omino pixel blog

This post will show a handful of simple tricks for “drawing” using Pixel Bender. That’s not what it’s for, especially in Flash. But it’s still interesting to see how it’s done.

But first, the demo:

And I’m sure the handy tabs across the top for the source code won’t escape your attention, either!

Pixel Bender Metadata

In the demo above, you can notice a couple of things. Some of the parameters are drawn as sliders, but also there’s a checkbox, some color pickers, and, in the drawing area, some draggable spots. This is done by a collusion between the Pixel Bender kernel, and the Flash viewer code. Here’s the parameters from the Pixel Bender kernel:

    parameter float3 backgroundColor<kind:"color";defaultValue:float3(1,1,1);>;

    parameter float spotRadius<defaultValue:50.0;minValue:1.0;maxValue:800.0;>;
    parameter float3 spotColor<kind:"color";defaultValue:float3(0,0,0);>;
    parameter float spotSquare<kind:"checkbox";defaultValue:0.0;>;

    // This parameter just gets poked with the rendering dimensions, always
    // Doesn't get shown to user. In my custom viewer, that is.
    parameter float2 dims<kind:"dstsize";defaultValue:float2(300,300);>;

    // "point" means it lives somewhere in the image, as a coordinate.
    parameter float2 lineStart<kind:"point";minValue:float2(0,0);maxValue:float2(400,400);defaultValue:float2(10,10);>;
    parameter float2 lineEnd<kind:"point";minValue:float2(0,0);maxValue:float2(400,400);defaultValue:float2(30,100);>;
    parameter float lineWidth<minValue:0.5;maxValue:30.0;defaultValue:2.0;>;

I’ve added a kind property to some of the parameters. Pixel Bender ignores it, but in ActionScript we can access it as part of the ShaderData. For example, it is true that shader.data.spotSquare.kind == "checkbox".

These aren’t special or magic! My Pixel Bender kernel says it, and my Flash viewer reads it. It’s a handy trick, if you happen to be in control of both parts.

How to Draw a Circle

It’s so easy! Given a center and a radius, you check each pixel to see if it’s within that distance of the center. Like so:

        float d = distance(co,center);
        if(d < spotRadius)
            dst = spotColor;

How to Draw a Square

This is ever so slightly trickier. Again, with a center and a radius, we want to see that both the x- and y-distances from the center are within the radius. Like so:

        float d = max(abs(co.x - center.x),abs(co.y - center.y));
        if(d < spotRadius)
            dst = spotColor;

How to Draw a Line

Now this is getting mathy. In an earlier post about Gradient fills, I derive an equation for “position between two points”, like so:

t = dot(uv,xy) / dot(xy,xy)

where a line segment is given by the endpoints (0,0) and (x,y), and some screen spot is given by (u,v). If t is within the range 0 to 1, then (u,v) is somewhere along that line segment if it’s drawn infinitely wide. That’s a short stubby line no matter how you slice it.

To constrain the width of the line, we need to know how far from the center (u,v) is, which is given by:

d = abs(length(xy) * dot(uv,yx) / dot(xy,xy))

(If you followed the Gradient post, it’s the right half — the y-component — of the final 2×2 matrix, times the length of the line, for scaling. But it’s not important.)

So, the combined code to draw a line between two endpoints, with a particular line width, and square-capped ends, is:

       // and now, a bit of fun math, as we plot a line between two points.
        float2 uv = co - lineStart;
        float2 xy = lineEnd - lineStart;
        float xy2 = dot(xy,xy);
        float g = dot(uv,xy) / xy2;
        // if we are between the two points, then g is between 0 and 1.
        float dl = abs(dot(uv,float2(-xy.y,xy.x)) / xy2 * length(xy));
        // dl is now the distance, in pixels, from outCoord to the line
        
        // if we're between the endpoints and close enough, draw.
        if(g >= 0.0 && g <= 1.0 && dl < lineWidth / 2.0)
            dst = float3(1,0,0); // draw the line in RED.

Ridiculous?

To reiterate: This is a ridiculous use for Pixel Bender. But the ideas may come in handy. Doing something with a squarish area-of-influence isn’t so outlandash… and while a solid-colored line is a bit unsubtle, a shaded field or beam area begins to seem plausible. Pixel Bender is so powerful and flexible, I know we’re going to continue to see unexpected and novel results from it.

Back to the cubes. This Pixel Bender generator shows a volume subdivided into cubes, and constrained to a spherical limit.

And here’s the source code.

