Owner: The Algorithmist URL:http://algorithmist.wordpress.com/ Join Date: Tue, 13 Mar 2007 16:45:20 -0500 Rating:0 Site Description: Applied mathematics in Flash and Flex. Site statistics:Click here
What’s next for Singularity? 2008-07-30 15:47:10 Seems to be a popular question as of late. I’m coming off a very intense project and getting ready to start a new one, so spare time is still short. I am planning an online demo of closest point to a Bezier (quad and cubic), possibly illustrating a couple different approaches to the [...]
100K Visits 1969-12-31 18:00:00 It was about 14 months ago that the blog formerly known as Singularity became ‘The Algorithmist.’ It’s kind of exciting to see the hit counter reach 100,000. Thanks to everyone who has linked to this blog and I hope people continue to find information of value here. On that note, I’m in [...]
Sometimes you see rewards beyond the payday 2008-07-25 17:26:29 We’ve all been there - we slave away on an app. - it gets changed a thousand times because the client or design team can’t make up their mind - then, finally it’s accepted and we get paid. Maybe it’s nothing more than a fancy site that looks cool but doesn’t even serve the [...] Read more:Sometimes
, beyond
New PureMVC Tutorial 2008-07-20 09:46:07 From Dave Keen - Flex/PureMVC/Jabber/XIFF3 - check it out here,
-tutorial-flex-puremvc-jabber-and-xiff-3-introduction/ Read more:Tutorial
Honda Fit Sport Update 2008-08-19 07:04:34 As a follow-on to this post, I’m now filling up every half tank. My two previous half-tank results have been 35.2 mpg and 35.4 mpg. A bit more local freeway driving on these two, so I’m getting the benefit of the highway mileage. I should point out again that I’m a very [...] Read more:Honda
, Update
Nadal wins Gold 2008-08-18 07:32:57 I thought Blake should have been in the final, but that’s another discussion for another time. Probably would not have made any difference in the outcome. Nadal
continues a streak that I can only compare to what Tiger achieved in winning four consecutive majors (although not in the same calendar year). Phelps’ [...]
Closest Point on Bezier Code 2008-08-15 07:35:27 The first pass at porting the classic Graphic Gem algorithm for closest point on a Bezier is complete and it works for both quadratic and cubic Beziers (the original Gem C code was hardcoded for cubics). This algorithm has important pedagogical significance beyond just being included in the Gems series. The embedded Bezier [...]
What’s wrong with Federer? 2008-08-14 12:24:40 So, another tournament, another early exit for Federer. Although I was glad to see an American (James Blake) win, it is always difficult to watch the slow decline of a great champion. They say the fall from the top is always the hardest. Some have speculated that Rodger’s timing has eroded with [...]
Closest Point on a Cubic Bezier Update 2008-08-13 07:10:54 I’m porting the classic Graphic Gem for computing the closest point on a Bezier curve to an arbitrary point from C to AS3. The Gem code only works for cubic Beziers, so that is the starting point for testing. My goal is to provide a utility that works for quadratic or cubic curves. [...] Read more:Update
Honda Fit Sport 2008-08-12 08:26:58 I purchased a Honda
Fit Sport recently (manual transmission), an interesting move from my Escape Hybrid. I really liked the Hybrid around town, but it was an expensive vehicle and the majority of my current driving is on the highway. On the highway, the Escape is just like any other SUV in terms [...]
K-th Order Bezier Subdivision 2008-08-11 07:39:56 One of the tools used in the Graphic Gem for computing the closest point to a cubic Bezier is a Bezier root finder. The elegance of this method lies in its use of geometric properties of Bezier curves to bracket roots. One of the computational tools in this process is subdivision of a [...] Read more:Order
New PV3D Demos 2008-08-10 10:17:11 As usual, I’m jammed up for time with another project, so the closest point to Bezier code is moving slowly. I’ve decided to port the Graphic Gem algorithm and expand it to support quad. and cubic Beziers. That will take a while
In the mean time, here are some new Papervision demos [...] Read more:Demos
Cubic Bezier 4-point Interpolation Part IV 2008-09-10 06:44:54 Previously, we saw that to computing the x-coordinates of P1 and P2 involved solving a 2×2 system of equations,
a11*P1x + a12*P2x = b1
a21*P1x+ a22*P2x = b2
where P1x represents the x-coordinate of P1, for example.
Cramer’s rule expresses the solution of a system of linear equations in terms of determinants. The determinant, det(A), is particularly simple for [...] Read more:point
Cubic Bezier 4-point Interpolation Part III 2008-09-09 07:25:18 Once the cubic Bezier curve is parameterized, i.e. B(t1) = V1 and B(t2) = V2, how do we solve for the x- and y-coordinates of P1 and P2? This problem can be addressed more easily by examining B(t) in power form (hopefully your browser supports superscript tags),
B(t) = c0 + c1*t + c2*t2 + c3*t3,
where [...] Read more:point
The FED Express 2008-09-08 18:06:42 Haven’t been this happy watching a tennis tournament in a long tiime. Congratulations Rodger!!!!
