GEOMETRIC MODELING OF THE CONTOUR ARCS PASSING THROUGH THE PREDEFINED POINTS

Abstract

Multidimensional interpolation is an important scientific task in demand of various science fields and technology. The geometrical theory of multidimensional interpolation has been further developed in terms of extending the shaping tools of geometrical modeling at the expense of the contour arcs passing through the predefined points. The proposed method is based on modification of Bezier’s curve with preservation of tangents in its initial and/or final points. Then the Bezier curve retains its geometrical properties of the arc, but additionally has the possibility to pass through several points set in advance. Examples are given of modifying a 5th-order Bezier curve arc into a curve arc passing through four predefined points and a 3rd-order Bezier curve arc passing through three predefined points and having a tangent in the initial point, which is proposed to be used as the onion dome surface forming arc. Such a method helps to reduce the piecewise character of composite curves when building curves. The introduction of such research results into computeraided design and solid-state modeling (CAD/CAM) systems will allow to expand their toolbox in terms of shaping surfaces and solids of technical shapes of various purposes.