if not modules then modules = { } end modules ['util-vec'] = {
    version   = 1.001,
    comment   = "support for vectors",
    author    = "Mikael Sundqvist & Hans Hagen",
    copyright = "PRAGMA ADE / ConTeXt Development Team",
    license   = "see context related readme files"
}

local newvector = vector.new

local sin, cos = math.sin, math.cos

local function xrotation(theta)
    return newvector {
        { 1,           0,          0, 0 },
        { 0,  cos(theta), sin(theta), 0 },
        { 0, -sin(theta), cos(theta), 0 },
        { 0,           0,          0, 1 },
    }
end

local function yrotation(phi)
    return newvector {
        { cos(phi), 0, -sin(phi), 0 },
        {        0, 1,         0, 0 },
        { sin(phi), 0,  cos(phi), 0 },
        {        0, 0,         0, 1 },
    }
end

local function zrotation(eta)
    return newvector {
        {  cos(eta), sin(eta), 0, 0 },
        { -sin(eta), cos(eta), 0, 0 },
        {         0,        0, 1, 0 },
        {         0,        0, 0, 1 },
    }
end

local function xyzscale(sx,sy,sz)
    return newvector {
        { sx or 1,       0,       0, 0 },
        {       0, sy or 1,       0, 0 },
        {       0,       0, sz or 1, 0 },
        {       0,       0,       0, 1 },
    }
end

-- local projz = newvector {
--     { 1, 0, 0, 0 },
--     { 0, 1, 0, 0 },
--     { 0, 0, 0, 0 },
--     { 0, 0, 0, 1 },
-- }

local function transform(eta,phi,theta,sx,sy,sz)
    if type(eta) == "table" then
        sz    = eta.sz
        sy    = eta.sy
        sx    = eta.sx
        theta = eta.theta
        phi   = eta.phi
        eta   = eta.eta
    end
    local v = xyzscale(sx,sy,sz)
    if eta then
        v = v * zrotation(eta)
    end
    if phi then
        v = v * yrotation(phi)
    end
    if theta then
        v = v * xrotation(theta)
    end
    return v -- * projz
end

local function points(M, N)
    if M then
        return newvector((M + 1) * ((N or M) + 1), 4)
    end
end

vector.helpers = {
    xrotation = xrotation,
    yrotation = yrotation,
    zrotation = zrotation,
    xyzscale  = xyzscale,
    transform = transform,
    points    = points,
}