Moving and Rotating with CFrame without sliding

[TimerHotel]

Basically, I am trying to make a ship go from one point to another, without sliding. Below is an example of what I mean.

Now, obviously this is math, but I would like some help figuring the math out, as I am not very good at it.
Would prefer implementation via CFrames. I am not asking for you to make the whole thing, just explain how I should go about it.

Edit: By the way, I do know how CFrames work.

[snorebear]

Have you tried something like the slope formula?

[Fm_Trick (Trick)]

You’re going to need to implement a series of points along a curve.

I am not great with math, however I know EgoMoose has a great tutorial on curves:

Modeling a projectile's motion

This guide was originally written for scriptinghelpers. The original can be found here. As a somewhat active member of the Scripting Helpers discord one of the most common questions I see is how to have a projectile travel an arc. Most people want to know how to do this for things like basketballs or cannon balls and so forth. Since this is such a popular question I thought it would be worth writing a blog post on it and talking about a few other things we can extend from our findings. Deriv…

[CodeWriter]

There is also a good tutorial about Bezier curves in the Roblox wiki:

https://developer.roblox.com/articles/Bezier-curves

[TimerHotel]

This seems to work fine, if the ship is already generally facing the position it will move toward, however when it has it’s back toward it, it rotates at crazy fast speeds, which still looks unrealistic.

[EgoMoose]

Haha this has ended up being an EgoMoose article thread. Everything posted so far has been written by me so hopefully if you have any questions I can answer them

Anyways, in regards to your problem check out this post:

Reparameterization: Tips and Tricks

This guide was originally written for scriptinghelpers. The original can be found here. Here’s a guide about reparameterization. It has a few nifty tricks that can be applied to all sorts of things outside the topic. Awhile back I wrote an article on the wiki discussing Bezier curves. Near the end of the article I started to talk about reparameterization (arc-length parameterization) and how it could be done without calculus. Today we are going to talk about how it can be done with calculus …

[TimerHotel]

This is nice, but I am still having trouble rotating the ship correctly while it’s travelling across the curve.

[wevetments]

Something you could try is using the Archimedes plugin to create 1/4 circles which will be the path of the ship. You could set the CFrame to each part of the 1/4 circle and set the orientation of the ship of the each of those parts.

[EgoMoose]

Well you have some function which gives you a point on the curve, say f(x). Thus if you can use the CFrame constructor CFrame.new(origin, lookAt) in the form CFrame.new(f(x), f(x+0.001)) to get a CFrame that rotates with the curve

[TimerHotel]

These are both great solutions, and I will definitely use a mix, however, @wevetments’ idea is perfect to make sure the ship turns in a realistic way, which was the biggest issue, so I will mark that as the solution.