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
Quantum Keys sent 200KM 2007-06-04 12:22:03 I was watching a Discovery or History Channel program that touched on crypto — at that time, the record distance for a quantum packet was about 50 klicks - now they’re up to 200. Don’t blink or technology will change
http://www.sciencedaily.com/releases/2007/06/070601162438.htm
Spider Defense Game @bit-101 2007-06-07 10:04:19 Keith Peters is working on an interesting game, currently called ‘SpiderDefense
’. I really like the way the ‘bad guys’ walk and follow the terrain — this is really good work.
Now, I want to see them start shooting green laser beams from their heads, as promised
Check it out here.
New TechNotes Delayed 2007-06-13 08:49:10 I’m currently involved in contract work that requires substantial overtime due to another developer leaving the project. With commute time and family considerations, that leaves virtually no week at the end of my time. This means that the TechNote series on skeletal animation I had hoped to start this month is probably delayed until fall (this project has an early Sept. delivery date).
I am working on adding closed-loop support and arc-length parameterization to the Bezier spline. After finishing, I will probably also add some sort of closed-loop support for the Catmull-Rom spline. 3D versions of these splines will be made available for camera and other path animation in Papervision 3D.
FITC Toronto 2007 Videos 2007-06-21 09:17:21 Daily summary, session, and conversations videos from FITC Toronto
2007 are now online. I hope they add some more session videos as I missed several due to schedule conflicts. The conversation between Joshua Davis and John Maeda was very interesting. Check it out here.
Learning ASP.net 2007-06-26 13:52:30 In the past, I’ve always used PHP/MySQL for back-end programming. For a new project, it’s time to learn ASP.net with SQL Server 2005 . Who knows, maybe there will be some new gigs in the future as a result of my experimentation with the M$ dark side
Anyone have any good book or tutorial site recommendations?
Read more:Learning
Moock’s EAS3 Now Shipping 2007-07-01 11:20:51 From Colin Moock, Essential Actionscript 3 is now shipping. Order here and enjoy!
Read more:Shipping
Die Hard 2007-07-05 08:12:59 I’ve been extremely busy on a gig (and handling family issues), so it’s taken me a while to finally see Die Hard 4. I’m a die-hard Bruce Willis fan, so you would probably expect my review to be positive. Aside from the semi-trailer/F-35 scene that was over the top, I really enjoyed the flick. I also took away numerous tips for improving myself such as how to get additional help on a gig (dial 1-800-HENCHMEN) and how to take out a chopper with a car. Good stuff to add to a resume
Closed Loop Bezier Spline 2007-07-12 19:06:25 I finally found a bit of free time to upgrade the cubic Bezier spline, adding arc-length parameterization and closed-loop support. Curve closure is automatic and handled by a new ‘closed’ setter function in the BezierSpline class. The new BezierClosed
Spline.mxml demo is illustrated in the following diagram,
C-1 continuity is preserved through the loop by using the tangent to the angle bisector from knots n-2, 0, 1 (as knots 0 and n-1 are the same). The control cages for each cubic segment are illustrated in the following diagram.
The spline now supports arc-length parameterization. The orange markers in the above diagrams show the original knots. The green markers are generated from a default uniform parameterization. The demo illustrates the difference between uniform and approximate arc-length paramterization. This allows the spline to be used in path animation with velocity control.
The Singularity package download and a more detailed description of the AS 3 paramteric
Online Demo - Spline Parameterization 2007-07-17 18:58:00 The previous post on closed-loop Bezier splines prompted some questions regarding arc-length parameterization. A curve’s parameterization does not generally affect the way the curve is drawn (I will show a counter-example in a future post). Parameterization does affect how sprites are animated along the curve. More detail may be obtained from this TechNote.
A common misconception is that the parameter value t = 0.5 always represents one half the distance along the curve. Not only is this generally untrue for single-segment curves, it can be dramatically incorrect for composite curves. With a common parameterization such as uniform or chord-length, a distribution of sprites along the curve at equal parameter increments (i.e. 0, 0.1, 0.2, … 1) does not necessarily result in equal distance (along the curve) between the sprites. This is the goal behind an arc-length parameterization.
The difference between uniform and arc-length parameterization can be illustrated by animati
Quadratic Bezier, 3-point interpolation 2007-07-20 21:29:35 Using a quadratic bezier curve to interpolate three point
s is a very old algorithm, dating back to the early 1970’s. It’s been around quite some time in Flash, although in a simplified form sometimes called midpoint interpolation. This is because the parameter, or t-value, at which the curve passes through the second point is arbitrary. The formula happens to be compact when t = 0.5. So, that is taken as the ‘interpolation formula’. The midpoint formula has been passed around online and published in some Flash books. The relationship of this formula to the actual parameterization of the curve is discussed in this TechNote.
Choosing a parameter value to interpolate the second point affects the placement of the middle Bezier control point. Since the control points form the set of geometric constraints for the curve, this is an example of a case where parameterization actually affects the shape of the curve.
