# 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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### How can a quad be triangulated consistently in 3D? [duplicate]

I'm making a building game and the terrain and modelling system are based on cubes made out of 8 corners each. Players can manipulate the corners to make other shapes. When you take a quad (ABCD), ...
11 views

### Implementing 3d isometric like camera in Unreal BP

Im trying to learn Blueprints and started by implementing my own isometric view from scratch. I have a pawn, with a camera component, the view is supposed to rotate and scroll. I have implemented ...
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### How do large physics based games (space engineers) deal with coordinates

I have recently been looking into physics engines and low level computing. At some point id like to make my own engine down the road. Something I can't seem to find an aswer for is how physics based ...
76 views

### Normals deformation with FFD

I am developing an FFD tool in Unity for the needs of a level designer. It works similarly to FFD box in 3DS Max. I used the implementation described by Sederberg and Parry with a lattice and ...
1 vote
68 views

### Inconsistent Movement Behaviour between built Game and Playmode

I'm using a simple MonoBehaviour that causes GameObjects to change their position based on a ...
119 views

### How to calculate the center of mass of a irregular polygon in Godot?

Or to calculate the centroid of a 2D polygon assuming uniform mass density, which is my case. The polygon can be either concave or convex.
1 vote
114 views

### How to calculate the surface area of a irregular 2D polygon in Godot?

I have a irregular 2D polygon, it is a PackedVector2Array, how do I get its area?
123 views

### How to live on sphere?

What I want to achieve I want to generate sphere planet world, seamless of course, for RTS game like Planetary Annihilation: TITANS, which means I want: place walking agents on sphere, move them on a ...
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### How to find offsets of Vector2's give number of points row, amount of points, and centered vertically?

Say that I want to make a grid that contains 5 points and up to 3 points on each row. starting from the top I should have 3 points followed by 2 points underneath centered by the same distance like so:...
37 views

### Calculating semicircle points of a scaled CapsuleCollider2D

I have a very simple code that draws the shape of a pre-defined capsule. It handles everything well, except the case when the GameObject to which the ...
57 views

### Collision of two rigid spheres with spin

I'm trying to create a particle simulation (solar system kind). Until now my particles have no spin so the collision is rather simple ...
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43 views

### 2d top down movement physics: speed, max speed, acceleration, friction, velocity, delta

I am creating a 2d top down game and am trying to implement movement. My current approach is very simple and looks like this ...
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1 vote
48 views

### Predictive Aim to shoot a moving target with a constant velocity while the projectile is affected by gravity (2D/Platformer view)

I've been working on creating stationary gun turrets that can shoot down missiles in my game. The bullets are affected by gravity while the missile moves in a linear path at a constant rate as if it ...
44 views

### How to make an object keep same relative position and orientation using only velocity

I have object A, I can get any information I want from object A (global position, velocity, etc) I have object B, which is positioned and oriented in a certain way relative to object B. There is no ...
1 vote
20 views

### 2 object snapping using bounding boxes in Unity Runtime

I am using boundary boxes for all calculations. In the image below you may see a case where this objects need to be snapped. Currently the calculations go as following, the rotation is changed by the ...
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### Normalize an angle in unity

How can I normalize angle between min value and max value? like normalizing -1136316.78186234° between 0° , 360° or between 180° , 360°. Node: for now I'm using double value as angle. Thanks for ...
16 views

### Selection Box Not Positioning Correctly

I found some code that generates a selection box, but when I tried it the box was not starting where the mouse was and I couldn't find the issue. ...
45 views

### Matrix parent-child transformation for 2D positioning

I am working with matrix math for parent / child transformations. I have to modify existing calculations to keep child scale constant while also keeping child position relative to its parent. Here's ...
35 views

### Texture space Raytracing of cylinder primitive in godot shader for Helix interception

I have been trying to do raytracing of an helix in a spatial shader in godot 4.2, but apparently I missed something because the result is bloby and melty at the cylinder level. The basics is that I ...
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61 views

### How to calculate velocity based on force at an angle

I have a 2D top-down jetboat that is moving (has a x, y velocity). I apply the velocity by multiplying against the delta time <...
1 vote
97 views

### Mirroring a Character's Position In a Shadow After Rotating 180 Degrees

Description: I am creating a 2.5D RPG. When my character moves from left to right, they rotate 180 degrees to face the new direction. Just like this example. They also have a blob shadow sprite that ...
• 312
3k views

### How hard to brake to perfectly smoothly reach the destination?

Goal I want the get the required minimum deceleration to perfectly smoothly reach a target. (The car's AI should know how hard it has to brake to be the perfect valet.) Research "How can I ...
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### How to rotate spaceship quaternion to face target direction with constant angular speed?

I have an enemy spaceship, and I want to make it turn to face the player with (for now) a constant angular speed. The ship's orientation is a quaternion. How do I do this? Since this is totally free ...
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1 vote
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### How to calculate rotation needed to cancel out perspective shift

I have a direction vector that's pointing to (0,0,1) in local object space. How can I calculate rotation needed to rotate it on Y axis so that from camera's point of view it would look as if it's ...
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113 views

### Max velocity for smooth deceleration to destination

I am able to update velocity of my agent every 0.5 seconds. My agents max speed is 5f/s and max acceleration/deceleration is 2f/s. I know how far away I am from the destination. How to determine ...
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47 views

### Camera (View) in Euler angles

This is code (below) from original game project (90s years), I it study now. Used fixed point math. ...
• 215
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### How to make calculating the inverse matrix more robust?

