isolining package for ActionScript 3

A week or so back I wrote about a package I ported/modified to create the Delaunay triangulation in Flash with a few AS3 classes. As I noted there, such a triangulated irregular network (TIN) allows us to interpolate isolines — lines of constant value (aka isarithms, commonly called contours).

So, given a field of points (weather stations, say)…

weather stations

…with one or more attributes attached (temperature, say)…

weather stations for interpolation

…a TIN can be constructed.

triangulated irregular network

With the above TIN, values can be interpolated along each edge between the points of known values (control points). The interpolation is strictly linear (that is, the value 50 would be interpolated halfway along an edge whose control points were valued 48 and 52).

interpolated points for isolining

With a given contouring interval (I’m using 4 degrees F here), we can connect some of these interpolated points, creating our contour lines.

rigid isolines, ready for smoothing

With the previous steps stripped away, this creates a passable isoline map.

masked isolines

The lines are rigid, though, and should be smoothed for presentation. I allow two methods for this. You can use the “simple” method, which just uses the built-in graphics method curveTo between the midpoint of each isoline segment (below with the isoline interval decreased to 3 degrees).

simple curves for isolining

The above looks alright, but the curves are not continuous, closed loops can still have hard corners, and the isolines no longer pass through the interpolated points (we have therefore generalized an already-inaccurate interpolation). My compatriot Andy Woodruff, author of the glorious new Cartogrammar blog, offered to write a nice continuous curve method that ensured isolines would still pass through the interpolated values. You can read about the method in his post. Here she blows:

continuous curves for isolining

Bringing it all together, then, and incorporating the only extra feature I wrote (tinting of isolines), here’s a nice finished isoline map of temperature across the U.S.

finished isoline map of U.S. temperature

My new isolining package for Flash/ActionScript3 accomplishes all of the above, requiring only an array of point data with attribute values attached. The above example, was accomplished with the following lines of code (after drawing the U.S. states from a shapefile).

//first, generate the array of triangles (ITriangle objects) from the point data
var triangles:Array = Delaunay.triangulate(points);
Delaunay.drawDelaunay(triangles, points, triClip, false); //comment this out if you don't want to draw the triangulation
//generate an array of isolines (isoline objects)
var isos:Array = IsoUtils.isoline(triangles, points, triClip, 3, 0);
//create color and class arrays for tinting the isolines
var classesArray:Array = new Array(40, 44, 48, 52, 56, 60, 64, 68, 72, 76);
var colorsArray:Array = new Array(0x051CFD, 0x4602FD, 0x6D0EEB, 0x8400FF, 0xC400FF, 0xEA00FF, 0xFF00E2, 0xFF0095, 0xFF0030, 0xFF0015, 0xFB3507);
//then, actually draw them, using a continuous curve
IsoUtils.drawIsolines(isos, triClip, "continuous", colorsArray, classesArray, .5, .95);

The full example is included in the .zip distribution. Get that here:

Keep in mind: triangulation is just one interpolation method, and is many ways the least technical (and accurate). More accurate interpolation techniques include inverse-distance and kriging. ***If you’re having trouble, and your isoline interval is not an integer, check out the comment at line 171 of Please fix that, BTW.

I meant to add other features, but since I started work this past week, I’m posting the package as-is, and invite others to modify. On my wishlist:

  • hypsometric tinting, or color between the lines, would allow for more effective terrain or temperature mapping
  • support for projections and other coordinate conversions in the drawIsolines method. I have packages for converting lat/long to a number of map projections, but currently the drawIsolines method doesn’t have support for passing a point coordinate conversion method.
  • an animated demo. This thing’s lightning-fast, so why not?
  • something that would be super wicked would be if someone would implement Tanaka’s illuminated contours [pdf] method, that thickens/thins and darkens/lightens lines like so…
    tanaka method
    …creating beautiful relief maps like the one below
    tanaka illuminated contours

If you add anything to the package, feel free to post a link to your revised version in the comments.


  1. Great stuff, thanks for taking the time to explain it as well as post it!

    Illuminated contours look lovely, I wonder if a passable version of them could be achieved with a BevelFilter?

    Posted June 9, 2008 at 2:18 am | Permalink

    Posted July 28, 2008 at 11:11 am | Permalink
  3. ur api for contour is wonderful
    and thanks a lot to u
    i’d like to fill color between lines ,and want it bo be like

    how can i extend ur api?
    can u give me some hint?
    thanks a lot!

    Posted September 2, 2008 at 1:20 am | Permalink
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  7. Hey, this is awesome… well done!!

