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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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Is it possible to generate a 2D surface that approaches certain mesh, and then a specialised ray-tracing function for it?

As an example, suppose we are trying to ray-trace a sphere. There are two options. The first one is to build a mesh of triangles approximating the sphere and ray trace it. Unfortunately, the more ...
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0answers
22 views

Calculating Damage from from object collision

I need to calculate the damage resulting from a crash of two objects. I found the formula of the resulting kinetic energy: E = m * v² / 2 I guess I also have to ...
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2answers
331 views

clamp a 2D coordinate to fit within an ellipse

I need to clamp a 2D coordinate to fit within an ellipse. Call of Duty: Modern Warfare 2 does something similar where capture points are translated from a 3D vector in the world to a 2D screen ...
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2answers
864 views

Calculating pitch angle to hit a target using a projectile that has fixed speed

I am trying to calculate a vertical angle needed to hit a target at [distance, elevation] 2D coordinates relative to shooter given a fixed projectile velocity, air ...
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2answers
236 views

Integration error in high velocity

I've implemented a simple simulation of two planets (simple 2D disks really) in which the only force is gravity and there is also collision detection/response (collisions are completely elastic). I ...
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3answers
3k views

How do I disassemble a 3x3 transformation matrix into rotation and scaling matrices?

I have a transformation matrix that rotates and scales. Is there any easy way to disassemble it into the original rotation and scaling matrices? For instance: ...
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3answers
2k views

How can I launch a GameObject at a target if I am given everything except for its launch angle?

I am trying to launch an object at a target, given its position, its target position, the launch speed, and the gravity. I am following this formula from Wikipedia: $$ \theta = arctan \bigg( \frac{v^...
6
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1answer
1k views

How To Program a fully controllable spring (Damped) motion

i'm working on a project that needs realistic 2D Animation, none linear motion you might say, i have tried many things such as Hermite Curve and a few other motions and in the end Spring Motion. ...
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2answers
949 views

How can I manually construct a right-handed orthographic projection matrix?

I need the formula to create a orthographic projection matrix. I am using GLM math libary and DirectX11. The reason I cannot use GLM to create it is because the NDC spaces are different between DX11 ...
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1answer
750 views

How to achieve cavalier projection using OpenGL fixed pipeline?

I want to make a quick demo program showing a cube, or a user loaded model, rotating in screen rendered with one of three projections: perspective, isometric and cavalier. Using the fixed pipeline, ...
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1answer
20 views

Interpreting focal length in units of pixels

I am working on a renderer of sorts and I have some fundamental questions. Let's say I have a vector in a 3D virtual world space which is unitless, and I want to project it onto a 2D screen, so I need ...
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0answers
25 views

Mapping between a sphere and a cube

I'm developing a game that procedurally generates terrains with a voxel engine. These terrains are essentially flat cubes that trail off into infinity on the x and z axes. y is basically the altitude, ...
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1answer
26 views

Unity - Calculating a rotation based on game time

I have a simple script to make an object spin: Spin Speed is the speed to rotate the object on each axis (preferably in degrees per second). Local is whether the rotation should be done based on ...
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0answers
19 views

Rotate projectile toward target [on hold]

Rotating a projectile toward a target Say I had a bullet a character shoots at an enemy. If the enemy was directly above me I want the bullet to be rotated at a 90 degree angle. Or if the bullet ...
0
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1answer
23 views

draw concave polygon from set of edge points

I'm having troubles trying to rearrange a set of points where each point is part of the edge of a concave polygone. My set of points is not sorted in any order, they are just randomly put in an array. ...
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vote
1answer
404 views

How can I move a vehicle using speed and steering angle?

I want to drive a vehicle in x and y coordinate area with range from (0,0) to (6000,5000). I am using Visual Components (using Python API). On input I have speed data and steering angle of wheels ...
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2answers
216 views

Shrink a convex polygon

Shrinking a concave polygon is quite hard, to do well. But I expect shrinking a convex polygon would be easy. The naive approach of moving each vertex a certain distance to the centre gives me poor ...
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1answer
78 views

Acceleration in Unity

I am trying to emulate acceleration and deceleration in Unity. I have written to code to generate a track in Unity and place an object at a specific location on the track based on time. The result ...
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3answers
25k views

Sorting array of points in clockwise order

Is there such an algorithm to sort an array of 2D points in clockwise order? I'm specifically dealing with right triangle in my case so only 3 points. However I'm interested in knowing if such an ...
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1answer
17 views

Moving object with preset timelapse

I am a newbie game developer. I have one problem. Consider the following case. I have a simple game with only one object - a ball. A ball can move only up and down from one side to another. A User ...
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0answers
18 views

Drawing ortho outline of rotated elipsoid

I'm working on a collision system for a 2.5D game, and I'm stuck on the sphereoids. As long as scaling x=y=z, and it doesn't rotate, I can just use an r^2 check, but I'm trying to figure out a way to ...
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votes
3answers
390 views

How to use Moving Average to avoid lucky streaks in RNG

I spent the last week reading about Luck Mitigation and what a dev can do to avoid extreme cases where the player's psychology will be messed up. I came up to this question How do I avoid “too” lucky ...
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2answers
50 views

Getting Model View Matrix by hand

Right now I'm trying to calculate the model view MAtrix by hand... The App is 2D. I have Somethign like this.. ...
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1answer
140 views

