Providing destruction in games is usually achieved by having pre-calculated fracturingpoints, swapping models at appropriate times while hiding the crimes witha puff of smoke or an explosion. An area of continued research is procedural destructionwhere an object will fracture in a realistic way depending on appliedforces such as gravity, explosions or load. This thesis proposes and begins the implementation for a triangle based surfacerepresentation capable of supporting procedural destruction in real-time for anunderlying point-based simulation; deriving the methodology from the paper byM. Pauly et al [12]. Too wide project scoping prevented the implementation from fully realising theinitial goals; where the surface and physics simulations was never married intoa single simulation. It is one half of a larger project on procedural destruction,focusing primarily on the surface representation where the second half is detailedin the report by C. Stegmayr [14]. Even without a complete simulation, performance is an evidently limiting factor.For more detailed simulations, with a simple test mesh and a small step size whenpropagating a fracture, frame times quickly raise up to almost 247 ms/frame.There are multiple areas of improvement for the implementation to reduce frametimes; however, scalability and performance are still major points of concern dueto inherent challenges with running multiple fractures in parallel. Unless scalingcan be improved, it is worth pursuing alternative approaches.

This paper reports progress toward the development of a representation of significant surface changes in dense depth maps. We call the representation the Surface Primal Sketch by analogy with representation of intensity changes, image structure, and changes in curvature of planar curves. We describe an implemented program that detects, localizes, and symbolically describes: steps, where the surface height function is discontinuous; roofs, where the surface is continuous but the surface normal is discontinuous; smooth joins, where the surface normal is continuous but a principle curvature is discontinuous and changes sign; and shoulders, which consists of two roofs and correspond to a step viewed obliquely. We illustrate the performance of the program on range maps of objects of varying complexity.

The problems under consideration center around the interpretation of binocular stereo disparity. In particular, the goal is to establish a set of mappings from stereo disparity to corresponding three-dimensional scene geometry. An analysis has been developed that shows how disparity information can be interpreted in terms of three-dimensional scene properties, such as surface depth, discontinuities, and orientation. These theoretical developments have been embodied in a set of computer algorithms for the recovery of scene geometry from input stereo disparity. The results of applying these algorithms to several disparity maps are presented. Comparisons are made to the interpretation of stereo disparity by biological systems.

The Reproducing Kernel Element Method (RKEM) is a hybrid between finite elements and meshfree methods that provides shape functions of arbitrary order and continuity yet retains the Kronecker-delta property. To achieve these properties, the underlying mesh must meet certain regularity constraints, unique to RKEM. The aim of this dissertation is to develop a precise definition of these constraints, and a general algorithm for assessing a mesh is developed. This check is a critical step in the use of RKEM in any application. The general checking algorithm is made more specific to apply to two-dimensional triangular meshes with circular supports and to three-dimensional tetrahedral meshes with spherical supports. The checking algorithm features the output of the uncovered regions that are used to develop a mesh-mending technique for fixing offending meshes. The specific check is used in conjunction with standard quality meshing techniques to produce meshes suitable for use with RKEM. The RKEM quasi-uniformity definitions enable the use of RKEM in solving Galerkin weak forms as well as in general interpolation applications, such as the representation of geometries. A procedure for determining a RKEM representation of discrete point sets is presented with results for surfaces in three-dimensions. This capability is important to the analysis of geometries such as patient-specific organs or other biological objects.

Este trabalho consiste em introduzir uma nova abordagem de representação de superfície no ambiente de simulação Freeflow2D. Consiste em usar Partição da Unidade Implícita para estimar da superfície a geometria, normais e curvatura. Procurando se valer das vantagens de métodos do tipo meshless (sem malha) conservando no entanto a malha Lagrangiana, no interesse de manter o fácil acesso de vizinhança, inserção e eliminação de pontos / The objective of this work is to introduce a new approache of surface representation within the Freeflow system. It consists of using implicit functions by means of Partition of Unit Implicit to estimate surface geometry, normals and curvature. Aiming at the advantages of meshless methods of surface representation whilst keeping the Lagrangian mesh in order to preserve ease of access of geometric vicinity, particle insertion and removal

