Embedded Implicit Stand-ins for Animated Meshes: a Case of Hybrid Modelling

In this paper we address shape modelling problems, encountered in computer animation and computer games development that are difficult to solve just using polygonal meshes. Our approach is based on a hybrid modelling concept that combines polygonal meshes with implicit surfaces. A hybrid model consists of an animated polygonal mesh and an approximation of this mesh by a convolution surface stand-in that is embedded within it or is attached to it. The motions of both objects are synchronised using a rigging skeleton. This approach is used to model the interaction between an animated mesh object and a viscoelastic substance, normally modelled in implicit form. The adhesive behaviour of the viscous object is modelled using geometric blending operations on the corresponding implicit surfaces. Another application of this approach is the creation of metamorphosing implicit surface parts that are attached to an animated mesh. A prototype implementation of the proposed approach and several examples of modelling and animation with near real-time preview times are presented

Curve Skeleton and Moments of Area Supported Beam Parametrization in Multi-Objective Compliance Structural Optimization

This work addresses the end-to-end virtual automation of structural optimization up to the derivation of a parametric geometry model that can be used for application areas such as additive manufacturing or the verification of the structural optimization result with the finite element method. A holistic design in structural optimization can be achieved with the weighted sum method, which can be automatically parameterized with curve skeletonization and cross-section regression to virtually verify the result and control the local size for additive manufacturing. is investigated in general. In this paper, a holistic design is understood as a design that considers various compliances as an objective function. This parameterization uses the automated determination of beam parameters by so-called curve skeletonization with subsequent cross-section shape parameter estimation based on moments of area, especially for multi-objective optimized shapes. An essential contribution is the linking of the parameterization with the results of the structural optimization, e.g., to include properties such as boundary conditions, load conditions, sensitivities or even density variables in the curve skeleton parameterization. The parameterization focuses on guiding the skeletonization based on the information provided by the optimization and the finite element model. In addition, the cross-section detection considers circular, elliptical, and tensor product spline cross-sections that can be applied to various shape descriptors such as convolutional surfaces, subdivision surfaces, or constructive solid geometry. The shape parameters of these cross-sections are estimated using stiffness distributions, moments of area of 2D images, and convolutional neural networks with a tailored loss function to moments of area. Each final geometry is designed by extruding the cross-section along the appropriate curve segment of the beam and joining it to other beams by using only unification operations. The focus of multi-objective structural optimization considering 1D, 2D and 3D elements is on cases that can be modeled using equations by the Poisson equation and linear elasticity. This enables the development of designs in application areas such as thermal conduction, electrostatics, magnetostatics, potential flow, linear elasticity and diffusion, which can be optimized in combination or individually. Due to the simplicity of the cases defined by the Poisson equation, no experts are required, so that many conceptual designs can be generated and reconstructed by ordinary users with little effort. Specifically for 1D elements, a element stiffness matrices for tensor product spline cross-sections are derived, which can be used to optimize a variety of lattice structures and automatically convert them into free-form surfaces. For 2D elements, non-local trigonometric interpolation functions are used, which should significantly increase