##################################################################
##                                                              ##
##           FUNCTION FOR GETTING POLYGON INFORMATION           ##
##                                                              ##
##################################################################


getPolyCoords = function() {

    load("kaleidoscope.rda")
    # topLevel contains group polygons
    # subLevel contains polygons for subgroups within each group

    top.poly.coords = topLevel$k
    ### the number of top level groups
    n.groups = length(top.poly.coords)
    ### the number of subgroups in each group
    n.sub = sapply(subLevel, function(grp) length(grp$k))
    n.subsub = sapply(subsubLevel, function(grp) length(grp$k))
    total.subsubPgons = sum(n.subsub)
    total.subPgons = sum(n.sub)

    # which group each subgroup belongs in (numeric id)
    group.sub = rep(1:n.groups, n.sub)

    # which group each subsubgroup belongs to
    subsubs.per.group = numeric(n.groups)
    j = 1
    for (i in 1:n.groups) {
        subsubs.per.group[i] = sum(n.subsub[j:(j+n.sub[i]-1)])
        j = j + n.sub[i]
    }
    group.subsub = rep(1:n.groups, subsubs.per.group)


    ### These are the coordinates of the subgroups polygons
    sub.poly.coords = vector("list", total.subPgons)
    j0 = 1
    for (i in 1:n.groups) {
        subGroup = subLevel[[i]]$k
        j1 = j0 + n.sub[i] - 1
        sub.poly.coords[j0:j1] = subGroup
        j0 = j1 + 1
    }

    ### Coordinates of the subsubgroups polygons
    subsub.poly.coords = vector("list", total.subsubPgons)
    j0 = 1
    for (i in 1:total.subPgons) {
        subsubGroup = subsubLevel[[i]]$k
        j1 = j0 + n.subsub[i] - 1
        subsub.poly.coords[j0:j1] = subsubGroup
        j0 = j1 + 1
    }

    list(top.poly.coords = top.poly.coords,
         sub.poly.coords = sub.poly.coords,
         subsub.poly.coords = subsub.poly.coords,
         n.groups = n.groups,
         n.sub = n.sub,
         n.subsub = n.subsub,
         total.subPgons = total.subPgons,
         total.subsubPgons = total.subsubPgons,
         group.sub = group.sub,
         group.subsub = group.subsub,
         subsubs.per.group = subsubs.per.group,
         rdaTopLevel = topLevel,
         rdaSubLevel = subLevel,
         rdaSubsubLevel = subsubLevel)
}





#################################################################
##                                                             ##
##               FUNCTIONS FOR ROTATING POLYGONS               ##
##                                                             ##
#################################################################


rotatePgon =
    function(pgon, theta) {
        coords = rbind(pgon@pts[[1]]$x, pgon@pts[[1]]$y)
        theta.rad = theta * pi/180
        R = matrix(c(cos(theta.rad), -sin(theta.rad),
                     sin(theta.rad), cos(theta.rad)),
                   nr = 2, byrow = TRUE)
        rotated.coords = R %*% coords
        pgon@pts[[1]]$x = rotated.coords[1,]
        pgon@pts[[1]]$y = rotated.coords[2,]
        pgon
}

rotateImage =
    function(theta, polyVars) {

        tCoords = vector("list", polyVars$n.groups)
        sCoords = vector("list", polyVars$total.subPgons)

        for (i in seq(along = tCoords))
            tCoords[[i]] =
                rotatePgon(polyVars$top.poly.coords[[i]], theta)

        for (i in seq(along = sCoords))
            sCoords[[i]] =
                rotatePgon(polyVars$sub.poly.coords[[i]], theta)

        if (!is.null(polyVars$total.subsubPgons)) {
            ssCoords = vector("list", polyVars$total.subsubPgons)
            for (i in seq(along = ssCoords))
                ssCoords[[i]] =
                    rotatePgon(polyVars$subsub.poly.coords[[i]], theta)
        }
        else {
            ssCoords = NULL
        }

        list(top = tCoords, sub = sCoords, subsub = ssCoords)
}