USING SPLINE FUNCTIONS FOR THE SHAPE DESCRIPTION...
'2,JHLQ GRZEGORZ LENDA1
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21
GEOINFORMATICA POLONICA
USING SPLINE FUNCTIONS FOR THE SHAPE DESCRIPTION OF THE SURFACE OF SHELL STRUCTURES Key words: shell structures, quadrics, splines, approximation Abstract The assessment of the cover shape of shell structures makes an important issue both from the point of view of safety, as well as functionality of the construction. The most numerous group among this type of constructions are objects having the shape of a quadric (cooling towers, tanks with gas and liquids, radio-telescope dishes etc.). The material from observation of these objects (point sets), collected during periodic measurements is usually converted into a continuous form in the process of approximation, with the use of the quadric surface. The created models, are then applied in the assessment RIWKHGHIRUPDWLRQRIVXUIDFHLQWKHJLYHQSHULRGRIWLPH6XFKDSURFHGXUHKDVKRZHYHUVRPHVLJQL¿FDQWOLPLWDWLRQV7KH approximation with the use of quadrics, allows the determination of basic dimensions and location of the construction, KRZHYHULWUHVXOWVLQLGHDOREMHFWVQRWSURYLGLQJDQ\LQIRUPDWLRQRQORFDOVXUIDFHGHIRUPDWLRQV7KH\FDQRQO\EHGH¿QHG by comparison of the model with the point set of observations. If the periodic measurements are carried out in independent, VHSDUDWHSRLQWVWKHQLWZLOOEHLPSRVVLEOHWRGH¿QHWKHH[LVWLQJGHIRUPDWLRQVGLUHFWO\7KHVHFRQGSUREOHPUHVXOWVIURPWKH one-equation character of the ideal approximation model. Real deformations of the object change its basic parameters, inter alia the lengths of half-axis of main quadrics. The third problem appears when the construction is not a quadric; no information on the equation describing its shape is available either. Accepting wrong kind of approximation function, causes the creation of a model of large deviations from the observed points. All the mentioned above inconveniences can be avoided by applying splines to the shape description of the surface of shell structures. The use of the function of this type, however, comes across other types of limitations. This study deals with the above subject, presenting several methods allowing the increase of accuracy and decrease of the time of the modelling with the splines. WYKORZYSTANIE FUNKCJI SKLEJANYCH '223,68.6=7$à7832:,(5=&+1,%8'2:/,32:à2.2:
