AN ANALYTICAL DESCRIPTION OF MUTUAL PLACEMENT CONDITIONS FOR AN ELLIPSE AND A REGION RESTRICTED BY A PARABOLA
Keywords:
Ф- function, ellipse, parabola, non-intersection, inclusionAbstract
method of construction of a Ф-function of an ellipse and a parabola is considered. Ф-function allows to model nonintersection and inclusion conditions in different geometric design problems: packing, cutting, arrangement, etc. Necessary expressions for Ф-function construction can be obtained using the conditions of tangent coefficient equality in tangent points of the parabola and the homothetically transformed ellipse. To obtain inclusion condition a coordinate system transformation is applied. In the general case an application of second-order methods for optimum search is acceptable and gives a good result for finding the points of the ellipse and the parabola which determine Ф- function value.
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References
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