[Truncated abstract] Image transition effects are commonly used on television and human computer interfaces. The transition between images creates a perception of continuity which has aesthetic value in special effects and practical value in visualisation. The work in this thesis demonstrates that better image transition effects are obtained by incorporating properties of projective geometry into image transition algorithms. Current state-of-the-art techniques can be classified into two main categories namely shape interpolation and warp generation. Many shape interpolation algorithms aim to preserve rigidity but none preserve it with perspective effects. Most warp generation techniques focus on smoothness and lack the rigidity of perspective mapping. The affine transformation, a commonly used mapping between triangular patches, is rigid but not able to model perspective effects. Image transition techniques from the view interpolation community are effective in creating transitions with the correct perspective effect, however, those techniques usually require more feature points and algorithms of higher complexity. The motivation of this thesis is to enable different views of a planar surface to be interpolated with an appropriate perspective effect. The projective geometric relationship which produces the perspective effect can be specified by two quadrilaterals. This problem is equivalent to finding a perspectively appropriate interpolation for projective transformation matrices. I present two algorithms that enable smooth perspective transition between planar surfaces. The algorithms only require four point correspondences on two input images. ...The second algorithm generates transitions between shapes that lie on the same plane which exhibits a strong perspective effect. It recovers the perspective transformation which produces the perspective effect and constrains the transition so that the in-between shapes also lie on the same plane. For general image pairs with multiple quadrilateral patches, I present a novel algorithm that is transitionally symmetrical and exhibits good rigidity. The use of quadrilaterals, rather than triangles, allows an image to be represented by a small number of primitives. This algorithm uses a closed form force equilibrium scheme to correct the misalignment of the multiple transitional quadrilaterals. I also present an application for my quadrilateral interpolation algorithm in Seitz and Dyer's view morphing technique. This application automates and improves the calculation of the reprojection homography in the postwarping stage of their technique. Finally I unify different image transition research areas into a common framework, this enables analysis and comparison of the techniques and the quality of their results. I highlight that quantitative measures can greatly facilitate the comparisons among different techniques and present a quantitative measure based on epipolar geometry. This novel quantitative measure enables the quality of transitions between images of a scene from different viewpoints to be quantified by its estimated camera path.

Esta tesis investiga sobre el proceso de transformación de la forma arquitectónica, analizando una técnica específica denominada morphing. La técnica del morphing se utiliza en los gráficos por ordenador para la transformación de la forma entre dos o más objetos dados. Desde un punto de vista técnico, se revisan y actualizan las metodologías y aplicaciones existentes, sus características específicas y sus incidencias sobre la arquitectura. Desde un punto de vista práctico, se utilizan una serie de modelos de las casas Usonianas de Frank Lloyd Wright, con el fin de experimentar la técnica y ver qué utilidades se pueden obtener a partir de su lógica de diseño. Como resultado de este análisis se obtiene una metodología genérica para el procedimiento de un morphing arquitectónico. / This thesis investigates the transformation of architectural form, analyzing a specific technique called morphing. Morphing is a technique used in computer graphics to transform a form between two or more given objects. From a technical point of view, the existing techniques are reviewed and updated, as well as their specific characteristics and impact on architecture. From a practical point of view, some models of Usonian houses of Frank Lloyd Wright are used to experience the technique and see which utilities are available from his design logic. As a result of this analysis a generic methodology for the process of architectural morphing is obtained.

This thesis proposes an architecture of animation engine flexible enough to support large scale of animation algorithms with unified approach to each one of them. One of the major goals of the engine is to support creation of very complex animation seqences with high degree of animation execution control. The main animation technique used in the engine is skeletal animation and some variants of this technique are already implemented within, but it was never meant to be skeletal animation only engine and is designed that way.