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Yes / The complex formation of Islamic Geometric Patterns (IGP) is one of the distinctive features in Islamic art and architecture. Many have attempted to reproduce these patterns in digital form, using various pattern generation techniques, in 2D. Shape grammars are an e ective pattern generation method, providing good aesthetic results. In this pa- per we describe a novel approach in generating 3D IGP using the shape grammar method. The particular emphasis here is to generate the motifs (repeated units with the pattern) in 3D using parameterization. These can then be manipulated within the 3D space to construct architec- tural structures. In this work we have developed two distinctive Shape Grammars in 3D namely Parameterized Shape Grammar (PSG) and Auto-Parameterized Shape Grammar (APSG). Here the PSG generates the motifs and the APSG enables construction of the structures using the generated motifs. Both grammars are practically implemented as a 3D modelling tool within Autodesk Maya. The parameterization within each grammar is the key to generate both Islamic geometric motifs and Islamic geometric motif-based structures.

2023 / Topological properties are considered structural properties of objects because these properties are sustained under continuous deformations of objects. Topological invariance provides stability to representations across changes to objects and viewpoints and are therefore central to object representation. I examined the role of topological properties in the cognitive development of object representations in perception, working memory, and categorization. In Chapter 2, I examined the phenomenological perception of hole shape in 3-8-year-olds (N = 133) by exploiting sound-shape correspondence (bouba/kiki effect). I hypothesized that if children directly perceived hole shape, they would show the sound-shape correspondence effect for holes. As predicted, the study findings were that children showed congruency between object hole shapes and the nonsense labels “bouba” and “kiki” suggesting that children from 3 years of age assign the inner contour of an object with a hole to the hole and not the material surrounding the hole. In Chapter 3, I investigated whether topological properties are maintained similarly to surface features in working memory, and whether attention has a similar influence on the maintenance of these representations, in 24-30-month-old children (N = 43). I hypothesized that topological objects would be remembered better than surface features and that attention cues would support children’s encoding of both feature types. Contrary to the predictions, I found that children maintained topological representations on par with surface features, and attention did support encoding in children’s working memory. In Chapter 4, I examined whether 3-8-year-old children (N = 151) use topological properties to make inferences about objects’ categories using a name generalization task. I predicted that, if so, then topology should compete with or even supersede surface features (i.e., shape or color) as the target of children’s extension of novel nouns to novel objects. As predicted, I found that topological properties competed with both shape and color, suggesting a similar but distinct role for objects’ topological properties and objects’ surface features in children’s kind-based inferences. Taken together, these findings show the critical role of considering topological properties in addition to surface features in achieving a comprehensive understanding of the development of perception, working memory, and object categorization.

Presented is a model for predicting SMA-induced deformations in an unsymmetric cross ply laminate. A previously developed theory is used to predict the room-temperature shape of the cross-ply laminate by minimizing its total potential energy. Then, using the principle of virtual work, equations relating the shape of the laminate to a force applied on supports fastened to the laminate are derived. Induced strains and displacements are predicted as a function of the applied force. Experiments where the force is generated by known weights are conducted. Good correlations are established between the experimental results and the predictions. The developed theory is able to predict with good accuracy the shape, strains and, displacements of an unsymmetric cross-ply laminate to the force applied on the laminate. This theory is then used to develop a model relating the laminate response to forces produced by a SMA actuator, the actuator being a SMA wire. To describe the mechanics of the SMA actuator, constitutive equations derived by other researchers are used. These constitutive equations relate the temperature of the wire to forces generated in it. Experiments where a SMA wire is used as an actuator are conducted. These experiments consist of resistively heating a SMA wire attached to supports fastened to the laminate. During these experiments, laminate deformations are measured as a function of the applied voltage. Comparisons with the temperature-based constitutive model predictions are not made since the relation between the applied voltage and the SMA temperature is very difficult to establish. However, the experiments show that a SMA used in conjunction with cross-ply unsymmetric laminates can induce very large changes in the laminate shapes. Thus, the concept of using a SMA actuator to control the shape of cross-ply unsymmetric laminates is validated. / Master of Science

