# 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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36 views

### Frustum culling issue at oblique angles

I am using the following algorithm to test if my camera frustum contains an axis-aligned bounding box: ...
14 views

### Triangle area selection using BVH raycasting

Let's assume I'm already storing a BVH acceleration structure per mesh on my engine and I'd like start making area selection like on many DCC tools out there, for instance, blender. With blender you ...
15 views

### Rotate relative to set point in a specified direction in a 3D space

I know there's a geometry formula to calculate the next point in rotation relative to another point in 2D but I'm working in 3D and I want to calculate the next position in specified direction as well....
47 views

### How to decompose a 4x4 TRS transformation matrix with negative scale?

As the title says I need to decompose 4x4 TRS transformation matrices and extract the proper scale vectors and the proper rotation vectors (or rotation quaternions). I know how to extract those ...
31 views

### Rotate object relative to camera position

I am trying to write code that is able to rotate object, based on camera position. So far I ended up with a code posted below. Moving mouse up and down (y input) caused to rotate object in y axis, ...
36 views

### How to tell which face of a cube is most visible to the camera?

Imagine a camera that shows a randomly rotated cube at an arbitrary position: The cube's pivot is in the center of the cube. This way its six faces could be referred as positive/negative X, Y or Z. ...
44 views

### How do I calculate/weight a diminishing damage formula based on N targets?

I'm making a game and had a look at the questions about calculating damage/diminishing returns here and here but I haven't quite been able to come up with a logarithmic function that satisfies this ...
49 views

### Calculating probabilities for a custom drop table system

I have a "drop table" / "loot table" / "item table" / "whatever you want to call it" system and I need to solve two Problems. Apologies in advance for the text ...
51 views

### How to Generate Level Map Based on Golden Ratio

I am trying to generate a map based on the Golden Ratio: a+b is to a as a is to b. I was looking at a JavaScript math library that had a built-in phi, but I wasn'...
26 views

### Can I get world-space z-near-plane vertices from projection matrix + z-near distance?

I'm trying to port ShaderToy VR shaders to WebXR (the new browser API for AR/VR devices). ShaderToy VR shaders expect two extra parameters: ray origin (view translation) and ray direction (unit vector ...
50 views

### Aircraft trajectory prediction

I have an aircraft that is controlled by player and i need to predict it's position at needed time. It's not a problem if the plane is just moving straight but most of the time aircraft is maneuring. ...
124 views

### When are oblique triangles used in game development?

I'm working on a project that explains how trigonometry is used in video games, and I need to mention oblique triangles. However, as far as I know, only right triangle diagrams are used in video games ...
2k views

### Rotation grid positions

I'm dealing with objects on 15x15 chunks in my game. I'd like the chunks to rotate, for example, rotation version 0 is the original position of 2,5; (EDIT: Oops, rotation 2 and 3 names need switching ...
35 views

### Rotation matrix to look at point p

Assume a left-handed coordinate system where x is right, y is up, and z is into the screen. You have a unit vector pointing up along the y-axis. What's the rotation matrix for pointing the unit vector ...
24 views

### Formula to convert zoomed in game space co-ords to UI

I need to come up with a formula to convert variable zoomed-in game space co-ords to UI co-ords. The engine I'm using is not traditional so there's no inbuilt function (convertToUISpace etc). Now I ...
106 views

### Calculate aim angle dead zone range

In my top down 2D shooter game the player has a shoulder mounted gun which rotates and aims automatically at enemies - that part is all working fine. Since the player can rotate as well, the gun is ...
22 views

### How do I scale my spell target indicator to match the radius of OverlapSphere

I have a spell system in which some spells have an Area of Effect. To get the targets I use Physics.OverlapSphere. I show the player an indication of the spell's ...
46 views

### How do I calculate to and from a Non-Linear Acceleration?

I am looking at non-linear accelerations using the following values: initial_acceleration time_to_max_velocity max_velocity current_velocity Initial_acceleration is the per frame acceleration we ...
31 views

### Isometric tiles on wrong positions if the mouse points at a negative world coordinate

I am using this approach: http://clintbellanger.net/articles/isometric_math/ Basically, you can calculate the iso coordinates based on the screen coordinates. What I am doing is, getting the actual ...
30 views

### Find projectile initial velocity, and air time, given projectile elevation, distance, angle

I have a target X position (D). I have a turret Y elevation (E). Turret is always pointed at 45 degrees (A). I need to calculate the initial projectile velocity required to hit the target, with an ...
52 views

### How to rotate velocity Vector3 to always point the same direction so that it can be applied to 2d blendtree?

Given two variables, a Vector3 representing body velocity and a Quaternion representing body's local rotation, how could I normalize the velocity vector so that it's always oriented towards the ...
56 views

### Getting angle from current position and next position

I am using pathfinding to move a train along rails, but I need the train to rotate. I have the next intended position and the current position at my disposal, how would I go about this? Pseudocode ...
149 views

### How to make good combinations of xp tables and xp rewards?

Is there a known step by step (automatable) to define mean xp reward formula/table to bases specific challenges rewards (generically, not only defeating enemies) and total xp table that set character ...
31 views

