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The Medial Axis Transform (MAT) is a powerful tool for shape analysis and manipulation. Traditional methods for working with shapes usually define shapes as boundaries between some “inside” and some “outside” region. While this definition is simple and intuitive, it does not lend itself well to the construction of algorithms for a number of seemingly simple tasks such as classification, deformation, and collision detection. The MAT is an alternative representation of shape that defines the “inside” region by its center and thickness. We present a method of constructing the MAT which overcomes a significant limitation of its use with real-world data: instability. As classically defined, the MAT is unstable with respect to the shape boundary that it represents. For data sources afflicted by noise this is a serious problem. We propose an algorithm, LSMAT, which constructs a stable least squares approximation to the MAT. / Graduate

The desktop publishing revolution of the 1980s is currently repeating itself in 3D, referred to as desktop manufacturing. Online services such as Shapeways have become available, making personalized manufacturing on cutting edge additive manufacturing (AM) technologies accessible to a broad audience. Affordable desktop printers will soon take over, enabling people to fabricate / Engineering and Applied Sciences

No description available.

The need for increased product variety and improved aesthetics require the manufacturing enterprise to reduce time to market and to increase use of free-form surfaces in the form of the product. These changes lead to problems in the traditional approach for specification and verification of tolerances especially for a free form surfaces. In the case of freeform surfaces, the desired performance of a product depends on its geometry and is often controlled by intrinsic parameters such as curvature. Design intent therefore requires control on variations in these parameters. Ideally therefore, tolerances have to be applied on these parameters to prescribe allowable variations in the geometry of free-form surfaces. Since only the geometry of the product is controlled in manufacturing, tolerance specification has to ensure that the tolerances specified on the part geometry will ensure that the resulting value of the parameter of interest is within the limits prescribed by the designer. Relationship between allowable range in design parameters and that in geometry is not linear. Tolerance specification therefore becomes a trial and error process requiring considerable expertise and time. This thesis provides designers with a tool to automatically derive the corresponding tolerances to be specified to the manufacturing process to realize the final shape, such that the parameters that are used to control shape of the surface are within the prescribed variations. Automation in acquiring inspection data has brought dramatic changes in procedure for tolerance verification too. Optical scanners and similar non-contact devices provide large amount of points on the surface of the part quite rapidly. The unstructured point data are then processed to determine if the part complies with the given tolerance specifications. For freeform surfaces, current methods of verification uses minimum distance criterion between the nominal surface and unstructured point data. This ignores the correspondence between the points in the two data sets and may result in the rejection of good parts and acceptance of bad parts. There are other unresolved such as the singularity at corners of polyhedral shapes and handling datum. A new approach based on the Medial Axis Transform (MAT) has been proposed. It has been shown that reasoning on the MAT of the nominal model and the measured point set respectively enables the identification of corresponding points in the two sets. Verification of the tolerance allocated is therefore free from the problem mentioned above. MAT exhibits dimensional reduction and hence reduces verification time. It also eliminates surface fitting for detected feature. Results of implementation are provided for tolerance specification and verification using MAT.

Heterogeneous Objects are engineered with multiple materials to achieve multiple functionalities like high hardness, high toughness and low structural weight. Heterogeneous objects are increasingly used to achieve multiple and often conflicting behaviour within a single object. Developing heterogeneous objects needs computational model for design, analysis and manufacturing. The computational model should map the geometry of the object with the material composition. The most general model is the volume based model that decomposes the geometry exhaustively into simple elements and defines the material distribution over these elements. This approach can model a wide range of objects. However, defining material distribution needs manual intervention to select these elements for material continuity, and to segment or subdivide them for better material approximation. Volume based representation is quite large in size and is cumbersome to edit, query or reuse. Feature based approaches have been proposed to address some of these issues. However, current art can model only limited class of Heterogeneous Objects that includes simple material distribution over complex geometry or complex material distribution over simple geometry. The thesis presents a new method to overcome these limitations. The method, a hybrid of volume based and feature based approaches, allows the user to define the complex material distribution over complex geometries intuitively and represent the same. The complex material distribution is modelled using material reference entities that may be mixed-dimensional, inclusive of non-manifold entities. It uses Medial Axis Transform for automated segmentation of these entities into independent regions, where the material distribution can be intuitively prescribed starting from the entity and terminating at the medial axis. The spatial variation of the material is captured by a parameterized distance field from the material reference entities. It develops new constructive operators to build a complex heterogeneous object model that allows the reuse of the existing heterogeneous object models, automates handling of material continuity, and controls the gradation of the material in the interface of the constituent heterogeneous objects. Constructions using these operators can be geometry driven or material driven i.e. the geometric form controls the material distribution or the material distribution is independent of the geometric form. The proposed representation can be adaptively meshed for generation of mesh in the direction of gradation of the material for finite element analysis and process planning for additive manufacturing. An iso-material contour representation has been proposed for process planning of Heterogeneous Object Models. This avoids the stair case effect by depositing material in the direction of material gradation, and avoids over-deposition or under-deposition due to frequent start and stop of the nozzles. The proposed method has been implemented to show that it can model wide range of heterogeneous objects and can be integrated with additive manufacturing.

Dans cette thèse, nous étudions les problèmes de reconstruction statique et dynamique à partir de vues multiples et texturation, en s'appuyant sur des applications réelles et pratiques. Nous proposons trois méthodes de reconstruction destinées à l'estimation d'une représentation d'une scène statique/dynamique à partir d'un ensemble d'images/vidéos. Nous considérons ensuite le problème de texturation multi-vues en se concentrant sur la qualité visuelle de rendu..