## Part Ib – Butterfly intermezzo

In the previous post we talked about affine transforms and splitting rectangles into triangles. We only talked about one of the simplest scenarios: mapping a complete rectangular area of a bitmap into a drawn triangle/rectangle. The formulas for mapping an arbitrary triangle of a source bitmap into an arbitraty drawn triangle are a bit more involved and we will discuss them in the next post. But even with two triangles we can create something simple to create a feel of 3d. Far from being a correct implementation, this example experiments with a 3d butterfly based on two sources images (the front and back of a butterfly).

The 'model' exists of two triangles, one for each wing, which are folded and rotated using a couple of sinuses. The resulting coords are used to generate the transform matrices for the bitmap fills on the wings. Which bitmap is used to fill a triangle is decided using a cross product of the wing vectors, to check whether we are seeing the top or the bottom of the wing. Since there is no real perspective it is sometimes hard to see which side is in front, but nonetheless this opens up fun possibilities for a children's game where you can draw a butterfly and then have it fly off your paper into a garden or something like that (where 100% correct perspective wouldn't matter anyway).

One thing I've noted is that when you use smooth bitmapfills without explicitly closing the filled polygon the flash player will sometimes hang / lock up for seconds at a time. Not sure what causes this, and I hope closing the polygon is the 'real' fix.

Here is the complete example with sourcecode included: Butterfly2 (1260). It's a Flash IDE FlashDevelop project, meaning you can edit it in FlashDevelop but have to export it from the Flash IDE. If you don't have a flash ide, setup the butterfly swf as injection swf and specify another output.