I have recently been motivated to look at Quadratic Bézier curves.
Quadratic Bézier curves are a way of defining a smooth curve between three control points in space
Bézier curves are named after a French engineer Pierre Bézier, who used it in the 1960s for designing curves for the bodywork of Renault cars. Bézier curves are used primarily in computer-aided geometric design (CAGD), but are also used in robotics to generate smoother motion profiles to prevent wear and tear.
In order to explain Bézier curves we first need to understand linear interpolation.
Linear interpolation, is a mathematical function that returns a value between two values on a linear scale.
firstValue + ((secondValue – firstValue) * t) = lerpValue
where t is the interval between 0 and 1.
This can be broken down into two parts
The first part calculates the distance between two values
secondValue – firstValue = distance
i.e. 300 – 200= 100
The second part takes the distance, multiplies it by the t factor and then adds the first value
i.e. (distance * 0.5) +200 = 250
You can see below that as t changes the value moves from the first value to the second value in a linearly