Bounds for spiral and piecewise spiral splines

This note is the updated outline of the article “Interpolational properties of planar spiral curves”, Fund. and Applied Math., 2001, Vol.7, N.2, 441-463, published in Russian. The main result establishes boundary regions for spiral and piecewise spiral splines, matching given data. The width of such region can serve as the measure of fairness of the point set, subjected to interpolation. Application to tolerance control of curvilinear profiles is discussed.