Float--Double

Testing equality with float or double is always a bad idea because of rounding errors, so don't use them as a hash. Never.

For it's floating point arithmetic, Java uses a subset of IEEE754. IEEE754 is full of beautiful tricks to mimic the behavior of real numbers and do a wonderful job at it, so sometimes we forget that is has limitations. The main troubles are (in no specific order):

there is a gap between 0.0 and the next value (so non-zero numbers can be rounded to 0 if they are in this gap)
there are special values for +infinity and -infinity (so there is no overflow, but you can get "stuck" on an infinite value. Imagine a*b evaluates to infinity, then a*b/bwill also evaluate to infinity and not to à`)
there is a special value NaN that means not a number. (0.0 / 0.0 evaluates to NaN)
there are signed zeroes (+0.0 and -0.0) Signed zeroes are usually not that painful (-0.0 == +0.0 for the primitive types double and float but not for their object wrappers Double and Float)
To come back to your question, using Double as a key in the map is a terrible idea because of rounding problems. You do not need to use Math.PI for infinity since Double.POSITIVE_INFINITY is a legitimate value. Be careful though, you don't want to have positive and negative infinity mixed up. Look at the previous questions, the trick here is to represent a line by an equation ax+by+c=0 with a,b, and c of type int.

As a final note, I think it is important to know the limitations of the encoding you are using (overflow for int, signed zeroes, infinity, and NaN of floating point numbers, surrogate pair for UTF-16…)