On some interactive mesh deformations

Techniques devoted to deform 3D models are an important research field in Computer Graphics. They can be used in differentstages: the modelling phase, the animation process and also during some special simulations. Additionally, some applications may require the manipulation of 3D models under certain restrictions to preserve the volume of the modified object. Hence, thepresent PhD Dissertation explores new algorithms to perform flexible, robust and efficient 3D deformations. Apart from this, it also researches on a new methodology to restrict these deformations so that the volume of the manipulated model remains constant. Some of the most used methods to achieve smooth deformations are those included in the Cage-Based Deformation paradigm. Cage-based deformations enclose the model to be deformed in a coarse polyhedron, the cage. Then, they usually rely on Generalized Barycentric Coordinates to relate the model with the vertices, and other geometric elements, of this cage, which are the control points or the deformation handles. Finally, every time that one of these handles is dragged, the model is deformed accordingly. Although this paradigm is simple, elegant and performs efficient deformations, some cage-free space deformation techniques have recently appeared. They increase the flexibility of the deformation handles, which do not need to be connected, and define powerful tools that make the deformation process more versatile and intuitive. In this context, the Dissertation introduces new Generalized Barycentric Coordinate systems specially designed to be used in a cage-free environment. Any user who wants to use the presented schemes only needs to locate a set of control points in the vicinity of the model that he or she wants to deform. These handles can be placed wherever he or she considers mode suitable and the only requirement is that the model has to be enclosed in their convex hull. Up to now, there are few techniques to produce volume-preserving space deformations. However, in recent years there has been a growing interest in performing constrained deformations due to their more realistic and physically plausible results. Our contribution to this research line consists in a deformation framework that preserves the volume of the 3D models by means of its gradient and a control surface to restrict the movement of the handles. Moreover, the proposed methodology is not restricted to the cage-based schemes, but it can also be used in a cage-free environment. Finally, our research can be specially useful for spatial deformations of biological and medical models. This kind of models represent real organs and tissues, which are often soft and lack an internal rigid structure. In addition, they are elastic and incompressible. Any application designed to deal with this group of models and to train or assist doctors must be flexible, robust, efficient and user-friendly. The combination of the proposed cage-free systems with the presented volume-preserving deformation framework satisfiesLes deformacions de models 3D s'utilitzen en diverses etapes de la generació de continguts digitals: durant la fase de modelatge, durant el procés d'animació i en alguns tipus de simulacions. A més a més, hi ha aplicacions que necessiten que la manipulació dels models 3D es faci tenint en compte certes restriccions que permeten la conservació del volum de l'objecte modificat. Tot plegat fa que les tècniques de deformació 3D siguin un camp d'estudi molt important dins del món dels Gràfics. Per aquesta raó, aquesta Tesi Doctoral estudia nous algorismes que permetin realitzar deformacions 3D de manera flexible, robusta i eficient i que, a més a més, permetin conservar el volum dels objectes modificats. Un dels paradigmes més utilitzats per tal de realitzar deformacions suaus és el conegut amb el nom de Deformacions Basades en un Poliedre Englobant. Aquesta família de mètodes embolcalla el model que es vol deformar, normalment representat com una malla de triangles, dins d'un poliedre simple, amb poques cares. Un cop fet això, estableix un sistema de Coordenades Baricèntriques Generalitzades per tal de definir els vèrtexs del model a partir dels vèrtexs del poliedre englobant, els quals s'anomenen punts de control o controls de la deformació. D'aquesta manera, cada cop que s'arrossega o es modifica un d'aquests punts de control, el model que es troba dins del poliedre englobant es deforma segons el sistema de coordenades que s'ha definit. Tot i que aquest paradigma és simple, elegant i eficient, des de fa ja uns anys han començat a aparèixer noves tècniques que no necessiten el poliedre englobant per tal de realitzar la deformació. El seu principal objectiu és augmentar la flexibilitat dels controls de la deformació i definir eines que facin que el procés de deformació sigui més versàtil i intuïtiu. Tenint en compte aquest factor, aquesta Tesi també estudia sistemes de Coordenades Baricèntriques Generalitzades dissenyats per realitzar deformacions sense la necessitat de definir el poliedre englobant. D'aquesta manera, qualsevol usuari que vulgui utilitzar els mètodes que es presenten en aquesta Dissertació només s'ha d'encarregar de definir un conjunt de punts de control al voltant del model que vol deformar, podent-los posar allí on consideri més oportú segons la deformació que vulgui obtenir. L'únic requeriment necessari és que el model ha de quedar dins de l'envolupant convexa d'aquests punts de control. Actualment existeixen pocs mètodes que realitzin deformacions 3D amb preservació del volum. No obstant això, d'un temps ençà ha augmentat l'interès per realitzar deformacions subjectes a certes restriccions que fan que el resultat sigui més realista i físicament versemblant. La contribució d'aquesta Tesi dins d'aquesta línia de recerca consisteix en un sistema de deformació que preserva el volum dels objectes 3D gràcies a còmput del seu gradient i a una superfície de control que restringeix el moviment dels punts de control. Aquest mètode es pot aplicar tant als sistemes de deformació que necessiten un poliedre englobant com als que no el necessiten. Finalment, i ja per acabar, la recerca realitzada pot ser especialment útil per tal de realitzar deformacions de models mèdics i biològics. Aquests tipus de models poden representar òrgans i teixits reals, els quals, normalment, són tous, mancats d'una estructura rígida interna, elàstics i incompressibles. Qualsevol aplicació dissenyada per treballar amb aquest tipus de models i per entrenar i donar assistència a usuaris mèdics hauria de ser flexible, robusta, eficient i fàcil d'utilitzar. La combinació dels mètodes de deformació proposats conjuntament amb el sistema de preservació de volum satisfà totes aquestes condicions. Per aquesta raó es creu que les contribucions realitzades poden esdevenir eines importants per produir deformacions mèdiques.Postprint (published version

