# These functions all take references to arrays over [0..2] without
# modifying the arguments. Arguments assume Cartesian(x,y,z) geometry
# This could be expanded to a module.

# Cartesian 3-vector dot product
sub dot {
    $_[0]->[0]*$_[1]->[0]+$_[0]->[1]*$_[1]->[1]+$_[0]->[2]*$_[1]->[2];
}

# Cartesian 3-vector cross product
# returns reference to array over [0..2]
sub cross {
    [$_[0]->[1]*$_[1]->[2]-$_[0]->[2]*$_[1]->[1],
     $_[0]->[2]*$_[1]->[0]-$_[0]->[0]*$_[1]->[2],
     $_[0]->[0]*$_[1]->[1]-$_[0]->[1]*$_[1]->[0]];
}

# length of a Cartesian 3-vector
# returns number
sub norm {
    sqrt(dot($_[0],$_[0]));
}

# angle between two Cartesian 3-vectors
# returns number: angle in radians
sub arc {
    atan2 norm(cross($_[0],$_[1])), dot($_[0],$_[1]);
}
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