vector-concepts

A repository I use to adventure, explore, and understand geometry / vector mathematics.

View Experiments: click here

🗺 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

   var deg = rad * 180/Math.PI

Degree to Radian

   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):

 var x = length * Math.cos(angle)
 var y = length * Math.sin(angle)

DOT Product

The most mystical equation

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

// 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

sean-codes/vector-concepts