# Tagged Questions

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

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### Mesh slicing/knifing with multiple planes

I have a ginormous mesh which I want to cut with multiple planes. For simplicity I want to know how to cut a mesh with single plane and repeat the logic. Consider a X-Y plane (1,1,0,0) = (a,b,c,d), ...
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### Convert transform from world to local space

I have a hierarchical node system. Given a world space transform, I need to obtain the transform for a specific node in local space. My Node class has the following method. public void ...
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### 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 ...
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### Implementing time step in main game loop

So ive read both http://gameprogrammingpatterns.com/game-loop.html and http://gafferongames.com/game-physics/fix-your-timestep/ and I kind of understand how I'm supposed to do it, but some parts are ...
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### Get bullet movement direction?

I have two objects, A and B, at two different points. I want B to fire at A. B's shot moves so far x and y every frame. How do I get the angle it needs to travel at as two numbers, one representing ...
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### Euler angles to directional vector

I wanted to implement a directional light system in my game, and instead of passing the direction to the light, I chose to use an angle, and only later convert it to a directional vector, so it is a ...
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### Vector math to calculate the rotation and drift of a tectonic plate?

I've been following the excellent Experilous procedural planet generation post, trying to recreate it in Java using libGDX. My planet is simpler, as it lacks any distortion of the mesh. It's just ...
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### understanding spatial hash function behaviour and Knuth for int64

I implemented open-indexing sparse 2D spatial HashMap, and I'm quite satisified with performance ( ~30-70 CPU cycles to get object at particular location for size ~16 Milion objects ). However, I ...
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### What is the best way to check for intersection of two bounding boxes, given a minimum and maximum Vector3 for each one

I have a BoundingBox object which holds two Vector3's (x, y, z), one for the minimum point and one for the maximum point. (-1.5 0 9 | 1.5 3 10) What is the best way to check for any intersection or ...
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### How to enforce touching within a ring shape?

I'd like to have the player moving the finger within the shaded ring: The game should be able to detect "out-of-boundary" events once the finger moves outside the ring. How can I accomplish this?
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### How to avoid Gimbal Lock on Rubik's Cube [duplicate]

I am making a Rubik's cube program. That will simulate a Rubik's cube. I am having problems with gimbal lock. I need to know how to avoid it. To my understanding I can either multiply the x, y, z ...
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### How do idle games handle such large numbers?

Just wondering how games such as Tap titans and Cookie Clicker handle such large numbers. I am trying to implement an idle game however the largest number format supported by C# is decimal. I am ...
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### Frustum Culling: How to calculate if an angle is between another two angles

I am trying to implement frustum culling but got stuck on how to determine if the angle that the object is from the player is in the FOV of the player. So basically I have the following information: ...
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### How to find or compute or look for overall/max RPM by simply checking for rotation?

I find it hard to determine the wheel RPM since I'm only making a simple 2D game of rotating object via Z-axis. I wanna try this solution but I got no change since I'm trying to find the RPM from a ...
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### Is * calling *= (or *= calling *) slower than writing seperate functions (for math library)? [closed]

I have some vector classes where the arithmetic functions looks like this: template<typename T, typename U> auto operator*(const Vector3<T>& lhs, const Vector3<U>& rhs) { ...
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### How can I launch a GameObject at a target if I am given everything except for its launch angle?

I have been working on this one for a few weeks, and I have yet to succeed. I have searched every resource out there, and tried them all, but still without success, so I do not believe existing links ...
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### physics: formula for gradually changing force

I have two physics objects (lets call them a and b) pushing against each other and I need to determine the cumulative energy pushing them apart across a given time. Then I will divide it by each ...
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### How to make a bar showing the “percentage” of a maximum

so Im making a game and I need a 'bar' to show how much time has passed in ms (dont worry about the time 'mechanics' I only work with the correct numbers). So lets say that the bar is 128px wide and ...
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### Adjacency in procedural generation of dungeon

I wanted to make a procedural dungeon experimenting a new approach, it works nice for random-meaningless content (in example a procedural background to a level), however when I want it to be ...
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### Should I compute impact damage with energy or momentum?

My game uses physics (Box2D in particular). Just about every object in the game can be destroyed, and the primary method of combat is by slamming objects into one another at high speed. It makes ...
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### Accurately simulating the lots of dice rolls without loops?

OK so if your game rolls lots of dice you can just call a random number generator in a loop. But for any set of dice being rolled often enough you will get a distribution curve/histogram. So my ...
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### Better way to timestep?

So I know how timestepping works. As I understand it if I wanted to move a character at the same speed in real-world time I need to simply multiply the movement of the character by DT on each frame. ...
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### Test if Jump can reach target

I have an object that can jump. When it jumps, its Y velocity becomes -600 (pixels/second). For up to .2 seconds, it can ignore gravity. After .2 seconds, it begins to accelerate downward at 2100 ...
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### Computing a full revolution for an arbitrary orbit?

I'm making a game in which the goal is to get as many planets as possible to orbit around a star. The user launches planets at any distance away from the sun (as long as it's on-screen), and in any ...
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### How to pitch, yaw, roll, an object like a flight simulator in OpenGL?