interpretability of the density distribution. To further improve the optimization, a parameter-free mesh deformation is embedded so that the compliances can be further reduced by locally shifting the node positions. Finally, the proposed end-to-end optimization and parameterization is applied to verify a linear elasto-static optimization result for and to satisfy local size constraint for the manufacturing with selective laser melting of a heat transfer optimization result for a heat sink of a CPU. For the elasto-static case, the parameterization is adjusted until a certain criterion (displacement) is satisfied, while for the heat transfer case, the manufacturing constraints are satisfied by automatically changing the local size with the proposed parameterization. This heat sink is then manufactured without manual adjustment and experimentally validated to limit the temperature of a CPU to a certain level.:TABLE OF CONTENT III I LIST OF ABBREVIATIONS V II LIST OF SYMBOLS V III LIST OF FIGURES XIII IV LIST OF TABLES XVIII 1. INTRODUCTION 1 1.1 RESEARCH DESIGN AND MOTIVATION 6 1.2 RESEARCH THESES AND CHAPTER OVERVIEW 9 2. PRELIMINARIES OF TOPOLOGY OPTIMIZATION 12 2.1 MATERIAL INTERPOLATION 16 2.2 TOPOLOGY OPTIMIZATION WITH PARAMETER-FREE SHAPE OPTIMIZATION 17 2.3 MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION WITH THE WEIGHTED SUM METHOD 18 3. SIMULTANEOUS SIZE, TOPOLOGY AND PARAMETER-FREE SHAPE OPTIMIZATION OF WIREFRAMES WITH B-SPLINE CROSS-SECTIONS 21 3.1 FUNDAMENTALS IN WIREFRAME OPTIMIZATION 22 3.2 SIZE AND TOPOLOGY OPTIMIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 27 3.3 PARAMETER-FREE SHAPE OPTIMIZATION EMBEDDED IN SIZE OPTIMIZATION 32 3.4 WEIGHTED SUM SIZE AND TOPOLOGY OPTIMIZATION 36 3.5 CROSS-SECTION COMPARISON 39 4. NON-LOCAL TRIGONOMETRIC INTERPOLATION IN TOPOLOGY OPTIMIZATION 41 4.1 FUNDAMENTALS IN MATERIAL INTERPOLATIONS 43 4.2 NON-LOCAL TRIGONOMETRIC SHAPE FUNCTIONS 45 4.3 NON-LOCAL PARAMETER-FREE SHAPE OPTIMIZATION WITH TRIGONOMETRIC SHAPE FUNCTIONS 49 4.4 NON-LOCAL AND PARAMETER-FREE MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION 54 5. FUNDAMENTALS IN SKELETON GUIDED SHAPE PARAMETRIZATION IN TOPOLOGY OPTIMIZATION 58 5.1 SKELETONIZATION IN TOPOLOGY OPTIMIZATION 61 5.2 CROSS-SECTION RECOGNITION FOR IMAGES 66 5.3 SUBDIVISION SURFACES 67 5.4 CONVOLUTIONAL SURFACES WITH META BALL KERNEL 71 5.5 CONSTRUCTIVE SOLID GEOMETRY 73 6. CURVE SKELETON GUIDED BEAM PARAMETRIZATION OF TOPOLOGY OPTIMIZATION RESULTS 75 6.1 FUNDAMENTALS IN SKELETON SUPPORTED RECONSTRUCTION 76 6.2 SUBDIVISION SURFACE PARAMETRIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 78 6.3 CURVE SKELETONIZATION TAILORED TO TOPOLOGY OPTIMIZATION WITH PRE-PROCESSING 82 6.4 SURFACE RECONSTRUCTION USING LOCAL STIFFNESS DISTRIBUTION 86 7. CROSS-SECTION SHAPE PARAMETRIZATION FOR PERIODIC B-SPLINES 96 7.1 PRELIMINARIES IN B-SPLINE CONTROL GRID ESTIMATION 97 7.2 CROSS-SECTION EXTRACTION OF 2D IMAGES 101 7.3 TENSOR SPLINE PARAMETRIZATION WITH MOMENTS OF AREA 105 7.4 B-SPLINE PARAMETRIZATION WITH MOMENTS OF AREA GUIDED CONVOLUTIONAL NEURAL NETWORK 110 8. FULLY AUTOMATED COMPLIANCE OPTIMIZATION AND CURVE-SKELETON PARAMETRIZATION FOR A CPU HEAT SINK WITH SIZE CONTROL FOR SLM 115 8.1 AUTOMATED 1D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINED SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 118 8.2 AUTOMATED 2D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINT SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 120 8.3 USING THE HEAT SINK PROTOTYPES COOLING A CPU 123 9. CONCLUSION 127 10. OUTLOOK 131 LITERATURE 133 APPENDIX 147 A PREVIOUS STUDIES 147 B CROSS-SECTION PROPERTIES 149 C CASE STUDIES FOR THE CROSS-SECTION PARAMETRIZATION 155 D EXPERIMENTAL SETUP 15

Digital reconstruction of a ceratopsid pes

A complete and fully articulated right pes of a centrosaurine ceratopsid from the Dinossaur Park Formation of Alberta, Canada provides important information regarding the structure and function of the pelvic limb in this group. A reconstructed centrosaurine foot with all data coming directly from actual specimens could be accurately modeled in three-dimensional morphospace and provide the basis of a digital atlas of the elements

