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How to write down the affine transformation that transforms the plane $Ax+By+Cz+D=0$ onto the plane $z = 0$?

I cannot understand how to begin. I can express $z$ (if $C\neq 0$): $$ z=-\frac{D+Ax+By}{C} $$

And I need to get the plane $z = 0$. How to do this?

KateCh
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  • There are many such transformations, so you’ll have to narrow your question down with some more criteria. For example, do you want the transformation to be a rigid motion? – amd Aug 18 '17 at 19:21
  • Yes, let it be a rigid motion. – KateCh Aug 18 '17 at 23:34
  • OK. That’s narrows it down to an infinite number. It’s reasonable to assume that the mapping also preserves orientation, but that still leaves an infinite number of possible rotation/translation combinations. – amd Aug 18 '17 at 23:38
  • I need some example of such a mapping. Any example suits me. – KateCh Aug 18 '17 at 23:47
  • Here’s one example, which you could also have found by searching this site. – amd Aug 19 '17 at 00:53

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