In recent years, multiresolution models have progressed substantially. At the beginning, discrete models were employed in graphics applications, due mainly to the low degree of complexity involved in implementing them, which is the reason why nowadays they are still used in applications without high graphics requirements. Nevertheless, the increase in realism in graphics applications makes it necessary to use multiresolution models which are more exact in their approximations, which do not call for high storage costs and which are faster in visualization. This has given way to continuous models, where two consecutive levels of detail only differ by a few polygons and where, additionally, the duplication of information is avoided to a considerable extent, thus improving on the spatial cost offered by most discrete models.Advances have been made in the use of new graphics primitives which minimize the data transfer between the CPU and the GPU, apart from trying to make use of the connectivity information given by a polygonal mesh. For this purpose, graphics primitives with implicit connectivity, such as triangle strips and triangle fans, have been developed. Many continuous models based on this type of primitives have been recently developed. In these last few years, graphics hardware performance has evolved outstandingly, giving rise to new techniques which allow the continuous models to accelerate even more. In this work, we have improved the interactive render of polygonal meshes. To tackle the problem, we firstly studied fundamental techniques to efficiently render polygonal meshes and we later made use of geometry simplification and level of detail techniques. Thus, we defined a multiresolution model that represents a polygonal mesh at any given resolution. This approach is able to manage continuous level-of-detail by smoothly adapting mesh resolution to the application requirements. Moreover, the model was modified to take the maximum advantage of the recent GPU features. We also created a modified version of the model for being used in deforming meshes. Finally, we developed an independent library to integrate our model in real-time applications.

It is believed that structures and actuation systems should be tightly integrated together in the future to create fast moving, efficient, lightweight dynamic machines. Such actuated structures could be used for morphing aircraft wings, lightweight actuated space structures, or in robotics. This requires actuators to be distributed through the structure. A tensegrity structure is a very promising candidate for this future integration due to its potentially excellent stiffness and strength-to-weight ratio, and the inherent advantage of being a multi-element structure into which actuators can be embedded. Development of these machines will utilise expertise in several fields, involving kinematics, dynamics, actuation and multi-axis motion control. The research presented in this thesis concerns the study of multi-axis actuated tensegrity structures. A form-finding method has been developed to find stable geometries and determine stiffness properties of the type of tensegrity structure proposed. It has been shown that a tensegrity structure, with practical nodes of finite size, can be designed with actuated members to give shape-changing properties while potentially allowing a good stiffness to mass ratio. An antagonistic multi-axis control scheme has been developed for the tensegrity structure. The describing function technique has been used to analyse the dead band controller in the control scheme, giving a stability criterion. An experimental actuated tensegrity system has been designed and built incorporating pneumatic muscles controlled by switching valves. Mathematical models for the experimental actuated tensegrity system have been developed in detail, including the pneumatic actuation system and the structure geometry. The dynamic behaviour of the tensegrity system has been investigated via several simulation studies, using the developed models and the proposed control scheme. Experimental validation has been successfully conducted. The multi-axis control scheme can accurately control the tensegrity structure to achieve shape changes while maintaining a desired level of internal pre-load. The mathematical models can be used as a basis for further development.