Can’t wait to start incorporating this stuff into After Effects CS4… but haven’t uncovered any details on exactly how Pixel Bender integrates to it. Presumably some magic parameters may tell you things like the source or dest extant, and maybe you can add “typing” information to parameters. Looking for links… since it may be a little while before I can afford to upgrade.

I was trying to do something else. But, as you well know, sometimes bugs are really cool. Here’s my bug of the night. Click Go, once, and Scramble a few times.

Geometrical interpretation: a perfectly nonreflective sphere is in each cubical cell, getting cross-sected just like the cubes.

And here’s the source code. It’s based on “cubes” from a few posts back.

Featuring mix(), clamp(), and dot().

Very often I need a simple linear-gradient in After Effects, and end up sing the four-color gradient because that’s all I can find. And so, here, for your perusal, is a Pixel Bender implementation of a Linear Gradient Generator.

After that, we’ll see the code, and after that, a quick review of the math.

Here is the .swf. (With some improvements on the Pixel Bender viewer — you can drag any float2 parameters as points, now.)

Isn’t that fun? Well, I’m easily amused.

The Code

Here’s the Pixel Bender code.

kernel Gradient 
{
    output pixel4 dst;
    parameter float2 p1<minValue:float2(0,0);maxValue:float2(400,400);defaultValue:float2(10,10);>;
    parameter float2 p2<minValue:float2(0,0);maxValue:float2(400,400);defaultValue:float2(130,130);>;

    parameter float3 color1<defaultValue:float3(0,0,0);>;
    parameter float3 color2<defaultValue:float3(1,1,1);>;

    void evaluatePixel() 
    {
        float2 co = outCoord();
        
        // shift everything relative to p1.
        float2 uv = co - p1;
        float2 xy = p2 - p1;

        // the math.
        float g = dot(uv,xy) / dot(xy,xy);
        g = clamp(g,0.0,1.0);

        // the color.
        dst.a = 1.0;
        dst.rgb = mix(color1,color2,g);
    }
}

The Math

I’m ok at math, but not always fluent in it. I can remember what a matrix is, but not necessarily exactly what a cross-product is. Maybe you’re like me. In which case this quick run through the math and logic behind the gradient fill will be quite useful in your own Pixel Bender bending!

And be assured, a few pages of high-school-algebra-style scribblings, and the occasional google (How do I invert a rotation again? What’s the formula for perspective?) really can lead to workable results. Good clean fun!

Let’s go.

Consider a trivial gradient, where our two control points are at (0,0) and (1,0). That would be easy! Just take the x-value of any pixel, and that’s your color. (That is, the position on the ramp between your two gradient colors.)

By the way, this picture is from Ron Avitzur’s “Graphing Calculator”. The story of its development is legendary; less well known is that it’s actually a very powerful and useful tool.

I found the easiest way to think about a general two-point gradient was to ask, “How do we rotate and scale our control points back to this trivial gradient?” And let’s assume that the first control point is always at (0,0).

Here is matrix for a basic rotation, which moves any input point by a rotation around (0,0):

[1]

A rotate-and-scale matrix looks like that, times a constant on each element.

We want to think of our general gradient as a transformation on the trivial gradient. Let’s say our second control point is (X,Y), and our first control point is (0,0) as mentioned above. The rotate-and-scale matrix being applied, conceptually, is:

[2]

To figure out the 0-to-1 trivial position of any of our input points, we need to invert it. A matrix inversion looks like:

[3]

So, we invert the second equation [2] by plugging it in to [3] and get:

[4]

Now, let’s call each pixel position of our output (U,V). For our gradient, we actually don’t care about the resulting Y position; just X gives us our gradient value. So we get:

[5]

Now, the definition of the dot product of (A1,A2,A3,…) and (B1,B2,B3,…) is (A1B1 + A2B2 + A3B3 + …). So, from the above, UV+XY is, conveniently, (U,V) dot (X,Y). Similarly, X² + Y² is (X,Y) dot (X,Y).

And now, when you read this part of the code a second time, it should be much clearer what’s going on:

    void evaluatePixel() {
        float2 co = outCoord();
        
        // shift everything relative to p1.
        float2 uv = co - p1;
        float2 xy = p2 - p1;

        // the math.
        float g = dot(uv,xy) / dot(xy,xy);
        g = clamp(g,0.0,1.0);

        // the color.
        dst.a = 1.0;
        dst.rgb = mix(color1,color2,g);
    }

Simple and useful!

Next up, soon, more cubes.