Postponing an sqrt computation when comparing distances

In this example, we will show you how to use a proxy object in order to postpone, or even avoid, using the computationally heavy std::sqrt() method when comparing the distance between two dimensional points.

A simple two-dimensional point class

Let's start with a simple point class in 2D. It has x and y coordinates and a member function, which calculates the distance to another point:

class Point{
public:
  Point(float x, float y) : x_{x}, y_{y} {}
  auto distance(const Point& p) const {
    auto dist_sqrd = std::pow(x_-p.x_, 2) + std::pow(y_-p.y_, 2)
    return std::sqrt(dist_sqrd);
  }
private:
  float x_{};
  float y_{};
};

A simple usage example would be as follows:

auto target = Point{3, 5}; auto a = Point{6, 9}; auto b = Point{7, 4}; auto nearest_target = target.distance(a) < target.distance(b) ? a : b; auto a_to_b_distance = a.distance(b);

Distances from two arbitrary points to target...