### How to make a dynamic frontline system for my game?

My problem: Basically the units, units meaning soldiers or vehicles, influence the frontline by moving into the opponents territory (See example image). I'm trying to understand where to even start ...
23 views

### Why does this order of Quaternion multiplication not introduce roll into my fps-style character controller?

I'm working on an OpenGL based project (in C#), employing Quaternions to rotate my camera I first tried to: ...
40 views

### C++ Help with Separating Axis Theorem

I am trying to detect collision between two triangles using Separating Axis Theorem however I am unaware what is wrong with my code. The CollisionHelper::isTriangleIntersectingTriangle is called every ...
38 views

### Using enemy, player and gun position can player shoot enemy?

I was asked this question in an interview last week and I've been thinking about it but I'm unsure how to solve it. You are on a spaceship and want to shoot the enemy space ship. You have the enemy ...
16 views

### Formula to calculate Level and Current Experience from Total Xp [duplicate]

So I'm building a mobile game where I have simple XP progression system that goes like this: Level1: 0-399 Total XP Level2: 400-1199 Total XP Level3: 1200-2399 Total XP So basically for the first ...
25 views

### Upside down ground correction?

How would you go about making ground correction for a platformer but upside down(reversed gravity)? I used this formula: P.Y+=(P.Y-2)%8-1 but the character just ...
126 views

### How to check if two normals/directions “look at” each other?

I need to flip polygons in my application. How do I determine if two vectors face each other, like in the second image below? Note that the origin of the vectors is also important, in addition to the ...
61 views

### Getting points inside a circle with a given radius in a 2D array?

Let's say you have a system that removes everything within a square made up of 4 position points. This square is calculated by taking the center point and adding or subtracting the range from this ...
25 views

### Math: determining a proper procedural vector for sine-movement

My Problem Suppose you have an object moving along the x-axis, wobbling up and down. Movement code might look like this: x += 1; y = Sin(x); Move((x,y) * speed); ...
49 views

### How to predict where the soccer ball should be intercepted by an AI player after being kicked?

This question has been asked many times before, but most of the answers give solution to the problem where ball (target) is assumed to be moving at a constant velocity. In my scenario, I'm making a ...
23 views

### Calculate the starting position of a turning aircraft with inertial force to make it stop at desired position and heading

Continued from the answer here, I have some problem when the aircraft in my game has inertial forces after going forward and turning itself. To illustrate, from the following image (https://imgur.com/...
82 views

### Calculate the aircraft's movement path in which its side speed is required

I am working on an implementation problem in which given an aircraft and the objective of the system is to find the quickest route (optimal in terms of time) from point A (contains the information of ...
56 views

### Godot - Offscreen Target Indicator

I have a crosshair image that will lock onto enemies that are visible in the camera and will stay on the edge of the screen when the enemy is offscreen. This works until you face more than 90º away ...
87 views

### Rotate Object in world space - Raytracing

I’m programming a C raytracing project. I’ve been wanting to implement object rotations (square, cylinder) for several days but I can’t do it. For each object I have its position (x, y, z) in the ...
82 views

### Damage-calculating formula for turn-based RPG with a twist: I have developed a formula, do you the experts think it will scale up successfully?

I’m developing a turn-based combat system for an RPG. It’s a little different to your standard RPG though. The idea being, the faster the player solves the problem they are presented with each time it'...
26 views

### Getting the edge-cells in a list of cells on a 2d grid, and knowing which neighbor is missing

I create a "circle" on my 2d-grid using this code: ...
66 views

### Diamond shaped map: converting tile number to coordinates and back

I have a diamond shaped map that is displayed as follows: ...
208 views

### LibGDX Efficient way to reduce a vector's value gradually until it reaches 0,0

I can manage to achieve this but the code seems to be much longer than it should be. Velocity is given an initial value, either positive or negative and then is ...
59 views

### My arcball camera does a roll when it shouldnt be

I am trying to build an arcball camera and it's mostly working, the problem is that as you rotate around the object you have selected (orbit_target_pos in the code),...
65 views

### Trying to 'stamp' an arbitrary assortment of pixels to a texture2d that may be rotated at an arbitrary angle

This one is hard to explain but I'll try to not to overcomplicate it. Engine is Unity, for reference. I have a system where an object has a 2d texture to display a custom splat map. The user can '...
89 views

### Clamp quaternion relative to plane normal

How would one be able to clamp a quaternion based on the angle relative to a plane surface (defined by a normal)? My diagram below provides more of a visual explanation of exactly what I am talking ...
107 views

### Rotate quaternion around plane normal

How can one rotate a quaternion so that the rotation is around a plane normal? A graphic/diagram I made below gives more detail about what exactly I am implying. Note that the tip of the quaternions ...
63 views

### (Unity3D) Determine If Ray Intersects Given Rectangle

I'm building a city generator for my game and I want to ensure buildings are never placed in such a way that they overlap roads. Currently I have the system build the roads, then place buildings ...
78 views

### Need Help Figuring Out Damage Calculations for Diablo RPG Clone

I'm building a Diablo clone using Unreal Engine 4 and have been having trouble wrapping my head around how the combat calculations should work. I copied a lot of the core stats from the original ...
18 views

### tilemap movement bounderies

My active tilemap surface is 5x5 tiles, and I try to limit the player's movement inside this area with the following code: ...