Fixing curves, for me, is an every day activity. Sometimes they look oddly pointy, too steep or too wide, guiding my eyes to awkwardness.
And since I’m an optimization freak (as you could tell on my previous article on Bézier curves), I end up using some procedures to tackle problems.
So, today I want to share with you a couple of techniques I use a lot. Here we go!
1. Method 1
If you’ve read my article on Bézier curves (and you should for the sake of understanding this article), you’ve noticed that I stressed on how important point placement is. Here’s a summary of what I recommended:
But this doesn’t mean that you should immediately start drawing this way; these are only requirements for you final work.
With this said, consider the following lowercase n:
Let’s start by fixing the top curve:
And here’s the same process for the inside curve:
And a comparison between our original n and our corrected one:
So, what happened here? Here’s some observations:
1.1 Problems With This Method
This has some limitations, of course:
2. Method 2
And here we are. *awkard stare*
So, back to business: how do the point-addition algorithms distribute the handle length? Well, they keep the handle length proportionally equal, to keep the curve as smooth as possible.
With this in mind, when we have our handles in a 90º angle, we can fit our 4 points in a square. And with less than 90º, a trapezoid:
Let’s stick with the rectangle, for simplicity’s sake.
By now, your inquisitive mind might be asking:
What happens to the curve if one handle grows from the minimum to the maximum length, inscribed in the rectangle, while the other does the opposite?
And now you must be thinking how did I read your thoughts, right? Right.
But let’s not deviated from the subject; here’s what happens:
As you can see, the curve bulges slightly in the extended handle’s side and gets steeper in the retracted one.
Now, what happens if both handles go from minimum to maximum length?
You probably saw this coming.
Well, first of all, I apologize for the slow build up, but I wanted you to be aware of the two factors, because you’ll be dealing with them with this method.
By the way, I don’t know if you keep the habit of click-and-dragging curves, but if you don’t, start doing it. And in most drawing applications, holding the Shift key down keeps the handles in the same vector.
If we want to keep the handles’ lengths proportionally equal, the rectangle from their maximum length point to their actual position has to be proportional to the anchor’s rectangle. Here’s an image to clear this out:
So, here are the steps to do this:
With practice, you’ll be able to eyeball the entire process and still get some sweet and smooth curves.
3. Final Thoughts
I hope you’ve found this article helpful, since I find these make me work faster (I struggle less to achieve satisfactory results), while it keeps the overall look of my work consistent.
Thanks for reading this and if you like it, share the knowledge! Cheers!