# 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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### Vector games (Wireframe, Elite-like) theory and implementations?

I'm interesting in knowing more about how vector games like Elite and Star Wars Atari were built from grounds up. The question is not how to implement vector graphics with modern 3D APIs like OpenGL ...
3k views

### Implementing 2D CSG (for collision shapes)?

Are there any simple (or well documented) algorithms for basic CSG operations on 2D polygons? I'm looking for a way to 'add' a number of overlapping 2D collision shapes. These may be convex or ...
600 views

### Square Grid Polygonal Terrain Query algorithm?

I have a square, fixed-grid terrain with one terrain type per grid unit in my game, and I want to do an arbitrary polygonal terrain query which returns all of the grid units enclosed/intersected by ...
1k views

### How do I get the areas enclosed by an arbitrary 2D shape?

In my game I want users to be able to draw arbitrary 2D shapes of any length around game objects. The shapes must be closed and drawn with a single stroke that does not overlap. For example: I want ...
2k views

### AABB - AABB Collision, which face do I hit?

To allow my objects to slide when they collide, I need to : Know which face of the AABB they collide with. Calculate the normal to that face. Return the normal and calculate the impulse that to apply ...
299 views

### Adjust Aim Angle for Motion with Accelerating Bullet

So, here's my problem: I have a turret attached to a ship that moves at a variable speed through my game world, shooting at the centre of another ship travelling through the game world in a possibly ...
280 views

### Path following with Asteroids-like movement. Time to complete path

I'm currently learning about how to do this, but it's best to post the problem beforehand. (posting on Physics and GameDev, as you guys know your math) It's quite difficult to explain. This specific ...
564 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 ...
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 ...
2k views

### Are game programmers aware of all the physics derivatives?

I am trying to study XNA for game programming. XNA has many methods that can simplify developer's life, such as reflecting the vector when it hits a solid plane. I know these are good and developers ...
30k views

### Does a minor in math increase my hirability? [closed]

I've been pondering this question for some months now, and have been unable to get an answer from anyone in the industry (likely because I know no one in the industry). I am currently completing a B....
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### Why does the order matter in multiplication of matrixes?

I stumbled on this question because I had the same problem with my camera, and changing the multiplication order worked. I ran into a similar problem when scaling a model. This code produced the ...
16k views

### Rotate vector by matrix?

If I have a Vector, say (1,1), how can I rotate it around the origin (0,0)? I'm working in XNA if that helps.
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### What is the simplest way to calculate distance in a 3D environment?

What is the simplest way to programmatically calculate difference between two points in a 3D game environment? I am trying to sort a list of light sources by how close they are to an entity, so that ...
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### Why isn't this physics code scaling velocities separately?

I'm working my way through this book and I'm trying to work this code out: ...
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### How can I transform a point from world space to object space?

If I have an object space described by transformation matrix that should be applied to object to transform it to world space, what I have to do to transform point (world space) to that object space. ...
839 views

### How can I change the acceleration of an object to arrive at a particular time?

I'm trying to write some code to change an acceleration factor so a ball will arrive at a destination in a desired time. The problem is I don't know time (t) but I do know I want it to arrive at (t - ...
8k views

### What is an efficient 2D line-segment-versus-triangle intersection test?

In a 2D plane, I have a line segment (P0 and P1) and a triangle, defined by three points (t0, t1 and t2). My goal is to test, as efficiently as possible ( in terms of computational time), whether the ...
933 views

### Abstracting multiple math libraries with C++

I would like to create some level of abstraction above math in my code. I mean I don't want to be dependant on the implementation of math operations or even on class names, which are provided by some ...
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### 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: ...
406 views

### How would one generate a texture for cracks in different materials?

I would want to have the ability to simulate different variables like brittleness, or other variables to get varied end results. I would mainly need to generate impact cracks, so it would need to ...
2k views

Short version: What can happen to the output of a vertex shader that leads to no(or very few) pixels being drawn, especially in relation to a perspective matrix. Long version: My problem refers to ...
1k views

### Determining the probability of a successful attack based on the equipped weapon?

Take this example, a player has a sword composed of the handle and a blade. Together, they generate a strength of X and that combination adds qualitative attributes (induce more damage to fire ...
9k views

### How would I translate screen coordinates to Isometric coordinates?

I have a function isoToScreen(x, y) that converts Isometric coordinates to Screen coordinates. ...
591 views

### What is the best way to limit player movement?

I'm currently programming a 2d game where the player moves around on a rectangular playing field. The player has a direction and a velocity. What is the best way to limit the player's movement so he/...
310 views

