https://github.com/sean-codes/vector-concepts
Storing some vector math experiments
https://github.com/sean-codes/vector-concepts
Last synced: about 1 year ago
JSON representation
Storing some vector math experiments
- Host: GitHub
- URL: https://github.com/sean-codes/vector-concepts
- Owner: sean-codes
- Created: 2017-11-13T02:32:32.000Z (over 8 years ago)
- Default Branch: master
- Last Pushed: 2020-06-15T03:29:40.000Z (about 6 years ago)
- Last Synced: 2025-03-27T13:01:44.048Z (over 1 year ago)
- Language: JavaScript
- Homepage: https://sean-codes.github.io/vector-concepts/#/experiments/circleCollision.js
- Size: 3.48 MB
- Stars: 8
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
Awesome Lists containing this project
README
# vector-concepts
> A repository I use to adventure, explore, and understand geometry / vector mathematics.
View Experiments: [click here](https://sean-codes.github.io/vector-concepts/)
## 🗺 Explored
- Scene setup / Loop
- Unit Circle
- SIN/COS/TAN
- Basic Vector Math ( Adding, Subtracting, Scale, Distance )
- Rotation
- Dot Product
- Projection with Dot Product
- Axis Aligned Bounding Box Collision (AABB)
- Separate Axis Collisions (SAT)
## 📙 Journal
#### Radians
Half of a circle = 180deg or `Math.PI` radians. A entire circle is 360deg or `Math.PI*2` radians. That is 6.28 radians in a circle. In a unit circle the circumference if equal to Math.PI*2
Radian to Degree
```js
var deg = rad * 180/Math.PI
```
Degree to Radian
```js
var rad = deg * Math.PI/180
```
### Sin, Cos, Tan are ratios
When thinking about sin, cos, tan it can be intuitive to think of the unit circle and solve a triangle using the ratios
```
sin: From -1 to 1 the Y
cos: From -1 to 1 the X
tan: can go above 1. the heigth of the wall
```
#### Cartesian vs Polar
**Cartesian**: using x/y to define a position
**Polar**: Using angle and length to define a position
##### Polar to Cartesian conversion. angle and length to (x, y):
``` js
var x = length * Math.cos(angle)
var y = length * Math.sin(angle)
```
### DOT Product
The most mystical equation
```js
var dot = vector1.x * vector2.x + vector1.y * vector2.y
```
The dot product gives us a relationship of two vectors. It is useful for finding the angle
##### Finding the angle between two vectors using DOT Product
The angle is equal to the DOT product of the vectors divided by their lengths multiplied
```js
// cos(Angle) = dot(V1, V2) / (v1.length * v2.length)
var dot = vector1.dot(vector2)
var cosAngle = dot / (vector1.length() * vector2.length()) // -1 to 1
var angle = acos(cosAngle) // 180 - 0
```
## 📚 Library
- http://blog.wolfire.com/2009/07/linear-algebra-for-game-developers-part-1/
- http://www.helixsoft.nl/articles/circle/sincos.htm
- https://www.khanacademy.org/math/trigonometry
- http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Trigonometric_functions.html
- https://betterexplained.com/articles/intuitive-trigonometry/