Isophote curves on timelike surfaces in Minkowski 3-space

Isophote comprises a locus of the surface points whose normal vectors make a constant angle with a fixed vector. In this paper, isophote curves are studied on timelike surfaces in Minkowski 3-space E31. The axises of spacelike and timelike isophote curves are found via their Darboux frames. Subsequently, the relationship between isophotes and slant helices is shown on timelike surfaces.Comment: 11 pages. arXiv admin note: text overlap with arXiv:1203.438

Highlight-line algorithm for realtime surface-quality assessment

A new method of surface-quality assessment is presented. The model of highlight lines is introduced, and its properties and applications in surface-quality evaluation are demonstrated. The differential equation of the highlight-line model is derived, and the difficulty involved in seeking its analytical solutions is discussed. Alternatively, the creation of highlight lines is formulated as a surface-plane intersection problem, and solved using surface-contouring techniques. A fast highlight-line algorithm is developed utilizing an efficient traced contouring technique. The algorithm is robust, fully automatic, and, therefore, well suited for realtime quality-assessment tasks.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31671/1/0000607.pd

AUTOMATIC FAIRING OF TWO-PARAMETER RATIONAL B-SPLINE MOTION

This paper deals with the problem of automatic fairing of two-parameter B

Automatic constraint-based synthesis of non-uniform rational B-spline surfaces

In this dissertation a technique for the synthesis of sculptured surface models subject to several constraints based on design and manufacturability requirements is presented. A design environment is specified as a collection of polyhedral models which represent components in the vicinity of the surface to be designed, or regions which the surface should avoid. Non-uniform rational B-splines (NURBS) are used for surface representation, and the control point locations are the design variables. For some problems the NURBS surface knots and/or weights are included as additional design variables. The primary functional constraint is a proximity metric which induces the surface to avoid a tolerance envelope around each component. Other functional constraints include: an area/arc-length constraint to counteract the expansion effect of the proximity constraint, orthogonality and parametric flow constraints (to maintain consistent surface topology and improve machinability of the surface), and local constraints on surface derivatives to exploit part symmetry. In addition, constraints based on surface curvatures may be incorporated to enhance machinability and induce the synthesis of developable surfaces;The surface synthesis problem is formulated as an optimization problem. Traditional optimization techniques such as quasi-Newton, Nelder-Mead simplex and conjugate gradient, yield only locally good surface models. Consequently, simulated annealing (SA), a global optimization technique is implemented. SA successfully synthesizes several highly multimodal surface models where the traditional optimization methods failed. Results indicate that this technique has potential applications as a conceptual design tool supporting concurrent product and process development methods

Aide au choix du posage en usinage 5 axes continus par la modélisation du comportement cinématique des machines-outils

Ces travaux s'inscrivent dans le cadre de l'amélioration de la productivité en usinage 5 axes continus. La modélisation d'un centre d'usinage et de sa commande numérique est proposée en 3 axes et 5 axes continus. Un simulateur est alors réalisé. Il permet de prévoir la vitesse de déplacement sur chacun des axes et de modifier les vitesses de consigne afin de mieux respecter les besoins spécifiés par le programmeur FAO. De plus les sources de perte de productivité du processus sont identifiées. Dans le but de réduire le temps d'usinage, une optimisation de l'orientation et du positionnement de la pièce dans la machine est donc proposée. Pour cela des cartographies en couleur sont réalisées. Elles permettent à un opérateur de choisir aisément un posage optimisé. L'ensemble des modélisations et des optimisations sont validées expérimentalement. Un choix optimal de posage associé à une modification de la vitesse au cours du programme permettent de réduire de plus de 50% le temps d'usinage.These works deal with productivity improvement in 5-axis machining. A machine tool and its computed numerically control are modeled in continuous 3 and 5 axis machining. A simulator is then performed. It predicts the speed on each axis and can change the programmed feedrate to fit with the specifications of the CAM programmer. Besides, the productivity of the process is improved. In order to reduce the machining time, orientation and positioning of the workpiece in the machine are optimized and the results are summarized in colored maps. This tool allows the operator to choose easily an optimized setup. Both modeling and optimization are validated experimentally. The optimal choice of part setup associated with a change of speed during the program can reduce more than 50% the machining time