Reliable Solid Modelling Using Subdivision Surfaces

Les surfaces de subdivision fournissent une méthode alternative prometteuse dans la modélisation géométrique, et ont des avantages sur la représentation classique de trimmed-NURBS, en particulier dans la modélisation de surfaces lisses par morceaux. Dans ce mémoire, nous considérons le problème des opérations géométriques sur les surfaces de subdivision, avec l'exigence stricte de forme topologique correcte. Puisque ce problème peut être mal conditionné, nous proposons une approche pour la gestion de l'incertitude qui existe dans le calcul géométrique. Nous exigeons l'exactitude des informations topologiques lorsque l'on considère la nature de robustesse du problème des opérations géométriques sur les modèles de solides, et il devient clair que le problème peut être mal conditionné en présence de l'incertitude qui est omniprésente dans les données. Nous proposons donc une approche interactive de gestion de l'incertitude des opérations géométriques, dans le cadre d'un calcul basé sur la norme IEEE arithmétique et la modélisation en surfaces de subdivision. Un algorithme pour le problème planar-cut est alors présenté qui a comme but de satisfaire à l'exigence topologique mentionnée ci-dessus.

Graph matching with subdivision surfaces for texture synthesis on surfaces

Existing texture synthesis-from-example strategies for polygon meshes typically make use of three components: a multi-resolution mesh hierarchy that allows the overall nature of the pattern to be reproduced before filling in detail; a matching strategy that extends the synthesized texture using the best fit from a texture sample; and a transfer mechanism that copies the selected portion of the texture sample to the target surface. We introduce novel alternatives for each of these components. Use of p2-subdivision surfaces provides the mesh hierarchy and allows fine control over the surface complexity. Adaptive subdivision is used to create an even vertex distribution over the surface. Use of the graph defined by a surface region for matching, rather than a regular texture neighbourhood, provides for flexible control over the scale of the texture and allows simultaneous matching against multiple levels of an image pyramid created from the texture sample. We use graph cuts for texture transfer, adapting this scheme to the context of surface synthesis. The resulting surface textures are realistic, tolerant of local mesh detail and are comparable to results produced by texture neighbourhood sampling approaches.

Representing images using curvilinear feature driven subdivision surfaces.

This paper presents a subdivision-based vector graphics for image representation and creation. The graphics representation is a subdivision surface defined by a triangular mesh augmented with color attribute at vertices and feature attribute at edges. Special cubic B-splines are proposed to describe curvilinear features of an image. New subdivision rules are then designed accordingly, which are applied to the mesh and the color attribute to define the spatial distribution and piecewise-smoothly varying colors of the image. A sharpness factor is introduced to control the color transition across the curvilinear edges. In addition, an automatic algorithm is developed to convert a raster image into such a vector graphics representation. The algorithm first detects the curvilinear features of the image, then constructs a triangulation based on the curvilinear edges and feature attributes, and finally iteratively optimizes the vertex color attributes and updates the triangulation. Compared with existing vector-based image representations, the proposed representation and algorithm have the following advantages in addition to the common merits (such as editability and scalability): 1) they allow flexible mesh topology and handle images or objects with complicated boundaries or features effectively; 2) they are able to faithfully reconstruct curvilinear features, especially in modeling subtle shading effects around feature curves; and 3) they offer a simple way for the user to create images in a freehand style. The effectiveness of the proposed method has been demonstrated in experiments.

Extension of Wu-Peters bounds to Catmull-Clark and 4-8 subdivision

La méthode de subdivision Catmull-Clark ainsi que la méthode de subdivision Loop sont des normes industrielle de facto. D'autre part, la méthode de subdivision 4-8 est bien adaptée à la subdivision adaptative, parce que cette méthode augmente le nombre de faces ou de sommets par seulement un facteur de 2 à chaque raffinement. Cela promet d'être plus pratique pour atteindre un niveau donné de précision. Dans ce mémoire, nous présenterons une méthode permettant de paramétrer des surfaces de subdivision de la méthode Catmull-Clark et de la méthode 4-8. Par conséquent, de nombreux algorithmes mis au point pour des surfaces paramétriques pourrant être appliqués aux surfaces de subdivision Catmull-Clark et aux surfaces de subdivision 4-8. En particulier, nous pouvons calculer des bornes garanties et réalistes sur les patches, un peu comme les bornes correspondantes données par Wu-Peters pour la méthode de subdivision Loop.

