Yeah, it's hard to describe it as unforeseeable when it's happened to you before and is readily modelable.

The guardian states this phenomenon is difficult to model: http://www.theguardian.com/artanddesign/shortcuts/2013/sep/0...

It may be difficult to model precisely what will happen because of the little fiddly sub-millimeter differences in window positions mattering. It is not difficult to understanding that a generally concave surface facing the sun is very likely to have some sort of significant problem. To the extent that the exact result is hard to model, simple engineering prudence would suggest the "'Doctor, it hurts when I do this.' 'Don't do that then.'" response.

Yeah, this really seems...kind of obvious. A concave reflective surface will focus any light source, and in particular, the sun.

Whatever the guardian says, it's a very basic optics problem, and not at all difficult to model. It's mostly a matter of whether or not anyone bothers to do it.

In terms of difficulty, it's one step harder than modeling which direction something will fall if someone drops it off your building.

Well except you have to model the position of the sun for every hour and day of the year, but sure other than that just like it.

And the position of the sun relative to the building is also a simple formula based on time of year. Given that this is the country that gave us freakin' Stone Henge you have to expect that someone remembered that there is a formula to predict exactly where the sun will be relative to a spot in England every day of the year. The clever ones actually used that to tell them what day it was since they couldn't be bothered to invent the wrist watch.

The position of the sun is very easy to predict, 90% of the time, in England: it's behind the clouds!

* this summer being an exception!

Yes - apparently it'll be 2020 before we see a summer like this again, though.

upvoted for Stonehenge reference.

Or you could use a simple rule of thumb. Something like, "Let's not build skyscrapers that are giant parabolic reflectors aimed at things of value (people, cars, other buildings, etc.)"

This seems like a really stupid mistake to make. TWICE.

...or you could put the concave side on the North. That also solves the problem.

Then you build one in the southern hemisphere. Oops!

In the southern hemisphere everything is upside down too, so the rays would reflect off into the atmosphere, I expect.

I bet a modern calculating machine could run through all of the permutations in no more than a couple of weeks!

> Well except you have to model the position of the sun for every hour and day of the year

That sounds exactly like some things xkcd has done in the "what if?" series. He's done all sorts of variations on similar calculations.

And while xkcd is smart, he's not superhumanly so (his fame is due to the unique combination of creative thinking, humour, geekery and smarts).

In other words, this is possible and a good engineer should be able to calculate this. Especially when you know that any concave reflective surface is going to focus the light somewhere. In addition you know that due to the movements of the sun during the day and the year, this focal point will in 3D to different positions. So yes, odds are that it's going to hit some spot, somewhere, where it's going to be able to do damage, at some point during the year. Then you get to make a simple risk calculation about expected strength of sunlight that time of the year.

And then you will remember to realize that over the course of the lifetime of this building, climate always has a non-zero probability of powerful outliers[0], and the conclusion is:

Simply don't build gigantic concave mirrors in residential areas.

[0] I'm not 100% sure if this is the case for strength of sunlight, since it's mainly dependent on what angle the sunlight arrives, which is not really up to chance. Still, even in the winter when the sun is quite low, as long as the sky is clear, I can easily light an incense stick with an A4-size fresnel lens. And I guess a whole building-side has a "slightly" bigger margin of how narrow the point of focus needs to be.

In which case, it is much simpler.

To work out where an object will fall, you have to model the path of various objects of all shapes, masses and densities with wind of all strengths and directions (including shifting and gusting winds), and considering the original orientation of the object, and any spin placed on it at point of release (in three axes).

Just working out the angles at which light from a distant ball of fire will hit a surface should be a piece of cake. You could probably do it pretty easily for every point (assuming a certain size of point) at that distance at which it isn't completely hidden, just in case the planet suddenly changes its orientation.

That's not particularly computationally intensive.

So what? People have been doing that for centuries using almanacs. And with computers that sort of thing becomes stupidly simple. IIRC that functionality is even built in to Google Sketchup.

It's not - given an accurate geometry model and reflective window material, it'd be really easy to use a raytracer to test this:

* Renderers like Maxwell handle caustics nicely, and you could get away with rough photon-mapping (instead of time-consuming but very accurate MLT)

* Most renderers have very accurate physical sky light models which accurately model the intensity and position of the sun in the sky based on time of day and long/lat coords.

It'd be easy to python script a run of renders for each minute in the day (10 seconds for a render) over the next 5 years and then run an analysis of the rendered image for intensity on the ground. Just set the ground material to not be lit by any diffuse GI rays or direct lighting, and it would literally just render out the reflected sun on the ground (or off other buildings if you wanted to do it REALLY accurately).

It'd be time consuming and CPU intensive to do the rendering for all that: 2,630,880 renders for each minutes for 5 years, but you could probably work out an envelope you could skip (definitely the night time) after doing the first year.

7308 hours render time for the full 24-hour period for 5 years. But do-able, and very parallel over multiple machines.

