Abstract
A method of forming linear frameworks of surfaces based on an array of points has been developed. From the initial array of points, subsets are distinguished - point series, based on which the linear elements of the surface framework are formed. The frame is formed on the basis of a family of guides and a family of generating curves. At the moment, the task of forming frameworks that define surfaces, whose functional purpose is interaction with the environment, is relevant. Methods of forming linear elements of the frame are proposed with the provision of regular changes of geometric characteristics along the curve while controlling the occurrence of special points. The specified properties of the frame elements provide the necessary surface properties. A general feature of the formation of flat and spatial contours by the proposed method is the mandatory analysis of the original point series. As a result of the analysis, areas are determined that can be interpolated by a curved line with a monotonous change in geometric characteristics, and areas where the occurrence of special points is inevitable. The method allows you to form flat and spatial curved lines, in which the number of special points is minimal. A method of estimating the error with which the formed contour represents a given curve is proposed. The method allows you to increase the number of conditions imposed on the outline. This can be prevention of oscillation, monotonous change of curvature and twist along the curve, fixed values of geometric characteristics at the starting points. Each of the additional conditions leads to the localization of the region of the possible location of the curve and reduces the error with which it is represented by the contour. The developed method was tested in the modeling of functional surfaces limiting the interblade channel of the turbocharger impeller. The main field of application of the developed method is modeling of dynamic surfaces, including the use of reverse engineering technology. The greatest effect can be obtained when solving problems that require reaching a compromise between the functional qualities of the surface and additional requirements for layout, comfort, and aesthetics.
Published Version
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