Authors
Loktev M. A.
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Degree
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Postgraduate MSTU STANKIN |
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E-mail
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m.loktev@stankin.ru |
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Location
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Moscow |
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Articles
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Graphic techniques of computer-aided solving of few mathematical problemsThis paper is devoted to the application of computer graphics tools in order to devise graphic techniques of solving of mathematical problems. Examples of solving combined algebraic linear equations and mathematical programming problems are given.
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Method of a functional voxelization of polygonal objects on the basis of mathematical apparatus of R-functionsOne of the pressing problems arising at experts in the field of voxel modeling is development of algorithms
of a voxelization of the polygonal models, synthesized in modern CAD systems. Similar
tasks arise in process of development of systems of layer-by-layer synthesis where the formed image
represents layer-by-layer obtaining raster images. In the late nineties the beginning receives the direction
of the functional voxel modeling (FVM) allowing to consider a voxel image as some characteristic
of functional space (M-image). The paper considers the principles of construction functional voxel
geometrical objects on the closed contour on the basis of the R-functional description. The analysis
of the graphic images received by different ways of the description of the closed contour is provided.
Problems of obtaining monotony of the received functional space are considered. The provided analysis
confirms that the advanced piecewise-analytical method of obtaining the description of a contour
of object most conforms to requirements of smoothness and monotony. These requirements and
the received analytical description of a functional surface allow to expand considerably application
of such models in functional voxel modeling at automation of a wide class of problems for CAD and
automation technologies.
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