The algorithm for modeling curved surfaces, based on three-tier or four-tier closed contours. For shaping are applied to the segments of conic sections. The possibility of modeling the surface by way of increasing the dimensionality of the embedding space. The technique of formation of the surface using the curves of the second order and direction into ruled surfaces. The resulting equation of the surface is drawn on a flat triangular or quadrangular contour.
Keywords:four-dimensional space, hyperair the guide surface, the guide surface, the degree of freedom, the elliptical dome.