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You may know me for my interactive tutorials. But before that, I was writing visual but non-interactive tutorials. In particular, there wasn't a lot of information about A* on the web, so I decided to collect all my notes about pathfinding together in one place in the 1990s. But then in the 2010s I started making interactive pages. The newer pages are narrower in scope; I covered a broader set of
4 Jan 2023 Many of my interactive pages have a draggable object. I want the reader to move the object around, and I want the diagram to respond in some way. Here I’ll document the code I use to make this work with both mouse and touch input, using browser features that are widely supported since 2020. Here’s a common case I want to support: Drag the circle with mouse or touchThis is the simple mod
In addition to finding a shortest path, these algorithms can be used for distance maps, flow field pathfinding, connected components, map analysis, garbage collection algorithms, flow networks, and procedural map generation. There are many optimizations and specializations of these algorithms. Representing the map# The first thing to do when studying an algorithm is to understand the data. What is
Sep 2017 and Jan 2025 This map generator creates volcanic island style maps. The simplest way to explore the maps is to click the plus/minus arrows to change the Seed. Try clicking on the Seed input box and hold down the Up arrow key to quickly scan many different island shapes. Can you find an ice lake? They’re rare at the default temperature. You can right-click on the map to save a higher resol
Hi! I make interactive visual explanations of math and algorithms, using motivating examples from computer games.
Mar 2013, updated in Mar 2015, Apr 2018, Feb 2019, May 2020, Oct 2021, Dec 2022, Feb 2023, Oct 2024, Mar 2025 This guide will cover various ways to make hexagonal grids, the relationships between different approaches, and common formulas and algorithms. I've been collecting hex grid resources[1] for over 25 years. I wrote this guide to the most elegant approaches that lead to the simplest code, st
Note: this article is a companion guide to my guide to hex grids. The data structures and functions here implement the math and algorithms described on that page. The main page covers the theory for hex grid algorithms and math. Now let’s write a library to handle hex grids. The first thing to think about is what the core concepts will be. Since most of the algorithms work with cube coordinates, I
Feb 2014, updated Aug 2014, Nov 2018, Jul 2020 In a Tower Defense game, there are many enemies that are all headed to the same place. In many Tower Defense games, there is a predetermined path, or a small number of paths. In some, such as the classic Desktop Tower Defense[1], you can place towers anywhere, and they act as obstacles that affect the paths taken by enemies. Try it out, and click on t
2 Sep 2014 (Warning: these notes are rough – the main page is here and these are some notes I wrote for a few colleagues and then I kept adding to it until it became a longer page) Several people have asked me how I make the diagrams on my tutorials. I need to learn the algorithm and data structures I want to demonstrate. Sometimes I already know them. Sometimes I know nothing about them. It varie
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