High viscous fluid order

So I saw a video recently, and I can't find it on Youtube. Let me know if you have a copy:

A very viscous, transparent (I think sugar solution) fluid is in a beaker. A needle is used to inject a blob of ink, which remains suspended in the solution. A pole down the centre of the beaker is rotated, shearing the fluid and smearing out the blob into a ring. The pole rotates about 10 times, so that the blob is completely smeared out. The pole is then rotated back in the opposite direction and the blob reforms.

If I can't find a copy of the video I will try it myself.

Sails and aerofoils

As a windsurfer and physicist, the aerodynamics of aerofoils are important to get right.

At the most basic level, modelling molecules with Newton's laws will get you the right result when simulating an aerofoil. However, an aerofoil does not simply deflect air downwards.

Actually this is hard to describe unambiguously, I can see why there are arguments.

Thoughts on the nature of light

The wave-particle duality of light has always bugged me. I have recently been thinking about how to simulate diffraction in a raytracer - could a ray perhaps have a certain radius in which it bends towards objects it passes close to?

This does still not account for interference. The fact that a photon travels through both slits of a double-slit experiment can be viewed as a photon in a coherent superposition.

It is quite likely that I am about to embarrass myself in exposing a woeful lack of understanding of optical quantum computing.

Does this then mean that we can use a double slit as an optical quantum computer? Actually, now that I think of it, probably not, because we can't develop gates that change behaviour of certain paths based on whether a photon passed through one slit or the other.

The result of a double-slit experiment (making some idealising assumptions) can be computed through the Fourier transform of a the slit arrangement. This in fact works for any series of slits.

Finally, the clinching proof that this is not possible is that Feynman showed that a classical computer cannot simulate a quantum computer in reasonable time. If it were possible, Feynman would have been wrong somehow.

So rememeber, quantum computing requires a way of interacting your qubits. Interference effects are not enough. I have seen interference being used in several experiments, however.. I don't understand how that works. Photons only interact with themselves... except in non-linear media, I guess. That must be it.

Metropolis Light Transport is not unbiased

I believe MLT is a biased algorithm, as it doesn't sample rays randomly. Many papers discuss something called "start-up bias", which results from choosing the paths to be perturbed - those paths are rated as 'more important' by the algorithm.

One would think that as long as completely new paths to mutate are regularly chosen, then the algorithm will eventually converge to the same solution as normal path tracing with no mutating of paths. To take the extreme case, if every possible (within the computational accuracy of the machine) path is sampled an equal number of times, it doesn't matter if you did that using path mutation or not.

Another question, then, is whether or not the mutation process leads the renderer to implicitly favour some paths over others. For example, paths right on the edge of the light may have fewer valid paths near them and will thus be sampled less often. If this is the case, then I think MLT is ultimately biased.

World Peace

So, imagine we had world peace, guaranteed in some way.

Would that be a good thing? I think there would be a big risk of stagnation and decay.

Wavefront rendering

I've been thinking about path tracing a lot lately, and I came up with a bad idea. Why it's bad is interesting though, as it demonstrates partly why physically-based rendering is so hard (complexity). I think it also validates path tracing as a good approach.

So, my idea was to take each emitter mesh, and propagate a single wavefront out through the scene. The mesh would be simplified as it propagated (retopologising, perhaps using Delauney triangulation). Once the wavefront was at a low enough intensity, it would not be reflected. The camera would then either receive all wavefronts on an image plane (which could potentially be stored as a hologram) or just raytrace the lit scene (seemed similar to radiosity).

Such a scheme would be able to store polarisation and phase in the wavefront, and thus calculate interference effects at surfaces (if previous wavefronts that hit the surface were recorded), and diffraction around barriers would be possible as well.

The problem with this approach is complexity. An area light at the top of a Cornell box is square. The left side sends light to the right, and the right side sends light to the left. A single mesh is not able to capture that much information -- my approach above was too simplistic.

The next step, then, is to make each part of the mesh emit spherical waves. We could then propagate them using the Huygens-Kirchoff principle if we cared about diffraction effects. This gets very complicated, as we almost need to store the state of light throughout the volume of interest, at a resolution good enough to observe interference effects (otherwise there's not much point using secondary waves at all). If we do not use secondary waves during propagation, but merely propagate the spherical waves outward, then this is a very complicated way of doing photon mapping.

So I conclude that this method, while interesting, is not practical, except for very specific scenes which may require such modelling.

Diffraction and interference are probably still better done storing and propagating phase with rays and image pixels - e.g. having 8 images, each storing the accumulated intensity for photons with a certain phase, and combining them to show interference effects at the end of rendering. Actually that sounds kind of cool, I'll have to try that one day. Diffraction could be done by using fuzzy intersection code and bending rays a random amount toward an edge when they went past an edge.

Edit: Someone's already thought of this, and called it Beam tracing.

Coanda effect helicopters

The person who takes these things, puts a camera on them and sells them for use following the action in sports television will make a fortune.

The idea is patented in the US; electric versions may not last long; it would be easy to have several and recharge them while others are flying.

I suspect the main challenge (after licensing) is in the control software. You'd either need very experienced pilots, or a good control system. A system that had the camera mounted with a gyro for stability like those old bomber turrets in a swivel ball would make things a lot easier for the pilot.

In case the above link is broken, I am referring to helicopters with dome-shaped bodies and a small blade on top that pushes air around the body; they fly as a result of the Coanda effect (the same one that most aeroplane wings use: faster air = lower pressure), as discussed on Slashdot.

solid state QC fabrication daydreaming

Well. One way would be to get bricks, 10nm^3 with sheer edges, and a single dopant at the centre. Constructing your QC would then simply be a matter of positioning bricks, perhaps by immersing them in liquid and pouring them over something.

The best strategy for regular arrays involves natural alignment through chemistry of some sort, for example if donors could be made to repel each other over some range, that would be very useful.

An alternative is some sort of nano-periodic structure that can be filled in in some kind of regular fashion and then etched away.

Perhaps a long biological molecule could be periodic on the scale required, and laid flat and straight on a substrate? The unwanted bits could then be removed, and crystal grown around the remainder..

So yeah

I just finished this game,

and it was awesome,

and there's no SVG logo on the web.

So here it is.

Actually, the more surprising thing is that Double Fine doesn't sell a green turtleneck with this logo on it. I suppose they do have Kochamara...