### Self-righting agents that have fallen over

I need insect-like agents that have fallen/rolled on their back/side to naturally re-orient themselves. The agents are modeled as simple cuboids in the physics engine (Bullet) to approximate an ant-...
3k views

### How to calculate the exit speed of ball bouncing off a solid surface

Hey all, I am working on a simple game to include some rigid body dynamics, involving placing (moving & rotating) some springs to bounce a falling ball into a target area. My problem is correctly ...
798 views

### How to account for acceleration when aiming projectiles?

How do I aim a constant speed projectile to hit a target if there is a constant acceleration vector acting on it? (For example, the wind and gravity from Worms.)
23k views

### How do I find a point given an angle and distance to it?

I'm working on a school project creating a tank team in the programming game Robocode. (It's a tank battle game with self-programmed bots, in Java). I'm programming a scout bot that scans, finds ...
13k views

### How to calculate a direction vector for camera?

I have a vector that describes change in movement, and I have a 3d-vector, m_rot, that describes a rotation given to an object. I want to calculate a direction vector using both this data. How to ...
14k views

### How does atan2 work when getting angle of a vector?

I know that atan2 gives me the absolute angle of any vector. But it doesn't give a value from 0 to ...
391 views

### How can I get a 2D texture to rotate like a compass in XNA?

I'm working on a small maze puzzle game and I'm trying to add a compass to make it somewhat easier for the player to find their way around the maze. The problem is: I'm using XNA's draw method to ...
842 views

### Vector problem: which one is the left / centre / right one?

In aviation, runways are named according to their magnetic orientation seen from the pilot's perspective. For example: a strip of asphalt oriented along the east-west axis will be named ...
6k views

### How do I restrict the movement of a point to within a radius of another?

I have a situation where a sprite's center point needs to be constrained within a certain boundary in 2D space. The boundary is circular, so the sprite is constrained within a radius. This radius is ...
3k views

### How can I get a velocity vector for an object moving in a circle?

I am simply trying to make an object move in a circle around a point. Let's say I have an object with a position vector going from that point to the object, and also the angle of the object with the x ...
10k views

### How do I find rotation in 3D based on a vector/normal?

I've been playing with Blender and Python, doing basic things like accessing vertices/normals,etc. I can get the normal of each face of a mesh. I was wondering, how can I get the rotation of a face ...
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, ...
12k views

### Combining rotation,scaling around a pivot with translation into a matrix

In short: I need to combine rotation (in the form of a quaternion), scaling around a pivot point along with translation into a transformation matrix. The long: I am trying to implement a proprietary ...
2k views

### 2D car physics and high speed turning

I've been looking at the following page, which has been very helpful: http://www.asawicki.info/Mirror/Car%20Physics%20for%20Games/Car%20Physics%20for%20Games.html but have come into problems with the ...
1k views

### How to make my character slide (not bounce) off a slope

My character needs to slide and not bounce off a slope. The solutions I found here use a Reflection vector, but they make my character bouncy when they run downwards a slope. ...
3k views

### top down game - checking, drawing enemy's line of sight area with obstacles

Examples of what i'm going to need: I'm using cocos2d to draw a CCTMXTiledMap, on those tiles i'll have to draw the LOS cone. How would i test if the player is within that cone, taking obstacles ...
538 views

### Calculating and detecting curves

How can I detect the 'steepness' of a curve? For example, if the user swipes their finger across the screen in a curve, what's the best way of detecting whether the curve is almost a semi-circle, or ...
4k views

### snapping an angle to the closest cardinal direction

I'm developing a 2D sprite-based game, and I'm finding that I'm having trouble with making the sprites rotate correctly. In a nutshell, I've got spritesheets for each of 5 directions (the other 3 come ...
3k views

### How to think about 2D scaling/rotation transformations

This is a kind of embarassing question to me since I'm getting more in-depth with XNA but some times my way of thinking about things in my head contradicts an example and I need to re-think it to make ...
2k 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. ...
2k views

### Calculation correct position of object after collision (2d)

I have a circle, that bounces of walls. The circle is traveling at the speed defined by px/s for x and y. I have collision detection implemented and I use vectors to calculate the new x/y speed (and ...
186 views

### Evenly distributed checkpoints in a procedurally generated world?

Got a procedurally generated world. It's succinctly described as an undirected acyclic graph where vertices are junctions and edges weights/length note the amount of time/effort guesstimated to be ...
2k views

### A* for non grid network

For my specific case, I am trying to find a path finding implementation similar to what described here. I could see reference implementation for A* and HPA*, but I wonder how to extend A* to simple ...