Smooth union

The union of two shapes takes, at every point, the smaller of their two distances. Drag the two centres, then drag k up: wherever the two distances are within k of each other, between the dotted curves, that minimum is rounded off and a neck grows across, like two drops of water touching; at k = 0 it is the plain union. With a gap g between the circles, the two join once k reaches 2g. In the slice at the corner the faint lines are each circle's own distance and the bright one is the result.