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## Math and Physics Articles

#### DIY 2D Vector Physics

Category: Math and Physics

By Tom Novelli

#### Combining Material Friction and Restitution Values

Category: Math and Physics

By Peter Stock

Category: Math and Physics

By Álvaro Begué

#### 2D Transforms 101

Category: Math and Physics

By Sundaram Ramaswamy

#### Math for Game Developers: Advanced Vectors

Category: Math and Physics

By Jorge "BSVino" Rodriguez

#### Particle Systems using Constrained Dynamics

Category: Math and Physics

By Tim Bright

#### Math for Game Developers: Probability and Randomness

Category: Math and Physics

By Jorge "BSVino" Rodriguez

#### PID Control of Physics Bodies

Category: Math and Physics

By James Wucher

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### DIY 2D Vector PhysicsUNDER REVIEW

Dec 01 2015 07:32 PM | Posted By Tom Novelli in Math and Physics
Some algorithms to get you started should you opt to ditch the libraries & do it yourself.

Tagged With:  2D  physics  collision  intersection  algorithm
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8Likes
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### Combining Material Friction and Restitution ValuesUNDER REVIEW

Nov 13 2015 05:39 AM | Posted By Peter Stock in Math and Physics
Calculating the coefficients needed to use the Coulomb friction model in physics simulations

Tagged With:  Physics
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11Likes
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Nov 05 2015 06:45 AM | Posted By Álvaro Begué in Math and Physics
How do you compute where you have to aim to hit a moving target with a finite-speed projectile? This is a common question on gamedev.net's forums. This article presents a procedure to solve this problem and some variations thereof.

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14Likes
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### 2D Transforms 101

Nov 01 2015 06:40 PM | Posted By Sundaram Ramaswamy in Math and Physics
A presentation on 2D transforms with interactive animations.

Tagged With:  2d  math  transformations  geometry  linear-algebra  mapping  coordinate-systems
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7Likes
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### Math for Game Developers: Advanced Vectors

Sep 16 2015 12:19 AM | Posted By Jorge "BSVino" Rodriguez in Math and Physics
YouTube series for beginners explaining various mathematical concepts as applied to game development

Tagged With:  math  vector  dot product  linear interpolation  euler  cross product  aabb  projections
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11Likes
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### Particle Systems using Constrained Dynamics

Sep 06 2015 12:56 PM | Posted By Tim Bright in Math and Physics
A really cool way to simulate large numbers of particles with path constraints *without* using springs.

Tagged With:  numerical methods  physics  particles  dynamics
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12Likes
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### Math for Game Developers: Probability and Randomness

Jul 10 2015 12:19 PM | Posted By Jorge "BSVino" Rodriguez in Math and Physics
YouTube series for beginners explaining various mathematical concepts as applied to game development

Tagged With:  math  probability  randomness  rng  noise
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12Likes
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### PID Control of Physics Bodies

Jan 26 2015 11:39 AM | Posted By James Wucher in Math and Physics
Once you bite the bullet and decide to use a physics engine for your game pieces, you are going to have to come to terms with making them move naturally. Getting a handle on handling forces to make things "turn" can be a psychotic episode in the making. Instead, do what the engineers do in the real world and use a PID control loop.

Tagged With:  2D  Box2D  Physics  PID  Control Loop
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11Likes
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### Capsule Inertia Tensor

Jan 11 2015 11:38 PM | Posted By Bojan Lovrovic in Math and Physics
This article tries to simplify the math behind calculating inertia tensor of a cylinder as much as possible without skipping on any important details. Implementation in C/C++ is presented at the end.

Tagged With:  physics  programming  math  calculus
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18Likes
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### Towards a Simpler, Stiffer, and more Stable Spring

Dec 19 2014 01:53 AM | Posted By Michael Schmidt Nissen (h4tt3n) in Math and Physics
In this article we will look at a modified spring equation that is very easy to tune, displays maximum possible stiffnes and damping, and is guaranteed to keep any spring system stable under all conditions. The equation is tailored for 1st order symplectic Euler integration and impulse based simulation.

Tagged With:  spring  damping  mass-spring-damper  harmonic oscillator  reduced mass  game physics
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10Likes
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### Shooting At Stuff

Nov 15 2014 12:22 PM | Posted By James Wucher in Math and Physics
You never shoot directly at a moving target. You shoot at where the target is going to be when your shot gets there. Millions of years of biology make it easy for predators. Turns out it's pretty easy for computers as well...if you know the math.

