Click here to view the embedded video.

Click here to view the embedded video.

You can find the compounds and the scene used to make this image here.

Very cool. But, you say, it’s for softimage and my stinking studio makes me use Maya. Well,  Maya users, have hope. Jeremie has also been beta testing a Maya version, called MGEAR.

Let’s face it, there are more animators needing high quality rigs than there are high quality riggers. And rigging takes a lot of time. That’s why autoriggers came into being. If you are laboriously assembling all your rigs by hand and you just want to get to animating, you really, really need to be using a solution like Gear.

GEAR has the openness and enough well -thought tools to appeal to a dedicated rigging TD while also providing a fast and reliable way for animators to generate sophisticated rigs with a minimal learning curve. It’s modular in design, meaning it isn’t restricted to rigging only humanoids or quadrupeds, and it’s extensible, so riggers can use GEAR as a framework upon which they build in their own particular style.

It’s a very well thought out system and highly recommended for small studios and individual animators who need good rigs fast, as well as riggers interested in having the capabilities of an autorigging framework without the desire (or time) to make their own.

Click here to view the embedded video.

[Note: This topic has been covered (better) elsewhere on the web, but I thought it was interesting enough to preserve for myself on this blog. -am]

So how do you generate a random vector in 3D space? The natural inclination is to generate each point based on a simple random azimuth and elevation. But because the circumference of latitudes decreases from the equator towards the poles, the result is an uneven distribution. Generate a few vectors and things will seem fine. But if you generate a large set of thousands of points, you get this:

But we need an even distribution. How about this: generate random values between -1 and 1 for each X, Y and Z. Then normalize those vectors, and again you have a collection of random points on a sphere. But the distribution still isn’t even… you are basically projecting the points of a cubic volume onto the sphere surface:

You can solve this problem by culling points outside the radius of the sphere (magnitude >1) as they are being generated, and the result is an even distribution on a sphere. This is known as the rejection method, and it works, but it’s inefficient. You are computing a lot of rejected points. Additionally, as a practical matter “N iterations” yields some number less than “N” vectors, making it difficult to specify the total number of vectors to be created by such a function.

Enter the trigonometric method (something of a misnomer seeing as how the method involves the integral of the surface of revolution.)

θ = υ(-1,1)

And Φ = υ(0,2π)

Where υ(a,b) is equal to a uniform random scalar.

So, go from Polar to Cartesian coordinates, and you get:

x = cos(θ) cos(Φ)

y = sin(Φ)

z = cos(θ) sin(Φ)

And it works.

Digression: if you want to get down to the heart of things, getting a random scalar value, or more specifically a repeatable pseudo-random value based on a specified seed, is it’s own challenge. Here’s a snippet of GLSL code, a function written by Stephen Gustavson which generates a “random” scalar value from a scalar seed input… (cos and mod should be familiar…the “fract” function returns the fractional (decimal) portion of it’s input.)

float randomizer(const float x)
{
float z = mod(x, 5612.0);
z = mod(z, 3.1415927 * 2.0);
return(fract(cos(z) * 56812.5453));
}

Less “terrain-like” is this output from a reticulation compound, which uses as it’s basis the “computational” noise described by Stephen Gustafson et al:

Interestingly, I approached this project having not read Ken Musgrave’s various writing on the subject of terrain generation outside of white papers. Once I did, I found that much of what I have discovered anecdotally he thought through in detail long ago. This is awesome, because it shows that my thinking has validity (after all, there are few who have spent more time and energy on the subject than he) and also because it gives me more threads to pull. I now have a series of compounds at my disposal that do various “terrain stuff,” now I can take a step back and decide how to assemble those experimental compounds into a more user-friendly and extensible set of ICE building blocks…

Texture masks based on height, curvature and slope

River generation (I have one approach but it leaves a lot to be desired)

Additional fractal deforms (worley and other cell based schemes, “hill”, variants on multifractals)

Crater formation, ecosystem maps, more refined erosion, and mountain/valley range formation

So, there’s a lot to do. But one step at a time.