An ogive is the shape formed by the pointed Gothic style arches. It is formed by the intersection of two circular arcs such that a sharp point is formed at the point of intersection. Of more application to metalworkers, 'ogive' is also used to describe the three dimensional shape typical of a rocket nose cone. Its cross-section has the same mathematical description as the Gothic arch.
Ogives can be turned incrementally on a lathe by first developing a table of (x,y) values that define the shape, then making a series of plunge cuts based on those values. A final finish is then done with a file and emery paper.
The attached diagram shows the math to develop the (x,y) value pairs as a function of the parameters of the desired ogive. Tedious work at best; that's why I wrote a program (OGIVE.C) to do this. An input data file is used to specify the ogive parameters and the details of the 'x' step size and tool width then, when the program runs it produces a cutting schedule that can be carried to the lathe to guide the turning.