Cup lid with roll and spill limiting rim

A container assembly comprising:

• a beverage container having a substantially round container lip and a container wall extending downward therefrom to a substantially round container base;
• and
• a lid compatible for attachment to said beverage container so as to form therewith a container assembly, the lid comprising:
• a substantially round rim having a substantially uniform radius as measured from a center of the lid, the rim being configured for secure attachment to the container lip;
• a central lid portion surrounded and bounded by the rim;
• a spout extending upward from the central lid portion proximal to the rim, the spout being configured for consumption therethrough of beverage;
• and
• a flange extending outward beyond an outer edge of the rim at least in a region of the rim that is proximal to the spout, the flange having a non-uniform radius as measured from the center of the lid;
• an upper perimeter of the lid being formed by outer edges of the rim and the flange such that when the container assembly is tipped over onto a horizontal surface, the container assembly is supported by a lowest point of the round base and by at least one point on the upper perimeter of the lid;
• wherein a radius of the upper perimeter of the lid, measured as a function of angular orientation about the center of the lid, includes a plurality of local minimum radii terminating at minimum points and a plurality of local maximum radii terminating at minimum points, said local maximum radii including a first local maximum radius that passes through the spout and terminates in a first maximum point, such that when the container assembly is tipped over and when the first maximum point momentarily contacts the horizontal surface, the container is gravitationally induced to roll until it assumes an orientation in which a height of its center of gravity is at a local minimum wherein the container is required to roll through an angle of no more than 90 degrees so as to reach the orientation at which the height of its center of gravity is at a local minimum.