A morph between two drawings of the same graph can be thought of as a continuous deformation between the two given drawings. A morph is linear if every vertex moves along a straight line segment from its initial position to its final position. In this thesis we study algorithms for morphing, in which the morphs are given by sequences of linear morphing steps. In 1944, Cairns proved that it is possible to morph between any two planar drawings of a planar triangulation while preserving planarity during the morph. However this morph may require exponentially many steps. It was not until 2013 that Alamdari et al. proved that the morphing problem for planar triangulations can be solved using polynomially many steps. In 1990 it was shown by Schnyder that using special drawings that we call Schnyder drawings it is possible to draw a planar graph on a O(n)×O(n) grid, and moreover such drawings can be found in O(n) time (here n denotes the number of vertices of the graph). It still remains unknown whether there is an efficient algorithm for morphing in which all drawings are on a polynomially sized grid. In this thesis we give two different new solutions to the morphing problem for planar triangulations. Our first solution gives a strengthening of the result of Alamdari et al. where each step is a unidirectional morph. This also leads to a simpler proof of their result. Our second morphing algorithm finds a planar morph consisting of O(n²) steps between any two Schnyder drawings while remaining in an O(n)×O(n) grid. However, there are drawings of planar triangulations which are not Schnyder drawings, and for these drawings we show that a unidirectional morph consisting of O(n) steps that ends at a Schnyder drawing can be found. We conclude this work by showing that the basic steps from our morphs can be implemented using a Schnyder wood and weight shifts on the set of interior faces.

Over the last decade, advances in fluid simulation and rendering have helped animators synthesize photorealistic shots for movies that would have been virtually impossible to create by manually animating the liquid. Despite the advent of these computational methods, fluid simulation in movie production still involves a large degree of trial and error. In this dissertation, we propose a set of techniques for creating animations of liquids that meet desired artistic criteria without the customary tuning of numerous physical parameters. The basis for our work is the mesh-based representation of the liquid surface which lends itself to efficient algorithms that can control the output of simulations. First, we show how an animator can create animated characters and shapes that behave as if they were made of water using our mesh-based control method. Our approach allows for multiple levels of control over the simulation, ranging from the overall tracking of the desired shapes to highly detailed secondary effects. Next, we present a novel technique for interpolating between fluid simulations with free surfaces. We construct 4D spacetime meshes from animations and register them using a non-rigid ICP algorithm. By incorporating user input to align visually important regions, we can produce plausible animations that look like a blend of the two input sequences, all without re-simulating the fluid. We demonstrate how this could have applications in pre-visualization and video games.