    However for some reason the isolines mess up when the nodes/weather stations are square.

    It would be great if you could fix this.


    Posted January 15, 2009 at 11:51 am | Permalink
  8. This looks interesting. Iwas hoping to apply this to archaeological site densities…but not being all that computer savy I am not able to open the application files after unzipping. A little help please.

    Posted January 19, 2009 at 3:59 pm | Permalink
  9. @erik: Hello, this is a small library specifically for Flash, Flex, or ActionScript 3 projects. So if you want to display your data as an isoline on the web, it may be for you. But if you have no use for an ActionScript-specific solution, other options may be better for your needs. R & GRASS, for example, are free tools with lots of flexibility in contouring. Neither are very easy to get started with, but both would be easier to use (esp. importing your data) than my classes if you don’t need a Flash solution

    Posted January 20, 2009 at 6:54 pm | Permalink
  10. nice work you’ve done, congratulations! In our office we would like to generate our charts and diagramms esp. contour-maps with flash for interactive presentations. I’ve searched the web the last year and havn’t found the right stuff. I will try out your software, you are on the right way! The next weeks, I will also take a close look on alternative implementations for GIS-interpolations. For example:
    when we can push your software into this… it would be a great deal! Thanx for your posting

    Kind regards


    Moritz Wagner
    Posted January 21, 2009 at 2:59 am | Permalink
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    Posted June 17, 2009 at 7:53 pm | Permalink
  14. I have been looking for something like this for ages! It looks great.
    I just opened it up and I keep getting 8 of these compiler errors:
    Warning: 3596: Duplicate variable definition.

    Posted May 26, 2010 at 8:13 pm | Permalink
  15. 能给我一点资料吗?

    Posted May 28, 2010 at 10:04 am | Permalink
  16. Very impressive !. Congratulations and keep working as you do, your work is very useful !.

    Posted May 29, 2010 at 5:10 pm | Permalink
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  18. well done! Your AS Libarary is most valuable.

    Posted October 13, 2010 at 3:09 am | Permalink
  19. I think that if you give some examples such as organization of variable ‘points’ ,’triClip’, it will be easier to understand. However, your work is done very well, thanks for your share!

    Posted October 13, 2010 at 3:15 am | Permalink
  20. Very nice your implementation for AS. Do you know something like this for PHP or JS?

    Thanks in advance

    Vinicius Cordeiro
    Posted August 24, 2011 at 8:53 pm | Permalink
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  27. have you finished “hypsometric tinting”?

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  28. @zach’ry:Hello,have you finished “hypsometric tinting”?

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  29. @zach’ry:Hello,have you finished doing “hypsometric tinting”?

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Since I am a Cancer, I naturally nurture, love, protect and take care of her. Since she is on fixed income and cannot work, my job as the sole provider has been stressful at times. But I want to point out that if/when I leave I will be taking all of the bills with me. During this entire time, I have taken care of her when she has shoulder aches or migraines ..she’s not confined, she just can’t sit for very long. I would do the dishes, get her something to eat, go to the store for her .stuff like that. I’m always looked out for her best interest and tried to make her comfortable. Basically sacrificing my needs for hers. Sounds similar to what women do for men doesn’t it. She in turn, has been right there for me during my illnesses. 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8 Trackbacks

  1. [...] isolining package for ActionScript 3 You can use the “simple” method, which just uses the built-in graphics method curveTo between the midpoint of each isoline segment (below with the isoline interval decreased to 3 degrees). The above looks alright, but the curves are not … [...]

  2. [...] update: for a cool usage of Delaunay triangulation, see my isolining package for ActionScript 3 [...]

  3. By The Kraken - A Software Development Journal on February 15, 2011 at 1:14 am

    [...] specially aggregated data-structure into isoLines input Posted: February 15th, 2011 Categories: OOP Tags: Comments: No Comments. Write a comment [...]

  4. [...] your browser interpolate isolines is fun! I first did these in ActionScript 3 back in 2008. This JavaScript version works essentially the same way: generating a triangulated irregular [...]

  5. [...] uses these triangulations in his map-making, you’ve gotta check out the sequence of images on this page. It’s incredible how just a scattering of local temperature measurements can be extended to [...]

  6. [...] 原文:isolining package for ActionScript 3 [...]

  7. By 等值线算法-网站收藏 on May 21, 2013 at 10:17 pm

    [...] as版等值线 geoserver拓展的等值线 [...]

  8. [...] colorful contour lines that arise from the differential equation governing heat flow. The temperature maps by Zachary Forest Johnson from a few weeks ago also used contour lines. And I found some great [...]

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