sakri rosenstrom blog

I know this has been done before, probably much more efficiently, but I had an idea wednesday and had to pursue it to its conclusion

The other day Katopz pointed me to this snippet which triangulates polygons. I’ve also seen an approach to ear cutting by nicoptere.

I figured that by converting an “O” into a “C” leaves me with two polygons which are easy to triangulate. Allow me to elaborate:

So the idea is just to cut out a rectangle (two triangles), which connects the polygon and the hole. Triangulate the “cut shape” and then concat the extra two triangles to it. But which rectangle to choose?

I wrote a class called PolygonWithHoles.as . This contains a polygon (Vector.<Point>), and holes (Vector.<Vector.<Point>>). The idea is too loop through the “holes” one at a time (cue beavis and butthead). The safest bet is to find the shortest “connection” between a point on the main polygon and the hole (done by looping and using Point.dist()).

This too has one stipulation. In order to have a rectangle, the code has to find the “shortest connection” either before or after our initially picked “shortest connection”.

Once the “cut out rectangle” has been discovered, the perimeter of the main polygon and the hole are merged through a few loops. If there are more holes, the now modified main shape is chopped again and again, eventually resulting in a “hole free” polygon. This can then be triangulated, and the “removed rectangles” are appended as sets of triangles.

Click image for demo

This approach seems to work well over 90% of the time. A few characters in some fonts do throw an error… not sure why. The triangulation is pretty fast, you can see this in the tracebox in the demo. The vectorization of the text is the slow bit.

The next step, of course, is to extrude the characters using textures Maybe even add shading some day…

The code is more or less legible this time, eventually I hope to clean this up into some sort of an API… Once again, the download is a zip of my always expanding “FindBitmapPixelOutline” project… download it’s latest incarnation here. The project you want to look at is “TriangulationTest.mxml”. Warning, it’s 6 megs with tons of crap you probably don’t want

.

Here’s a demo I made for my presentation at multi-mania. I played around with verlet integration before and have long wanted to try this technique on text. Once I got the vectorization going, it was just a matter of connecting all the points to “Verlet Sticks”.

This turned out to be a little tougher than expected. The tricky thing about Verlet Sticks, is that if you connect the same Verlet Point to multiple Verlet Points, the calculations go berzerk, and your shape quickly vanishes from the canvas into the ether. So the challenge was to find a way to connect all the points of a vector shape, with a minimum number of “individual connections”, yet in a way that maintains the integrity of the shape. Keyboard cat played me off multiple times in my attempts .

Finally, the solution I landed on, was to create a grid out of all the points. The idea is to create a boundary rectangle, which maintains it’s shape via “cross sticks”:

Then, create a grid using all the points of your vector shape(s), in such a way that each point connects to a subdivision of the outlines of that “boundary Rectangle”:

In the image above you can see the “boundary rectangle” surrounding the vector shape. Then, each point is connected with a vertical and horizontal line. These verticals and horizontals are then connected to a “subdivided” boundary rectangle.

In the demo you can turn “render sticks” on and off to visualize the trick.

Strengths:

• Can handle pretty much any set of shapes and subshapes

Weaknesses:

• Due to the “Boundary Rectangle” the shapes “bouncing” is limited, a “T” for instance can’t lie diagonally, it always ends up on one of the four sides of the rectangle.
• The vertical and horizontal lines shouldn’t have more than two subdivisions. To fix this, the code first checks for all points along the same x and y, then shifts any instances above 2 by .5 pixels each. It’s practically invisible, but it’s there.
• Doesn’t support transparency, I guess this could be done with a blendmode or so…
• More complex shapes can still spazz out and disappear

Click to try out the demo here . Ignore the collision physics, it’s CRAP! The effect works best with “pixel fonts”. The controls are :

• RENDER : renders the input text with the selected font
• UPDATE : update one frame of animation (when stopped)
• PLAY : updates the animation on an enter frame
• BOUNCE : when the characters are just skidding the floor, spice things up by clicking this button

The code is DIRTY, but does the trick. I’ve uploaded the source for the brave (or desperate ). It’s the same project that I’ve been using for my last 5 or so blog posts, so there’s a lot of redundant code in there. Download it here.

ext steps:

• compose a clean “all purpose” class for generating such a grid
• Render shapes with curves, using the drawing api
• Use nicopteres vectorization code to do this with photos…
• Improve the curves and optimization, again I think I can use some code from nicopetre

I just wanted to put this out there because, well, it’s kind of nifty… More to come, enjoy!

.