chauvet dmx Mega

Saurabh Joshi says:

Well, I could partially understand what you want to say. Anyways, let me share a comment with you.

For any convex polygon the claim in problem 2 is trivially true. Now, Any concave polygon can be made by tiling up a few convex polygons. If we can show that for all convex polygons, each point on the surface of the polygon receives light from all directions then we are done. The reason is these points on surface receiving lights from entire 180 degree will act as a light source on the other side of the surface.

In fact, only one point in each edge of a convex polygon should exist such that it receives light from entire 180 degree. But alas, none of this happens. Let's take a regular triangle ( all sides equal ) and a light source somewhere inside it. Draw three mirror images of this triangle with each side acting as a mirror. You can fill up entire 2D plane this way. Now, there are countably infinite light source in the plane. You draw a straight line from any of these light source to a point on the edge of the original triangle. This line will tell you the way light will reflect in the from the light source of original triangle to reach this point. Thus, it is easy to see that receiving light from _all direction_ is not possible. But we can have dense ness, in a sense that given any angle $latex theta$ and $latex theta '$ we will have at least one ray which hits the point with angle lying between this range.

For non-regular convex polygon even this property is not easy to prove because while taking mirror images and trying to fill entire 2D plane, the images overlap which invalidates any ray path from a light source in a 2D plane to a point on the edge of the original polygon to be a physical possibility.

I hope you are able to visualize what I want to say. I guess a couple of figure would explain it better.

senthil r says:

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