for loop in Return - function

Question

I'm a beginner in C++ and i have a problem that i dont know how to solve it,
I have an int function that few parameters should be return on it:
int sphere(const float & X,const float & Y,const float & Z,
const int & Px, const int & Py, const int & Pz,
const int & diameterOfSphere, const int & number)
{
return pow(Px-X,2) + pow(Py+(diameterOfSphere * (number - 1))-Y,2)
+ pow(Pz-Z,2) <= pow(diameterOfSphere/2,2);
}
in this function, the integer "number" may should be start from 2 to for example 100. I need to do something that if i choose 100 for "number", the return statement should be repeated 99 times and separated by a plus ( + ).
for example i can do it manually but it is needed to write a lot of codes which is not logical
for example, i did it manually for just three times
return (pow(Px-X,2)+pow((Py+(diameterOfSphere * 2))-Y,2)+pow(Pz-Z,2)
<= pow(diameterOfSphere/2,2))
+ (pow(Px-X,2)+pow((Py+(diameterOfSphere * 3))-Y,2)+pow(Pz-Z,2)
<= pow(diameterOfSphere/2,2))
+ (pow(Px-X,2)+pow((Py+(diameterOfSphere * 4))-Y,2)+pow(Pz-Z,2)
<= pow(diameterOfSphere/2,2))
+ (pow(Px-X,2)+pow((Py+(diameterOfSphere * 5))-Y,2)+pow(Pz-Z,2)
<= pow(diameterOfSphere/2,2)) ;
Is there any easier way? I know i have to use a loop but i dont know how to do it in this case
Thanks a lot

Answer 1

Don't use pow() to do spheres squares, pow() is an exponential function that is quite slow. Break your formula and format your lines to make code readable. Your point's coordinates are integer, is that intentional? This variant is not only more readable, it's more likely to be optimized by compiler:
int sphere(const float & X,const float & Y, const float & Z,
const int & Px, const int & Py, const int & Pz,
const int & diameterOfSphere, const int & number)
{
const float dx = Px - X;
const float dy = Py + diameterOfSphere * (number - 1) - Y;
const float dz = Pz - Z;
const float D = dx*dx + dy*dy + dz*dz;
return D <= 0.25 * diameterOfSphere*diameterOfSphere;
}
Now if I understood you right, you need a recursion or a loop that emulates recursion. You actually can call function from itself, do you know that?
int sphere(const float & X,const float & Y, const float & Z,
const int & Px, const int & Py, const int & Pz,
const int & diameterOfSphere, const int & number)
{
const float dx = Px - X;
const float dy = Py + diameterOfSphere * (number - 1) - Y;
const float dz = Pz - Z;
const float D = dx*dx + dy*dy + dz*dz;
if(!(number>0))
return 0;
return D <= 0.25 * diameterOfSphere*diameterOfSphere
+ sphere(X,Y,Z,Px,Py,Pz,diameterOfSphere, number -1);
}
Negative side of recursion a) each function call fills stack with variables and parameters stored b) there is an extra call that returns immediately.
Py + diameterOfSphere * (number - 1) - Y expression throws me back, is that a mistake? Pretty much it almost never would cause comparison to be true. And it's still not clear what you're trying to do with those comparisons. So, while I modified code so it would be equal to your idea, it looks chaotic\senseless. The >= or <= would return 1 or 0 as result. Or did you mean this?
return ( D <= 0.25 * diameterOfSphere*diameterOfSphere )
+ sphere(X,Y,Z,Px,Py,Pz,diameterOfSphere, number -1);