Stadiums based on curvilinear geometry: Approximation of the ellipsoid offset surface

Abstract

Abstract This article provides an effective method of determining the coordinates of points and the angles for various surfaces approximating the ellipsoid surface. The stands of the stadium (with a capacity of up to 82,000 seats) with rows shaped by ellipse arcs were designed (in accordance with the European Standard EN 13200-1). An algorithm was proposed to determine the optimal height of the ring steps (with the guarantee of unobstructed vision of the entire playing field from each seat of the stands). The second algorithm ensures a comfortable space in each individual seating place in the stands (deviation of the depth of the row generated by ellipse arcs did not exceed 0.000009 m at any place of the stands). This article encourages readers to program DXF files (read in the AutoCAD system) to streamline design work.