# Questions tagged [mathematics]

Mathematics questions deal with the arithmetic, geometry, calculus, formulae and other calculations used in the development of a game.

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### Checking for collisions on a 3D heightmap

I have a 3D heightmap drawn using OpenGL (which isn't important). It's represented by a 2D array of height data. To draw this I go through the array using each point as a vertex. Three vertices are ...
3k views

### Calculate Position on Tile Map by single Index

I stumble about a Math Problem for calculating a Position on a dynamic tile-map. So i got a List of Tile Entities. Every Tile got his one unique Index Value and i have to set the parameters for Map ...
661 views

### Plotting entities on a radar

I'm trying to build a radar system like the one in the original X-Wing games. The way it works is that there are two circular radar systems, one for behind the ship, and one for infront. So, I've ...
2k views

### Orthographic Camera Zooming

In XNA I am using a spritebatch to render a board. I have created a camera class which can provide me a view and projection matrix. Currently I am supplying the view matrix to my sprite batch when I ...
687 views

### Inverting matrix then decomposing gives different quaternion than decomposing then inverting the quat

I'm getting different signs when I convert a matrix to quaternion and invert that, versus when I invert a matrix and then get the quaternion from it: ...
1k views

### Tangent to a circle through a point

I'm trying to figure out how to calculate the following angle: I know center (p1) and radius (r) of a circle. Given a point p3 I want to calculate the angle a such as the tangent (tan) of the circle ...
17k views

### Fast Ray Sphere collision code [closed]

I am looking at here and while it's well organized a lot of links are broken: http://www.realtimerendering.com/intersections.html I am trying to find fast code that will give me the hit point and the ...
103 views

### How to move points of a multi-segmented bezier curve to one side

I am trying to move points from a multi-segmented bezier curve to one end of the curve using the following code which modified for my use from here. Only the last segment seems to give the desired ...
147 views

### How to place a camera so that it always fits a plane?

I have a plane that can get its scale changed during the game, and I want to make the camera view it completely every time the plane has its scale changed. The only camera is set to perspective ...
13k views

### SIMD C++ library [closed]

In the past, I've used Visual Studio with the DirectX XNA math library. Now, I'm using the GNU compiler collection. Can anyone advise a SIMD math library with a good documentation?
6k views

### How to optimize the distance function?

While developing a reasonably simple RTS-like game, I noticed my distance calculations were causing an impact in performance. At all times, there are distance checks to know if a unit is in range to ...
2k views

### Beyond "Novice" Game Projects

I was reading this answer on the type of math a game developer should know and this part really stood out at me: ...
19k views

### How can you visualize a quaternion?

When I visualise a three dimensional rotation matrix, or scaling matrix I visualize it as three axes. Is there a similar way that I can visualize a rotation quaternion?
4k views

### Are there 3D projections other than orthographic and perspective? [closed]

The question is pretty much in the title. Are there notable 3D projections other than orthographic and perspective that could be used in a 3D system such as OpenGL? In particular, are there any that ...
43k views

### How do I use the dot product to get an angle between two vectors?

I am learning to use normalized vectors in my games. I've learned that in order to know the angle between two vectors, I can use the dot product. This gives me a value between -1 and 1, where 1 ...
5k views

### Can someone explain the (reasons for the) implications of colum vs row major in multiplication/concatenation?

I am trying to learn how to construct view and projection matrices, and keep reaching difficulties in my implementation owing to my confusion about the two standards for matrices. I know how to ...
2k views

### Terracing mountain features

I'm looking to replicate a procedural terrain effect I found on a portfolio/blog site a few days ago. Quoting the site, the terracing was generated through, "multiplying [the final height] by some ...
14k views

### How do I find the circumcenter of a triangle in 3D?

I want to find the circumcenter of a triangle. Wolfram only shows how to find the circumcircle of a triangle in R2. How can I find the circumcenter of a triangle in R3?
31k views

### How to detect 2D line on line collision?

I'm a flash actionscript game developer who is a bit backward with mathematics, though I find physics both interesting and cool. For reference this is a similar game to the one I'm making: Untangled ...
45k views

### How to extract euler angles from transformation matrix?

I have a simple realisation of entity/component game engine. Transform component have methods to set local position, local rotation, global position and global rotation. If transform is being set new ...
15k views

### 3D Camera Rotation

Please, forgive me, but I need help and I've been stuck on this for a few weeks now, I'm making no progress and everywhere I go and I see a different answer, everything I try doesn't work. I've had ...
10k views

### Are there any disadvantages of using Distance Squared checks rather than Distance?

I use distance squared checks for basically all my distance (vector3 length) checking, due to the performance increase from not incurring a square root (like in plain length checks). From the looks ...
3k views

### Re-create 2D side-on wave effect from Worms game

I'm trying to recreate the waves/water effect from Worms ( see here http://youtu.be/S6lrRqst9Z4?t=31s ) From what I understand its not actually a sprite, its procedurally generated by something like a ...
4k views

### What are the most common splines you will find in game development?

List here the most common splines found in game development, how many points the method needs to interpolate a curve, and how can you build a data type that allows you to get an interpolation of the ...
17k views

