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
Flex 3D Data Visualization with Papervision 2007-10-08 16:23:09 I’ve started yet another background project studying ways that Papervision
3D can be used for 3D data visualization. One of the earliest techniques in this area (for hierarchical data) was Cone Trees. The example below illustrates a very simple Papervision cone tree. Actual cones are used as the representation of the root node for a few reasons. First, I plan on having both free and target cameras available for tree/node visualization and fly-through. Cones are easily seen from any camera angle. Cones are already colored based on whether or not the node has children. The size of a cone may indicate the relative number of children (tall/thin -> few children, short/fat -> many children). This is helpful as I plan to add the ability to expand/contract nodes in the future.
Although visually unimpressive, the BaseCone class upon which the above image was created supports on-the-fly addition of children, with automatic repositioning of child nodes throughout the Read more:Visualization
We all use math every day 2007-10-04 14:46:31 After NCIS and The Unit, one of my favorite weekly shows is Numb3rs. Only on American TV can a math geek catch criminals and score chicks! I also like the offline learning community built around the show, providing teaching aids based on the math techniques used in the show.
If you are a teacher, you might want to check out the blog here. Each episode review has a set of learning activities along with links to other activities and additional information.
Read more:every
Five3D 2007-10-15 17:03:00 Five3D is another entry into the Flash 3D arena, but with an interesting approach - all vector graphics. Currently implemented in AS2. I’m tempted to download the package, but I already have too many background projects
For the right application, it could be very useful tool. Check it out here.
Update: If I had just visited Zeh Fernando’s site, I would have seen the link to the Five3D Lab.
Panel border dimensions 2007-10-21 13:46:37 I’ve received a couple questions regarding custom Flex components (in Actionscript) and how to position child elements relative to the parent borders. For example, consider a component extending Panel
that contains Text and Button child items. The Text control is to be placed near the top-left of the content area and its width is relative to the width of the content area. The (0,0) coordinate represents the top, left-hand corner of the Panel, not the content area. To position children relative to the content area, it is necessary to know the border dimensions.
If the parent container extends mx.core.Container, you might consider using the viewMetrics property, which returns an instance of mx.core.EdgeMetrics. The EdgeMetrics instance contains four properties (bottom, left, right, top) containing the extents of the borders surrounding the content area.
If you are just starting out with custom Actionscript components for Flex, maybe this will help you out. Good luck!
Flex File Upload with ASP.NET 2007-10-19 08:46:48 In my ongoing efforts to learn asp.net, I recently read about web handlers. Hmmm … seems like a convenient way to handle file upload from a Flex app. Although I’m much more comfortable with PHP, I hacked something together that worked okay on my server (.NET 2.0). I suspect others have blogged about this, but another example never hurts and I tried to distill this one down to a very simple level. Hopefully, it will be easy for other asp.net beginners to pick up on and expand.
There are some hacks in the .ashx file, including hardcoding the physical location of the upload folder on my server (which no longer exists after testing). I believe there is a more elegant way to specify the upload folder in the web.config file and then access it in the script using WebConfigurationManager.AppSettings. Haven’t had time to try that.
If you’re an experienced .NET pro, go ahead and laugh (although suggestions on making the process better are quite welcome). Begi Read more:Upload
Moock AS3 SFO Tour Recap 2007-10-30 08:10:02 From Lee Brimelow - check out this cool video recapping Colin’s AS 3 From the Group Up tour stop in San Francisco. Includes an interview. If you’re just getting into AS 3 and live in one of the tour cities, at least try to get yourself on the wait list!
Lee’s blog is full of good content as well - worth a bookmark.
Read more:Recap
mathschallenge.net 2007-10-27 16:54:18 Although I enjoy programming, I enjoy math more. Pretty much everyone has heard of Dr. Math. One of the lesser-known sites that I enjoy for a quick break is mathschallenge.net . In addition to problems (I’ve forgotten a lot about number theory over the years), they have a nice FAQ section, which is great for students.
Org Charts in Flex 2007-11-01 10:55:07 I’ve responded to a blog post and a few private e-mails recently on this topic. Two companies seem to have solutions - OrgPlus from Human Concepts and ILOG Elixir. I don’t have any experience with Human Concepts, but I did work extensively with ILOG in my SGI days. I have high confidence in anything they develop.
CMOrgChart was an entry in the Flex Derby, but not sure if the source is available.
Read more:Charts
Flare 2007-11-01 09:51:28 If you are interested in an AS 3 library for data visualization, here’s a good bookmark for you - check out Flare
.
Demos - Tutorial - API Documentation
enjoy!
Logitech Alto 2007-11-09 08:04:54 I rarely comment on products as there is plenty of that available from other blogs. Every now and then, I come across something really worth a comment. The keyboard on my Dell M60 has become sticky after several years of use (or abuse). I recently started using an external keyboard, but that setup was clumsy, especially for travel.
