Approach Outline Polygonal-Functional Hybrids for Computer Animation and Games The modern world of computer graphics is mostly dominated by polygonal models. Due to their scalability and ease of rendering such models have various applications in a wide range of fields. Unfortunately some shape modelling and animation problems can not easily be resolved using polygonal models alone. For example, dramatic changes of the shape (involving changes of its topology) or metamorphosis between different shapes can not easily be performed. The Function Representation (FRep) [Pasko95] allows us to overcome some of these problems and simplify the process of major model modification. Our system is based on a hybrid modelling concept, where polygonal and FRep models are combined together and can be evaluated in real time or near real time [Kravtsov08]. This system allows us to: produce animations involving dramatic changes of a shape (e.g. metamorphosis, mimicking viscoelastic behaviour, character modifications etc) in short time intervals integrate existing animated polygonal models and FRep models within a single model interactively create complex shapes with changing topology and/or specified level of detail (LOD) Abstract NCCA The National Centre for Computer Animation, UK D. Kravtsov*, O. Fryazinov, V. Adzhiev, A. Pasko and P. Comninos bmth.ac.uk We use convolution surfaces [Sherstyuk99] to approximate an animated mesh. Such implicit surfaces can easily be manipulated using an underlying lower dimensional skeleton and can be blended with each other smoothly. Resulting surface can be blended with any FRep object using blending union [Pasko95]. Related Work Update skeleton Evaluate scalar field produced by the skeleton Evaluate scalar field produced by the “object” Combine scalar fields Extract polygons from combined scalar field Deform polygonal model Combine models Update parameters Implementation We have implemented the proposed approach as a plug-in for Maya™. Our plug-in requires the user to specify both the skeletons and polygonal meshes, which are used to calculate the initial parameters of all the skeletal primitives of the convolution surface. Intermediate results of the implicit surface polygonisation can be seen in the editor window in near real-time. Each parameter can be animated over time B. Synchronise skeletons for the polygonal and functional models Maya™ plug-in CPU implementation Performance scales almost linearly with the number of processors/cores. Additional optimisation techniques can be used to accelerate model evaluation: - employing time coherence (avoiding unnecessary evaluations outside regions of interest) - skipping surface extraction between certain frames - using faster function approximation A. Generate an FRep model approximating the mesh, either “embedding” or “attaching” the FRep model to the mesh GPU implementation The task can easily be parallelised due to independent function evaluations in the volume. Function evaluation, mesh extraction and rendering were performed entirely on the GPU. Current implementation is based on CUDA. Our technique can be implemented using DirectX or OpenGL, provided that geometry shaders are available. Skeleton Mesh Embedding Attachment 1. Initialisation step 2. Process Effects that are hard to achieve with purely polygonal models Automatic geometric LOD due to resolution independence of the FRep model Scalability Simplified point membership classification and collision detection Easy integration into existing pipelines with intuitive control Large number of potential applications (user generated content, new special effects, advanced interactions with environment etc) Advantages Embedding Attachment approximation [Kravtsov08] Kravtsov, D., Fryazinov, O., Adzhiev, V., Pasko, A., Comninos, P., “Embedded Implicit Stand-ins for Animated Meshes: a Case of Hybrid Modelling”. Technical report. The National Centre for Computer Animation, Bournemouth University, UK, 2008 [Pasko95] Pasko, A., Adzhiev, V., Sourin, A., Savchenko, V., "Function representation in geometric modeling: concepts, implementation and applications", The Visual Computer, vol.11, No.8, 1995, pp [Sherstyuk99] McCormack, J., Sherstyuk, A. “Creating and Rendering Convolution Surfaces”, Computer Graphics Forum”17 (2), 1998, pp s References Results thus providing the user with more flexibility to produce various effects. No blending Blending union with varying parameters “Andy” model is courtesy of John Doublestein

Skeleton Mesh EmbeddingAttachment approximation