The default parameterization for the Singularity Be
Papervision 3D V1.5 2007-07-20 08:38:58 Just a quick note to say congrats to the Papervision
team on the V1.5 release - read about it and download here. Once my current gig is complete, I hope to release 3D versions of the Catmull-Rom and Cubic Bezier splines for use in P3D path animation. In the mean time, back to implementing change requests
Catmull-Rom Spline Animation 2007-07-27 17:47:43 A new online demo is now available, illustrating the animation of a Catmull-Rom spline from beginning to end. The curve is drawn from t=0 to t=1 in an ENTER_FRAME handler. This emulates how the spline might look if it were drawn by hand.
This demo provides a good introduction to working with C-R splines. Studying how the drawing speed varies with knot placement is a subtle introduction to spline parameterization.
Thanks, by the way, to Mario Klingemann for helping test some of the C-R spline methods.
Check out the demo here (includes a link to download the full Singularity package).
Read more:Animation
Some interesting stuff 2007-07-31 12:57:46 Some recent observations from the department of the new and interesting
,
Colin Moock on inheritance-vs-composition in AS 3.
hxASM - Flash 9 assembler (mmmm … tasty).
Jesse Warden’s cool Flex preloader tutorial.
Ralph Hauert (Papervision 3D) FlashCulture interview.
Ted Patrick’s Flash 9 install counter.
Acress Danica McKellar on making math cool for girls.
and … the list would not be complete without something from John Grden - now appearing at MAX 2007.
Read more:stuff
Actionscript Convex Hull Class 2007-08-02 14:32:49 The last time I programmed a convex hull algorithm, it was waaaay back in the day when I was coding in Fortran — I’m a pathetic old dude. Reviewing this example from Lost In Actionscript was a great way to end a hard day of application testing.
Check it out here. I think Lost in Actionscript is one of my new favorite blogs. It would be the top favorite if it played the LIS theme in the background
Closed-Loop Catmull-Rom Spline 2007-08-19 10:40:45 Blogging has been slow the last couple weeks, dealing with gigs and migraines, but I found a little time to add closed-loop support to the Catmull-Rom spline. It’s a simple algorithm for adjusting the outer control points for a smooth transition through the first knot, as illustrated below.
The red marker indicates the first auxiliary control point. The green marker indicates the outermost auxiliary control point. The direction of the vector from initial knot to each control point is along the chord emanating from the first knot. The distance from first knot to both the second and next-to-last knots determines the distance along each chord to place the auxiliary control points. The first auxiliary control point is placed along the chord from the first knot to the next-to-last knot, but at a distance equal to that from the first to second knot. The process is reversed for the outermost auxiliary control point.
The graphic illustration should convince you of at least G-1 continui Read more:Closed
2A Jonathan Moore Interview 2007-08-17 08:34:08 Jonathan Moore
of 2Advanced was recently interviewed at Behance. Interesting stuff. It’s often fun to take a break from applied math and see what’s going on inside the mind of the creative geniuses in the industry. In case you have not noticed, PLAT4M is back with new content. Enjoy!
Read more:Jonathan
Path Animation with Papervision 3D 2007-08-26 16:50:11 I finally got around to implementing a 3D version of the Catmull-Rom spline. My primary intended use is for path animation in Papervision
3D. The 3D version of the C-R spline does not have the 2D draw() method, but it maintains support for arc-length parameterization and automatic closure (with smooth transition through the closure).
The former property is useful for velocity control and proper easing during path animation while the latter is useful for continuous fly-throughs. An online demo is available, but be warned. It is distilled down to a very simple level in order to make the code easier to understand. The result is probably the ugliest PV3D demo you will ever see
The red cubes represent markers, indicating control-point placement in 3D space. The green sphere is animated (using arc-length parameterization) along the path.
Check out the online demo here, which includes a link to download the Singularity package (now containing the alpha 3D Catmull-Rom spline).
Read more:Animation
AS 3 Optimizations 2007-08-24 12:27:12 John Grden started with a blog post on the topic of AS 3 optimization that has now grown into its own standalone page at osflash.org . The new page also includes links to other experiments on the topic. Check it out here and thanks to John for yet another great contribution to the Flash/Flex community!
New Tweener Class from the.laboratory 2007-08-29 08:57:04 There is a new Tweener class at the laboratory (Eduardo Dias da Costa’s blog) along with some cool demos. I particularly liked the Catmull-Rom tween :) Check it out here.
Lemniscate of Bernoulli 2007-08-31 15:14:15 Or, a fancy name for a figure-8 or infinty shape. Some curves do not have simple, closed-form equations for plotting. In rectangular coordinates, the equation for the Lemniscate of Bernoulli is (x^2 + y^2)^2 = a^2(x^2 - y^2) . In polor form, the equation is r^2 = a^2cos(2t) . Because of the radical and the range of the cosine funtion, the polar form is used in a principal quadrant. Symmetry and reflection may be used to generate the remainder of the curve.
What if we were required to animate sprites along the curve?
Since a highly accurate plot is not desired, it is easy to sample the curve to generate control points for a closed-loop Catmull-Rom spline (automatic closure saves having to generate the final control point). Arc-length parameterization assures smooth motion during the animation.
This is illustrated in an online demo, which you may view here. The demo page includes a link to download the entire Singularity package.
