Introduction
Video games are amazing! They can be fun, educational, and even therapeutic. But how do they work? How do you develop a game that can move around or shoot lasers? The answer: math. Even if you never need more than basic addition and subtraction during your game design studies, you will use them a lot. After that, it's all up to you.
Even if you never need more than basic addition and subtraction during your game design studies, you will use them a lot. After that, it's all up to you.
Even if you never need more than basic addition and subtraction during your game design studies, you will use them a lot. After that, it's all up to you.
You may still have to do some trigonometry in order to solve problems related to collisions and distances between objects. Vectors are also good for calculating movement and rotation of objects within the game world.
Many people think that advanced math skills are needed for creating games, but this is not usually the case.
Many people think that math skills are absolutely necessary for creating video games, but the truth is that not all game designers and programmers need to be math whizzes. In fact, in many cases, it's not even necessary to have a background in computer science or engineering.
While there may be some aspects of your job where you will use advanced mathematics, most of the time you'll be using basic math skills like addition and subtraction (though sometimes multiplication and division). Many of the equations and formulas used in programming won't require much more than basics. For example:
The formula for determining how much damage an item does on impact with an enemy uses simple multiplication: damage = base damage * bonus multiplier * skill coefficient * environment bonus coefficient * current HP / max HP * armor class bonus coefficient
A simple equation for determining if a hit box collides with another hit box looks like this: (1 - (dist(hitbox1) / dist(hitbox2))^2), where "dist" stands for distance between two points
Math is used in many different aspects of game design and programming.
Let's take a look at some of the ways math is used in video game design and programming.
Game theory: Game theory is the study of how getting into one strategy affects what other players will do, and vice versa. It's used to help understand how people make decisions in gaming situations, especially when there are multiple players involved.
Physics: Math underlies all things physical (and non-physical), from gravity and force to motion and velocity. In terms of games, it's important for calculating how objects move through space—for example, knowing if your spaceship can change direction quickly enough to avoid an asteroid field or whether an enemy bullet can hit your character before they dodge out of the way.* Artificial intelligence: Computer scientists often use stochastic methods (like Monte Carlo simulation) to determine things like where enemies or other characters should appear on screen; this type of process uses random numbers generated by computers rather than using strict mathematical formulas.* Data analysis: When designing complex games with many moving pieces—like a massively multiplayer online roleplaying game (MMORPG)—it helps developers keep track of everything going on while they're programming each new feature into their project by analyzing large amounts of data from previous versions.* Debugging: Debugging means fixing errors that occur during development stages so as not to interfere with testing efforts later down the line.* 3D modeling: Developers use trigonometry extensively for creating models within virtual environments like video games or virtual reality systems like Oculus Rift; for example, calculating distances between points so that polygons stay within certain bounds when rendered onto screens allows users' eyesight not be overwhelmed by too much information at once
Game designers generally use math to solve problems that pertain to movement, physics, and time.
Game designers generally use math to solve problems that pertain to movement, physics, and time.
Movement: Game designers are often tasked with creating a player's avatar in the game world. These avatars can be controlled by a player or they can move on their own as AI. The way they move is dictated by the rules of physics in the game world (gravity, air resistance, friction). If there's not enough real life data available for how an object should behave in a certain situation (e.g., how fast a thrown ball will fly), developers must come up with their own equations to estimate this behavior accurately enough to make gameplay possible while still keeping it interesting and fun for players who want challenging experiences but aren't interested in spending hours learning calculus in order to get them!
3D gaming requires more advanced math than 2D gaming does.
3D games require more advanced math than 2D games do. This is because in 3D gaming, you have to account for the third dimension of space (depth). If you don't take into account how far away objects are from each other, your game will look and feel very weird. For example, if you were playing a racing game where cars were constantly crashing into each other and going through walls of buildings, it would be really weird to see them behave like that in real life!
Math is also used to determine other factors such as damage and health, speed, acceleration, and gravity.
Math is also used to determine other factors such as damage and health, speed, acceleration, and gravity.
3D gaming requires more advanced math than 2D gaming does.
Trigonometry and Vectors
Remember your trigonometry class? Trig is a branch of mathematics that deals with triangles. The sine, cosine, and tangent of an angle (a/k/a sin π/2 = 0) are the sides of a triangle's three angles. They can be used to calculate the value of any angle by knowing two other values for that angle: for example if you know one side length and one angle measurement then you can calculate all three sides using trigonometry.
Trigonometric functions (sine 90 degrees etc.) are also known as circular functions because they're used to describe how things move around in circles. In video games it is common practice to use these functions as part of collision detection algorithms which detect whether two objects are moving towards each other at specific speeds - this way we can tell whether they'll collide or not!
To learn more about trigonometric functions check out this article by Khan Academy: https://www.khanacademy.org/math/trigonometry/#SIN_COS_TAN
Calculating Acceleration and Velocity
Acceleration and velocity are important concepts in game design, since they determine how fast objects move through a game world. If a player has to run across a platform that is moving at constant speed, you must calculate the acceleration so that the player doesn't fall off.
Vectors are used to represent the direction and position of objects in the game world. They can be very useful for determining whether two objects collide or not, since you don't have to perform calculations on every single pixel for each object involved in an interaction. They also allow for easy collision detection through simple calculations based on vector math!
Rotating Objects Using Angles
Rotating objects is a common operation in video games. You might have seen objects rotate like cars or players running around on the screen. But what exactly does it mean to rotate an object?
Rotating an object means turning it around some point. This can be done using angles, which are measured in degrees, clockwise from the x-axis or counterclockwise from the x-axis. The angle used for rotating is called the rotation angle or axis angle, and we'll use this term throughout this article to refer to both concepts interchangeably.
Creating a Spinning Laser Cannon
A laser cannon is a weapon that shoots lasers. It can be used to destroy other things, like planets or spaceships. The way it works is by spinning around. The more rotations per second (sp/s), the faster it fires its beams of light.
The variables involved in creating a spinning laser cannon include:
Rotations per second (sp/s)
Length of beam (mm)
Diameter of beam (mm)
Calculating the Angle of Rotation for Sprites Facing a Target Location
Calculating the angle of rotation for sprites facing a target location is a common practice in video game design. The process of calculating this angle requires the use of trigonometry, vectors and matrix multiplication. The formula used to calculate this angle is:
A = acos(x/y) + B
This formula uses the x-axis lengths of both sprites as inputs and returns an angle value that represents how far from their original orientation each sprite's heading should be rotated so that they are facing one another in perfect alignment. You can also use this formula for objects other than sprites—for example, you could use it to determine whether or not two blocks need to be moved further apart so that they're touching at all points except at their corners (this would allow them to rotate without overlapping).
Conclusion
Video games are an amazing way to bring math into your life. When you play a video game, you'll use math in every aspect of the design and programming process. Whether it's calculating how many lives each player has left, or figuring out how far someone can jump before falling off a ledge - there's plenty of opportunity for learning!