As Nadal moves onward in Rome, having won back-to-back Master’s events on the clay circuit, I was reflecting on Nadal’s overall record on clay. He could retire today and still be counted as the greatest clay-court player of all time. Here is the record,
- Acapulco (2005)
- Barcelona (2005, 2006, 2007, 2008,2009)
- Bastad (2005)
- Costa do Sauipe (2005)
- Roland Garros (2005, 2006, 2007, 2008)
- Hamburg (2008)
- Monte Carlo (2005, 2006, 2007, 2008, 2009)
- Rome (2005, 2006, 2007)
- Sopot (2004)
- Stuttgart (2005, 2007)
He is only 22 and barring injury will compete for several more Roland Garros titles. Four of his six current slams are at RG. Although his success extends beyond clay, he seems to be without equal on this surface.
Spent some time this weekend catching up with blogs/sites that I’ve bookmarked to go back and check out at a later time. Out of the dozen or so reviewed this weekend, one really stood out above the rest.
Want to give some props to Eugene’s astatic notes blog and the interesing 3D experiments there (some of which require FP10 to view). This is the latest addition to my blogroll.
I had been playing with Babolat Pro Hurricane Tour 17 on the mains for some time, and had almost decided on xCel Premium for the crosses. Babolat offers a hybrid string package with VS Team 16 for the crosses. I have always loved playing with VS Team for the entire racquet, but it’s difficult to play 100% gut all the time in Texas weather. I felt that the 16-gauge cross would hold up better against the Pro Hurricane Tour ‘cutting into’ it, so wanted to give it a try.
Glad I did. I love the power and feel and still get good access to spin from the mains. I have to worry a bit in humid or sprinkling weather like this morning, but I’ve found if I put some powder or rosin over the strings before working out and after playing that they hold up quite well.
Having seen Monica interviewed a couple times on TV, I was contemplating getting the book. Nice to see Tennis Channel offering a sample chapter.
Visited InsideRIA this afternoon and noticed the interesting optimization article. We’ve seen lots of information on AS 3 optimization. What makes this article different is the inclusion of Flex practices for good app. performance.
This is something I started many years ago and put on the shelf because I never had an immediate use for it. Two utilities are forthcoming in Degrafa; spline->Bezier anad function->Bezier. These utilities approximate functions and specific splines over an interval with quadratic Bezier curves. With these utilities, splines such as natural cubic, parametric, and Catmull-Rom will be easily plottable in the normal Degrafa geometry pipeline.
Following is a screen shot of work in progress on a natural cubic spline. This was originally a derivative test as the spline slope at various points is required for the algorithm. The derivative formula is covered in this TechNote. There is no overlap between successive knot intervals. The blue curve shows a simple point-to-point plot of the natural cubic spline. The red curve shows the quadratic Bezier approximation.
Well over a hundred small lines are used in the traditional plot. There are ten quads. in the above example.
Instead of trying to minimize the total number of quad. Bezier curves, the algorithm produces a modest number of quads in exchange for exact representation at knots and an integral number of quads. per spline segment. This makes it very easy to create specific shapes out of the quad. approximation between knots which could be useful in charting applications.
More to come!
It’s that time of year again. I’ve spoken at several Flash conferences in the past and FITC Toronto is by far my favorite. Won’t be able to attend this year, but if you have the flexibility in your schedule, I highly recommend this event.
And, it’s in the home country of my favorite band, RUSH!
Just got back from a long day of family activities and watching 12 Rounds (gave it a C+). Missed the announcement that Roger and Mirka got married. Best wishes to Mr. and Mrs. Federer.
Oh yes, thanks to TennisElbowRoom & Twitter
I get about 60 e-mails a day (either direct or through the contact form on my web site) requesting solutions to various math/Flash/Flex problems. When possible, I try to answer some of them here on the blog. This one was interesting as it provides an opportunity to illustrate some of the new Degrafa math utilities.
Drawing an ellipse whose major axis is either horizontal or vertical is pretty easy. This question was how to animate a sprite along a rotated ellipse. Animation along any path requires arc-length parameterization for precise velocity control.
If arc-length as a function of natural parameter is a smooth function, a natural cubic spline can be used for arc-length parameterization as illustrated in this TechNote. One observation about ellipse arc length is that it is invariant with respect to rotation. So, we can parameterize the ellipse as if it were horizontally oriented and centered at the origin.
Evaluating the path requires a rotation followed by translation. The example below applies a counter-clockwise rotation to an ellipse and then animates a sprite around the ellipse. Path orientation is applied as illustrated in the above TechNote.
To use the demo, drag a rectangle to define a horizontal ellipse. The rotation value is hardcoded into the Flex example (currently 45 degrees CCW). Click the ‘Animate’ button to animate the rectangle sprite around the ellipse.
The ParameterizedEllipse class is provided as a standalone file and the demo uses the Degrafa natural cubic spline and Gaussian quadrature utilities. The example also illustrates the dashed-line decorator. The ellipse parameterization is either the classic parameteric (some would say polar) form or on arc-length. I haven’t tested every aspect of this code, so view it as a general outline for a solution to this problem.