This paper proposes a non-photorealistic rendering method that creates an artistic effect called mosaicing. The proposed method converts images provided by the user into the mosaic images. Commercial image editing applications also provide a similar function. However, these applications often trade results for low-cost computing. It is desirable to create high quality images even if the computa...

In this paper we will extend the concept of Voronoi diagrams to parameterized surfuces where distance between two points is defined as infimum over the lengths of surface paths connecting these points. We will present a method to compute Voronoi diagrams on these surfuces.

We present linear-time algorithms to construct tree-like Voronoi diagrams with disconnected regions after the sequence of their faces along an enclosing boundary (or at infinity) is known. We focus on the farthest-segment Voronoi diagram, however, our techniques are also applicable to constructing the order-(k+1) subdivision within an order-k Voronoi region of segments and updating a nearest-ne...

We give a new geometric interpretation of quantum pure states. Using Voronoi diagrams, we reinterpret the structure of the space of pure states as a subspace of the quantum state space. In addition to the known coincidence of some Voronoi diagrams for one-qubit pure states, we will show that even for mixed one-qubit states, as far as sites are given as pure states, the Voronoi diagram with resp...

Recently, the Arrangement 2 package of Cgal, the Computational Geometry Algorithms Library, has been greatly extended to support arrangements of curves embedded on two-dimensional parametric surfaces. The general framework for sweeping a set of curves embedded on a two-dimensional parametric surface was introduced in [3]. In this paper we concentrate on the specific algorithms and implementatio...