--begin vector functions
function addv(v1, v2)
  return {x=v1.x+v2.x, y=v1.y+v2.y}
end

function subv(v1,v2)
  return {x=v1.x-v2.x, y=v1.y-v2.y}
end

function multv(v,n)
  return {x=v.x*n, y=v.y*n}
end

function divv(v, n)
  return {x=v.x/n, y=v.y/n}
end

function magsqrv(v)
  return (v.x*v.x)+(v.y*v.y)
end

function distsqrv(v1, v2)
  return (v1.x-v2.x) * (v1.x-v2.x) + (v1.y-v2.y) * (v1.y-v2.y)
end
--end vector functions