Offset on camera following object that accelerates

I have camera a that is actively following an object (a plane) from behind. This object can accelerate or decelerate. I would like to have a camera offset when I move the plane, so it doesn't look so ...
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0answers
23 views

btRigidBody world transform and scale issue

When I create a collision shape for rigid body (in this case box) I use vertices positions and scale from the opengl matrix, the code looks this way: ...
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6answers
10k views

Moving ships between two planets along a bezier, missing some equations for acceleration

OK, I already posted this over at math.stackechange.com but didn't get any answers :( First of here's a picture of my problem, the description follows afterwards: So I got all the points and ...
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1answer
131 views

Calculating real time moment of inertia around arbitrary axis in 3d

I have a 3d rigid body consisting of multiple triangles forming a closed mesh. I know how to calculate the moment of inertia around an arbitrary axis by splitting up the mesh into simpler shapes and ...
161
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16answers
126k views

What math should all game programmers know? [closed]

Simple enough question: What math should all game programmers have a firm grasp of in order to be successful? I'm not specifically talking about rendering math or anything in the niche areas of game ...
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vote
2answers
350 views

How to get the point of collision in Separating Axis Theorem?

I'm interested in the relatively precise point (not line) of collision for calculating angular velocity on impact for use in a impulse calculation. At first I thought, perhaps naively, that I could ...
0
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1answer
115 views

Rendering an isometric tilemap

I have a tile which is 512x256 pixels and I'm trying to render it in an isometric fashion. I have this helper function: ...
0
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1answer
35 views

Top down off-screen indicator, Unity3D C#

I'm working on a top-down 3D game where things spawn off camera. Movement only occurs on 2 axis (x and z). Rotation is about y axis. The player is in the center of the camera and needs to have ...
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1answer
38 views

Wrong angles given by atan2

I have a method to calculate angle between two vectors, but it is giving wrong values. here is the code : ...
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1answer
47 views

Third Person SpaceShip Camera Directx9 follows objekt but gets weird after moving object

We have the following code. It should follow the game Object in every step but it does not. In the beginning we can rotate the object where ever we want and it works but after moving it some the ...
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1answer
13 views

Get closest point on box to line

Eventually this problem will be 3D. My player is looking forwards. There is an axis-aligned box on the screen (FOV is guaranteed to be 90, so boxes behind the player aren't considered.) I want to ...
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3answers
5k views

How to calculate the closing speed of two objects

I have the 2D positions and 2D velocity vectors of two objects. How do I calculate the closing velocity ? I want to get the closing speed. Think of one jet tracks another jet with radar and you want ...
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0answers
47 views

How can I make this tile map correctly?

I'm having the following problem creating this hexa tiled map. this is what I wanted : [EDIT] Ok I've Managed to do this: ...
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0answers
10 views

Find The Angle Needed for Hitting a Target with Air Resistance [duplicate]

I'm looking for a formula to hit a target on an xy plane. How can I calculate the angle needed to hit the target with a given distance and projectile velocity? I want to incorporate simulated air ...
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vote
1answer
506 views

Converting Euler rotation angles from Z up to Y up (Max to OpenGL)

I'm working on pulling geometry and it's transformation from a 3DS Max exported FBX (Z-up) to an OpenGL model format (Y-up). The main problem is I intend to keep the transformations as Translation and ...
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1answer
82 views

AABB test does not consistently detect edge-to-edge contact when bounds are very different in size

My function compares two AABBs for collision detection, and when they are around the same size it works fine, but I noticed that if I greatly decreased the size of one of them (or augmented the size ...
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0answers
21 views

Python Pygame collision help with my game

I'm creating a game in Pygame where a snowboarder will be going down a hill in 2D. I need to figure out how I can detect collision when the snowboarder (shape of line) hits another line (hill) on one ...
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1answer
67 views

libgdx - how to make enemies not overlap

I'm currently making a roguelike shooter in libgdx to get a better understanding of the library but I recently just stumped onto a problem where enemies would overlap each other while tracking the ...
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0answers
38 views

2:1 Diametric Projection in 2D

I'm trying to implement a 2D isometric game, well diametric with a 2:1 pixel ratio. Trouble is the rotation matrix I made doesn't seem to work. It's off by a little bit and doesn't line up: I'm not ...
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1answer
44 views

How to implement level-player collisions resolution?

I want to create simple collision response system (physical simulation is not required now). It is needed just that player can't go through walls. I consider some variants: - Just create a set of ...
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1answer
62 views

How is raycasting implemented

I know what it's used for, I know what it does. What I am essentially asking is what is the math/code behind how it works? I'm aware that any custom implementation would likely be slower than an ...
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1answer
98 views

How to fit rectangles in a page?

Here's my problem: I need to fit rectangles in a polygon but in "certain way". I have few rectangular shapes (of different sizes) and I need to put them on a polygon. My first idea was to always ...
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3answers
58 views

Find Entity Orientation In Degrees Given Two Coordinates

I'm trying to find the orientation for an entity, as an angle in [0º-360º). I've searched for an answer and tried to implement something of my own, but it always fails on the edge cases. For a better ...
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1answer
3k views

Quaternion Look At with Up vector

I have implemented a "look at" method for my screen elements and it almost works how I want it to work. The ScreenElement class uses a R3 Vector and a Quaternion to determine the position and ...
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3answers
129 views

How to find the degree of interpolation?

I have two quaternions: A and B. I want to lerp between them. Given another quaternion C, I ...
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1answer
162 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: ...
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1answer
65 views

Perspective Matrix doesn't work OpenGL 4

I tried to implement my own perspective matrix and it doesn't work. I don't understand why. With just with my view matrix (without Perspective Matrix) I can see my mesh. Here my view matrix : ...