Coarse-to-fine skeleton extraction for high resolution 3D meshes

This paper presents a novel algorithm for medial surfaces extraction that is based on the density-corrected Hamiltonian analysis of Torsello and Hancock [1]. In order to cope with the exponential growth of the number of voxels, we compute a first coarse discretization of the mesh which is iteratively refined until a desired resolution is achieved. The refinement criterion relies on the analysis of the momentum field, where only the voxels with a suitable value of the divergence are exploded to a lower level of the hierarchy. In order to compensate for the discretization errors incurred at the coarser levels, a dilation procedure is added at the end of each iteration. Finally we design a simple alignment procedure to correct the displacement of the extracted skeleton with respect to the true underlying medial surface. We evaluate the proposed approach with an extensive series of qualitative and quantitative experiments

Large-scale Geometric Data Decomposition, Processing and Structured Mesh Generation

Mesh generation is a fundamental and critical problem in geometric data modeling and processing. In most scientific and engineering tasks that involve numerical computations and simulations on 2D/3D regions or on curved geometric objects, discretizing or approximating the geometric data using a polygonal or polyhedral meshes is always the first step of the procedure. The quality of this tessellation often dictates the subsequent computation accuracy, efficiency, and numerical stability. When compared with unstructured meshes, the structured meshes are favored in many scientific/engineering tasks due to their good properties. However, generating high-quality structured mesh remains challenging, especially for complex or large-scale geometric data. In industrial Computer-aided Design/Engineering (CAD/CAE) pipelines, the geometry processing to create a desirable structural mesh of the complex model is the most costly step. This step is semi-manual, and often takes up to several weeks to finish. Several technical challenges remains unsolved in existing structured mesh generation techniques. This dissertation studies the effective generation of structural mesh on large and complex geometric data. We study a general geometric computation paradigm to solve this problem via model partitioning and divide-and-conquer. To apply effective divide-and-conquer, we study two key technical components: the shape decomposition in the divide stage, and the structured meshing in the conquer stage. We test our algorithm on vairous data set, the results demonstrate the efficiency and effectiveness of our framework. The comparisons also show our algorithm outperforms existing partitioning methods in final meshing quality. We also show our pipeline scales up efficiently on HPC environment

Doctor of Philosophy

dissertationShape analysis is a well-established tool for processing surfaces. It is often a first step in performing tasks such as segmentation, symmetry detection, and finding correspondences between shapes. Shape analysis is traditionally employed on well-sampled surfaces where the geometry and topology is precisely known. When the form of the surface is that of a point cloud containing nonuniform sampling, noise, and incomplete measurements, traditional shape analysis methods perform poorly. Although one may first perform reconstruction on such a point cloud prior to performing shape analysis, if the geometry and topology is far from the true surface, then this can have an adverse impact on the subsequent analysis. Furthermore, for triangulated surfaces containing noise, thin sheets, and poorly shaped triangles, existing shape analysis methods can be highly unstable. This thesis explores methods of shape analysis applied directly to such defect-laden shapes. We first study the problem of surface reconstruction, in order to obtain a better understanding of the types of point clouds for which reconstruction methods contain difficulties. To this end, we have devised a benchmark for surface reconstruction, establishing a standard for measuring error in reconstruction. We then develop a new method for consistently orienting normals of such challenging point clouds by using a collection of harmonic functions, intrinsically defined on the point cloud. Next, we develop a new shape analysis tool which is tolerant to imperfections, by constructing distances directly on the point cloud defined as the likelihood of two points belonging to a mutually common medial ball, and apply this for segmentation and reconstruction. We extend this distance measure to define a diffusion process on the point cloud, tolerant to missing data, which is used for the purposes of matching incomplete shapes undergoing a nonrigid deformation. Lastly, we have developed an intrinsic method for multiresolution remeshing of a poor-quality triangulated surface via spectral bisection

