Generating Well-Distributed Point Sets with a Self-Similar Hierarchical Tile

We present a method for generating well-distributed point according to a given density. Our method is based on a single precomputed tile. The tile is both self-similar and hierarchical. A selfsimilar tile allows to increase the density of points in large steps by recursively subdividing the tile. A hierarchical tile allows to smoothly adjust the density of points. We present an interesting method to construct a self-similar point distribution, we show how to construct a well-distributed self-similar point distribution, and how to make a point distribution hierarchical. Our method is capable of generating well-distributed point sets in real time, using an algorithm that is easy to implement. However, because only a single tile is used, noticeable periodicity is introduced in the generated point distributions. Therefore, our method is somewhat better suited for applications that do not require point distributions with a high visual quality, such as sampling. Volume xx (200y), Number z, pp. 1–8 Generating Well-Distributed Point Sets with a Self-Similar Hierarchical Tile Ares Lagae & Philip Dutré Department of Computer Science Katholieke Universiteit Leuven † Abstract We present a method for generating well-distributed point according to a given density. Our method is based on a single precomputed tile. The tile is both self-similar and hierarchical. A self-similar tile allows to increase the density of points in large steps by recursively subdividing the tile. A hierarchical tile allows to smoothly adjust the density of points. We present an interesting method to construct a self-similar point distribution, we show how to construct a well-distributed self-similar point distribution, and how to make a point distribution hierarchical. Our method is capable of generating well-distributed point sets in real time, using an algorithm that is easy to implement. However, because only a single tile is used, noticeable periodicity is introduced in the generated point distributions. Therefore, our method is somewhat better suited for applications that do not require point distributions with a high visual quality, such as sampling.We present a method for generating well-distributed point according to a given density. Our method is based on a single precomputed tile. The tile is both self-similar and hierarchical. A self-similar tile allows to increase the density of points in large steps by recursively subdividing the tile. A hierarchical tile allows to smoothly adjust the density of points. We present an interesting method to construct a self-similar point distribution, we show how to construct a well-distributed self-similar point distribution, and how to make a point distribution hierarchical. Our method is capable of generating well-distributed point sets in real time, using an algorithm that is easy to implement. However, because only a single tile is used, noticeable periodicity is introduced in the generated point distributions. Therefore, our method is somewhat better suited for applications that do not require point distributions with a high visual quality, such as sampling.