May the Fed Express
roll on!
Cubic Bezier 4-point Interpolation Part II 2008-09-08 06:25:11 I finished the basic version of the demo, but it’s evident that several aspects require some discussion. I don’t have time for a full TechNote, so I’ll go over each issue in a separate blog post. This will make it a lot easier to understand the code.
To review, the problem is as follows. Given four [...] Read more:point
My Apology to Murray 2008-09-07 17:13:30 I was watching the Nadal-Murray
match over the last two days, always rooting for the underdog. It seemed like Murray was dialed in yesterday, but got a bad break with the rain delay. It’s really hard to play with the same intensity and shotmaking two days in a row, especially against a machine like Nadal.
After [...] Read more:Apology
Cubic Bezier 4-point Interpolation Preview 2008-09-05 09:39:02 The next online demo will be four-point
interpolation for a cubic Bezier curve. This TechNote shows the general algorithm for three-point interpolation using a quadratic Bezier. It may seem as if the only variable is where to place the middle control point so that the quadratic Bezier passes through the specified second point. The classic [...] Read more:Preview
Easing Along Parametric Curves Demo 2008-09-03 07:46:34 The Bezier easing demo is now online. It only illustrates ease-out for a few ease types, but it should be enough to get the idea across. The following screenshot illustrates the difference between natural and arc-length parameterization for a cubic Bezier curve with cubic ease-out.
The red marker illustrates application of the ease without arc-length parameterization. [...] Read more:Curves
Easing along parametric curves, part II 2008-09-02 07:15:53 I think it’s fair to say that most people apply easing functions as arguments to a method in a tweening library instead of direct application. So, how does one directly apply Penner-style easing functions to path animation along
a parametric curve?
The previous post in this series illustrated the importance of arc-length parameterization in proper application [...]
Easing along parametric curves part I 2008-08-29 08:00:45 Over the holiday weekend, I hope to work on a demo illustrating how to apply easing to animating a sprite along
a path represented by a parameteric curve. The specific curve will be a cubic Bezier. I’ve talked about velocity control in path animation in the past and the importance of arc-length parameterization. [...]
Jacobian and IK 2008-08-27 07:40:58 Not sure where this came from, but I received three e-mails yesterday asking ‘what is a Jacobian,’ one of which wanted to know how it was used in IK. When something is asked multiple times, I try to respond in the blog and my first response is always check Wikipedia for a basic definition. [...]
46th Mersenne Prime 2008-09-28 11:18:38 UCLA team discovers 46th Mersenne prime on a network of 75 XP Computers - 13 million digits (I’m a PC). Amazing how high-performance computing has changed over the years
Read more here.
Papervision Daily 2008-09-26 08:45:23 So, are you looking for a regular fix of Papervision
coolness (lucky you - no 3D in my immediate future)? Then, look no further than the Daily
Papervision 3D blog. Adding this one to the blogroll and I do check it daily
enjoy!
Good Programmers Into Great Programmers 2008-09-24 06:33:35 Interesting article here by Jeff Cogswell, author of ‘Designing Highly Usable Software.’ I particularly liked the point about programmers understanding where things can go wrong. In my current gig, I receive specs all the time that indicate how something should work and be displayed under average use conditions. It’s the extreme cases where the UI [...] Read more:Programmers
, Great
PureMVC Fabrication 2008-09-22 07:22:05 Loosely stated, Fabrication is an abstract layer for PureMVC and Multicore Pipes, which facilitates faster development of Multicore PureMVC applications. You can read about it here and there is a great blog post here as well with some additional links.
Good luck!
Prince Speedport Black Team and Flash 2008-09-19 07:08:22 I’m really enjoying my new racquet - a Prince
03 Speedport Black
Team. The racket is light and very maneuverable. Still deciding on the right strings and tension. I like playing Babolat VS Team 17, but you can only play with gut a limited time in the Texas weather (and I like the 17-gauge strings [...] Read more:Flash
Joining Degrafa 2008-09-18 08:22:16 I started the parameteric curve library back in 2004, with the first TechNote appearing in 2005. My original goal for this library was to have a code repository to illustrate mathematical concepts discussed in TechNotes. My strong belief is that fundamental principles of computational geometry should be freely available (with mathematical and code details) to [...] Read more:Joining
Spline Tangents Part III 2008-09-17 07:32:20 Once again, there were a few questions regarding this post; namely, how to draw the normal vector to the spline. One person suggested using the fact that slopes of perpendicular lines are negative reciprocals. Since we already know the slope of the tangent line, we know the slope of the normal line (although there are [...]
Spline Tangents Part II 2008-09-16 07:01:00 I received a couple questions regarding this post relative to computing the angle of the tangent line relative to the horizontal. It’s a matter of a little trig once you recall the geometric interpretation of a curve’s derivative at a point. Our old friend, Math.atan2() is just what the doctor ordered. To illustrate, I modified [...]
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