Improving automatic rigging for 3D humanoid characters

In the field of computer animation the process of creating an animated character is usually a long and tedious task. An animation character is usually efined by a 3D mesh (a set of triangles in the space) that gives its external appearance or shape to the character. It also used to have an inner structure, the skeleton. When a skeleton is associated to a character mesh, this association is called skeleton binding, and a skeleton bound to a character mesh is an animation rig. Rigging from scratch a character can be a very boring process. The definition and creation of a centered skeleton together with the ’painting’, by an artist,of the influence parameters between the skeleton and the mesh (the skinning) s the most demanding part to achieve an acceptable behavior for a character. This rigging process can be simplified and accelerated using an automatic rigging method. Automatic rigging methods consist in taking as input a 3D mesh, generate a skeleton based in the shape of the original model, bound the input mesh to the generated skeleton, and finally to compute a set of parameters based in a chosen skinning method. The main objective of this thesis is to generate a method for rigging a 3D arbitrary model with minimum user interaction. This can be useful to people without experience in the animation field or to experienced people to accelerate the rigging process from days to hours or minutes depending the needed quality. Having in mind this situation we have designed our method as a set of tools that can be applied to general input models defined by an artist. The contributions made in the development of this thesis can be summarized as: • Generation of an animation Rig: Having an arbitrary closed mesh we have implemented a thinning method to create first an unrefined geometry skeleton that captures the topology and pose of the input character. Using this geometric skeleton as starting point we use a refining method that creates an adjusted logic skeleton based in a template, or may be defined by the user, that is compatible with the current animation formats. The output logic skeleton is specific for each character, and it is bounded to the input mesh to create an animation rig. • Skinning: Having defined an animation rig for an arbitrary mesh we have developed an improved skinning method; this method is based on the Linear Blend Skinning(LBS) algorithm. Our contributions in the skinning field can be sub-divided in: – We propose a segmentation method that works as the core element in a weight assigning algorithm and a skinning lgorithm, we also have developed an automatic algorithm to compute the skin weights of the LBS Skinning of a rigged polygonal mesh. – Our proposed skinning algorithm uses as base the features of the LBS Skinning. The main purpose of the developed algorithm is to solve the well-known ”candy wrap” artifact; that produces a substantial loss of volume when a link of an animation skeleton is rotated over its own axis. We have compared our results with the most important methods in the skinning field, such as Dual Quaternion Skinning (DQS) and LBS, achieving a better performance over DQS and an improvement in quality over LBS. • Animation tools: We have developed a set of Autodesk Maya commands that works together as rig tool, using our previous proposed methods. • Animation loader: Moreover, an animation loader tool has been implemented, that allows the user to load animations from a skeleton with different structure to a rigged 3D model. The contributions previously described has been published in 3 research papers, the first two were presented in international congresses and the third one was acepted for its publication in an JCR indexed journal.En el campo de la animación por computadora el proceso de crear un personaje de animación es comúnmente una tarea larga y tediosa. Un personaje de animación está definido usualmente por una malla tridimensional (un conjunto de triángulos en el espacio) que le dan su apariencia externa y forma al personaje. Es igualmente común que este tenga una estructura interna, un esqueleto de animación. Cuando un esqueleto esta asociado con una malla tridimensional, a esta asociación se le llama ligado de esqueleto, y un esqueleto ligado a la mallade un personaje es conocido en inglés como "animation rig" (el conjunto de elementos necesarios, que unidos sirven para animar un personaje). Hacer el rigging desde cero de un personaje puede ser un proceso muy tedioso. La definición y creación de un esqueleto centrado en la malla junto con el "pintado" por medio de un artista de los parámetros de influencia entre el esqueleto y la malla 3D (lo que se conoce como skinning) es la parte mas demandante para alcanzar un compartimiento aceptable al deformase (moverse) la malla de un personaje. Los métodos de rigging automáticos consisten en tomar una malla tridimensional como elemento de entrada, generar un esqueleto basado en la forma del modelo original, ligar la malla de entrada al esqueleto generado y finamente calcular el conjunto de parámetros utilizados por el método de skinning elegido. El principal objetivo de esta tesis es el generar un método de rigging para un modelo tridimensional arbitrario con una interacción mínima del usuario. Este método puede ser útil para gente con poca experiencia en el campo de la animación, o para gente experimentada que quiera acelerar el proceso de rigging de días a horas o inclusive minutos, dependiendo de la calidad requerida. Teniendo en mente esta situación, hemos diseñado nuestro método como un conjunto de herramientas las cuales pueden ser aplicadas a modelos de entrada generados por cualquier artista. Las contribuciones hechas en el desarrollo de esta tesis pueden resumirse a: -Generación de un rig de animación: Teniendo una malla cerrada cualquiera, hemos implementado un método para crear primero un esqueleto geométrico sin refinar, el cual capture la pose y la topología del personaje usado como elemento de entrada. Tomando este esqueleto geométrico como punto de partida usamos un método de refinado que crea un "esqueleto lógico" adaptado a la forma del geométrico basándonos en una plantilla definida por el usuario o previamente definida, que sea compatible con los formatos actuales de animación. El esqueleto lógico generado será especifico para cada personaje, y esta ligado a la malla de entrada para así crear un rig de animación. - Skinning: Teniendo definido un rig de animación para una malla de entrada arbitraria, hemos desarrollado un método mejorado de skinning, este método sera basado en el algoritmo "Linear Blending Skinnig" (algoritmo de skinning por combinación lineal, LBS por sus siglas en inglés). Nuestras contribuciones en el campo del skinnig son: - Proponemos un nuevo método de segmentación de mallas que sea la parte medular para algoritmos de asignación automática de pesos y de skinning, también hemos desarrollado un algoritmo automático que calcule los pesos utilizados por el algoritmo LBS para una malla poligonal que tenga un rig de animación. - Nuestro algoritmo de skinning propuesto usará como base las características del algoritmo LBS. El principal propósito del algoritmo desarrollado es el solucionar el defecto conocido como "envoltura de caramelo" (candy wrapper artifact), que produce una substancial perdida de volumen al rotar una de las articulaciones del esqueleto de animación sobre su propio eje. Nuestros resultados son comparados con los métodos mas importantes en el campo del skinning tal como Cuaterniones Duales (Dual Quaternions Skinning, DQS) y LBS, alcanzando un mejor desempeño que DQS y una mejora importante sobre LBSPostprint (published version