Dissertação (mestrado)—Universidade de Brasília, Instituto de Psicologia, Departamento de Processos Psicológicos Básicos, Programa de Pós-Graduação em Ciências do Comportamento, 2016. / Submitted by Albânia Cézar de Melo (albania@bce.unb.br) on 2016-04-18T16:12:03Z No. of bitstreams: 1 2016_JulianaSilvaRochaAguiar.pdf: 884788 bytes, checksum: 5d540c6518298000167a09bcf3f4391e (MD5) / Approved for entry into archive by Raquel Viana(raquelviana@bce.unb.br) on 2016-04-27T20:32:42Z (GMT) No. of bitstreams: 1 2016_JulianaSilvaRochaAguiar.pdf: 884788 bytes, checksum: 5d540c6518298000167a09bcf3f4391e (MD5) / Made available in DSpace on 2016-04-27T20:32:42Z (GMT). No. of bitstreams: 1 2016_JulianaSilvaRochaAguiar.pdf: 884788 bytes, checksum: 5d540c6518298000167a09bcf3f4391e (MD5) / A capacidade de reconhecer emoções em faces é uma habilidade essencial à interação humana e fornece informações relevantes, ao permitir predizer comportamentos de outras pessoas. Tal aptidão está presente desde a infância e avança ao longo do desenvolvimento humano. Pesquisas que utilizam a técnica morphing com crianças sugerem haver variação da habilidade de reconhecer emoções em faces em continuum, com algumas necessitando de maior ou menor intensidade da expressão emocional para percebê-las. Portanto, o objetivo deste estudo consistiu em examinar o reconhecimento emocional em faces na infância, utilizando uma tarefa com variação da intensidade emocional, a fim de verificar se o nível de intensidade influencia seu desempenho. Participaram da pesquisa 28 crianças entre 7 e 11 anos, de ambos os sexos, do 1o ao 6o ano do Ensino Fundamental. Queixas comportamentais e QI foram critérios de exclusão. Naquelas selecionadas, foi aplicado um Teste de Reconhecimento de Emoções em Face Infantil, que apresentou 168 imagens manipuladas pela técnica morphing, contendo expressões das seis emoções básicas. Os resultados indicaram idade como tendência de crescimento sobre a probabilidade de acerto no julgamento da emoção avaliada. Bem como taxas mais altas de acerto diante da emoção de alegria, enquanto piores desempenhos perante faces de medo. O principal achado foi que a intensidade emocional previu a probabilidade de acertos, aumentando em 42% a chance de acerto a cada aumento de unidade da intensidade. Tais achados são relevantes porque corroboram que o reconhecimento de emoções em diferentes níveis pode ser mais sensível às diferenças individuais. _______________________________________________________________________________________________ ABSTRACT / The ability to recognize emotions in faces is an essential skill to human interaction. This recognition provides relevant information by allowing to predict behaviors of others. Such ability is present since childhood and continues to progress along the human development. Research using the morphing technique with children suggest a change in the ability to recognize emotions in faces on a continuum, and some require greater or lesser intensity to perceive it. Therefore, the aim of this study was to examine the emotional recognition in faces over childhood, using a task with range of emotional intensity to verify that the level of emotional intensity influences their performances. The participants were 28 children between 7 and 11 years of age, of both sexes, students from 1st to 6th grade of elementary school. Measures of IQ and behavioral complaints were used as exclusion criteria. In selected children, it was applied a Test of Facial Emotion Recognition for Children, which presented 168 images manipulated by the morphing technique, containing expressions of the six basic emotions. Results indicated age as a trend of growth over the likelihood of success. As well as higher rates of success on the emotion of happiness, while worst performances before faces of fear. The main finding was that the emotional intensity predicted the likelihood of participants’ successes, increasing by 42% the chance to increase at every unit in intensity. These results are important because they confirm that the recognition of emotions in different intensity may be more sensitive to differences among individuals.

An investigation into two distinct novel adaptive structures concepts is performed with a view to improving the aerodynamic efficiency of aircraft wings.The main focus of the work is on the development of a rotating spars concept that enables the adaptive aeroelastic shape control of aircraft wings in order to reduce drag. By altering the orientation of the internal wing structure, it becomes possible to control the flexural and torsional stiffnesses of the wing, as well as the position of the elastic axis. It follows then that control of the aeroelastic deformation is also possible. Consequently, the aerodynamic performance can be tailored, and more specifically the lift-to-drag ratio can be maximised through continuous adjustment of the structure.To gain a thorough understanding of the effect of the concept on a wing, an assumed modes static aeroelastic model is developed, and studies are performed using this. These studies establish guidelines with regards to the effective design of a wing incorporating the rotating spars concept. The findings of these studies are then used to establish a baseline design for a wind tunnel model. A finite element model of this is constructed and aeroelastic analyses are used to improve the model and arrive at the final experimental wing design. The wind tunnel tests confirm analytical trends and the robustness of an approach to automaticallyadapt the structure to maintain an aerodynamic performance objective.The remainder of the work investigates the application of an all-moving wing tip device with an adaptive torsional stiffness attachment as a passive loads alleviation system. Through consideration of the attachment stiffness and position, it is possible to tune the device throughout flight in order to minimise the loads that are introduced into the aircraft structure in response to a gust or manoeuvre. A dynamic aeroelastic wing model incorporating the device is developed and used to perform parameter studies; this gives an insight into the sizing and placement of the device. Next, a finite element representation of a conceptual High Altitude Long Endurance (HALE) aircraft is used as a baseline platform for the device. Aeroelastic analyses are performed for the baseline and modified models to investigate the effect of the attachment stiffness and position on the gust response and aeroelastic stability of the system. The reduced loading within thestructure of the modified aircraft then enables the model to be optimised in order to reduce the mass of the aircraft.