On compact Riemann surfaces, the Laplacian $\Delta$ has a discrete, non-negative spectrum of eigenvalues $\{\lambda_{i}\}$ of finite multiplicity. The spectrum is intrinsically linked to the geometry of the surface. In this work, we consider surfaces of constant negative curvature with a large symmetry group. It is not possible to explicitly calculate the eigenvalues for surfaces in this class, so we combine group theoretic and analytical methods to derive results about the spectrum. In particular, we focus on the Bolza surface and the Klein quartic. These have the highest order symmetry groups among compact Riemann surfaces of genera 2 and 3 respectively. The full automorphism group of the Bolza surface is isomorphic to $\mathrm{GL}_{2}(\mathbb{Z}_{3})\rtimes\mathbb{Z}_{2}. We analyze the irreducible representations of this group and prove that the multiplicity of $\lambda_{1}$ is 3, building on the work of Jenni, and identify the irreducible representation that corresponds to this eigenspace. This proof relies on a certain conjecture, for which we give substantial numerical evidence and a hopeful method for proving. We go on to show that $\lambda_{2}$ has multiplicity 4.

The low-level interpretation of images provides constraints on 3D surface shape at multiple resolutions, but typically only at scattered locations over the visual field. Subsequent visual processing can be facilitated substantially if the scattered shape constraints are immediately transformed into visible-surface representations that unambiguously specify surface shape at every image point. The required transformation is shown to lead to an ill-posed surface reconstruction problem. A well-posed variational principle formulation is obtained by invoking 'controlled continuity,' a physically nonrestrictive (generic) assumption about surfaces which is nonetheless strong enough to guarantee unique solutions. The variational principle, which admits an appealing physical interpretation, is locally discretized by applying the finite element method to a piecewise, finite element representation of surfaces. This forms the mathematical basis of a unified and general framework for computing visible-surface representations. The computational framework unifies formal solutions to the key problems of (i) integrating multiscale constraints on surface depth and orientation from multiple visual sources, (ii) interpolating these scattered constraints into dense, piecewise smooth surfaces, (iii) discovering surface depth and orientation discontinuities and allowing them to restrict interpolation appropriately, and (iv) overcoming the immense computational burden of fine resolution surface reconstruction. An efficient surface reconstruction algorithm is developed. It exploits multiresolution hierarchies of cooperative relaxation processes and is suitable for implementation on massively parallel networks of simple, locally interconnected processors. The algorithm is evaluated empirically in a diversity of applications.

Este trabalho consiste em introduzir uma nova abordagem de representação de superfície no ambiente de simulação Freeflow2D. Consiste em usar Partição da Unidade Implícita para estimar da superfície a geometria, normais e curvatura. Procurando se valer das vantagens de métodos do tipo meshless (sem malha) conservando no entanto a malha Lagrangiana, no interesse de manter o fácil acesso de vizinhança, inserção e eliminação de pontos / The objective of this work is to introduce a new approache of surface representation within the Freeflow system. It consists of using implicit functions by means of Partition of Unit Implicit to estimate surface geometry, normals and curvature. Aiming at the advantages of meshless methods of surface representation whilst keeping the Lagrangian mesh in order to preserve ease of access of geometric vicinity, particle insertion and removal

Yes / In this work we propose a talking head system for animating facial expressions using a template face generated from Partial Differen- tial Equations (PDEs). It uses a set of preconfigured curves to calculate an internal template surface face. This surface is then used to associate various facial features with a given 3D face object. Motion retargeting is then used to transfer the deformations in these areas from the template to the target object. The procedure is continued until all the expressions in the database are calculated and transferred to the target 3D human face object. Additionally the system interacts with the user using an artificial intelligence (AI) chatterbot to generate response from a given text. Speech and facial animation are synchronized using the Microsoft Speech API, where the response from the AI bot is converted to speech.

yes / Detailed design of pharmaceutical tablets is essential nowadays in order to produce robust tablets with tailor-made properties. Compressibility and compactibility are the main compaction properties involved in the design and development of solid dosage forms. The data obtained from measured forces and displacements of the punch are normally analysed using the Heckel model to assess the mechanical behaviour of pharmaceutical powders. In this paper, we present a technique for shape modelling of pharmaceutical tablets based on the PDE method. We extended the formulation of the PDE method to a higher dimensional space in order to generate a solid tablet and a cuboid mesh is created to represent the tablet’s components. We also modelled the displacement components of a compressed PDE-based representation of a tablet by utilising the solution of the axisymmetric boundary value problem for a finite cylinder subject to a uniform axial load. The experimental data and the results obtained from the developed model are shown in Heckel plots and a good agreement is found between both. / Available in full text since 5th Feb 2013 following the publisher's embargo period.