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In this video, we'll take a look at the foundation of organic modeling, the B-spline, and compare to it's far more well known cousin, the Bezier curve for which it is often mistaken. The Bezier is the curve widely used in 2D applications like Illustrator and Photoshop, and let's you draw or edit using points connected to handlebars, which are then used to adjust the shape of the curve. Let's first take a look at a Bezier and note the handles that make it easy to draw and edit. So, Bezier curves, first and foremost, are formula-based for infinite smoothness.
It has the handlebar controls, which we've mentioned, which are connected via center point, and the two end points of the handles. It's also extremely useful for 2D, like Illustrator and Photoshop as mentioned, but not so much for 3D. Let's take a look at the B-spline. Again, this curve is also formula- based, and generates infinite smoothness. However, it doesn't have handlebars on the curve. It uses a control cage. That cage is outside of the curve. It only touches at the very end points.
This curve was invented specifically for 3D for which it's excellent, but not so much for 2D. Now, let's take a look at the B-spline in 3D. Here is a Freeform Curve that has been drawn in Rhino. You can see the control points are highlighted there. So, if your curve does not display the control points, you can easily turn them on with the Control Point icon or using the F10 keyboard shortcut. You can see the cage, which allows editing. So, these can be moved back and forth changing the shape of the curve.
So, I am going to zoom out and let you see that we have three of these curves. Those were used to generate a 3D surface, so here's the resulting surface from those curves. This is the term you might have heard called N.U.R.B.S. The technical definition is Non Uniform Rational B-Spline, so that's what the B.S stands for. It means surfaces that have been generated from these Freeform Curves called B-splines. The surface has the advantage of being editable, just like the curves were.
So, I am going to select the surface. Let me turn on the control points for the surface. Here is a similar pattern from curves to the surface, as far as the location of these points. I am going to grab a couple of these guys and just pull them in one direction and see what happens. So, just like the curve that this generated from, this surface is infinitely smooth. I'll try one more little tweak here.
Check it out from the back side. So, this hopefully illustrates why we don't use the Bezier curves from 2D. Any handlebars that were on this surface would be way too difficult to navigate or manage. You would have not only the center point, but also both of the handlebar ends, which would then need to be both moved and rotated, which would be extremely difficult. So, note that these control points for the surface, can only move. There is no really rotation about them. We can also move them in groups and scale them.
So, the word B-spline does sound familiar to Bezier, but B-splines are mandatory and superior when you start working in 3D. B-Splines, with their cage of control points off of the line, do take a little getting used to, especially if you have loads of experience with 2D and Illustrator. But here is the good news. You can import an illustrator file, drawn with Beziers, and easily convert them to B-splines to generate 3D surfaces, as we have just seen.
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