Compare doubles in c++

Question

I want to determine whether a point is inside a circle or not. So I do this :

(x - center_x)^2 + (y - center_y)^2 < radius^2

But my coordinates are double and I think I should do it with epsilon, so is fabs ((x - center_x)^2 + (y - center_y)^2 - radius^2 ) < EPS better?

related: http://stackoverflow.com/questions/17333/most-effective-way-for-float-and-double-comparison — NathanOliver, Jun 28 '16 at 14:20
You seem to be under the impression that `^2` raises something to the second power. That's not the case. In C++ `^` is "bitwise XOR" - http://en.cppreference.com/w/cpp/language/operator_arithmetic#Bitwise_logic_operators — Jesper Juhl, Jun 28 '16 at 14:36

score 5 · Accepted Answer · answered Jun 28 '16 at 14:21

5

You don't need the epsilon when you're comparing using < or >, those are perfectly fine. You need it instead of ==. In your case, you've just added a small amount to radius, which is probably undesirable. Also note that ^ is not the same as pow(a, b).

answered Jun 28 '16 at 14:21

lorro

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Thank you, I knew that I should use `EPS` with `==` but always been wondering about `<` and `>`. This made it clear to me! P.S I know I can't use `^` as pow :P – Gigata Jun 28 '16 at 14:26
either case is better to do `x*x + y*y` than `pow(x, 2) + pow(y, 2)`, which only does a multiplation avoiding complex logarithm calculations. – Luis Colorado Jun 30 '16 at 06:27

score 4 · Answer 2 · answered Jun 28 '16 at 14:20

4

You cannot use '^' in C++ for this purpose. Instead of (x - center_x)^2 + (y - center_y)^2 < radius^2 do (x - center_x)*(x - center_x) + (y - center_y)*(y - center_y) < radius*radius. It is no problem for the coordinates to be double.

answered Jun 28 '16 at 14:20

Shiro

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I really do not think this is code but the formula the OP is using. – NathanOliver Jun 28 '16 at 14:21
@NathanOliver, either case, SO rules recommend to post full testable code, so Shiro is right assuming the OP is trying to use the formula he posts. – Luis Colorado Jun 30 '16 at 06:29

eerorika · Answer 3 · 2016-06-28T14:32:12.483

It depends.

Naiive ordered inequality comparison is usually most appropriate for testing whether a floating point value is on one side of a threshold.

Due to floating point errors, a result that should be on one side of the threshold may end up on the other side. If it is important to guarantee no false negatives, while increasing the chance of false positives, then your suggested alternative may be appropriate.

Note that constant epsilon based error compensation is not effective when the input values vary in magnitude.

score 4 · Answer 4 · answered Jun 28 '16 at 14:28

No. As others mentioned, the operator ^ in C is bitwise exclusive or, not power. But you could use an inline function:

inline double Sqr(double x) {return x*x;}
// ...
if (Sqr(x - center_x) + Sqr(y - center_y) < Sqr(radius)) // ...

As for your question,

fabs (Sqr(x - center_x) + Sqr(y - center_y) - Sqr(radius) ) < EPS

means that (x,y) is at the circumference of the circle.

Compare doubles in c++

4 Answers4