A mirror that reflects all of the Skydome

Artwork Blender Tests
1

I wonder what kind of shape the mirror that can reflect all of the Skydome is like… :confused:

I tried to calculate the shape and created a mesh in Blender. Here is that.
http://bp0.blogger.com/_d4nbesSwQqc/R8JrkIuw4BI/AAAAAAAAAPw/W79qMGmr5Lw/s400/MakeMirror+Shape.jpg

In order to make sure the mirror can really reflect all of the Skydome exactly as I expected, I took a test by putting it in the center of the Skydome and looking at it from the top with a camera. It could be seen as follows.
http://bp0.blogger.com/_d4nbesSwQqc/R8JrkIuw4AI/AAAAAAAAAPo/gLZbB4cMd08/s400/MakeMirror+Reflection.jpg
As you can see, it is not perfect. The ideal image that I wanted to get as a result of the mirror is like:
http://bp2.blogger.com/_d4nbesSwQqc/R8Jrkouw4DI/AAAAAAAAAQA/vB8J81YEeBM/s400/Sky_5B.jpg

I have learned about a rough shape for the mirror, but it is not a correct shape. Does anybody know the shape and the way to create? :spin:

2

What exactly is the purpose of this? Couldn’t you just set that texture as the skydome in the first place?

3

The purpose is to play with mirrors.

However, it could be useful when you want to know what the skydome is really like, because you can’t watch all of the world around 360 degrees with a single camera at a time. Only looking at this mirror from the top will tell you that information easily.

Therefore, you can make sure there are no mistakes in your settings of the skydome with your eyes.

4

I’ve mistaken the formulas of the normal vector of the mirror, and here is an improved one.

http://bp2.blogger.com/_d4nbesSwQqc/R8N4wYuw4EI/AAAAAAAAAQI/fGWz63_3gmc/s400/MakeSurface.jpg

I have the formulas and I think it’s correct, but I can’t calculate and create the surface from the formulas of the normal by integrating. How do I get a surface from the formulas of a normal.