Top down

Top down processes depart from an assumed final result and work their way to meet this result. The final result, within this scope, is evaluated as the profile curve responsible for shaping the structure in its vertical sections, ultimately functioning as the main responsible for the forces discharge (along with the thickness and angles of contact faces). Top down processes depart from a given curve as the vertical profile curve (e.g., circle, oval, catenary) to generate a resulting shape whose structural efficiency is only then evaluated.

A quick survey of various openings in masonry walls in the last two thousand years allows us to enumerate several types of curves in arches which, often, are also the profile used for vaults. Of these, we find as common denominator a symmetric curved profile that connects the top of both jambs and its tip is above them. The large array of possibilities, characteristic of different geographic regions, culture and ultimately architecture styles, was categorized by Chaix according to the proportion between the width and the height. The usage of diffused template shapes characterizes this type of solutions. Given an arch profile, a top down vault surface is produced by a geometric operation that transforms this generatrix into a surface.