The research presented in this thesis examines the use of an estimated "actuator work" value as a performance parameter for the comparison of various aerodynamic control device configurations. This estimated "actuator work," or practical work as it will be referred to as in this thesis, is based on the aerodynamic and structural resistance to a control surface deflection. It is meant to represent the actuator energy cost required to deflect a general configuration of conventional or unconventional control surface. Thin airfoil theory is used to predict the aerodynamic load distribution required for this work calculation. The details of applying thin airfoil theory to many different types of control surface arrangements are presented. Convenient equations for the aerodynamic load distributions and aerodynamic coefficients are obtained. Using the developed practical work equations, and considering only the aerodynamic load component, the practical work required for a given change in lift is compared between different control surface arrangements. For single control surface cases, it is found that a quadratic (morphing) trailing edge flap requires less practical work than a linear flap of the same size. As the angle of attack at which the change in lift occurs increases, the benefit of the quadratic flap becomes greater. For multiple control surface cases, it is necessary to determine the set of control deflections that require the minimum practical work for a given change in lift. For small values of the initial angle of attack, it is found that a two-segment quadratic trailing edge flap (MTE) requires more work than a two-segment linear flap (TETAB). But, above a small value of angle of attack, the MTE case becomes superior to the TETAB case. Similar results are found when a 1-DOF static aeroelastic model is included in the calculation. The minimum work control deflections for the aeroelastic cases are shown to be strongly dependent on the dynamic pressure. / Master of Science

No / A methodology for shape morphing using partial differential equation (PDE) surfaces is presented in this work. The use of the PDE formulation shows how shape morphing can be based on a boundary-value approach by which intermediate shapes can be created. Furthermore, the mathematical properties of the method give rise to several alternatives in which morphing one shape into another can be achieved. Three of these alternatives are presented here. The first one is based on the gradual variation of the weighted sum of the boundary conditions for each surface, the second one consists of varying the Fourier mode for which the PDE is solved whilst the third results from a combination of the first two. Examples showing the efficiency of these methodologies are presented. Thus, it is shown that the PDE based approach for morphing, when combined with a parametric variation of the boundary conditions, is capable of obtaining smooth intermediate surfaces automatically.

The following work is directed towards an evaluation of aircraft that undergo structural shape change for the purpose of optimized flight and maneuvering control authority. Dynamical equations are derived for a morphing aircraft based on two primary representations; a general non-rigid model and a multi-rigid-body. A simplified model is then proposed by considering the altering structural portions to be composed of a small number of mass particles. The equations are then extended to consider atmospheric flight representations where the longitudinal and lateral equations are derived. Two aspects of morphing control are considered. The first is a regulation problem in which it is desired to maintain stability in the presence of large changes in both aerodynamic and inertial properties. From a baseline aircraft model various wing planform designs were constructed using Datcom to determine the required aerodynamic contributions. Based on nonlinear numerical evaluations adequate stabilization control was demonstrated using a robust linear control design. In maneuvering, divergent characteristics were observed at high structural transition rates. The second aspect considered is the use of structural changes for improved flight performance. A variable span aircraft is then considered in which asymmetric wing extension is used to effect the rolling moment. An evaluation of the variable span aircraft is performed in the context of bank-to-turn guidance in which an input-output control law is implemented. / Ph. D.

