Interactive design of smooth genus n objects over a single domain

Recently, there have been some developments in constructing infinitely smooth genus-n objects over a single domain using the so-called topological design method. Compared with existing geometric design methods, it provides many advantages: a simpler data structure, a compact data set and infinite continuity. Improvement in the user interface, however, is still needed for designing free-form genus-n objects. This research improves the topological design interface by incorporating a radial-basis scattered data interpolating function for designing infinitely smooth genus-n objects over a single domain. As part of this research, a constrained Delaunay triangulation over the given unstructured data on the single domain is activated. This allows visualization of a polygonized genus-n object in the object space as well as providing interactive data control behavior in the object space. This method is characterized by the unconstrained control points inside the boundaries and by the small-size data set needed to design a free-form genus-n object.