When I calculated the inverse matrix, I found that the error in using the float data type would cause the inverse matrix calculation error. Is there any good solution? ...
81 views

### Software rendering - compose View matrix

There is function compose View Matrix, it's software rendering project. Used fixed point math. phd_sin() and phd_cos() user defined functions implement sin() and cos(). Please explain this ...
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115 views

### Normalized coordinates not translating to screen coordinates the way I need them to

I am making a simple game in C# using pictureboxes. I want to move a picturebox on a form. Once this picturebox is placed in a new location, I normalize its X,Y coordinates between [0, 1] and then ...
46 views

### Checking if I am looking through a window using angles

I am developing a mod for a game with a Lua api. I am trying to detect if I am looking through from behind a window when I shoot an enemy. For context, when I shoot through this window I apply a ...
45 views

### Determining a direction/projection/heading for an object in 3D space after it has been rotated

I hope this is a good place to find an answer. I'm not a math wiz and I've tried to tackle this problem many times over the past decade or so. I have a 3D space world, and I'm in a little space ship. ...
67 views

### Calculate damage when attacker has bonus but defender has resist

Let's say an archer does base damage of 50. But their equipment provides +30% bow damage to make the damage ...
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1 vote
186 views

### Calculate path segments size

I have a problem more closely described on a picture below. The idea is that I have my agent in point A and I want to get to the point B. The problem is, that agents rotation towards point B is alpha ...
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75 views

### How to correctly instantiate a cube over another, or side-by-side another one

In a Minecraft spawn system like, I can't make works correctly following code. Specifically, if I use Code 1 it works only when I instantiate a cube over another one, not one aside other. The ...
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### How does vector raised to the power of another vector work?

I was watching this tutorial and at timestamp 3:03 he did this: This blows my mind because I didn't expect that to actually work, how the heck does that work ???? For example, if I have vector (2, 3, ...
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112 views

### Angry Birds style aiming (ballistic trajectory)

Could you please provide guidance on how to create the curved part? regard,
130 views

### Min - Max Weapon Damage formula in video games

I currently working on an RPG game and I'm looking for are formula for creating/generating a min-max weapon damage for an item. Why in Diablo for example, when a weapon is dropped from an enemy, the ...
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31 views

### Difference of angle by Y value

This code from game 90s years. For example on scene there is tiger as "item" and main character as "enemy". This code calculate vector or direction of attack tiger to main ...
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### What this code do?

I investigate source code old game for 90s, dont understand math stuff. ...
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112 views

### How to compute XP thresholds when scaling changes for each level range?

I am developing mobile game and I am stuck on an issue regarding proper player stats scaling based on level. As a parameters for the computation we have: base XP value multiple increment values (for ...
63 views

### Is this gimbal lock I'm hitting even with rotation matrices / quaternions?

I'm spawning a trigger box relative to another object using local offset. The engine I'm using does not provide a native function to make that conversion (at least in a way accessible to me), so I am ...
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### When does normalization happen in the perspective projection matrix

I am currently watching this video where the instructor shows how the perspective project matrix is actually derived. There are a few things that I am still unclear of. Firstly he says we need to ...
297 views

### Simulate Velocity For A Projectile Moving Along A Spline

I'm using Unity's latest Splines package(v2.5) to move a projectile across a spline with speed. It works perfectly and the projectile moves across the spline to it's target with linear speed. But I'd ...
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1 vote
114 views

### How to properly split damage against armor?

I am developing a third-person shooting style game and I want to implement an armor system. The system that I have envisioned does not reduce the damage to 0, but by half. So the incoming damage is ...
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148 views

### Inconsistent Speed Of A Projectile Traveling On A Bezier Curve

What I'm doing: I'm moving a projectile to it's target along a Bézier curve with one control point. The projectile moves from Transform A to ...
• 312
163 views

### Calculating average ttk given accuracy and healing

I'm trying to calculate the expected ttk for weapons in my game but I'm having trouble because players can miss and enemies can heal. Let's say an enemy has 100 health and every second you have a $p$...
157 views

### How to tell whether an expression is independent from frame rate?

I'm working on a videogame where part of the logic involves increasing a value each render frame (a render frame is equivalent to a simulation step where the result is drawn on the screen). Frames can ...
56 views

### Determining meters per second in scaled terrain

I have a terrain with a width of 199 and height of 99 and I'm scaling this train by 500. What would be 1 meter in the new terrain, would it be 500? I'm trying to move my character in meters per second ...
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### Test if a point is inside a 3D cuboid, given the 8 corner positions, through code

I'm trying to find to obtain if a point, let's call it "v" is inside a cuboid which every corner position named P1 to P8 I am trying to achieve this and in fact found some answers in some ...
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