Introduction 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 hardly be overcome using polygonal models only. For example, dramatic changes of the shape (involving change of topology) or metamorphosis between different shapes can not be performed easily. The Function Representation (FRep) [Pasko et al. 1995] allows us to overcome some of the problems and simplify the process of the 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 near-real or real time. It allows us to: produce animations involving dramatic changes of the shape (e.g. metamorphosis, viscoelastic behaviour, character modifications etc) in short times (Fig.) interactively create complex shapes with changing topology (Fig.) and specified level of detail (LOD) integrate existing animated polygonal models and FRep models within a single model Generate FRep model approximating the mesh. Either embedding or attaching FRep model to the mesh Synchronize skeletons for polygonal model and functional model Effects hardly achievable with pure polygonal models Automatic geometric LOD (can be tweaked depending on hardware) Scalability Easy integration into existing pipelines Large number of potential applications (new special effects, user generated content, SMTH ELSE etc) 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 polygonization can be seen in the editor window in near real- time. Each parameter can be animated over time thus providing the user with more flexibility to produce various effects. Task is easily parallelized (independent function evaluations). Mesh from scalar field can be extracted using simple polygonization algorithm. CUDA generates volume data and after polygonization fills the vertex buffer. DirectX or OpenGL with geometry shaders. Performance scales almost linearly with the num of processers, time coherence, skipping frames

Компактное представление Высокая вычислительная сложность Независимость от разрешения Вычисление модели в произвольной последовательности Ограниченный объем разделяемой и кэш памяти Большое число независимых АЛУ («аппаратных потоков») Постоянное улучшение технических характеристик Упрощение параллелизации Моделирование с помощью FRep Интерактивная визуализация FRep GPU