In this study, four different NiTi-based shape memory alloys (SMAs) compositions were processed, shape-set, and characterized to evaluate their effectiveness as SMA actuation component for satellite antennas. Three of the compositions were commercially available NiTi wires (90°C Flexinol® actuator NiTi wire and Confluent ADB SE508 NiTi wire), NiTi SM495 plates (ATI Specialty Alloys and Components) and the other composition was in house lab-produced NiTiCu plate. Different shape-setting techniques were performed such as pin and plate, fixtures and dies, and finally a sandwich fixture. The two most promising outcomes were the SE NiTi 508 wire and the NiTiCu plate. A SE NiTi 508 wire was first heat-treated at 550 °C for 3 hours and then it was shape-set at 450 °C for 30 min using a Cu tube which was previously deformed to the desired deployment curvature and fixed on a steel rig. The wire was kept inside the Cu tube during the shape-setting process to obtain the desired curvature. After shape-setting, the wire was thermally cycled multiple times. The results showed that the SE NiTi 508 wire was able to retain its deployment shape successfully after each thermal cycle. Furthermore, a NiTiCu plate was sandwiched between two steel sheets which were shaped into the desired full-deployment shape beforehand. The NiTiCu plate was shape-set at 450 °C for 30 min and then thermally cycled multiple times to test its effectiveness. The NiTiCu plate retained its full-deployment shape successfully after every thermal cycle.

In this thesis, we investigate the formulation, optimization and ambiguities in single-image 3D surface reconstruction from geometric and photometric constraints. We examine linear, discrete and quadratic constraints for shape from planar curves, shape from texture, and shape from shading. The problem of recovering 3D shape from the projection of planar curves on a surface is strongly motivated by perception studies. Applications include single-view modeling and uncalibrated structured light. When the curves intersect, the problem leads to a linear system for which a direct least-squares method is sensitive to noise. We derive a more stable solution and show examples where the same method produces plausible surfaces from the projection of parallel (non-intersecting) planar cross sections. The problem of reconstructing a smooth surface under constraints that have discrete ambiguities arise in areas such as shape from texture, shape from shading, photometric stereo and shape from defocus. While the problem is computationally hard, heuristics based on semidefinite programming may reveal the shape of the surface. Finally, we examine the shape from shading problem without boundary conditions as a polynomial system. This formulation allows, in generic cases, a complete solution for ideal polyhedral objects. For the general case we propose a semidefinite programming relaxation procedure, and an exact line search iterative procedure with a new smoothness term that favors folds at edges. We use this numerical technique to inspect shading ambiguities.

Cette thèse porte sur la reconnaissance et l’appariement de formes 3D pour des systèmes intelligents de vision par ordinateur. Elle décrit deux contributions principales à ce domaine. La première contribution est une implémentation d'un nouveau descripteur de formes construit à la base de la géométrie spectrale de l'opérateur de Laplace-Beltrami ; nous proposons une signature de point globale avancée (AGPS). Ce descripteur exploite la structure intrinsèque de l'objet et organise ses informations de manière efficace. De plus, AGPS est extrêmement compact puisque seulement quelques paires propres étaient nécessaires pour obtenir une description de forme précise. La seconde contribution est une amélioration de la signature du noyau d'onde ; nous proposons une signature du noyau d'onde optimisée (OWKS). La perfectionnement est avec un algorithme heuristique d'optimisation par essaim de particules modifié pour mieux rapprocher une requête aux autres formes appartenant à la même classe dans la base de données. L'approche proposée améliore de manière significative la capacité discriminante de la signature. Pour évaluer la performance de l'approche proposée pour la récupération de forme 3D non rigide, nous comparons le descripteur global d'une requête aux descripteurs globaux du reste des formes de l'ensemble de données en utilisant une mesure de dissimilarité et trouvons la forme la plus proche. Les résultats expérimentaux sur différentes bases de données de formes 3D standards démontrent l'efficacité des approches d'appariement et de récupération proposées par rapport aux autres méthodes de l'état de l'art. / This thesis concerns recognition and matching of 3D shapes for intelligent computer vision systems. It describes two main contributions to this domain. The first contribution is an implementation of a new shape descriptor built on the basis of the spectral geometry of the Laplace-Beltrami operator; we propose an Advanced Global Point Signature (AGPS). This descriptor exploits the intrinsic structure of the object and organizes its information in an efficient way. In addition, AGPS is extremely compact since only a few eigenpairs were necessary to obtain an accurate shape description. The second contribution is an improvement of the wave kernel signature; we propose an optimized wave kernel signature (OWKS). The refinement is with a modified particle swarm optimization heuristic algorithm to better match a query to other shapes belonging to the same class in the database. The proposed approach significantly improves the discriminant capacity of the signature. To assess the performance of the proposed approach for nonrigid 3D shape retrieval, we compare the global descriptor of a query to the global descriptors of the rest of shapes in the dataset using a dissimilarity measure and find the closest shape. Experimental results on different standard 3D shape benchmarks demonstrate the effectiveness of the proposed matching and retrieval approaches in comparison with other state-of-the-art methods.

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.