Piecewise-smooth Subdivision

Below are some examples from our paper Piecewise-smooth subdivision with normal control (H. Biermann, A. Levin, D. Zorin, SIGGRAPH 2000). In this paper, we present a complete set of subdivision rules for piecewise-smooth surfaces.


Quite often, standard subdivision rules don't produce satisfying results: In this example, we want to interpolate the boundary of the control mesh (left). We would expect a smooth surface of similar shape as the control mesh (middle), but the standard corner rules produce the surface on the right.

control mesh concave corners convex corners

Rather than adding ad-hoc rules for various special cases, we define the class of piecewise-smooth surfaces, which is sufficiently general for modeling applications. The class contains surfaces with boundaries and corners. There are two corner types, which are not equivalent: convex (left) and concave (middle). Combining convex and concave sectors results in complex corners (right).

convex corner concave corner complex corner

We present a uniform framework to generate piecewise-smooth surfaces. Moreover, the same algorithm allows to prescribe normal directions on the surface. By manipulating the normals, one can bend the surface in an intuitive way without changing the control mesh.

normal manipulation

In our reference implementation, the user applies features to the surface by tagging the control mesh. This example shows the surface without tags (left), convex and concave corners (center), and a complex corner of three sectors (right).

pipes pipes with corners pipes with complex corner