The applet was built using the Graphic, Algebra and Spreadsheet Views. Six free points define the profile of an object of revolution about the y-axis.
The seventh point slides on the axis of symmetry to control the shapes of the ellipses which give the appearance of a 3D view.
The profile curve consists of 5 cubic arcs which join smoothly in the sense that at each join the first and second derivatives of the neighbouring arcs are the same either side of the join. The technique is called "natural cubic spline fitting". The implementation just requires the Algebra of GeoGebra to find the inverse of a 4x4 symmetric matrix. Each arc is drawn as a locus controlled by a parameter t between 0 and 1 which is defined by a slider hidden from the field of view.
