New Geometric Data Structures for Collision Detection

We present new geometric data structures for collision detection and more, including: Inner Sphere Trees - the first data structure to compute the peneration volume efficiently. Protosphere - an new algorithm to compute space filling sphere packings for arbitrary objects. Kinetic AABBs - a bounding volume hierarchy that is optimal in the number of updates when the objects deform. Kinetic Separation-List - an algorithm that is able to perform continuous collision detection for complex deformable objects in real-time. Moreover, we present applications of these new approaches to hand animation, real-time collision avoidance in dynamic environments for robots and haptic rendering, including a user study that exploits the influence of the degrees of freedom in complex haptic interactions. Last but not least, we present a new benchmarking suite for both, peformance and quality benchmarks, and a theoretic analysis of the running-time of bounding volume-based collision detection algorithms

Realistic Hair Simulation: Animation and Rendering

International audienceThe last five years have seen a profusion of innovative solutions to one of the most challenging tasks in character synthesis: hair simulation. This class covers both recent and novel research ideas in hair animation and rendering, and presents time tested industrial practices that resulted in spectacular imagery

Distance based heterogeneous volume modelling.

Natural objects, such as bones and watermelons, often have a heterogeneous composition and complex internal structures. Material properties inside the object can change abruptly or gradually, and representing such changes digitally can be problematic. Attribute functions represent physical properties distribution in the volumetric object. Modelling complex attributes within a volume is a complex task. There are several approaches to modelling attributes, but distance functions have gained popularity for heterogeneous object modelling because, in addition to their usefulness, they lead to predictability and intuitiveness. In this thesis, we consider a unified framework for heterogeneous volume modelling, specifically using distance fields. In particular, we tackle various issues associated with them such as the interpolation of volumetric attributes through time for shape transformation and intuitive and predictable interpolation of attributes inside a shape. To achieve these results, we rely on smooth approximate distance fields and interior distances. This thesis deals with outstanding issues in heterogeneous object modelling, and more specifically in modelling functionally graded materials and structures using different types of distances and approximation thereof. We demonstrate the benefits of heterogeneous volume modelling using smooth approximate distance fields with various applications, such as adaptive microstructures, morphological shape generation, shape driven interpolation of material properties through time and shape conforming interpolation of properties. Distance based modelling of attributes allows us to have a better parametrization of the object volume and design gradient properties across an object. This becomes more important nowadays with the growing interest in rapid prototyping and digital fabrication of heterogeneous objects and can find practical applications in different industries

Interactive visualization tools for topological exploration

Thesis (Ph.D.) - Indiana University, Computer Science, 1992This thesis concerns using computer graphics methods to visualize mathematical objects. Abstract mathematical concepts are extremely difficult to visualize, particularly when higher dimensions are involved; I therefore concentrate on subject areas such as the topology and geometry of four dimensions which provide a very challenging domain for visualization techniques. In the first stage of this research, I applied existing three-dimensional computer graphics techniques to visualize projected four-dimensional mathematical objects in an interactive manner. I carried out experiments with direct object manipulation and constraint-based interaction and implemented tools for visualizing mathematical transformations. As an application, I applied these techniques to visualizing the conjecture known as Fermat's Last Theorem. Four-dimensional objects would best be perceived through four-dimensional eyes. Even though we do not have four-dimensional eyes, we can use computer graphics techniques to simulate the effect of a virtual four-dimensional camera viewing a scene where four-dimensional objects are being illuminated by four-dimensional light sources. I extended standard three-dimensional lighting and shading methods to work in the fourth dimension. This involved replacing the standard "z-buffer" algorithm by a "w-buffer" algorithm for handling occlusion, and replacing the standard "scan-line" conversion method by a new "scan-plane" conversion method. Furthermore, I implemented a new "thickening" technique that made it possible to illuminate surfaces correctly in four dimensions. Our new techniques generate smoothly shaded, highlighted view-volume images of mathematical objects as they would appear from a four-dimensional viewpoint. These images reveal fascinating structures of mathematical objects that could not be seen with standard 3D computer graphics techniques. As applications, we generated still images and animation sequences for mathematical objects such as the Steiner surface, the four-dimensional torus, and a knotted 2-sphere. The images of surfaces embedded in 4D that have been generated using our methods are unique in the history of mathematical visualization. Finally, I adapted these techniques to visualize volumetric data (3D scalar fields) generated by other scientific applications. Compared to other volume visualization techniques, this method provides a new approach that researchers can use to look at and manipulate certain classes of volume data

