Variables after the colon in a constructor [duplicate]

Answer 1

In your example point3 is the constructor of the class with the same name (point3), and the stuff to the right of the colon : before the opening bracket { is the initialization list, which in turn constructs (i.e. initializes) point3's member variables (and can also be used to pass arguments to constructors in the base class[es], if any.)

Answer 2

It's a way of invoking the constructors of members of the point3 class. if x,y, and z are floats, then this is just a more efficient way of writing this

point3( float X, float Y, float Z):
{
   x = X;
   y = Y;
   z = Z;
}

But if x, y & z are classes, then this is the only way to pass parameters into their constructors

Answer 3

Member initialization as others have pointed out. But it is more important to know the following:

When the arguments are of the type float or other built-in types, there's no clear advantages except that using member initialization rather than assignment (in the body of the constructor) is more idiomatic in C++.

The clear advantage is if the arguments are of user-defined classes, this member initialization would result in calls to copy constructors as opposed to default constructors if done using assignments (in the constructor's body).