Efficient and precise interactive hand tracking through joint, continuous optimization of pose and correspondences

Fully articulated hand tracking promises to enable fundamentally new interactions with virtual and augmented worlds, but the limited accuracy and efficiency of current systems has prevented widespread adoption. Today's dominant paradigm uses machine learning for initialization and recovery followed by iterative model-fitting optimization to achieve a detailed pose fit. We follow this paradigm, but make several changes to the model-fitting, namely using: (1) a more discriminative objective function; (2) a smooth-surface model that provides gradients for non-linear optimization; and (3) joint optimization over both the model pose and the correspondences between observed data points and the model surface. While each of these changes may actually increase the cost per fitting iteration, we find a compensating decrease in the number of iterations. Further, the wide basin of convergence means that fewer starting points are needed for successful model fitting. Our system runs in real-time on CPU only, which frees up the commonly over-burdened GPU for experience designers. The hand tracker is efficient enough to run on low-power devices such as tablets. We can track up to several meters from the camera to provide a large working volume for interaction, even using the noisy data from current-generation depth cameras. Quantitative assessments on standard datasets show that the new approach exceeds the state of the art in accuracy. Qualitative results take the form of live recordings of a range of interactive experiences enabled by this new approach.

Visibility and proximity on triangulated surfaces

En aquesta tesi es solucionen problemes de visibilitat i proximitat sobre superfícies triangulades considerant elements generalitzats. Com a elements generalitzats considerem: punts, segments, poligonals i polígons. Les estrategies que proposem utilitzen algoritmes de geometria computacional i hardware gràfic. Comencem tractant els problemes de visibilitat sobre models de terrenys triangulats considerant un conjunt d'elements de visió generalitzats. Es presenten dos mètodes per obtenir, de forma aproximada, mapes de multi-visibilitat. Un mapa de multi-visibilitat és la subdivisió del domini del terreny que codifica la visibilitat d'acord amb diferents criteris. El primer mètode, de difícil implementació, utilitza informació de visibilitat exacte per reconstruir de forma aproximada el mapa de multi-visibilitat. El segon, que va acompanyat de resultats d'implementació, obté informació de visibilitat aproximada per calcular i visualitzar mapes de multi-visibilitat discrets mitjançant hardware gràfic. Com a aplicacions es resolen problemes de multi-visibilitat entre regions i es responen preguntes sobre la multi-visibilitat d'un punt o d'una regió. A continuació tractem els problemes de proximitat sobre superfícies polièdriques triangulades considerant seus generalitzades. Es presenten dos mètodes, amb resultats d'implementació, per calcular distàncies des de seus generalitzades sobre superfícies polièdriques on hi poden haver obstacles generalitzats. El primer mètode calcula, de forma exacte, les distàncies definides pels camins més curts des de les seus als punts del poliedre. El segon mètode calcula, de forma aproximada, distàncies considerant els camins més curts sobre superfícies polièdriques amb pesos. Com a aplicacions, es calculen diagrames de Voronoi d'ordre k, i es resolen, de forma aproximada, alguns problemes de localització de serveis. També es proporciona un estudi teòric sobre la complexitat dels diagrames de Voronoi d'ordre k d'un conjunt de seus generalitzades en un poliedre sense pesos.

Some surface profiles of a strip after plane-strain indentation by rigid bodies with serrated surfaces

This paper is concerned with the surface profiles of a strip after rigid bodies with serrated (saw-teeth) surfaces indent the strip and are subsequently removed. Plane-strain conditions are assumed. This has application in roughness transfer of final metal forming process. The effects of the semi-angle of the teeth, the depth of indentation and the friction on the contact surface on the profile are considered.

Understanding the physical processes of pollutant build-up and wash-off on roof surfaces

Pollutants originating with roof runoff can have a significant impact to urban stormwater quality. This signifies the importance of understanding pollutant processes on roof surfaces. Additionally, knowledge of pollutant processes on roof surfaces is important as roofs are used as the primary catchment surface for domestic rainwater harvesting. In recent years, rainwater harvesting has become one of the primary sustainable water management techniques to counteract the growing demand for potable water. Similar to all impervious services, pollutants associated with roof runoff undergo two primary processes: build-up and wash-off. The knowledge relating to these processes is limited. This paper presents outcomes of an in-depth research study into pollutant build-up and wash-off for roof surfaces. The knowledge will be important in order to develop appropriate strategies to safeguard rainwater users from possible health risks.