Multi-Surface Simplex Spine Segmentation for Spine Surgery Simulation and Planning

This research proposes to develop a knowledge-based multi-surface simplex deformable model for segmentation of healthy as well as pathological lumbar spine data. It aims to provide a more accurate and robust segmentation scheme for identification of intervertebral disc pathologies to assist with spine surgery planning. A robust technique that combines multi-surface and shape statistics-aware variants of the deformable simplex model is presented. Statistical shape variation within the dataset has been captured by application of principal component analysis and incorporated during the segmentation process to refine results. In the case where shape statistics hinder detection of the pathological region, user-assistance is allowed to disable the prior shape influence during deformation. Results have been validated against user-assisted expert segmentation

The aging frontal lobe in health and disease : a structural magnetic resonance imaging study

Cortical and subcortical regions of the brain decrease in volume in normal as well as pathological aging. Previous studies indicate that certain parts of the brain, like the prefrontal cortex, may be particularly vulnerable to age-related processes which are manifested by significant volume loss in this region. Cortical volume loss may be further enhanced by different kinds of pathology in the brain. The purpose of this study was to further investigate regional volumetric changes of the frontal lobe in normal aging and in aging patients with dementia. In study I-III patients with frontotemporal lobar degeneration (FTLD), Alzheimer’s disease (AD) and healthy controls are investigated. Cortical atrophy is related to clinical symptoms (study I), discussed in relation to gross morphology and cytoarchitecture (study II), and compared with the atrophy in the hippocampus (study III). In study IV a large number of normal elderly participants are investigated. Age-related volume loss in the limbic system (the dorsal anterior cingulate cortex and the hippocampus) is compared with atrophy of a region of the prefrontal cortex (the orbitofrontal cortex). Volumetric data of frontal and temporal cortical regions and the hippocampus was acquired by manual delineation on structural magnetic resonance images. Results of study I and III reveal that the clinical symptoms displayed by the subtypes of FTLD are commonly reflected in a specific pattern of atrophy in frontotemporal cortices as well as in the hippocampus. Study II suggests that the surface morphology of sulci and gyri may be unreliable landmarks for cyto-architectonic regions of the frontal cortex. Study IV finally indicates that a common characteristic of limbic regions may be that age-related volume loss is delayed in comparison to regions of the prefrontal cortex. Results also suggest that the dorsal anterior cingulate is more resistant to age-related volume loss than hippocampus, which implies that age-related volume loss occurs at different rates for different regions also within the limbic system