Abstract: A logical generalization of point skeletons based on a novel definition of distance from any point to a skeleton is presented. Unlike the two existing generalization ways: distance surfaces and convolution surfaces, this way preserves all good properties of point skeletons: (1) Skeletons are equidistant from any point on their features, this means that skeletons strongly resemble their features and we can use these resemblances intuitively to construct and control a geometric object through the manipulation of its skeletons; (2) The features of skeletons are convex; (3) The features of skeletons are highly smooth; (4) Skeletons are compact, highly abstract representation of their features, this means that we can use a group of very easily constructed and controlled skeletons to construct and control a complex glamorous geometric object; and besides, it has another property: (5) When a skeleton fluidly changes into another one of different dimension, its feature also varies fluidly. Moreover, a new way of combining, i.e. multiplying the fields generated by individual skeletons has been proposed. This way of combining has some better properties than the traditional way of combining, i.e. summing the fields generated by individual skeletons.