Coding Math: Episode 20 - More on Bezier Curves

This week we discover a couple of neat tricks to using Bezier curves.

[milen]

"Well, I don't suppose you're buying this drama" HAH that's just gold.
Love the series! Learning a lot. I have a decent background in physics and programming but combining the two would've been very hard without you so keep up the good work! Loving it!!!

[naraksama]

I had a hard time understanding your multicurve function, but now I get it. It's basically: start at point 0, calculate the mid of the next two points (1 and 2). Create a loop for t for quadraticBezier(0, 1, mid, t, pFinal). At the end of the iteration, the mid point is the new starting point (0 = mid).

[johnconley]

You are really good, like watching NETFLIX, I can't stop watching and coding. My lesson fav so far ? Edge the springs(!), though I had to do them

[AngelHdzMultimedia]

I am deeply thankful for this! Blessings!

[jgcooper]

if you rearrange the terms it becomes really easy to understand the formula, and thus to extrapolate it to use more control points (probably as many as you like), and even to automate it as a for loop fed with an array of points.
allow me to illustrate the reordered terms:

Bezier ( a, b, c, v ){ // a b c are points, v is the interpolation value

w = 1 - v;

result = a * (w*w)
+ b * (w*v) * 2
+ c * (v*v);

}


Bezier ( a, b, c, d, v ){ // a b c d are points, v is the interpolation value

w = 1 - v;

result = a * (w*w*w)
+ b * (w*w*v) * 3
+ c * (w*v*v) * 3
+ d * (v*v*v);

}


Bezier ( a, b, c, d, e, v ){ // a b c d e, are points, v is the interpolation value

w = 1 - v;

result = a * (w*w*w*w)
+ b * (w*w*w*v) * 4
+ c * (w*w*v*v) * 4
+ d * (w*v*v*v) * 4
+ e * (v*v*v*v);

}

and so on, it's easy to see how this could be automated into a generalized function with n points

[World_Theory]

I'd love to know how to find any points of intersection (accurately) of two different Bézier curves. And also of different types of paths, such as arcs, lines. (Intersections between all type, not just intersections between the same types.)

Finding the points of intersection is an important step in adding and subtracting shapes without relying on clips and masks. (The stroke of two shapes may acquire strange effects if someone relies on clips and masks.)

[goikk]

You are my hero 😍 Thank you for the video 💪

[FerchoNossa]

javascript :) ... absolute useful man. thanks

[begrateful]

Did you wrote a paper about this because i really wanna use it in my bachelorthesis about curves in gamedevelopment

[jim_o]

10:10 I really want to know the difference of your function and the canvas function. is it just run with more iterations or with more detailed numbers, are canvas functions run differently than custom JavaScript functions?

[zaibaas]

Can we calculate control points with start and end point given ? I want to draw a curve with certain given inclination every time for any given start & end points

[nicolaigd]

Thanks for making this video! I'm wondering, is it possible to keep the curve on every point when calculating a multicurve? The formula in the start of the video doesn't work then (the curves don't line up properly).