Collision Detection and Merging of Deformable B-Spline Surfaces in Virtual Reality Environment

This thesis presents a computational framework for representing, manipulating and merging rigid and deformable freeform objects in virtual reality (VR) environment. The core algorithms for collision detection, merging, and physics-based modeling used within this framework assume that all 3D deformable objects are B-spline surfaces. The interactive design tool can be represented as a B-spline surface, an implicit surface or a point, to allow the user a variety of rigid or deformable tools. The collision detection system utilizes the fact that the blending matrices used to discretize the B-spline surface are independent of the position of the control points and, therefore, can be pre-calculated. Complex B-spline surfaces can be generated by merging various B-spline surface patches using the B-spline surface patches merging algorithm presented in this thesis. Finally, the physics-based modeling system uses the mass-spring representation to determine the deformation and the reaction force values provided to the user. This helps to simulate realistic material behaviour of the model and assist the user in validating the design before performing extensive product detailing or finite element analysis using commercially available CAD software. The novelty of the proposed method stems from the pre-calculated blending matrices used to generate the points for graphical rendering, collision detection, merging of B-spline patches, and nodes for the mass spring system. This approach reduces computational time by avoiding the need to solve complex equations for blending functions of B-splines and perform the inversion of large matrices. This alternative approach to the mechanical concept design will also help to do away with the need to build prototypes for conceptualization and preliminary validation of the idea thereby reducing the time and cost of concept design phase and the wastage of resources

Virtual prototyping with surface reconstruction and freeform geometric modeling using level-set method

More and more products with complex geometries are being designed and manufactured by computer aided design (CAD) and rapid prototyping (RP) technologies. Freeform surface is a geometrical feature widely used in modern products like car bodies, airfoils and turbine blades as well as in aesthetic artifacts. How to efficiently design and generate digital prototypes with freeform surfaces is an important issue in CAD. This paper presents the development of a Virtual Sculpting system and addresses the issues of surface reconstruction from dexel data structures and freeform geometric modeling using the level-set method from distance field structure. Our virtual sculpting method is based on the metaphor of carving a solid block into a 3D freeform object using a 3D haptic input device integrated with the computer visualization. This dissertation presents the result of the study and consists primarily of four papers --Abstract, page iv

Doctor of Philosophy

dissertationWhile boundary representations, such as nonuniform rational B-spline (NURBS) surfaces, have traditionally well served the needs of the modeling community, they have not seen widespread adoption among the wider engineering discipline. There is a common perception that NURBS are slow to evaluate and complex to implement. Whereas computer-aided design commonly deals with surfaces, the engineering community must deal with materials that have thickness. Traditional visualization techniques have avoided NURBS, and there has been little cross-talk between the rich spline approximation community and the larger engineering field. Recently there has been a strong desire to marry the modeling and analysis phases of the iterative design cycle, be it in car design, turbulent flow simulation around an airfoil, or lighting design. Research has demonstrated that employing a single representation throughout the cycle has key advantages. Furthermore, novel manufacturing techniques employing heterogeneous materials require the introduction of volumetric modeling representations. There is little question that fields such as scientific visualization and mechanical engineering could benefit from the powerful approximation properties of splines. In this dissertation, we remove several hurdles to the application of NURBS to problems in engineering and demonstrate how their unique properties can be leveraged to solve problems of interest