Tagged With:  2d intercept position  2D  vector  target  intercept  moving target  algorithm
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15Likes
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### Math for Game Developers: Calculus

Oct 10 2014 06:42 AM | Posted By Jorge "BSVino" Rodriguez in Math and Physics
The popular series continues with applications for calculus as related to game development

Tagged With:  math  calculus
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15Likes
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### Simple but Effective Collisions Part 1: Radial Collision Handling

Aug 15 2014 08:00 AM | Posted By George Kristiansen in Math and Physics
Smooth collision detection is a requirement for any game, whether you're running around in an FPS or landing a spacecraft on the Moon. This article talks through the first of two methods for implementing simple collision detection for objects commonly encountered in games. It will use DirectX syntax, but it is easy enough to apply to other APIs.

Tagged With:  collision detection  trees  bounding  cylinder
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11Likes
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### Matrix Inversion using LU Decomposition

Apr 25 2014 02:05 PM | Posted By Tim Bright in Math and Physics

Tagged With:  matrix  inversion  LU decomposition  numerical methods
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14Likes
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### Math for Game Developers: Fragment Shaders

Mar 26 2014 11:45 PM | Posted By Jorge "BSVino" Rodriguez in Math and Physics
A series of videos on the mathematics behind shaders, covering topics including normal mapping, lambertian surfaces, specularity, sprite lamp normal generation and fog

Tagged With:  shaders  normal maps  lambertian surfaces  specularity  fog  sprite lamp  normals
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7Likes
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### Making a Game Engine: Transformations

Feb 15 2014 01:17 PM | Posted By James Lambert in Math and Physics
Any graphical game needs a way to place objects on the screen, move them, rotate them, and even grow or shrink them. Transformation matrices offer a very elegant solution to this problem.

Tagged With:  game engine  transforms  matrices
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6Likes
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### Math for Game Developers: Triangle Meshes

Feb 07 2014 04:30 AM | Posted By Jorge "BSVino" Rodriguez in Math and Physics
Math for Game Developers is exactly what it sounds like - a weekly instructional YouTube series wherein I show you how to use math to make your games. Every Thursday we'll learn how to implement one game design, starting from the underlying mathematical concept and ending with its C++ implementation. The videos will teach you everything you need to know, all you need is a basic understanding of...

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12Likes
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### Math for Game Developers: Geometry Testing

Jan 30 2014 08:58 AM | Posted By Jorge "BSVino" Rodriguez in Math and Physics
Learn the math behind firing a bullet and detecting collisions in a scene with the line/box intersection algorithm

Tagged With:  vector  aabb  matrices  matrix  plane intersection  line intersection  collisions  projections
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15Likes
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Jan 21 2014 04:51 PM | Posted By Tim Bright in Math and Physics
This advanced article on intersection tests is primarily about curve intersection, but it also contains useful information for primitive intersection tests, such as point-line, line-line, and line-circle. These can be extended to 3D primitives as well.

Tagged With:  geometry  intersections  lines  plane  curves  parametric  implicit
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20Likes
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### Problem Solving Using Vectors

Dec 23 2013 04:45 AM | Posted By James Lambert in Math and Physics
Anybody who has dealt with rotating sprites probably has dealt with angles. Representing a sprite's rotation as an angle makes certain operations, such as rotating towards another angle, much more complicated than it should be. There is a better way. Use unit vectors.

Tagged With:  vectors
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23Likes
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### Practical Guide to Bezier Curves

Nov 07 2013 09:05 AM | Posted By Tim Bright in Math and Physics
There's a lot about the basics of Bezier curves around, but how about actually using them? This will show a few new things about Bezier curves, a few techniques in coding up curves, and serve as a primer for Bezier surfaces and B-splines.

Tagged With:  math  Bezier curves  geometry
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9Likes
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### Math for Game Developers: Advanced Matrices

Sep 24 2013 01:05 PM | Posted By Jorge "BSVino" Rodriguez in Math and Physics
The popular video tutorial series continues with new videos on advanced ways to use matrices in game development

Tagged With:  matrices
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19Likes
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### Math for Game Developers: Quaternions

Aug 21 2013 09:10 AM | Posted By Jorge "BSVino" Rodriguez in Math and Physics
The popular video tutorial series returns with new videos on how to use quaternions in game development

Tagged With:  quaternions  axis-angle  rotation  inverse
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16Likes
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### Math for Game Developers: Advanced Vectors

Aug 07 2013 02:30 PM | Posted By Jorge "BSVino" Rodriguez in Math and Physics
These videos cover dot products, cross products, euler angles, and box intersection as applied to game problems

Tagged With:  dot product  cross product  euler angles  box intersection
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25Likes
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### Math for Game Developers: Intro to Matrices

Aug 05 2013 03:57 PM | Posted By Jorge "BSVino" Rodriguez in Math and Physics
Explores various game development techniques that utilize a basic understanding of matrices

Tagged With:  matrices  basis vectors  scaling  rotation  translation  inverse