### RPG Formula - Attack and defense

I'm making a game and I'm struggling with the formula to calculate the real damage the player does. I have skills which can do for example 10 hits of 20% weapon damage each of a total of 200% damage. ...
8k views

### How can I render a circular progress bar procedurally?

I'm working in Flash AS3, but pseudo-code or any other language is fine. How can I make a circular progress bar? Akin to the ship bars in Pax Britanica, you can see them in the screenshot here. ...
5k views

### Browser RPG fight calculation formula

I am making a simple browser rpg game, similar to battleknight. To keep the game simple, I have just Strength, Constitution, and Luck, but since Luck is based on randomness, I'm struggling with combat ...
10k views

### Moving a particle around an Archimedean spiral at a constant speed

I want to move a particle in a spiral at a constant speed. Note that that is not a constant angular speed. This is proving rather difficult, and I'll go through my method so far below. The spiral in ...
1k views

### Converting time of day into a smooth day/night variable?

I'm trying to make a smooth day/night cycle for a game project that I've been working on. I've already set up a clock that adds deltaTime to seconds, wraps seconds to gameMinutes, etc. The issue that ...
2k views

### How to rotate directional billboard particle sprites toward the direction the particle is moving

Behavior: With the following texture I get a weird behavior when I try to rotate my particles in the direction they are moving. Essentially, the quad seems to rotate, but just barely so that when ...
867 views

### How can I maintain a rectangular formation when units are added or removed?

I've got bots in a rectangular formation with rows and columns. A problem arises when a bot is added or removed from the formation. When this happens, the bots have to rearrange themselves so that the ...
4k views

### Attack vs Defence and who is the winner? [closed]

I am in the process of creating a new simple game in mobile and I've spent several days on the following part. For simplicity, let's say that I have two fighters. The only attribute of them is Attack ...
10k views

### How to move an object along a circumference of another object?

I am so out of math that it hurts, but for some of you this should be a piece of cake. I want to move an object around another along its ages or circumference on a simple circular path. At the moment ...
3k views

### Adding air drag to a golf ball trajectory equation

I'm developing a 2D golf game in VB.NET 2005, but I am stuck on how to implement air or wind drag that should affect the ball. Already I have these equations for projectile: $v_0$ for the initial ...
1k views

### Projected trajectory of a vehicle?

In the game I am developing, I have to calculate if my vehicle (1) which in the example is travelling north with a speed V, can reach its target (2). The example depict the problem from atop: There ...
2k views

### Orbital mechanics: orbit as a function of time. Universal variable formulation?

I am trying to model a two dimensional orbit for a two body Kepler problem but have gotten stuck when introducing the time variable. For a satellite with known semi major axis (a), eccentricity (e), ...
3k views

### How to render metaballs?

How to render metaballs? I am a Python programmer familiar with the Panda3d and Blender3d APIs. My math kinda sucks, but I know enough to write game logic code and procedural model generation code, ...
1k views

### Zooming and panning a camera simultaneously causes a swooping effect

In a 2d game, I have a basic camera class. The guts of the class creates a transformation matrix that is later passed to the Begin() method of a SpriteBatch. The transformation is done like this: <...
2k views

### Understanding normal maps on terrain

I'm having trouble understanding some of the math behind normal map textures even though I've got it to work using borrowed code, I want to understand it. I have a terrain based on a heightmap. I'm ...
1k views

### In a semi-infinite procedural (chunk based) map, how do you handle objects larger than a single chunk?

I'll use an example to try and be more specific. Assume this is for a 2D top-down game. Chunks in this are made up of 32x32 tiles. If procedural buildings were to be generated based on some kind of ...
1k views

### Vary speed of enemy smoothly

Hey. I'm trying to create an enemy that travels at a speed s on screen but I'm having trouble with trying to make the speed vary in a smooth motion. Basically, I ...
5k views

### The correct way to transform a ray with a matrix?

Playing with XNA Triangle Picking Sample I found out that it does not work well if you scale the world matrix of the objects you want to pick. When I dug into the implementation I found this comment ...
7k views

### How to calculate the surface area of a mesh

I am looking for a way to calculate surface area of a 3D mesh object and found this code from a Unity forum: ...
20k views

### How to get translation from view matrix

How can I retrieve the camera's world-space position from its view matrix? The only answers I've seen to this question suggest the translation is in the last row/col but this wouldn't work since the ...
18k views

### Changing coordinate system from Z-up to Y-up

Blender's coordinate system is different from what I'm used to, in that Z points upwards instead of Y. What would be the simplest way of converting all the world data (so that all animations, texture ...
2k views

### Elliptical orbit modeling

I'm playing with orbits in a simple 2-d game where a ship flies around in space and is attracted to massive things. The ship's velocity is stored in a vector and acceleration is applied to it every ...
1k views

### Circular Bullet Spread Is Not Even

I'm creating a bullet shooter much in the style of Touhou. Right now I want to have a very simple circular shot being fired from the enemy. However, the spacing is very uneven, which isn't very good ...
264 views

### Get local coords from global coords

I need to get local coords from global coords. I did not find ready-made examples. Please help me how to do it on the example image. Thank you! UPDATED: Here's the method in the java, created ...