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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6
votes
1answer
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 ...
4
votes
2answers
13k views

Moving a 2D object along circular arc between two points

I have a sprite which I need to move along a curve between two points in 2D space. Speed must be consistent all the way. No physics involved. How can I achieve this? The object is sun sprite.
5
votes
1answer
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 ...
7
votes
3answers
4k views

building a game for different resolution phones

I am starting some tests for building a game on the Android program. So far everything is working and seems nice. However I do not understand how to make sure my game looks correct on all phones as ...
1
vote
1answer
11k views

RPG Logarithmic leveling formula?

I'm working on a RPG game, however, I am not the amazing person at math that I wish I was, although someone suggested a logarithmic equation would work well. My current idea is for this: You start ...
6
votes
1answer
4k views

Ray Intersecting Plane Formula in C++/DirectX

I'm developing a picking system that will use rays that intersect volumes and I'm having trouble with ray intersection versus a plane. I was able to figure out spheres fairly easily, but planes are ...
4
votes
2answers
266 views

Determining the first future intersection possible between ships and a planet

Somewhat of an extension of this. The Problem I have a ship being launched from a planet, and I would like it to travel at a constant speed and direction such that it intersects another planet the ...
1
vote
3answers
2k views

Code to generate a color gradient within a texture using a diagonal line

I want to generate a color gradient between two colors from x1,y1 to x2,y2. I'm unsure how to do this though. I can use Color.Lerp to get all of the color steps, but the problem is that I don't ...
0
votes
1answer
52 views

How to keep objects in the same position relative to their parent?

I'm writing a simple game in C# and i'm having some difficulty to calculate the local position of a sprite. What i'm aiming to achieve: Calculate the sprite "local position" relative to the ...
0
votes
1answer
101 views

how do I move an object based on rotation of another object?

This question is related to my other question about camera rotation. I hope its acceptable to ask a second question. I cannot figure out the math of how to calculate moving the camera to stay behind ...
47
votes
4answers
8k views

A ball hits the corner, where will it deflect?

I need to brush up my trigonometry and hope you can help here with a simple mathematical model. Here is my model so far in the image attached. I am aware that the frame animation has other problems ...
34
votes
5answers
12k views

How can I calculate current level from total XP, when each level requires proportionally more XP?

In my game, XP needed to reach the next level is Current Level × Level Threshold. Given that, how can I get my current level from the total XP ever earned? For example: ...
22
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6answers
11k views

What is a good linear algebra book for game programmers? [closed]

I was told that I should start learning Linear Algebra in order to create good games with good physics. I'm reading Linear Algebra book and it's completely foreign to me. The author starts out with ...
33
votes
7answers
31k views

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 ...
53
votes
2answers
10k views

What is a quaternion?

What is a quaternion, and do how they work? Also, what advantages do you gain using three points on a 2D plane? Finally, when is it considered good practice to use quaternions?
21
votes
1answer
9k views

Determine arc-length of a Catmull-Rom spline to move at a constant speed

I have a path that is defined by a concatenation of Catmull-Rom splines. I use the static method Vector2.CatmullRom in XNA that allows for interpolation between points with a value going from 0 to 1. ...
13
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4answers
9k views

Staggered Isometric Map: Calculate map coordinates for point on screen

I know there are already a lot of resources about this, but I haven't found one that matches my coordinate system and I'm having massive trouble adjusting any of those solutions to my needs. What I ...
18
votes
6answers
32k views

Best C++ Math Library for Game Engine? [closed]

I'm looking for a fast opensource C++ math-library for my game engine with the following features: fast (sse?) vectors matrices quaternions suitable for both opengl and directx
16
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6answers
5k views

How could you parallelise a 2D boids simulation

How could you program a 2D boids simulation in such a way that it could use processing power from different sources (clusters, gpu). In the above example, the non-coloured particles move around ...
24
votes
5answers
11k views

How to quickly calculate the sight area in a 2D tiled game?

I have a matrix of tiles, on some of that tiles there are objects. I want to calculate which tiles are visible to player, and which are not, and I need to do it quite efficiently (so it would compute ...
31
votes
4answers
14k views

How can I move an object in an "infinity" or "figure 8" trajectory?

When I want to move object around point I do: point.x *= cosf(timer.timeElapsed); point.y *= sinf(timer.timeElapsed); How to make point move on eight or ...
27
votes
4answers
17k views

Bezier curve arc length

See also: same question on Math.SE How can I find the arclength of a Bezier curve? For example, a linear Bezier curve has the length: ...
17
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2answers
40k views

How do I linearly interpolate between two vectors?

I have a velocity vector where my client is at and where its going, and I have the same vector that comes from the server telling where the client should be. Sometimes its a bit different, so I want ...
15
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2answers
3k views

Why do people use quaternions?

I have been using them as a black box for a while, I'm just learning about of the maths but I'd just like some definitive answers to this question. So far the only benefit I've come across personally ...
15
votes
6answers
15k views

What is the purpose of the canonical view volume?

