Primary-geodesic least surface shapes for predetermined ground plots and functions

Abstract

A means to create the shape for a structure that holds the most space under the least area for any predetermined polygonal ground plot. The ground plot is cut into a sheet material as an open window, called a plot-frame 2 . The plot-frame 2 could also be created on the ground itself. A membrane 1 is placed over the plot-frame 2 and a pressure differential is created on both sides of the membrane 1 . Functions that take on polygonal shapes are placed on the membrane 1 that would be entryways; connection planes and other flat polygons are achieved by means of constraints 4. The final static display shape of the membrane 1 shows the shape of the intended structure above ground.

I. I claim a least surface geodesic shaped structure that matches up to any ground-plot and has the required polygonal functions such as connection-planes, entryways, view-ports and other flat or curved predetermined surfaces that could be demanded upon its surface by, 
 fixing the shape of any plot of ground that the structure is required to cover to an open window within a plot-frame ( 2 );  
 expanding the membrane ( 1 ) from the open window within the plot-frame ( 2 ) with a even pressure force between the plot-frame and the base ( 3 );  
 while creating functions on the membrane ( 1 ) as polygonal surfaces whereby, 
 constraints ( 4 ) hold the membrane ( 1 ) to points/lines/planes by fixing the surface of the membrane ( 1 ) to the places that it needs to be for the polygonal shapes that it is required to have,  
 so that the membrane ( 1 ) shows the least surface above the plot-frame ( 2 ) with the proper shapes for the functions that the structure is required to have.