How to fit rectangular polygon into irregular polygon using R?

Question

How to fit a rectangular polygon into an irregular polygon? Or better; how to get the maximum-rectangular-polygon fitting into an irregular polygon?

Background : I have got a bunch of overlapping raster files which represent different datatakes of a spaceborne sensorsystem. For further analysis, I want to get the maximum-rectangular-polygon (all 4 corners with 90degree angle) which fits into the footprints/outline of all these datasets, to mask and crop my datasets. In other words; How to fit a rectangular polygon of maximum size into the green outline (see image below)?

Idea : First get the outline or footprint for every dataset, then dissolve all the footprints to get the outline and finally fit a rectangular polygon of maximum extent into that irregular polygon

Answer 1

Does the following do what you need?

library(raster)
library(rgeos)
library(mapview)
raster1 <- raster(xmn=-2,xmx=0.1,ymn=50.3,ymx=51.5,vals=1)
raster2 <- raster(xmn=-2.1,xmx=0.5,ymn=50.4,ymx=51.4,vals=1)
raster3 <- raster(xmn=-2.2,xmx=-0.3,ymn=50.2,ymx=51.6,vals=1)

r1 <- extent(raster1)
r1p <- as(r1, 'SpatialPolygons')
r2 <- extent(raster2)
r2p <- as(r2, 'SpatialPolygons')
r3 <- extent(raster3)
r3p <- as(r3, 'SpatialPolygons')
r1p$data <- 1
r2p$data <- 2
r3p$data <- 3

rr <- bind(r1p, r2p, r3p)
rrsp <- as(extent(rr), 'SpatialPolygons')
rrsp$data <- 1
crs(rrsp) <- crs(r1p) <- crs(r2p) <- crs(r3p) <- crs(raster1)

mm <-
    mapview(rrsp, col.regions = 'green', col='green', alpha.regions = 0.1) + 
    mapview(r1p, col.regions = 'red', col='red', alpha.regions = 0.1) + 
    mapview(r2p, col.regions = 'red', col='red', alpha.regions = 0.1) + 
    mapview(r3p, col.regions = 'red', col='red', alpha.regions = 0.1)

mm

It finds the extents of each raster, makes spatial polygons from them, and then binds them together. The extent of this is then found, again as a spatial polygon.

The mapview code makes the following plot.

The green rectangle encompasses all of the rasters which are in red.