decker labs

So over the last week or so, I restructured my 3D engine. Nothing that would be visibly noticeable, but I feel better about where it is at right now. What I like about it, though, is that it is still not what would be probably considered “the right way” to do it. The reason I am happy about this is that it makes it my own, and I understand exactly why and how it works. Once I have a really solid understanding, then I can move towards doing it the “correct way,” but for now, my little hacked together experiment makes me happy.

One of the changes I did make is to the shaders. I added a PseudoGouraudShader, which uses gradients to draw each polygon face to try and smooth out the hard lines created by using a flat shader. I doubt this method would ever produce 100% accurate results that are identical to a gouraud shader, but it makes for interesting results. The method I am using is pretty slow, as it needs to draw each face four times, three of them being gradient fills. Each vertex’s normal is calculated from the sum of all the faces it is a part of, and that brightness value is used to draw a radial gradient on that face, the center point being the vertex. (Two examples: RGB example and dot example, the circle areas are ‘painted’ on via gradient fill) This can produce some fun effects too when played with.

I had an example of the PseudoGouraudShader last week, but it was off, it looked like alternating faces had different brightness values. Just playing around last night I found the issue, it lies with how I was calculating my normal.  When getting the cross product of the vectors, it is better to normalize the result instead of normalizing the vector before. The example below shows the two results and code snippets:

Still not perfect, but I’m not sure how close I can get using this method. I think there might still be some slight errors in the core math, which could be producing the results that look similar to the image on the left (although less intense). You can check out the live demo here.

On a last note, calculating normals and centroid over and over again for rendering can get pretty intense. In the case like this, the same normal gets calculated multiple times a render even though it hasn’t changed (because each vertex needs to get the normal of each face it is connect to). In order to boost speed, I created a caching system. When the normal is calculated, it saves it to a “stale normal” and updates an object (which I called the cached face) that tracks the position of each vertex in the face. Then, the next time the normal is called, if that cached face is not different then the real one, it just uses the stale normal instead of re-calculating.

Quick update on my current experiment building a 3D engine in Flash – I’ve added light and shaders. Shaders are special materials that are effected by the direction each face is pointing (called the normal) and another vector, in this case, a light direction. During the render process, each face calculates its brightness thus giving the illusion that light is reflection off of the mesh.

Upon researching, I found on a few occasions that the way to calculate lighting is to simply add the normalized normal and normalized light vector. This, however, seems to be slightly incorrect applicable to this situation. First, the result is another Point3D, where instead I am looking for a brightness value. Upon consulting coworker Mathieu Badimon, he suggested using the dot product of the normal and light vector. This returns a single number value, and when used to calculate brightness seems to work perfectly.

Next step? Finally tackling bitmap distortion in 3D, allowing for bitmap materials. (Which opens the doors to different types of shades as well, such as bump maps and dot3 normal mapping.) Once I’ve tackled that, I plan to completely restructure the engine, as I have a better idea now of how it can work while still sticking to my original plan of excluding a view3D. In the process of restructuring, I plan to write up the core math equations used in the most simplified way that I can, as finding some of these equations in a non-language specific explanation or simplified manor can be difficult.

Check out the new demo here. Click and drag the white dot to move the light source.

A few weeks ago I had to create a simple X-axis based parallax ‘engine’ for a project. Just basic horizontal movement, which is scaled based on an abstract z value. Well, somehow that turned into a full 3D engine. So I am continuing to build on what I had started in order to create my own Flash 3D engine, not because I think I can build a better Papervision, Away3D, or Five3D, (because I’m sure I can’t) but rather in order to learn. Since I end up using 3D engines fairly often now, I figure it’s good experience for me to build my own and see how it can work from the ground up.

So the first thing I learned, which really surprised me, is that building a 3D engine is easy. I’ll be the first to admit that math isn’t necessarily my strong suite, so believe me when I say it’s not too difficult. There are only a few tricky equations you need, and there’s plenty of information on the web since almost everyone it seems has created a 3D engine at one point or another. The tricky part, however, is getting the engine optimized and to run smoothly. That’s really what my challenge is.

I was able to get basic translation (which runs horrendously slow right now) as well as rotation implemented. I expanded on that to create a mesh, which can accept data imported by an .obj file (very easy to write a parser for) and create geometry. The mesh, like most in other 3D engines, consists of an array of vertex points and faces, which themselves are a collection of references to those vertex points. The mesh overall or individual faces can accept a material, as well as an optional back material for the reverse of the normal for when single sided is false. I calculate the z-depth for sorting based on the centroid of the polygon, which is probably not the fastest or most accurate way, but so far it has seems to work pretty well. Currently I have not yet tackled bitmaps or lighting, but that’s an interesting challenge for down the road.

On the note of optimization, I’ve noticed that Papervision, Away3D, and Five3D all use a scene3D and/or view3D. That said, all of your 3D ends up in more or less abstract container that handles the rendering. I suspect the reasoning for this is so that a render function only has to be called once, and all the appropriate transforms can happen here. In my experiment, I have decided against this, and probably at the stake of performance. The reason I don’t want to include a viewport or scene is so that the user can have more direct access to how the ‘Sprite3D’ is placed on the stage and it’s relation to other elements. I would also like to see how much can be achieved without having to use a container for the rendering process. Regardless, it’s been a fun learning experience so far.

Some demos below. The first example shows some of the basics. The second shows an experimental gradientFill material (creates a voronoi effect) and the third show an experimental shader that colors the faces in relation to their space in 3D.