A couple months ago, I saw the Logitech
Alto in a Dell store and ordered one for myself.
This product has delivered beyond my best expectations. I feel more like I’m working on a desktop system and the entire setup folds easily for travel. After using the Alto day-to-day and during over half a dozen business trips, I feel comfortable recommending it to others who may be interested in a better setup for their notebook.
Calling all Leopards 2007-11-13 12:41:04 After living in the clutches of the M$ empire for most of my career, I’m seriously considering joining the rebel alliance and purchasing a Mac Book Pro (17″). I’m interested in all opinions from current owners; in particular, those currently running FlexBuilder and/or Flash CS3 with Leopard. Thanks!!
Read more:Calling
Swift3D Export to Papervision 2007-11-17 08:35:31 From Electric Rain,
“Electric Rain is opening new doors for Adobe® Flash® designers with an update to Swift 3D® v5.0 enabling export to the increasingly popular Papervision
3D format. This new feature will be available in conjunction with the release of Swift 3D v5.0 for the Macintosh® platform, as well as a free update to existing Swift 3D v5.0 Windows users, adding even more export flexibility to the industry leading 3D tool for Flash.“
Sounds very interesting for those wanting a solid, entry-level modeling tool for Papervision work.
Mindomo 2007-11-29 07:34:35 I may experiment with this product some during my upcoming vacation (yeah, I also told myself that about Flare and Five3D). The Business and Education products look somewhat interesting. Anyone have any experience with this tool? Thoughts and opinions are welcome.
Papervision 3D Team Interviews 2007-11-27 08:28:22 Want more insight into the killer team creating a killer product? Check out some recent interviews with the PV3D core team.
Read more:Papervision
, Interviews
Let’s Make a Deal 2007-11-26 17:49:31 I originally discussed this problem in the old Singularity blog as a result of it having been mentioned on a Numb3rs episode. Numerous people asked me if the show made a mistake. I’ve been around enough to recognize the old “Let’s Make a Deal” problem from the famous old game show of the same name.
When the problem was first posed to me (a very long time ago), I made the correct choice but only because I took the ‘intuitive’ answer and chose the opposite. My first analysis of the problem (done in the early 90’s along with a Fortran simulator) is reposted below. Shortly after the first Singularity post, a Flash simulator was provided at the lessrain blog.
A recent conversation about the non-intuitive nature of many results from Statistics lead me to druge this up. Perhaps I’ll do a Flex simulator some time in the future.
Original Singularity post follows
——
Here is the modern version of “Let’s Make a Deal&rd
Lagrange Multipliers II 2007-12-06 14:09:24 As I head out for vacation, here is a simple question. What is the distance from the plane
ax + by + cz = d
to the origin? The answer is a simple click away (Mathworld). For fun, suppose we also wanted to know the coordinates of the point on the plane closest to the origin. This can be solved as a constrained optimization problem, serving as another example of the technique of Lagrange multipliers.
Informally, we wish to minimize x2 + y2 + z2 subject to the constraint ax + by + cz - d = 0. Relax the constraint into the objective and form the function,
L(x,y,z) = x2 + y2 + z2 - λ(ax + by + cz - d) .
The stationary points are determined from
δL/δx = 2x - aλ = 0 , or x = aλ/2 [1]
δL/δy = 2y - bλ = 0 , or y = bλ/2 [2]
δL/δz = 2z - cλ = 0 , or z = cλ/2 [3]
δL/δλ = 0 implies the original constraint, ax + by + cz = d [4]
Subsititue x, y, and z from [1-3] into [4] to obtain λ = 2d/(a2 + b2 + c2) [5].
Substitute the λ value from [5] into [1-3] to obtain the coordi
Lagrange Multipliers 2007-12-03 07:58:38 I never expected one Twitter comment to generate so many e-mails. There are a lot of college students in the Flash community, many of which are taking calculus courses, so it probably makes sense. I could say check out Wikipedia, but there are a lot of topics for which a theoretical introduction is difficult to comprehend. When I work with calc. III students studying extrema of functions, I like to start out with this problem.
minimize x2 + y2 + z2
on the hyperbolic cylinder x2 - z2 = 1 [1]
This is a constrained optimization problem. Set the partial derivatives of the objective to zero. The partials are only zero at the point (0, 0, 0) which is not in the domain of the constraint. From the constraint, z2 = x2 - 1. Eliminate z from the objective which becomes
minimize w = 2x2 + y2 - 1 [2]
Now, δw/δx = 4x and δw/δy = 2y . These are only zero at x = 0 and y = 0. From [1], this implies z2 = -1 , yielding an imaginary solution. As an exercise, eliminate x from the obj
Testing Equation Formatting 2007-12-02 09:06:02 Just testing how to format equations from within Wordpress. Press Alt-Shift-v in Firefox (Alt-v in IE and make sure the editor has focus) to bring up the advanced toolbar (I work directly in the Code editor). From the advanced toolbar, click the ‘Omega’ symbol to insert special characters (you can see the specific codes in the editor).
