Automatic Bezier Arcs in Degrafa

An interesting problem is to draw an eye-pleasing arc between two points.  This can be used for anything from drawing origin-destination route arcs to approximating trajectories in animation.  Since we already know how to interpolate a quadratic Bezier between three points, one possible solution is to parameterize the generation of a middle interpolation point given two initial points.

I’ve used an algorithm along these lines since about 1982.  It takes two parameters, one of which determines the concavity of the arc.  The second parameter controls the distance between the midpoint of the line segment from first to last point and the middle interpolation point.  This provides a large amount of control over the generated arc.

A closely related problem is animating the arc.  This is trivial with a quadratic Bezier as the section of arc at any parameter value can be drawn with a single curveTo command using deCasteljau subdivision.

The auto-arc generation is now in the BezierUtils class and the subdivision method has been added to the AdvancedQuadraticBezier class.  A screen shot from the rather plain and simple demo is shown below.

Quadratic Bezier auto-fit between two points

The code has been checked into the Origin branch.

View demo.

View source.

Speaking at Dallas TechFest

If you’re in the D/FW area and are interested in attending Dallas TechFest, then I hope to see you at the session on computational geometry in Flex and Degrafa. Little knowledge of Flex is required; only a desire to add cool geometry buzzwords to your vocabulary. I’ll introduce Degrafa, highlight some differences between Degrafa and FXG, and then launch into the low-level computational geometry capability in Degrafa. In addition to declarative drawing, you can see how to perform more advanced tasks in Actionscript ranging from possible charting applications to animating route arcs.

More on the conference below – see you at the end of July!

Babolat RPM Blast Review

I wanted to postpone this review for a couple weeks in order to hit with the strings for a substantial amount of time under a variety of conditions. My prior configuration was a hybrid of Pro Hurricane Tour 17/VS Team Gut 17. I replaced that with RPM Blast 17 on the mains. Tension is 53lb on a Prince EXO3 Black frame. In general, I think strings like PHT/RPM need to be on stiffer frames. Interestingly, Rafa’s stick, the AeroPro Drive GT (stock frame) has a stiffness of 70, swingweight of 331, and balance is 4pt HL. The EXO3 Black has a stiffness of 71, swingweight of 328, and equivalent balance. Nadal can afford to swing away with a fullbed; I prefer a gut hybrid for a little more control and feel. Maybe that’s why he’s French Open champ and I’m writing Flex applications for a living 🙂

The observation I want to counter with this review is that RPM Blast is just PHT in a different color. On the subject of color, black is a great choice. The difference does not stop there. I could tell from the very first hit that this was a different string. The responsiveness was there, but with a little something extra. The ball even sounds a bit different at impact. I do not have specific measurements, but over the course of several weeks, I can see increased spin on the ball. This is generally from getting a bit more dip on the ball with the same stroke. If I really try to put some spin on the ball, I can get some wicked action 🙂

Two other observations of note. First, I always disliked restringing because I thought it took several days of hitting before the PHT/VS Team hybrid started to ‘feel’ right. Some of that may be that I’ve always thought gut plays better after it starts to fray. With the RPM Blast/VS Team hybrid, I liked the feel from the very first hit and it’s even better after a few weeks of hitting.

Second, the RPM Blast silicone coating does seem to let the strings slip more, but I kind of have a habit of adjusting the strings after every point anyway. The side effect is that the mains do not cut into the gut as much, which will probably increase the durability of the hybrid configuration. I rarely worry about that in any event because at the low tension the hybrid becomes mushy before it breaks.

Now, for what you really want to know about – power. Revenge was marketed as a power string, but it kind of underwhelmed me. RPM Blast delivers the goods, although to achieve the string’s potential you will probably want to string a bit lower than you are used to. I can’t vouch for feel in a fullbed and you may lose some control depending on your current configuration. It may be okay in a fullbed for very advanced players, but intermediate or between intermediate and advanced may prefer it in a hybrid.

For me, the extra feel and control from crossing it with gut is worth the extra cost. I also found RPM to be easier on the arm than PHT, a nice bonus recovering from an arm injury.

RPM Blast is an upgrade over PHT in every aspect of the game. Serve, volley, groundstroke, overhead, drop shot, whatever. So, if you don’t mind a bit more coinage for a poly, go string up some bad-ass black RPM Blast and kick some on the court!