This plots a classic Bézier curve, with a bit of a twist - this curve can have infinite control points! Well, at least until Scratch starts going into really high numbers and coming out with NaN in it's operators, but not much can be done about that. All there is for you to do in this project is to click wherever you want to add a point, it's simple as that! You can drag points around. Have fun and enjoy the maths. You can click the green flag to reset the points. Keep your mouse still as you click, or it will be a drag and won't generate a new point. If this is slow for you, use Turbowarp (it also looks nicer): https://turbowarp.org/1074037217?hqpen How does this work, you may be wondering? Well, it's actually kind of simple. You need to assign each point a weight, for each position along t. The weights of all of the points are added together to form a position. When t=0, you're at the start of the curve, on the first point, and it should be assigned a weight of 1, and everything else should be assigned 0, so you are put where you want. Similarly on the last point when t=1. In the in-betweens, it gets a little trickier. We can give points a value of (1-t)^(n-i)*t^i*P*B, where n is the number of points, i is the number of the point we're assigning weight to, P is it's position (x or y), and B is the binomial coefficient. This last one can be calculated by n!/(i!(n-i)!, and for those who don't know, ! denotes factorial. If you'd like to know more, you can find many results on the web, or feel free to ask me. Heaps of effort has gone into putting this together for you, so if you like it, consider leaving a love and favourite, maybe even a follow if you'd like to see more like this. It means a lot to see people enjoying what I make. Infinite Béziers have heaps of cool uses! I'd love to see what you can make, so feel free to use this code with credit, and let me know, so I can see what you've made. Follow the discussion here: https://scratch.mit.edu/discuss/topic/782995/ #all #math (can't we just all settle to call it the same thing? xD)
