Efficient way of finding distance between two 3D points

Question

I am writing a code in C++ and want to compute distance between two points. Question 1:

I have two points P(x1, y1, z1) and Q(x2, y2, z2) , where x,

Answer 1

As far as Question 1 goes, the performance penalty is the calculation of the square root itself. The formula for calculating the distance using the square root of paired coordinate differences is what it is.

I would highly recommend to read this A-M-A-Z-I-N-G square root implementation by John Carmack of ID software he used in his engine in Quake III. It is simply MAGICAL.