In character animation achieving realistic deformations of the skin is a challenging task. Geometric skinning techniques, such as smooth blending or dual-quaternions, are very popular for their high performance but fail to produce convincing deformations. They look too soft compared to human skin deformation at a rigid bone joint. In addition advanced effects such as skin contacts or bulges are not taken into account. Other methods make use of physical simulation or volume control to better capture the skin behavior, yet they cannot deliver real-time feedback. We developed a novel skinning framework called implicit skinning. Our method produces visually plausible deformations in real-time by handling realistic skin contacts and bulges between limbs. Implicit skinning exploits the ability of implicit surfaces to be robustly combined as well as their efficient collision detection. By approximating the mesh by a set of implicit surfaces, we are able to guide the deformation of a mesh character. we can combine the implicit surfaces in real-time, and use the final implicit surface to adjust the position of mesh vertices at each animation step. Since collision detection is very efficient using implicit surfaces we achieve skin contacts between limbs at interactive to real-time frame rates. In this thesis we present the complete implicit skinning framework, that is, the conversion of a mesh character to implicit surfaces, the composition operators and the mesh deformation algorithm on top of the implicit surface. Two deformation algorithms are studied: a fast history dependent algorithm which acts as a post process on top of dual-quaternions skinning and a slower yet more robust history dependent algorithm. / Graduate

In this thesis, I analyze the weight functions used in moving least squares (MLS) methods to construct implicit surfaces that interpolate or approximate polygon soup. I found that one previous method that presented an analytic solution to the integrated moving least squares method has issues with degeneracies because they changed the weight functions to decrease too slowly. Inspired by their method, I derived a bound for the choice of weight function for implicit moving least squares (IMLS) methods to avoid these degeneracies in two-dimensions and in three-dimensions. Based on this bound, I give a theoretical proof of the correctness of the moving least squares interpolation and approximation scheme with weight function used in Shen et al. when used on closed polyhedrons. Further, previous IMLS implicit surface reconstruction algorithms that ll holes and gaps create surfaces with obvious bulges due to an intrinsic property of MLS. I propose a generalized IMLS method using a Gaussian distribution function to re-weight each polygon, making nearer polygons dominate and reducing the bulges on holes and gaps.

Free-form surfaces and implicit surfaces must be tessellated before being rendered with rasterization techniques. However ray tracing provides the means to directly render such objects without the need to first convert into polygonal meshes. Since ray tracing can handle triangle meshes as well, the question of which method is most suitable in terms of performance, quality and memory usage is addressed in this thesis. Bézier surfaces and NURBS surfaces along with basic algebraic implicit surfaces are implemented in order to test the performance relative to polygonal meshes approximating the same objects. The parametric surfaces are implemented using an iterative Newtonian method that converges on the point of intersection using a bounding volume hierarchy that stores the initial guesses. Research into intersecting rays with parametric surfaces is surveyed in order to find additional methods that speed up the computation. The implicit surfaces are implemented using common direct algebraic methods. All of the intersection tests are implemented using the Embree ray tracing API as well as a SIMD library in order to achieve interactive framerates on a CPU. The results show that both Bézier surfaces and NURBS surfaces can achieve interactive framerates on a CPU using SIMD computation, with Bézier surfaces coming close to the performance of polygonal counterparts. The implicit surfaces implemented outperform even the simplest polygonal approximations.

