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CURDIS： A template for incremental curve discretization algorithms and its application to conics

虚拟现实与智能硬件 2024年第5期6卷 358-382页

作者： Philippe LATOUR marc van droogenbroeck Belgium 4000

We introduce CURDIS, a template for algorithms to discretize arcs of regular curves by incrementally producing a list of support pixels covering the arc. In this template, algorithms proceed by finding the tangent quadrant at each point of the arc and determining which side the curve exits the pixel according to a tailored criterion. These two elements can be adapted for any type of curve, leading to algorithms dedicated to the shape of specific curves. While the calculation of the tangent quadrant for various curves, such as lines, conics, or cubics, is simple, it is more complex to analyze how pixels are traversed by the curve. In the case of conic arcs, we found a criterion for determining the pixel exit side. This leads us to present a new algorithm, called CURDIS-C, specific to the discretization of conics, for which we provide all the details. Surprisingly, the criterion for conics requires between one and three sign tests and four additions per pixel, making the algorithm efficient for resource-constrained systems and feasible for fixed-point or integer arithmetic implementations. Our algorithm also perfectly handles the pathological cases in which the conic intersects a pixel twice or changes quadrants multiple times within this pixel, achieving this generality at the cost of potentially computing up to two square roots per arc. We illustrate the use of CURDIS for the discretization of different curves, such as ellipses, hyperbolas, and parabolas, even when they degenerate into lines or corners.

关键词： Computer graphics Curve discretization Conics Rasterization Ellipse drawing Conic spline Conic pencil

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CURDIS: A template for incremental curve discretization algorithms and its application to conics

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虚拟现实与智能硬件(中英文) 2024年第05期 358-382页

作者： Philippe LATOUR marc van droogenbroeck Montefiore Institute University of Liège

We introduce CURDIS, a template for algorithms to discretize arcs of regular curves by incrementally producing a list of support pixels covering the arc. In this template, algorithms proceed by finding the tangent quadrant at each point of the arc and determining which side the curve exits the pixel according to a tailored criterion. These two elements can be adapted for any type of curve, leading to algorithms dedicated to the shape of specific curves. While the calculation of the tangent quadrant for various curves, such as lines, conics, or cubics, is simple, it is more complex to analyze how pixels are traversed by the curve. In the case of conic arcs, we found a criterion for determining the pixel exit side. This leads us to present a new algorithm, called CURDIS-C, specific to the discretization of conics, for which we provide all the details. Surprisingly, the criterion for conics requires between one and three sign tests and four additions per pixel, making the algorithm efficient for resourceconstrained systems and feasible for fixed-point or integer arithmetic implementations. Our algorithm also perfectly handles the pathological cases in which the conic intersects a pixel twice or changes quadrants multiple times within this pixel, achieving this generality at the cost of potentially computing up to two square roots per arc. We illustrate the use of CURDIS for the discretization of different curves, such as ellipses, hyperbolas, and parabolas, even when they degenerate into lines or corners.

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CFD Analysis of Can Heating Process

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Fluid Dynamics & Materials Processing 2022年第4期18卷 1129-1136页

作者： David Alonso de Mezquia Uxue Arrieta MMounir Bou-Ali Ferruh Erdogdu Huseyin Topcam Bart van droogenbroeck Dagbjørn Skipnes Mechanical and Industrial Manufacturing Department Engineering Faculty of Mondragon UnibertsitateaMondragon20500Spain Department of Food Engineering Ankara UniversityGolbasi KampusuGolbasiAnkara06830Turkey Institute for Agricultural Fisheries and Food Research ILVOMerelbeke9820Belgium NOFIMA Research Center Stavanger4068Norway

In this work,the thermal sterilization process in food cans has been analyzed using Computational Fluid Dynamics(CFD).STAR CCM+software has been used in order to develop a numerical model to study the heating process of standard and the recently proposed toroidal shaped *** model has been validated comparing the results with the ones obtained experimentally and numerically that can be found in the literature.A good agreement between the obtained numerical results and the experimental ones has been *** results also agree with other numerical models previously developed in the *** the model has been validated,taking advance of the possibility to easily introduce movement in the simulations,new variables have been analyzed in the system using this model,such as rotational movement of the *** model developed has been used to study the efficiency of the sterilization process with the two types of cans by means of calculating the temperature inside the systems and calculating the F0 *** can be seen that the efficiency of the sterilization process is better in the toroidal *** has been also checked that CFD models can be very helpful in analyzing the temperature profiles inside the cans and making sure that the correct temperature has been obtained inside the can and the sterilization process has been correctly carried out.

关键词： Toroidal can heat transfer CFD retor

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