Without the A frame we have a discontinuity for C1 at the third black point from the left - a cusp.
I can see that one of the advantages of using bezier curves over the other interpolation methods we've learned is the ability to introduce corners. Are there other benefits of this method too? And are there other interpolation methods that can also give us curves and corners.
This connects back to the hermite functions where we can represent every cubic curve between two points by using two tangent vectors. I can see that Bezier curve extends from it to free up some constraints by letting the end point of a pair and first point of the next pair use different tangent vectors.
Beautiful property: The tangents have to match for the points to be continuous. But as another student has already pointed out, this isn't required and there is a benefit to being able to produce corners in our interpolations. I can't see it just yet, but does this imply that the previous versions wouldn't allow for such corners?
@alexkassil If we actually look back at the example of geometry in typography, we can see how the letter Q is constructed -- using bezier curves with handles parallel to the axis, we can keep a continuous curve along the vector
An interesting application similar to the demo link is the use of this "path tool" in animation, where animators can use these curves to translate, scale, and rotate objects plotted against time.