the algorithms that will result during the course of this research, after reaching sufficient maturity, will be implemented in the form of a standalone software package or a plug-in to an existing modelling and animation software such as Maya. Thus, the potential applications of this research are numerous. The techniques can be used anywhere that efficient modelling and animation are called for e.g. development of computer games, digital broadcast and 3D avatars. Moreover, the movie industry will benefit from this new technology. At present in computer animations and special effects especially for movie making there is a tremendous amount of manual work involved. With the proposed research, where both modelling and animation are combined into a single layer with efficient parameterisation, such efforts will be significantly reduced.

Dissemination and Exploitation The academic results of this research will be disseminated via relevant high quality peer-reviewed scientific journals and conference proceedings as well as by the maintenance of a web presence. Any resultant publication will be submitted to our respective research offices before publication to determine whether the content has value worthy of IP protection.

The results of this research will be highly relevant to industry. We will, therefore, seek opportunities to demonstrate the new technologies in relevant trade shows and fairs in order to attract potential industrial partners to exploit the work for commercial benefit.

Dr Ugail’s previous work on PDE surfaces has already received industrial attention through his recent presentations of some the work at SIGGRAPH 2004. As part of Yorkshire Forward’s sponsored event, Dr Ugail recently had the opportunity to present some of this work to senior executives of a number of high-profile companies including Alias/SGI, Discreet and Curious Labs. In particular, Curious Labs has expressed an interest in integrating some of our recent work in their geometry modelling software called Shade 3D, which has over 20,000 customers in Japan. We will exploit similar industrial opportunities for our current proposed research.

Project management and resources Each of the investigators brings specific expertise to the project. The work will be managed between the two sites accordingly, with the surface modelling being led by Bradford and the animation being led by Bath. However, there is sufficient overlap of skills to ensure progress without the need for constant reference to the other site.

7 Professor Willis has expertise in the use of novel techniques for the control, rendering and animation in both 2D and 3D. In addition he continues to work in 3D facial animation and has worked on NURBS surfaces/outlines for animation. In addition, there is extensive experience at writing robust, portable system software at Bath.

Dr Ugail has expertise in the practical applications of the PDE method, especially its applicability to shape parameterisation. Dr Palmer has expertise in 3D animation systems and the development of intelligent control methods for animation. In addition, there is extensive experience of Maya at Bradford.

We seek support for two research assistants (RAs) to work with the investigators to undertake the proposed research. The Bath RA will primarily need software and interface skills, coupled with animation experience. The Bradford RA will have to be a person with considerable mathematical and programming expertise. Therefore, we wish to seek two RAs with research and technical experience at post PhD level.

The main technical activities of the project will be carried out by the RAs and will be directed jointly by the investigators. At each site there will be weekly technical meetings between the RA and the relevant investigators. Besides email and telephone communications between the members from both sites, there will be formal meetings every 6 months among all the members of the research team and informal meetings as needed in between. Each formal meeting will consider progress against the Milestones and consider how to make the best of the forthcoming 6 months.

The project requires computing hardware resources that combine high performance 3D interactive graphics with substantial CPU power. Therefore, on the hardware side the requirement is for two fast desktop PCs, one for each site. The costs of travel to 4 overseas and 4 European conferences as well as the travel costs between Bath and Bradford have also been included.

References B. Allen, B. Curless and Z. Popović, The Space of Human Body Shapes: Reconstruction and Parameterization from Range Scans, ACM Transactions on Graphics, 22 (3) (2003) 587-594. A. Aubel, Anatomically-Based Human Body Deformations, Ph.D. Thesis No 2573, EPFL, May 2002. A. Aubel and D. Thalmann, Realistic Deformation of Human Body Shapes, Proceedings of Computer Animation and Simulation 2000, Interlaken, (2000) 125-135. M.I.G., Bloor, and M.J. Wilson, Using Partial Differential Equations to Generate Freeform Surfaces, Computer-Aided Design, 22 (1990) 202-212. G. Farin, Curves and Surfaces for CAGD: A Practical Guide, Morgan Kaufmann Publications, 2001. S. King, R. Parent, A Parametric Tongue Model for Animated Speech, In Computer Animation and Simulation 2000: Proceedings of the Eurographics Workshop, (2000) 3-13. J. Kundert-Gibbs and P. Lee, Maya Savvy, Sybex, (2003) 335-341. D. Lavender, Maya Manual, Springer-Verlag, (2003) 114-116. J. Lee and S. Y. Shin, A hierarchical approach to interactive motion editing for human like figures. In Proceedings of SIGGRAPH 1999, (1999) 39-48. A. Mohr and M. Gleicher, Building Efficient, Accurate Character Skins from Examples, ACM Transactions on Graphics, 22(3) (2003) 562-568. M. Simmons, J. Wilhelms and A. V. Gelder, Skinning: Model-Based Reconstruction for Creature Animation, In Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation, (2002) 139 -146. H. Seo, F. Cordier and N. Magnenat-Thalmann, Modeling and Animating Hands & Bodies: Synthesizing Animatable Body Models with Parameterized Shape Modifications, In Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, (2003) 120-125. K. Yamane, J. J. Kuffner and J. K. Hodgins, Data Driven Character Animation: Synthesizing Animations of Human Manipulation Tasks, ACM Transactions on Graphics, 23(3) (2004) 532-539. L You, J. J. Zhang and P. Comninos, Generating Blending Surfaces with a Pseudo-Lévy Series Solution to Fourth Order Partial Differential Equations, Computing, 71(4) (2003) 353-373.

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