Bézier Curves

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

$\text{Bézier curve general formula}$
$B(t)=\sum _{i=0}^n(\genfrac{}{}{0ex}{}{n}{i})(1-t{)}^{n-i}{t}^i{P}_i$
$\therefore B(t)=\sum _{i=0}^n\frac{n!}{i!(n-i)!}(1-t{)}^{n-i}{t}^i{P}_i$
$\because (\genfrac{}{}{0ex}{}{n}{k})=\frac{n!}{k!(n-k)!}$
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