∫dx/√(a2-x2) = sin-1(x/a) + C
A bit cumbersome, but much easier than converting something else to images and inlining the images
Read more:Testing
, Equation
, Formatting
Kennedy Space Center 2007-12-09 07:27:29 Spent most of the day, yesterday at KennedySpaceCenter
. It was the space program in the 1960’s and early 70’s that got me interested in math and science in the first place (okay, the original Star Trek series had some influence as well). If you ever have the opportunity to visit, it’s well worth the $$$. Unfortunately, due to the latest schedule update, it looks like I’m going to miss the STS-122 launch today.
Blog posts are on hold until I get back from the cruise. Until then, enjoy the artwork of Alan Foxx - I met him last night at his shop in Downtown Disney. The online images don’t do justice to the actual prints, though.
Limit Proofs 2007-12-22 10:17:22 At first, I thought someone was sending me their calculus homework, but this time of the semester, it’s most likely a question that was asked on a final. Anyway, I don’t mind posting solutions on topics that are of general interest to high-school and college students … whenever I have the time
Question: What is the limit as x→2 of the function x2 + 3 , using only the definition of a limit?
So-called epsilon-delta proofs can be cumbersome for polynomials of degree greater than one because of the apparent lack of a single delta value. To review, limit as x→c of f(x) = f(c) means that for any ε > 0, there exists δ > 0 such that |x - c| < δ ==> |f(c) - f(x)| < ε . Intuitively, the definition means we can make f(x) arbitrarily close to f(c) by making x ’sufficiently’ close to c.
For the problem at hand, it appears that the limit as x→2 is 7. To prove this assertion using the definition, then given any ε > 0 , we must show Read more:Limit
UltraShock V2 2007-12-18 08:00:51 Just got back from vacation and noticed that the very long-awaited UltraShock V2 now appears to be up and running. Check it out here.
Going Underground 2008-02-23 17:56:35 I’ve started a very large project that will keep me occupied 7 days as week for quite some time. Just a quick note to inform everyone that blog posts will be very sparse for quite a while. Thanks. Read more:Going
Red Bull Flight Lab 2008-02-20 08:16:32 This impressive work was created by Lessrain in Papervision 3D. I can really appreciate the effort that went into this one.
Check out the Red BullFlight
Lab.
Famous Black Mathematicians 2008-02-18 07:32:16 In celebration of black history month, I thought it interesting to point out the large number of black mathematicians who have made significant contributions to the field. Even as an undergraduate, I recall being introduced to William Claytor’s work. If you are interested in pursuing this topic futher (especially if you are a teacher of [...] Read more:Famous
, Black
New PureMVC Example 2008-02-14 07:49:31 Josh Spoon at SWF It Good has posted a new PureMVC example at his blog.
Continue reading “How to Create a PureMVC Application with AS3.” Read more:Example
Having the Right Friends 2008-02-12 07:22:03 From Science News,
“Girls in high school take as many math courses as boys, influenced by close friends and peers who are doing well in school. More than boys, girls look to their close friends when they make important decisions, such as whether to take math and what math classes to take, confirming how significant peers [...] Read more:Having
, Right
, Friends
PI for President! 2008-02-06 08:47:23 If you are dissatisfied with the goon currently in office as well as the crop of goons campaigning to replace him, then it’s time to support the real candidate for change - infinite change, that is. Yes, we’re talking about the number ∏ . MathematicianPictures.com has launched a campaign to support PI for president. [...] Read more:President
Cubic Bezier Y at X 2008-02-03 15:22:30 One of the requests for the Singularity Bezier curves is the ability to return a y-value, given an x-value. This is often used for interpolation in easing. Many 3D packages, for example, have the ability to specify a functional relationship between two parameters using a cubic Bezier curve as a visual design tool. [...]
FiTC Toronto 2008 Lineup 2008-02-01 10:17:42 I’m not sure I’ll even have time to think about conferences this year, much less attend any. I’ve always liked FiTC Toronto
and this year’s speaker lineup looks as impressive as ever. I’m going to miss a chance to see Jared Tarbell. If you have a chance to attend, take it!
[...]
FK Experiment in PV3D 2008-01-30 10:26:57 My backlog of ‘background’ projects seems to only keep growing and one of the casualties over the last several months has been kinematic experiments in PV3D. Fortunately, Lee Felarca seems to be making some inroads in this area. Check out a recent experiment from his blog - hope to see more from him over time.
Maybe [...] Read more:Experiment
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