I have updated the Reference for Functional Equations. I have added several entries to the tables, updated the graphs, added some new graphs, added some explanations and additional notes on notation, corrected a few typos, and re-organised the document slightly. Get the new version here.
(Original Image by Valerie Everett)
It is sometime necessary to move an object in a physics simulation to a specific point. On the one hand, it can be difficult to analyse the exact force you have to apply; on the other hand it might not look so good if you animate the object’s position directly.
A compromise that works well in many situations is to use a spring-damper system to move the object.
The trick is simple: we apply two forces—the one is proportional to the displacement; the other is proportional to the velocity. Tweaked correctly, they combine to give realistic movement to the desired point.
Tags: damper, force, Game Development, game programming, physics, PID controller, Simulation, spring
(Original image by GoAwayStupidAI).
Below are four C++ implementations of the region quadtree (the kind used for image compression, for example). The different implementations were made in an attempt to optimise construction of quadtrees. (For a tutorial on implementing region quadtrees, see Issue 26 [6.39 MB zip] of Dev.Mag).
- NaiveQuadtree is the straightforward implementation.
- AreaSumTableQuadtree uses a summed area table to perform fast calculations of the mean and variance of regions in the data grid.
- AugmentedAreaSumTableQuadtree is the same, except that the area sum table has an extra row and column of zeros to prevents if-then logic that slows it down and makes it tricky to understand.
- SimpleQuadtree is the same as AugmentedAreaSumTableQuadtree , except that no distinction is made (at a class level) between different node types.
Tags: C++, image partitioning, Image Processing, quadtree, spatial partitioning
When implementing image algorithms, I am prone to make these mistakes:
- swapping x and y;
- working on the wrong channel;
- making off-by-one errors, especially in window algorithms;
- making division-by-zero errors;
- handling borders incorrectly; and
- handling non-power-of-two sized images incorrectly.
Since these types of errors are prevalent in many image-processing algorithms, it would be useful to develop, once and for all, general tests that will catch these errors quickly for any algorithm.
This post is about such tests.
Tags: algorithm, C++, compression, Image Processing, Python, unit testing
*Fast = not toooo slow…
For the image restoration tool I had to implement min and max filters (also erosion and dilation—in this case with a square structuring element). Implementing these efficiently is not so easy. The naive approach is to simply check all the pixels in the window, and select the maximum or minimum value. This algorithm’s run time is quadratic in the window width, which can be a bit slow for the bigger windows that I am interested in. There are some very efficient algorithms available, but they are quite complicated to implement properly (some require esoteric data structures, for example monotonic wedges (PDF)), and many are not suitable for floating point images.
So I came up with this approximation scheme. It uses some expensive floating point operations, but its run time is constant in the window width.
Tags: algorithm, dilation, erosion, filtering, Image Processing, maximum filter, minimum filter, morphology
Many textures used for 3D art start from photographs. Ideally, such textures should be uniformly lit so that the texture does not interfere with the lighting applied by the 3D software. Often, lighting artefacts must be removed by hand. This can be tedious and time consuming.
The tool provided here aims to automate this process. It is still in an experimental phase, so it is very crude. Below you can see some of the before and after pictures.
Tags: filtering, game tools, Image Processing
I decided to put the Poisson disk sampling code here for download since the site that hosted it is down. The code accompanies the tutorial on Dev.Mag: Poisson Disk Sampling.
Download
| poisson_disk_java.zip (184 KB) poisson_disk_python.zip (912 KB) poisson_disk_ruby.zip (59 KB) |
(Original Image by everyone’s idle.)
This post was a originally published on Luma Labs, now dead.
As old as stimulus-response techniques are, they still form an important part of many AI systems, even if it is a thin layer underneath a sophisticated decision, planning, or learning system. In this tutorial I give some advice to their design and implementation, mostly out of experience gained from implementing the AI for some racing games.
A stimulus response agent (or a reactive agent) is an agent that takes inputs from its world through sensors, and then takes action based on those inputs through actuators. Between the stimulus and response, there is a processing unit that can be arbitrarily complex. An example of such an agent is one that controls a vehicle in a racing game: the agent “looks” at the road and nearby vehicles, and then decides how much to turn and break.
Tags: AI, artificial intelligence, convolution, filtering, Kalman filter, Mathematics, PID controller, racing game ai, random, random steering, response curve, Special Numbers Library, stimilus response agent, system design
Tools for editing game levels and AI for your own games are nice to have, but it is not always practical to implement these for small projects, nor is it affordable to buy them off-the-shelf or bundled with expensive middleware.
In the Dev.Mag article Guerrilla Tool Development, I give some ideas for getting some useful tools on a tight budget. Check it out!
(Original image by Hljod.Huskona / CC BY-SA 2.0).
I used to hate neural nets. Mostly, I realise now, because I struggled to implement them correctly. Texts explaining the working of neural nets focus heavily on the mathematical mechanics, and this is good for theoretical understanding and correct usage. However, this approach is terrible for the poor implementer, neglecting many of the details that concern him or her.
This tutorial is an implementation guide. It is not an explanation of how or why neural nets work, or when they should or should not be used. This tutorial will tell you step by step how to implement a very basic neural network. It comes with a simple example problem, and I include several results that you can compare with those that you find.
Tags: AI, artificial intelligence, Matlab, neural network, Octave, optimisation, pattern recognition, random, sampling
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