Derivation of Mean Value Coordinates Using Interior Distance and Their Application on Mesh Deformation

The deformation methods based on cage controls became a subject of considerable interest due its simplicity and intuitive results. In this technique, the model is enclosed within a simpler mesh (the cage) and its points are expressed as function of the cage elements. Then, by manipulating the cage, the respective deformation is obtained on the model in its interior.In this direction, in the last years, extensions of barycentric coordinates, such as Mean Value coordinates, Positive Mean Value Coordinates, Harmonic coordinates and Green's coordinates, have been proposed to write the points of the model as a function of the cage elements.The Mean Value coordinates, proposed by Floater in two dimensions and extended later to three dimensions by Ju et al. and also by Floater, stands out from the other coordinates because of their simple derivation. However the existence of negative coordinates in regions bounded by non-convex cage control results in a unexpected behavior of the deformation in some regions of the model.In this work, we propose a modification in the derivation of Mean Value Coordinates proposed by Floater. Our derivation maintains the simplicity of the construction of the coordinates and eliminates the undesired behavior in the deformation by diminishing the negative influence of a control vertex on regions ofthe model not related to it. We also compare the deformation generated with our coordinates and the deformations obtained with the original Mean Value coordinates and Harmonic coordinates

Development and validation of real-time simulation of X-ray imaging with respiratory motion

International audienceWe present a framework that combines evolutionary optimisation, soft tissue modelling and ray tracing on GPU to simultaneously compute the respiratory motion and X-ray imaging in real-time. Our aim is to provide validated building blocks with high fidelity to closely match both the human physiology and the physics of X-rays. A CPU-based set of algorithms is presented to model organ behaviours during respiration. Soft tissue deformation is computed with an extension of the Chain Mail method. Rigid elements move according to kinematic laws. A GPU-based surface rendering method is proposed to compute the X-ray image using the Beer-Lambert law. It is provided as an open-source library. A quantitative validation study is provided to objectively assess the accuracy of both components: i) the respiration against anatomical data, and ii) the X-ray against the Beer-Lambert law and the results of Monte Carlo simulations. Our implementation can be used in various applications, such as interactive medical virtual environment to train percutaneous transhepatic cholangiography in interventional radiology, 2D/3D registration, computation of digitally reconstructed radiograph, simulation of 4D sinograms to test tomography reconstruction tools

3D model deformations with arbitrary control points

Cage-based space deformations are often used to edit and animate images and geometric models. The deformations of the cage are easily transferred to the model by recomputing fixed convex combinations of the vertices of the cage, the control points. In current cage-based schemes the configuration of edges and facets between these control points affects the resulting deformations. In this paper we present a family of similar schemes that includes some of the current techniques, but also new schemes that depend only on the positions of the control points. We prove that these methods afford a solution under fairly general conditions and result in an easy and flexible way to deform objects using freely placed control points, with the necessary conditions of positivity and continuity.Peer ReviewedPostprint (author's final draft

A Framework for the Semantics-aware Modelling of Objects

The evolution of 3D visual content calls for innovative methods for modelling shapes based on their intended usage, function and role in a complex scenario. Even if different attempts have been done in this direction, shape modelling still mainly focuses on geometry. However, 3D models have a structure, given by the arrangement of salient parts, and shape and structure are deeply related to semantics and functionality. Changing geometry without semantic clues may invalidate such functionalities or the meaning of objects or their parts. We approach the problem by considering semantics as the formalised knowledge related to a category of objects; the geometry can vary provided that the semantics is preserved. We represent the semantics and the variable geometry of a class of shapes through the parametric template: an annotated 3D model whose geometry can be deformed provided that some semantic constraints remain satisfied. In this work, we design and develop a framework for the semantics-aware modelling of shapes, offering the user a single application environment where the whole workflow of defining the parametric template and applying semantics-aware deformations can take place. In particular, the system provides tools for the selection and annotation of geometry based on a formalised contextual knowledge; shape analysis methods to derive new knowledge implicitly encoded in the geometry, and possibly enrich the given semantics; a set of constraints that the user can apply to salient parts and a deformation operation that takes into account the semantic constraints and provides an optimal solution. The framework is modular so that new tools can be continuously added. While producing some innovative results in specific areas, the goal of this work is the development of a comprehensive framework combining state of the art techniques and new algorithms, thus enabling the user to conceptualise her/his knowledge and model geometric shapes. The original contributions regard the formalisation of the concept of annotation, with attached properties, and of the relations between significant parts of objects; a new technique for guaranteeing the persistence of annotations after significant changes in shape's resolution; the exploitation of shape descriptors for the extraction of quantitative information and the assessment of shape variability within a class; and the extension of the popular cage-based deformation techniques to include constraints on the allowed displacement of vertices. In this thesis, we report the design and development of the framework as well as results in two application scenarios, namely product design and archaeological reconstruction