I have had an experience that invisible objects' shadows appear.
 
 I'm not sure that this phenomenon is worth to report on this news group.
 Because I don't know if this phenomenon had been reported or described in the document of POV-ray language very well.
 But I try to report this hoping this report is helpful.
( And permit me to write in poor English and correct wrong expression if I wrote.)
 
 I tried to make a shape by subtracting some objects from a base object. And I have had some unexpected results. The expected result is Fig.4.
 I guess the problem is the invisible objects' shadows written in chapter 3 and Fig.3 below. I attached the scene file. Please see it if you would like to know about the scene file in detail.
 
1. Result of coincident surfaces
 I rendered the scene file I made. Then the result was as shown Fig.1.
 This result commonly happens because the scene file included some coincident surfaces.
 I used two casts shown below to cut (subtract) base object.
 
Fig.1
Fig.1
 
Cast1Cast 1    Cast2Cast2
 
 
 
2. Result of coincident surface
  I moved the Cast2 little bit. Then the result altered as below.
 Some of the partial surface because of coincident surfaces was reduced. But something is wrong inside the circle. I cannot see the surface made by Cast1. Is this also some problem concerning to next chapter?
Fig.2
Fig.2
 
3. The shadow of invisible objects
 Next, I moved the Cast1 same distance as Cast2. Then the strange shadow appeared. According to the shape of this shadow, this problem have something to do with number of times of intersection. (e.g. intersection time is odd number, then rendered expectedly.)
Fig.3
Fig.3
 
4. Expected result
 Finally I moved the Cast1 to opposite direction. Then I could get expected result.
Fig.4
Fig.4
 
 
 
That's all. Bye (^_^)/
 
Best regards
 
Masanori Imazu