PV3D and Flex Examples 2007-09-27 10:01:53 Stephen Downs (aka Tink) has posted some really good examples of using Papervision 3D with Flex. If you are starting out with PV3D and plan on using Flex, check out the examples here!
Read more:Examples
Bezier Tweening and Velocity 2007-09-23 11:53:36 Someone once remarked to me that tweening with Bezier curves seemed to have a ‘natural’ easing. In some cases, a sprite moving along the curve might appear to move slowly out of the first control point, noticeably speeding up moving into the last control point.
The issue is not easing, but parameterization. The subject of parameterization has been dealt with in detail in this blog and in TechNotes, although mostly for composite curves. The Singularity Bezier curves now support approximate arc-length parameterization (implemented in the base Parametric class).
A person drawing a quadratic Bezier with curveTo() might be inclined to state that the point corresponding to t=0.5 was exactly halfway along the length of the Bezier curve. If markers were distributed at say t=0, t=0.1, t=0.2 … t=1, one might expect them to be uniformly distributed along the curve.
In fact, the marker distribution depends on the curve’s geometric constraints (control point placement). Read more:Velocity
Learn AS 3 For Free From Colin Moock 2007-09-19 18:05:49 So, how do you score a free AS 3 class from the man himself? Well, you have to be in the right city at the right time. Check it out here and move fast. I suspect classes will fill up fast!
Read more:Colin
Spline to XML MaxScript 2007-09-18 16:39:59 The post on exporting splines to XML
for path animation in Papervision 3D proved to be pretty popular :) I’ve received some requests for the Maxscript used in the export. It’s pretty pathetic as scripts go, but here you go!
Place the script in the {3ds max root}/scripts folder. Run the SplineToXML.ms script, then open a listener window. Select a curve in MAX. In the listener window, type
exportAsXML(”camerapath.xml”)
Move the camerapath.xml file from the scripts folder to the bin folder of your Flex app. Animate and have fun!
Caveat: My 3ds max install is very old (V6), so I can’t vouch that the script runs on later versions of the software.
Papervision 3D Path Animation from 3ds max 2007-09-16 10:55:57 The previous experiments with path animation in Papervision
3D were interesting, but of little practical use as very few applications generate path information programmatically at runtime. A more common workflow is to generate paths in a 3d application. The latest addition to the Singularity parametric curve library is a 3D Bezier spline that is suitable for working with cubic spline paths generated from other applications.
The 2D bezier spline took knots (or CV’s) as inputs and automatically generated tangents. The 3D version simply accepts CV, in-, and out-tangent information generated from a 3D package. To test this spline with 3ds max, I wrote a simple MAXScript to export spline data to XML. A Flex program reads the XML data (E4X is very cool) and transfers the data to the 3D Bezier spline. An example is shown below,
whose exported XML is
<spline name=’Line01′ knots=’7′ closed=’true’>
<knot x=’-123.018′ Read more:Animation
Papervision 3D Figure-8’s 2007-09-04 18:24:38 The 2D Lemniscate of Bernoulli example proved to be rather popular, so I thought a 3D extension would make a good test for the 3D closed-loop Catmull-Rom spline. This example animates a series of markers (boxes) along three figure-8 paths in the XY, XZ, and YZ planes.
Arc-length parameterization produces smooth motion along all three paths. The online demo may be viewed here, which includes a link to download the entire Singularity package.
Read more:Papervision
Flex for Business Decision Analytics 2007-09-28 07:50:29 I’ve been asked a lot about what’s next for Singularity. The parameteric curve library seems to be pretty far along, so I need to go back and try to finish off the 2D rigging classes. In tandem with that effort, I’ve decided to revive an old background project for which Flex seems to be much better suited than Flash. Adobe has made some noise about using Flex for business intelligence, but only in terms of displaying dashboards. A dashboard is driven by analysis of data which could range from simple statistics to advanced methodologies from the field of Operations Research.
In terms of the latter, Flex/AS 3 is well suited for model assembly and analysis, while FDS/RPC in tandem with suitable server-side software can handle the solution of OR models. So, the big question is how do you put it all together? I guess I’m going to have fun working up some demos
For some light bedtime reading,
Managing Supply-Chain Risk
Multiobjective Programming
Lagran Read more:Business
, Analytics
Papervision Renderable Spline with Path Following 2007-10-11 16:45:07 Visualizing a spline path is not only useful, it may be required for some applications. Fortunately, the new Lines3D and Line3D classes in the Phunky branch make renderable splines possible. Path animation also requires orientation control. To provide these capabilities, I extended the Singularity P3D.BezierSpline to create a PV3DSpline class. This allows the 3D BezierSpline class to remain generic while providing Papervision
-specific controls for drawing the spline in 3D space and better path following.
I still need to add detailed roll control. That’s on the ever-growing ‘to do’ list. An online demo is available if this is something you want to check out.
A MaterialsList material is applied to the test object to identify the top (blue) and front (green). You can observe the demo here, which includes a link to download the Singularity library. You *must* use the Papervision code from the Phunky branch in order to build your own standalone application.
Read more:Following
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