http://www.businessinsider.com/architect-behind-the-walkie-t...
This seems like a really stupid mistake to make. TWICE.
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 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.
* 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.
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.
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.
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.
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.
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).
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.
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...
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.
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