Interval set: a volume rendering technique generalizing isosurface extraction

A scalar volume V={(x,f(x))|x∈R} is described by a function f(x) defined over some region R of the three dimensional space. The paper presents a simple technique for rendering interval sets of the form I_g(a,b)={(x,f(x))|a⩽g(x)⩽b}, where a and b are either real numbers of infinities. We describe an algorithm for triangulating interval sets as α shapes, which can be accurately and efficiently rendered as surfaces or semi transparent clouds. On the theoretical side, interval sets provide an unified approach to isosurface extraction and direct volume rendering. On the practical side, interval sets add flexibility to scalar volume visualization-we may choose to, for example, have an interactive, high quality display of the volume surrounding or “inside” an isosurface when such display for the entire volume is too expensive to produce