You can do it on the back of an envelope. Radius of curvature sets the focal length and the min and max elevations of the sun are set by your latitude. If there's any elevation between the min and max where the reflection will hit the ground even close to the focal length of the building, you will have a problem.

It's the same optics calculations anyone designing a concentrating solar power system would do, and while you need to be careful if you want accurate answers, it's not complicated to see if it has the slightest chance of working.

You know, indirect lighting surely doesn't melt plastic, so you absolutely don't need Metropolis Light Transport here. And also you don't need to use photon maps. The computations to map the intensity of specular reflections from the building's windows would the equivalent to creating a photon map on a scene, not using the photon map to render a complete scene.

> You know, indirect lighting surely doesn't melt plastic ...

That depends on the light's intensity. If with the term "indirect" you include specular and diffuse reflection, then yes, in the right circumstances, the energy level can be spectacularly high.

But computer simulations need to be done very carefully, because the issue isn't visible light reflection, it's infrared reflection. For the building in question, the windows are glazed with a coating meant specifically to pass visible light to the interior but reflect infrared radiation (both to preserve building heat in the winter and reject heat in the summer).

What that means is that, as bad as the reflected visible glare seems to those passing by, the infrared energy levels are much higher, and easily explain the damage.

> If with the term "indirect" you include specular

But you don't. "lighting in which the light emitted by a source is diffusely reflected" (merriam-webster.com)

In normal computer graphics speak, indirect lighting means light that has had at least one diffuse reflection on its path.

What? It's the indirect reflection of the sun, specularly reflected (and focused) off the building.

You need the light source (sun) reflected onto the ground (or whereever it's reflected) from off the building.

You can't use standard path-tracing / ray tracing for that, as that traces rays from the camera outwards, and wouldn't show the caustics (well, you might be lucky and get one or two fireflies, but that wouldn't be the result needed for analysis).

At the very least, you'd need BDPT. Photon mapping would be a much faster (but cruder) solution.

Basically what you're saying is you need classic ray-tracing from light sources, such as one can get with Pov-Ray and similar old-school ray-tracing programs.

Well, I'd define classic as standard "from camera" outwards.

POV Ray does classic (which won't give you what you need as it doesn't handle caustics) or photon mapping which will.

Bi-directional path tracing (tracing rays from both the camera and lights in the scene and joining the respective light paths in the middle), and Metropolis Light Transport (a progressive variation of BDPT) are the most accurate, but are often slow to converge to a noise-free result, mainly due to the fact they do handle caustics (reflections of bright light focal patterns) accurately, which introduces noise (over the standard GI noise).

But photon mapping would give reasonable results in a few seconds.

> Well, I'd define classic as standard "from camera" outwards.

Fair enough. I was thinking of optical ray tracing, not graphic ray tracing. In optical ray tracing the point is to analyze the paths of light beams through lenses and from mirrors, not the POV of a camera necessarily.

I've been able to get pretty useful optical ray tracing out of Pov-Ray:

http://www.arachnoid.com/raytracing/csg.html (note the animation toward the bottom of the page).

Yeah, I work in the VFX industry, so I'm a bit biased :)

Cool - actually, that would be a lot less computationally expensive (assuming you just modelled the sun as a disc) tracing it backwards without any GI at all. Photon mapping's pretty similar though, you've just got a final gather process at the end of sending out the light rays. The difference is photon mapping records all the hits to all surfaces. If you limited it to specular ones (at least for the first ray bounce) you'd probably have something very similar.

This is what I tried to say 5 or 6 messages ago, when I first replied to you.

> What? It's the indirect reflection of the sun, specularly reflected

I am pretty sure the standard use of "indirect lighting" in normal computer graphics jargon means light that has had at least one diffuse reflection on its path. Even Merriam-Webster lists this meaning [1].

You'd just need to run the ray-tracing from light sources algorithm, to map the intensity of the specular reflection of the building. This would be equivalent to just creating the photon map. Then you could just view the photon map directly, to see the intensity of the death ray. There would be no need to render the scene (although you could, if you wanted a photorealistic view).

[1] http://www.merriam-webster.com/dictionary/indirect%20lightin...

Everything is obvious once you know the answer.

This is true, and we often forget it. But since they knew the answer after the Las Vegas building, the risk that this might happen should have been obvious.

Perhaps as a child he had a fatal attraction towards frying ants on sidewalks with lenses?

one can only wonder how so many minutiae things can violate building code while a huge death ray building is just fine with the building department.

Had to think about the same Las Vegas building.

But the Vegas one even has a curve. So there is a potential lethal focal point.

Sensational news item: http://www.youtube.com/watch?v=R-hV_AawLSE

this one also does..

Here's your xenophobic headline: "Uruguayan National Responsible for Construction of Solar Death Rays in Major US and UK Cities"

I wonder if the differing climates between Las Vegas and London played a part.

Glass is cool