This thesis presents results of the application of energy-based large-scale optimization of a two-subsystem (propulsion subsystem (PS) and airframe subsystem-aerodynamics (AFS-A)) air-to-air fighter (AAF) with two types of AFS-A models: a fixed-wing AFS-A and a morphing-wing AFS-A. The AAF flies 19 mission segments of a supersonic fighter aircraft mission and the results of the study show that for very large structural weight penalties and fuel penalties applied to account for the morphing technology, the morphing-wing aircraft can significantly outperform a fixed-wing AAF counterpart in terms of fuel burned over the mission. The optimization drives the fixed-wing AAF wing-geometry design to be at its best flying the supersonic mission segment, while the morphing-wing AFS-A wing design is able to effectively adapt to different flight conditions, cruising at subsonic speeds much more efficiently than the fixed-wing AAF and, thus yielding significant fuel savings. Also presented in this thesis are partially optimized results of the application of a decomposition strategy for large-scale optimization applied to a nine-subsystem AAF consisting of a morphing-wing AFS-A, turbofan propulsion subsystem (PS), environmental controls subsystem (ECS), fuel loop subsystem (FLS), vapor compression/polyalphaolefin loop subsystem (VC/PAOS), electrical subsystem (ES), central hydraulics subsystem (CHS), oil loop subsystem (OLS), and flight controls subsystem (FCS). The decomposition strategy called Iterative Local-Global Optimization (ILGO) is incorporated into a new engineering aircraft simulation and optimization software called iSCRIPT™ which also incorporates the models developed as part of this thesis work for the nine-subsystem AAF. The AAF flies 21 mission segments of a supersonic fighter aircraft mission with a payload drop simulating a combat situation. The partially optimized results are extrapolated to a synthesis/design which is believed to be close to the system-level optimum using previously published results of the application of ILGO to a five-subsystem AAF to which the partially optimized results of the nine-subsystem AAF compare relatively well. In addition to the optimization results, a parametric study of the morphing AFS-A geometry is conducted. Three mission segments are studied: subsonic climb, subsonic cruise, and supersonic cruise. Four wing geometry parameters are studied: leading-edge wing sweep angle, wing aspect ratio, wing thickness-to-chord ratio, and wing taper ratio. The partially optimized AAF is used as the baseline, and the values for these geometric parameters are increased or decreased up to 20% relative to an established baseline to see the effect, if any, on AAF fuel consumption for these mission segments. The only significant effects seen in any of the mission segments arise from changes in the leading-edge sweep angle and wing aspect ratio. The wing thickness-to-chord ratio shows some effect during the subsonic climb segment, but otherwise shows no effect along with the taper ratio in any of the three mission segments studied. It should be emphasized, however, that these changes are made about a point (i.e. synthesis/design), which is already optimal or nearly so. Thus, the conclusions drawn cannot be generalized to syntheses/designs, which may be far from optimal. Also note that the results upon which these conclusions are based may very likely highlight a weakness in the conceptual-level drag-buildup method used in this thesis work. Further optimization studies using this drag-buildup method may warrant setting the thickness-to-chord ratios and taper ratios rather than having them participate in the optimization as degrees of freedom (DOF). The final set of results is a parametric study conducted to highlight the correlation between the fuel consumption and the total exergy destruction in the AFS-A. The results for the subsonic cruise and supersonic cruise mission segments show that at least for the case when the AFS-A is optimized by itself for a fixed specific fuel consumption that there is a direct correlation between the fuel burned and total exergy destruction. However, as shown in earlier work where a three-subsystem AAF with AFS-A, PS, and ECS is optimized, this may not always be the case. Furthermore, based on the results presented in this thesis, there is a smoothing effect observed in the exergy response curves compared to the fuel-burned response curves to changes in AFS-A geometry. This indicates that the exergy destruction is slightly less sensitive to such changes. / Master of Science

