Compendium of Publications on: Differential Operators on Manifolds for CAD CAM CAE and Computer Graphics
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This Doctoral Thesis develops novel articulations of Differential Operators on Manifolds for applications on Computer Aided Design, Manufacture and Computer Graphics, as follows: (1) Mesh Parameterization and Segmentation. Development and application of Laplace-Beltrami, Hessian, Geodesic and Curvature operators for topology and geometry – driven segmentations and parameterizations of 2-manifold triangular meshes. Applications in Reverse Engineering, Manufacturing and Medicine. (2) Computing of Laser-driven Temperature Maps in thin plates. Spectral domain - based analytic solutions of the transient, non-homogeneous heat equation for simulation of temperature maps in multi-laser heated thin plates, modeled as 2-manifolds plus thickness. (3) Real-time estimation of dimensional compliance of hot out-of-forge workpieces. A Special Orthogonal SO(3) transformation between 2-manifolds is found, which enables a distance operator between 2-manifolds in R^3 (or m-manifolds in R^n). This process instruments the real-time assessment of dimensional compliance of hot workpieces, in the factory floor shop. (4) Slicing or Level-Set computation for 2-manifold triangular meshes in Additive Manufacturing. Development of a classification of non-degenerate (i.e. non-singular Hessian) and degenerate (i.e. singular Hessian) critical points of non-Morse functions on 2-manifold objects, followed by computation of level sets for Additive Manufacturing. Most of the aforementioned contributions have been screened and accepted by the international scientific community (and published). Non-published material corresponds to confidential developments which are commercially exploited by the sponsors and therefore banned from dissemination.
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Educative Visuals - Digital Delivery of Architectural Information for (potential) Heritage Buildings Kwee, Verdy; Radford, Antony; Bruton, Dean (The Eurographics Association, 2006)The paper proposes models that address current issues and considerations at several key levels relating to treatment of architectural information, its presentation and delivery methods specific to architecture education ...
Miller, Chris M.; Jones, Mark W. (The Eurographics Association, 2005)Texture mapping is an extremely powerful and flexible tool for adding complex surface detail to an object. This paper introduces a method of surface texturing and hypertexturing complex volumetric objects in real-time. We ...
Cubero, Francisco; Mas, Albert; Patow, Gustavo (The Eurographics Association, 2012)This paper presents a new general purpose procedural geometrical modeling system. It is focused on providing flexibility, modularity and scalability. Furthermore, it is taylored to manage huge geometric models, with millions ...