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#' morphomapMoment
#'
#' Calculate the moment of inertia around the x and y axes and the product of inertia
#' @param cp matrix: coordinates of the external outline
#' @param mp matrix: coordinates of the internal outline
#' @param delta numeric: picture elements of adjustable side length
#' @return Ix numeric: moment of inertia around the x axis
#' @return Iy numeric: moment of inertia around the y axis
#' @return Ixy numeric: product of inertia around the x and y axis
#' @author Antonio Profico, Luca Bondioli, Pasquale Raia, Paul O'Higgins, Damiano Marchi
#' @examples
#' #create a section
#' extsec<-morphomapCircle(10,1000)
#' intsec<-morphomapCircle(8,1000)
#' InMs<-morphomapMoment(extsec,intsec,delta=0.1)
#' @export
morphomapMoment<-function(cp,mp,delta=0.1){
maxx<-max(cp[,1],na.rm=T)
minx<-min(cp[,1],na.rm=T)
maxy<-max(cp[,2],na.rm=T)
miny<-min(cp[,2],na.rm=T)
X<-seq(minx+delta/2,maxx-delta/2,delta)
Y<-seq(miny+delta/2,maxy-delta/2,delta)
grid_sect<-as.matrix(expand.grid(X, Y))
A<-point.in.polygon(grid_sect[,1], grid_sect[,2], cp[,1], cp[,2], mode.checked=FALSE)
B<-point.in.polygon(grid_sect[,1], grid_sect[,2], mp[,1], mp[,2], mode.checked=FALSE)
sel<-which(A==1 & B==0)
delta2=delta*delta
Ix<-sum((grid_sect[sel,2]^2)*delta2)
Iy<-sum((grid_sect[sel,1]^2)*delta2)
Ixy<-sum((grid_sect[sel,1]*grid_sect[sel,2])*delta2)
names(Ix)<-"Ix"
names(Iy)<-"Iy"
names(Ixy)<-"Ixy"
return(c(Ix,Iy,Ixy))
}
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