A Primer on Bézier Curves – So What Makes a Bézier Curve?(pomax.github.io) |
A Primer on Bézier Curves – So What Makes a Bézier Curve?(pomax.github.io) |
If you're reading this text block, then you have scripts disabled: thankfully, that's perfectly fine, and this site is not going to punish you for making smart choices around privacy and security in your browser. All the content will show just fine, you can still read the text, navigate to sections, and see the graphics that are used to illustrate the concepts that individual sections talk about."
That is how I'd like to the rest of the internet to work as well.
I think I'm gonna make `primersprimer.graphics` to list them or something.
This, however, is pretty damn nifty, esp relative to most 'let me explain to you with prettier pictures what google (now chatgpt) just explained to me' fluff.
Also, the math of quadratic beziers made it so even if you did get the handles of each control point the right length to avoid a bump, you could get a "pumping" effect as the radius of curvature changed from wide to narrow and back to wide, though you could avoid this by avoiding trying to create circles in your track design.
No Limits 2 eventually came out which uses a different type of curve which was far easier to make smooth. It also included a way to define the track by graphing out the ride's G-forces and banking changes, and it would plot the control points for you. It was an absolute game changer for making smooth track.
- You have one polynomial describing the x-coordinate and one describing the y-coordinate, and both polynomials have the same degree (two for quadratic, three for cubic Bézier curves)
- The two polynomials share the same parameter t, which runs from 0 to 1.
That's all.
If I just want to get a working product I only need the basic algorithm, but understanding "all" of it is never wrong
Concepts coming from french mathematicians were made more obscure just to raise the bar. The irony is, in french Universities.
I recall a student who had enough failing the computer based assessments. He kindly asked the lead lecturer to show us all that he, at least, could land a perfect score. He made the mistake to try, got 8 points out of 20.
He admitted it wasn't easy when not prepared, and moved on with the next mined field.