I'm currently learning OpenGL and haven't been able to find an answer to this question. After the projection matrix is applied to the view space, the view space is "normalized" so that all the points ...
11
votes
1answer
8k views

Circle-Line Collision Detection Problem

I am currently developing a breakout clone and I have hit a roadblock in getting collision detection between a ball (circle) and a brick (convex polygon) working correctly. I am using a Circle-Line ...
8
votes
2answers
1k views

Modular spaceship control

I am developing a physics based game with spaceships. A spaceship is constructed from circles connected by joints. Some of the circles have engines attached. Engines can rotate around the center ...
16
votes
3answers
34k 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 ...
6
votes
1answer
970 views

rotating an object from sourceAngle to destAngle, both 0-359, clockwise or counter clockwise?

I've got a game object i need to rotate. It's current angle is player.rotation, the destination is targetAngle, both in degress, 0 to 359. I've got a function named rotateDirection(float sourceAngle, ...
12
votes
4answers
7k views

How do I implement deceleration?

I say "deceleration" because I'm not using acceleration at the moment; what I mean is moving the velocity back towards zero, eventually stopping. I'm new to vectors and not so great with physics and ...
7
votes
1answer
2k views

Converting between Spiral Honeycomb Mosaic and axial hex coordinates

There seems to be quite a lot of logic in dealing with hexagonal grids using a system of axial coordinates like the one described here. In doing some reading about hex grids, though, I ran across the ...
8
votes
3answers
6k views

Kepler orbit : get position on the orbit over time

I'm developing a space-simulation related game, and I am having some trouble implementing the movement of binary stars, like this: The two stars orbit their centroid, and their trajectories are ...
5
votes
3answers
9k views

Getting isometric grid coordinates from standard X,Y coordinates

I'm currently trying to add sprites to an isometric Tiled TMX map using Objects in cocos2d. The problem is the X and Y metadata from TMX object are in standard 2d format (pixels x, pixels y), instead ...
5
votes
2answers
790 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.)
4
votes
3answers
2k views

Simulated Economic Factors Based on Supply and Demand in MMO Resource Trading Game

I'm working on a gam (naturally), and the primary activity for the player is to buy and sell commodities at various marketplaces. Each commodity has the following properties: Base Price: if all ...
15
votes
1answer
5k views

What are the maths behind 'Raiden 2' purple laser?

The path of the laser is affected by user input and enemies present on the screen. Here is a video, at 5:00 minutes the laser in question is shown : Raiden II (PS) - 1 Loop Clear - Part 2 UPDATE ...
7
votes
1answer
3k views

Spherical to Cartesian Coordinates

Well I'm reading the Frank's Luna DirectX10 book and, while I'm trying to understand the first demo, I found something that's not very clear at least for me. In the updateScene method, when I press A, ...
3
votes
3answers
5k views

simplest way of making a sphere roll in a realistic way

rather than just moving a sphere across a plane, I want to make it roll like a ball. What is the simplest way of doing this? I assume it will have something to do with the circumference of the ball ...
10
votes
3answers
1k views

Can I jump from A to B?

I'm making some rudimentary AI for my side-scroller and I need to know whether an AI unit can reach point B from point A simply by taking a jump. Flight trajectory of my characters is a bit unusal as ...
9
votes
2answers
1k views

Render 3d object to 2d surface (embedded system)

i am working on an embedded system of a sort, and in some free time i would like to test its drawing capabilities. System in question is ARM Cortex M3 microcontroller attached to EasyMX Stellaris ...
7
votes
1answer
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 ...
6
votes
1answer
4k views

Predicting physics/trajectory for pool/billiards games

I'm thinking of making a quick proof of concept of a billiard-style game mechanic, where the player has perfect information of what is about to happen. Here's a good example: I'm only mildly ...
6
votes
4answers
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 ...
5
votes
1answer
1k views

How to do perspective projection “parallax” but without changing the scale or offset of objects?

Hello everyone I have this problem that I have tried everything I could think of. The problem: I am making a 2D game with parallax effect but I am using 3d space so am not simulating the parallax but ...
2
votes
1answer
147 views

Modeling complex requirements for populating loot/drop tables

I have a set of items and a data structure that describes where and how those items may be dropped. I'm looking to implement a roguelike/randomizer element to the game and want to include the special ...
6
votes
1answer
714 views

Finding roots/zeros for collision detection?

For the most simple of 2D games, I have implemented a posteriori collision detection (overlapping rectangles) on the x/y Cartesian plane, but am now interested in understanding the basics of a priori ...
6
votes
1answer
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/...
6
votes
2answers
5k views

Matrix for 2D perspective

I'm trying to determine whether what I'm attempting to achieve is even possible mathematically. I'm obviously not a seasoned game developer so I'm having trouble even coming up with the terminology to ...
2
votes
2answers
4k views

Calculate matrix transformation components separately

It is possible to calculate the translation, rotation and scale that were used to build a matrix? I mean if I have a matrix M can I calculate the rotation, scale, ...
2
votes
4answers
7k views

Checking for collisions on a 3D heightmap

I have a 3D heightmap drawn using OpenGL (which isn't important). It's represented by a 2D array of height data. To draw this I go through the array using each point as a vertex. Three vertices are ...