Mathematics

Calculating Vectors for AI Ship Movement Vectors are essential mathematical constructs for defining the desired direction and magnitude of movement for AI controlled ships. At their core, vectors contain numeric x and y components that denote direction using trigonometric principles. By normalizing vector lengths and mapping vector directions to intended ship headings, smooth trajectories can…

What is a Projectile? A projectile is any object that once launched or fired, continues moving under its own inertia and is influenced only by the downward force of gravity. Common examples of projectiles include balls, arrows, and bullets. Key terms related to projectile motion include: Launch angle: The angle a projectile is initially launched…

The goal of launching a projectile to precisely strike a target involves carefully determining the initial velocity that will enable the projectile to follow the ideal trajectory. The key variables that influence this include the location of the target, the launch location and orientation of the weapon or launcher, the mass and dimensions of the…

Using Beta Distributions for Dynamic Randomness Beta distributions are continuous probability distributions defined over the interval [0, 1] parameterized by two positive shape parameters, commonly labeled α and β. Unlike the uniform distribution which assigns equal probability over the [0, 1] range, beta distributions allow for a variety of distribution shapes based on the choice…

Defining Uniform Distributions A uniform distribution refers to a probability distribution in which all outcomes have an equal likelihood of occurring. Some key properties of uniform distributions include: The probability density function (PDF) is constant over the distribution’s support range. All values within the distribution’s bounds have equal probability. The distribution has maximum entropy out…

Speeding Up Non-Uniform Random Number Generation Generating non-uniform random numbers is a common task in statistical sampling, Monte Carlo simulations, and other applications. However, basic algorithms for generating non-uniform distributions are often inefficient. As the number of random values needed grows into the millions or billions, the computational costs can become prohibitive. This article examines…

Getting Started with Math for Game Graphics Programming Game graphics programming relies heavily on mathematics to model 3D worlds and render them efficiently. Before diving into graphics APIs like Direct3D or Vulkan, it’s important to build a solid math foundation covering topics like linear algebra, calculus, statistics, and probability. This article provides an overview of…

Determining Aim with Trigonometry The foundation of aim calculation in shooting games relies on basic trigonometric functions. By determining the angles and distances between the barrel of the gun to the target, we can use sine, cosine, and tangent functions to aim precisely. The key is translating the geometric relationship between barrel, target and the…

Predicting Future Positions In order to aim properly at a moving target, we first need to predict where that target will be in the future. This requires an understanding of position vectors, which locate objects in space, and velocity vectors, which describe their speed and direction of motion. A position vector P locates a game…

Understanding Projectile Motion Physics Predicting accurate aim points for moving targets requires a strong grasp of the physics of projectile motion. Specifically, factors like gravity, acceleration, velocity vectors, and kinematic equations that relate these variables need to be internalized. Only with an intuition for how these physical factors intersect can one start to derive the…