LONGRHO<-function(bingout) {
#takes confidence region produced by BINGHAM or BINGROT and projects it onto (long,rho) and (lat,rho) planes
#Bingham "type 1" regions (region is a nice football shaped region in lat long rho space) only
#all regions produced by LONGRHO, BINGROT, and BINGHAM are simultaneous
#bingout is a list with components bound, uppmat, lowmat
if (bingout$icase != 1) stop(message="bingham type 1 case only")
bound<-bingout$bound
uppmat<-bingout$uppmat
lowmat<-bingout$lowmat
nlong<-nrow(uppmat)
nlat<-ncol(lowmat)
long0<-floor(min(bound[,1]))
long1<-ceiling(max(bound[,1]))
lat0<-floor(min(bound[,2]))
lat1<-ceiling(max(bound[,2]))
dlong<-(long1-long0)/(nlong-1)
dlat<-(lat1-lat0)/(nlat-1)
xlong<-long0+(0:(nlong-1))*dlong
xlat<-lat0+(0:(nlat-1))*dlat
rho.u<-ifelse(is.finite(uppmat),uppmat,-200)
rho.l<-ifelse(is.finite(lowmat),lowmat,200)

up<-apply(rho.u,1,max)
lo<-apply(rho.l,1,min)
indu<- (up > -200)
indl<- (lo < 200)
bound.long.rho<-cbind(xlong[indu],up[indu])
bound.long.rho<-rbind(bound.long.rho,cbind(rev(xlong[indl]),rev(lo[indl])),bound.long.rho[1,])

up<-apply(rho.u,2,max)
lo<-apply(rho.l,2,min)
indu<- (up > -200)
indl<- (lo < 200)
bound.lat.rho<-cbind(xlat[indu],up[indu])
bound.lat.rho<-rbind(bound.lat.rho,cbind(rev(xlat[indl]),rev(lo[indl])),bound.lat.rho[1,])

c(bingout,list(bound.lat.rho=bound.lat.rho,bound.long.rho=bound.long.rho))
}