Heterogeneous volumetric data mapping and its medical applications

With the advance of data acquisition techniques, massive solid geometries are being collected routinely in scientific tasks, these complex and unstructured data need to be effectively correlated for various processing and analysis. Volumetric mapping solves bijective low-distortion correspondence between/among 3D geometric data, and can serve as an important preprocessing step in many tasks in compute-aided design and analysis, industrial manufacturing, medical image analysis, to name a few. This dissertation studied two important volumetric mapping problems: the mapping of heterogeneous volumes (with nonuniform inner structures/layers) and the mapping of sequential dynamic volumes. To effectively handle heterogeneous volumes, first, we studied the feature-aligned harmonic volumetric mapping. Compared to previous harmonic mapping, it supports the point, curve, and iso-surface alignment, which are important low-dimensional structures in heterogeneous volumetric data. Second, we proposed a biharmonic model for volumetric mapping. Unlike the conventional harmonic volumetric mapping that only supports positional continuity on the boundary, this new model allows us to have higher order continuity $C^1$ along the boundary surface. This suggests a potential model to solve the volumetric mapping of complex and big geometries through divide-and-conquer. We also studied the medical applications of our volumetric mapping in lung tumor respiratory motion modeling. We were building an effective digital platform for lung tumor radiotherapy based on effective volumetric CT/MRI image matching and analysis. We developed and integrated in this platform a set of geometric/image processing techniques including advanced image segmentation, finite element meshing, volumetric registration and interpolation. The lung organ/tumor and surrounding tissues are treated as a heterogeneous region and a dynamic 4D registration framework is developed for lung tumor motion modeling and tracking. Compared to the previous 3D pairwise registration, our new 4D parameterization model leads to a significantly improved registration accuracy. The constructed deforming model can hence approximate the deformation of the tissues and tumor

Shape deformations based on vector fields

This thesis explores applications of vector field processing to shape deformations. We present a novel method to construct divergence-free vector fields which are used to deform shapes by vector field integration (Chapter 2). The resulting deformation is volume-preserving and no self-intersections occur. We add more controllability to this approach by introducing implicit boundaries (Chapter 3), a shape editing method which resembles the well-known boundary constraint modeling metaphor. While the vector fields are originally defined in space, we also present a surface-based version of this approach which allows for more exact boundary selection and deformation control (Chapter 4). We show that vectorfield- based shape deformations can be used to animate elastic motions without complex physical simulations (Chapter 5). We also introduce an alternative approach to exactly preserve the volume of skinned triangle meshes (Chapter 6). This is accomplished by constructing a displacement field on the mesh surface which restores the original volume after deformation. Finally, we demonstrate that shape deformation by vector field integration can also be used to visualize smoke-like streak surfaces in dynamic flow fields (Chapter 7).In dieser Dissertation werden verschiedene Anwendungen der Vektorfeldverarbeitung im Bereich Objektdeformation untersucht. Wir präsentieren eine neuartige Methode zur Konstruktion von divergenzfreien Vektorfeldern, welche mittels Integration zum Deformieren von Objekten verwendet werden (Kapitel 2). Die so entstehende Deformation ist volumenerhaltend und keine Selbstüberschneidungen treten auf. Inspiriert von etablierten, auf Randbedingungen beruhenden Methoden, erweitern wir diese Idee hinsichtlich Kontrollierbarkeit mittels impliziten Abgrenzungen (Kapitel 3). Während die ursprüngliche Konstruktion im Raum definiert ist, präsentieren wir auch eine oberflächenbasierte Version, welche ein genaueres Festlegen der Abgrenzungen und bessere Kontrolle ermöglicht (Kapitel 4). Wir zeigen, dass vektorfeldbasierte Deformationen auch zur Animation von elastischen Bewegungen benutzt werden können, ohne dass komplexe Simulationen nötig sind (Kapitel 5). Des weiteren zeigen wir eine alternative Möglichkeit, mit der man das Volumen von Dreiecksnetzen erhalten kann, welche mittels Skelett-Animation deformiert werden (Kapitel 6). Dies erreichen wir durch ein Deformationsfeld auf der Oberfläche, das das ursprüngliche Volumen wieder hergestellt. Wir zeigen außerdem, dass Deformierungen mittels Vektorfeld-Integration auch zur Visualisierung von Rauch in dynamischen Flüssen genutzt werden können(Kapitel 7)