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The advancements in robotic perception in the recent years have empowered robots to better execute tasks in various environments. The perception of objects in the robot work space significantly relies on how sensory data is represented. In this context, 3D models of object’s surfaces have been studied as a means to provide useful insights on shape of objects and ultimately enhance robotic perception. This involves several challenges, because sensory data generally presents artifacts, such as noise and incompleteness. To tackle this problem, we employ Gaussian Process Implicit Surface (GPIS), a non-parametric probabilistic reconstruction of object’s surfaces from 3D data points. This thesis investigates different configurations for GPIS, as a means to tackle the extraction of shape information. In our approach we interpret an object’s surface as the level-set of an underlying sparse Gaussian Process (GP) with variational formulation. Results show that the variational formulation for sparse GP enables a reliable approximation to the full GP solution. Experiments are performed on a synthetic and a real sensory data set. We evaluate results by assessing how close the reconstructed surfaces are to the ground-truth correspondences, and how well objects from different categories are clustered based on the obtained representation. Finally we conclude that the proposed solution derives adequate surface representations to reason about object shape and to discriminate objects based on shape information. / Framsteg inom robotperception de senaste åren har resulterat i robotar som är bättre på attutföra uppgifter i olika miljöer. Perception av objekt i robotens arbetsmiljö är beroende avhur sensorisk data representeras. I det här sammanhanget har 3D-modeller av objektytorstuderats för att ge användbar insikt om objektens form och i slutändan bättre robotperception. Detta innebär flera utmaningar, eftersom sensoriska data ofta innehåller artefakter, såsom brus och brist på data. För att hantera detta problem använder vi oss av Gaussian Process Implicit Surface (GPIS), som är en icke-parametrisk probabilistisk rekonstruktion av ett objekts yta utifrån 3D-punkter. Detta examensarbete undersöker olika konfigurationer av GPIS för att på detta sätt kunna extrahera forminformation. I vår metod tolkar vi ett objekts yta som nivåkurvor hos en underliggande gles variational Gaussian Process (GP) modell. Resultat visar att en gles variational GP möjliggör en tillförlitlig approximation av en komplett GP-lösningen. Experiment utförs på ett syntetisk och ett reellt sensorisk dataset. Vi utvärderar resultat genom att bedöma hur nära de rekonstruerade ytorna är till grundtruth- korrespondenser, och hur väl objektkategorier klustras utifrån den erhållna representationen. Slutligen konstaterar vi att den föreslagna lösningen leder till tillräckligt goda representationer av ytor för tolkning av objektens form och för att diskriminera objekt utifrån forminformation.

This thesis deals with blobs modeling and visualizing (iso-surfaces, implicit-surfaces). It includes implementation of full-featured editor of these objects. It provides real-time operations over surfaces. The work also contains its motivation - where this modeling technique comes from, required equations and computations needed for surface rendering and algorithms used for blobs visualization.

La 3D s'impose comme un nouveau média dont l'adoption généralisée passe par la conception d'outils, accessibles au grand public, de création et de manipulation de formes tridimensionnelles quelconques. Les outils actuels reposent fortement sur la modélisation sous-jacente des formes, généralement surfacique, et sont alors peu intuitifs ou limitatifs dans l'expressivité offerte à l'utilisateur.Nous souhaitons, dans ces travaux, définir une approche ne présentant pas ces défauts et permettant à l'utilisateur de se concentrer sur le processus créatif. En nous inspirant de l'utilisation séculaire de l'argile, nous proposons une approche modélisant la matière sous forme lagrangienne.Une forme est ainsi décrite par un système de particules, où chaque particule représente un petit volume du volume global.Dans ce cadre lagrangien, la méthode Smoothed Particle Hydrodynamics (SPH) permet l'approximation de grandeurs physiques en tout point de l'espace. Nous proposons alors une modélisation de matériaux à deux couches, l'une décrivant la topologie et l'autre décrivant la géométrie du système global.La méthode SPH permet, entre autres, d'évaluer la densité de matière. Ceci nous permet de définir une surface implicite basée sur les propriétés physiques du système de particules pour redonner un aspect continu à la matière.Ces matériaux peuvent alors être manipulés au moyen d'interactions locales reproduisant le maniement de la pâte à modeler, et de déformations globales. L'intérêt de notre approche est démontrée par plusieurs prototypes fonctionnant sur des stations de travail standard ou dans des environnements immersifs. / 3D is emerging as a new media. Its widespread adoption requires the implementation of userfriendly tools to create and manipulate three-dimensional shapes. Current softwares heavily rely on underlying shape modeling, usually a surfacic one, and are then often counter-intuitive orlimiting. Our objective is the design of an approach alleviating those limitations and allowing the user to only focus on the process of creating forms. Drawing inspiration from the ancient use of clay,we propose to model a material in a lagrangian description. A shape is described by a particles system, where each particle represents a small fraction of the total volume of the shape. In this framework, the Smoothed Particle Hydrodynamics method enables to approximate physical values anywhere in space. Relying on this method, we propose a modeling of material with two levels, one level representing the topology and the other one describing local geometry of the shape.The SPH method especially enables to evaluate a density of matter. We use this property todefine an implicit surface based on the physical properties of the particles system to reproduce the continuous aspect of matter. Those virtual materials can then be manipulated locally through interactions reproducing the handling of dough in the real world or through global shape deformation. Our approach is demonstrated by several prototypes running either on typical desktop workstation or in immersive environment system.