I'm working on a college Graphics project using LWJGL (OpenGL in Java). I've done most of the scene but I got a problem in figuring out the jet's orientation. Here's how I tried it at the very ...
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### ELO Rating System & Multiple Games Against the Same Player

I've decided to use the ELO rating system for my chess-like strategy game. I've implemented the algorithm but I don't really understand it completely (I'm not a maths person)... I've decided to give ...
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### Implementing Separating Axis Theorem in 3D with C++/OpenGL

Using an Octree data structure provided to me by an acquaintance that gives min/max bounding box values, I've been able to write an algorithm that takes the global centre points, face normals and half ...
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### 2D circular with elliptical orbit interference

Given 2 object (a spaceship and a planet), which are both orbiting the same sun. I have the spaceships position and velocity (and therefore also it's elliptical curve equation). And for the planet I ...
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### Object orbiting a 3d sphere

I'm developing in libgdx java/android but not using any high-level environment like Unity. I have a sphere at [0,0,0], with a PerspectiveCamera looking at it. Through the main game loop I have ...
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### Help With Rotating Turret and Muzzle Flare Sprites

I am making a top down game that involved tanks rotating their turrets and firing at other tanks. I have the turrets rotating independently of the tank itself about the center. However, I am now ...
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### How can I make bullets go to the cursor in Pygame properly

So hey, I'm new into making games and programming at all, I tried to make a small game thingy in Pygame that would include a dude shooting bullets and stuff. However, I can't really get the shooting ...
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### Calculating Linear force required to hit a specific vertex on a parabola

The idea is a user presses somewhere on the screen and the program will fire an object in a parabola shape from a defined start position that has it's vertex where the user touched the screen. I have ...
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### How do I convert 3D vertices and faces to 2D shapes?

I'm assuming all the math is done with projection matrices from linear algebra, but I don't yet understand how they work, and haven't found much information on them. What I'm mainly curious about is ...
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### Generate Geodesic Sphere from Hex and Pentagons

I have two polygonal meshes, a hexagon and a pentagon (They are tiles in a strategy game). I want to use them to construct a geodesic sphere ...
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### List cells in a 2D grid that belong in a sector / portion of a circle

Are there any algorithms to find out which cells in a 2D grid lie inside/is part of a slice of a circle - a pie slice shaped region? Essentially, as per image below, I need to list out all the green ...
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### How to generate tangent and binormal(bitangent) of a triangle polygon mesh

I am currently using FBX sdk to acquire mesh information from obj and fbx files. However, not all meshes contain tangent and binormal(bitangent) information so I have to use the method ...
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### How to calculate Joystick margins/tresholds?

On Joystick that gives Float position values from -1 to 1 on either of x and y axis, how to implement proper math, that adds "lower" and "higher" circular margin? For example if lower margin is 25% ...
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### Finding pitch/yaw values from lookat vector

I have a camera class that contains a position, a pitch, and a yaw (the pitch and the yaw correspond to y and x rotation values). I want to implement a lookAt function that takes a vector and the ...
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### Timed Line Drawing

I'm trying to program a remake of the classic Missile Command Atari game from scratch, but I've run into a problem. So I have a function that can draw a line from one point to another. I figured I ...
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### 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), ...
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### RPG Damage Calculation Logartihm in Java

I'm trying to make a damage calculation formula for my RPG game, there are 12 levels for both the Player and the Enemy, I've come as far as making a Reverse Exponential formula, but I want the damage ...
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### How to calculate a vector for multi-axis rotations from sphere coordinates?

I'm working on a SceneKit project in iOS, trying to rotate a sphere (representing a planet) so that a point at a given longitude/latitude coordinate is facing "forward" (i.e. that point moves to the ...
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### Find your value between four values in a grid based on distance, Unity

Please note: Originally posted in stack overflow, redirected due to nature of problem. I am making a procedural mesh game. I am trying to calculate the temperature for the player's current chunk by ...
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### How do RPGs balance linear damage formulas?

I'm developing a damage formula for an RPG. I've checked many popular titles formulas for reference (Final Fantasy, Chrono Trigger, Golden Sun and Castlevania) and most seem to use linear functions. ...
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### Cumulative transformation matrices for hierarchical object transformations

I'm having a small issue with my design for hierarchical 3D objects. I'll try to sum things up concisely. Every object has a vector3 for its position, scale, and rotation, as well as a std::vector of ...
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### calculating the weights for direction vectors to a target

I have an entity that is allowed to move in a fixed amount of directions. Let's call a the angle between two directions. r is the length of each direction vector. Now the entity wants to head from its ...
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### Does the sound need to be fixed?

Are there special requirements for audio for different devices? I have been stuck on this for around two days now, and would really appreciate all the help I can get. I have some audio in my code. ...
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### How do you rotate all the objects around the camera?

If I'm correct, the way that you can "look around" in an environment is that you rotate all the objects around the camera. This is the code that I've created using JavaFX 3D. So what's the algorithm? ...