The research presented in this thesis investigates the mechanical properties of candidate materials that could be used as a skin for a morphing wing. A morphing wing is defined as a wing that changes shape. Although engineers have been designing different morphing wing configurations, there has been limited research investigating materials that could be used as a skin for a morphing wing. Specifically, after investigating the different morphing wing abilities engineers at Virginia Tech are designing, criteria were determined for candidate materials. A suitable skin material for a morphing wing will have to be elastic, flexible, have high recovery, resistant to different weather conditions, resistant to abrasions and chemicals, and have a hardness number high enough to handle the aerodynamic loads of the aircraft while in flight. Using some of the preceding criteria, different materials were selected that are readily available in the commercial market. The materials tested were a type of thermoplastic polyurethanes, copolyester elastomer, shape memory polymer, or woven materials that are made out of elastane yarns. The first study determined the required forces to strain the material in a uniaxial direction. A test stand was designed with a gripping device to hold the material. By grounding one side of the material, the other side of the material was pulled using a winch. Using a force transducer and a string potentiometer the required forces and the amount the material was strained was recorded, respectively. Utilizing the same test stand, the amount the material recovered was also acquired. Also, by measuring how much the material necked the elongation ratio was calculated. The final test determined if the forces "relaxed" after being strained to a stationary position. It was found that each material performed differently, but some materials were definitely better suited for morphing wing material. The materials that were made out of thermoplastic polyurethanes, copolyester elastomer, and shape memory polymer required less force and were able to strain more, when compared to the woven materials. The second study determined if the material could be strained in a biaxial direction. The reason for this was for a better understand how the material would perform if the material was strained to an extreme condition. A test stand was designed using the same principles and components as the uniaxial test stand. The only difference was additional sensors were required to measure the force and strain along the other axis. Although a recovery analysis was warranted for the biaxial experiments, most of the materials test failed while being strained a small amount. Also, the material strained a lot less before ripping, when compared to the straining capabilities when only being strained in the uniaxial direction. After conducting the experiments, the results were similar to the uniaxial experimental results. In terms of required forces to strain the material, the thermoplastic polyurethanes and the copolyester elastomer required less force, when compared to the woven materials. The only advantage of the woven materials was they did not break. The final study determined how much the material deflected while being subjected to a pressure load before breaking. The test stand used an air compressor to supply a pressure load to the material, while a laser vibrometer measured how much the material deflected. A regulator was used to control the amount of pressure that was applied to the material. As the pressure load was increased, the material deflected more. The test stand also determined the maximum sustained pressure load the material could handle before breaking. After conducting all the experiments and analyzing the data, it was found woven materials are not suitable as a skin material. The reason air is allowed to pass through the woven material. Therefore, woven materials could not sustain the aerodynamic loads of an aircraft while in flight. The rest of the materials performed differently. Specifically if the material strained well and required less force while conducting the uniaxial and biaxial experiments, those materials could not sustain a high pressure load. Yet, the materials that did not strain well and required more force were able to handle a larger sustained pressure load. / Master of Science

This thesis work presents detailed results of the application of energy- and exergy-based methods to the integrated synthesis/design of an Air-to-Air Fighter (AAF) aircraft with and without wing-morphing capability. In particular, a morphing-wing AAF is compared to a traditional fixed-wing AAF by applying large-scale optimization using exergy- and energy-based objective functions to the synthesis/design and operation of the AAF which consists of an Airframe Subsystem (AFS-A) and Propulsion Subsystem (PS). A number of key synthesis/design and operational decision variables are identified which govern the performance of the AFS-A and PS during flight, and detailed models of the components of each of the subsystems are developed. Rates of exergy destruction and exergy loss resulting from irreversible loss mechanisms are determined in each of the AAF vehicle subsystems and their respective components. Multiple optimizations are performed on both types of AAF for a typical fighter aircraft mission consisting of 22 segments. Four different objective functions are used in order to compare exergy-based performance measures to the more traditional energy-based ones. The results show that the morphing-wing AAF syntheses/designs outperform those for the fixed-wing aircraft in terms of exergy destroyed/lost and fuel consumed. These results also show that the exergy-based objectives not only produce the "best" of the optimal syntheses/designs for both types of AAF in terms of exergy destroyed/lost and fuel consumed but as well provide details of where in each subsystem/component and how much specifically each source of irreversibility contributes to the optimal syntheses/designs found. This is not directly possible with an energy-based approach. Finally, after completion of the synthesis/design optimizations, a parametric study is performed to explore the effect on morphing-wing effectiveness of changing the weight and energy penalties used to model the actuations required for morphing. The results show that the morphing-wing AAF exhibits significant benefits over the fixed-wing aircraft even for unrealistic weight and energy penalties. / Master of Science