A5 Pentagons Are the New Bestagons скачать в хорошем качестве

A5 Pentagons Are the New Bestagons

How can you accurately aggregate and compare point-based data from different parts of the world? When analyzing crime rates, population, or environmental factors, how do you divide the entire globe into equal, comparable units for analysis?   For data scientists and geospatial analysts, these are fundamental challenges. The solution lies in a powerful class of tools called Discrete Global Grid Systems (DGGS). These systems provide a consistent framework for partitioning the Earth's surface into a hierarchy of cells, each with a unique identifier. The most well-known systems, Google's S2 and Uber's H3, have become industry standards for everything from database optimization to logistics.   However, these systems come with inherent trade-offs. Now, a new DGGS called A5 has been developed to solve some of the critical limitations of its predecessors, particularly concerning area distortion and analytical accuracy.   Why Gridding the Globe is Harder Than It Looks The core mathematical challenge of any DGGS is simple to state but difficult to solve: it is impossible to perfectly flatten a sphere onto a 2D grid without introducing some form of distortion. Think of trying to apply a perfect chessboard or honeycomb pattern to the surface of a ball; the shapes will inevitably have to stretch or warp to fit together without gaps.   All DGGS work by starting with a simple 3D shape, a polyhedron, and projecting its flat faces onto the Earth's surface. The choice of this initial shape and the specific projection method used are what determine the system's final characteristics. As a simple analogy, consider which object you’d rather be hit on the head with: a smooth ball or a spiky cube? The ball is a better approximation of a sphere. When you "inflate" a spiky polyhedron to the size of the Earth, the regions nearest the sharp vertices get stretched out the most, creating the greatest distortion.   A Quick Look at the Incumbents: S2 and H3   To understand what makes A5 different, it's essential to have some context on the most popular existing systems.   Google's S2: The Cube-Based Grid The S2 system is based on projecting a cube onto the sphere. On each face of this conceptual cube, a grid like a chessboard is applied. This approach is relatively simple but introduces significant distortion at the cube’s vertices, or "spikes." As the grid is projected onto the sphere, the cells near these vertices become stretched into diamond shapes instead of remaining square. S2 is widely used under the hood for optimizing geospatial queries in database systems like Google BigQuery.   Uber's H3: The Hexagonal Standard Uber's H3 system starts with an icosahedron—a 20-sided shape made of triangles. Because an icosahedron is a less "spiky" shape than a cube, H3 suffers from far less angular distortion. Its hexagonal cells look more consistent across the globe, making it popular for visualization. H3's immense success is also due to its excellent and user-friendly ecosystem of tools and libraries, making it easy for developers to adopt. However, H3 has one critical limitation for data analysis: it is not an equal-area system. This was a deliberate trade-off, not a flaw; H3 was built by a ride-sharing company trying to match drivers to riders, a use case where exact equal area doesn't particularly matter. To wrap a sphere in hexagons, you must also include exactly 12 pentagons—just like on a soccer ball. If you look closely at a football, you'll see the pentagonal panels are slightly smaller than the hexagonal ones. This same principle causes H3 cells to vary in size. The largest and smallest hexagons at a given resolution can differ in area by a factor of two, meaning that comparing raw counts in different cells is like comparing distances in miles and kilometers without conversion. For example, cells near Buenos Aires are smaller because of their proximity to one of the system's core pentagons, creating a potential source of error if not properly normalized.   Introducing A5: A New System Built for Accuracy A5 is a new DGGS designed from the ground up to prioritize analytical accuracy. It is based on a dodecahedron, a 12-sided shape with pentagonal faces that is, in the words of its creator, "even less spiky" than H3's icosahedron.   The motivation for A5 came from a moment of discovery. Its creator, Felix Palmer, stumbled upon a unique 2D tiling pattern made of irregular pentagons. This led to a key question: could this pattern be extended to cover the entire globe? The answer was yes, and it felt like uncovering something "very, very fundamental." This sense of intellectual curiosity, rather than a narrow business need, is the foundation upon which A5 is built. A5's single most important feature is that it is a true equal-area system. Using a specific mathematical projection, A5 ensures that every single cell at a given resolution level has the exact same area. This guarantee even accounts for the Earth's true shape as a slightly ...