README.md

Bézier Curves

https://serve.bubner.me/unity/bezier

$$\text{Bézier curve general formula}$$
$$B(t) = \sum_{i=0}^{n} \binom{n}{i} (1-t)^{n-i} t^i P_i$$
$$\therefore B(t) = \sum_{i=0}^{n} \frac{n!}{i!(n-i)!} (1-t)^{n-i} t^i P_i$$
$$\because \binom{n}{k} = \frac{n!}{k!(n-k)!}$$
This small Unity app generates Bézier curves using the explicit definition of summated binomial coefficients and linear interpolation. Created as a proof-of-concept and for fun to learn more about the math involved in computer graphics.

Features

• Add up to 171 points (double datatype precision)
• Remove individual or all points
• Edit points and reflect changes dynamically and instantly (like Desmos)
• Scrub along a vector by interpolation ratio t with a slider or animation
  • Draw-point scrubbing t shows construction lines as a set of linear interpolations
• Adjust resolution (delta t) of rendered curve
• Real-time curve rendering