Point.h

/*
 * A point with x-y coordinates.
 */

#ifndef POINT_H_
#define POINT_H_

#include <cmath>

struct Point {
  float x, y;
  Point operator-(Point &p);
  Point operator+(Point &p);
  Point operator*(double k);
  bool operator==(const Point &other) const;

  bool operator<(const Point &other) const;

  static Point getUnitVector(Point vector) {
    double length = getLengthOfVector(vector);
    return {vector.x / (float)length, vector.y / (float)length};
  }

  static double getDistanceBetweenPoints(Point point1, Point point2) {
    double diffX = point1.x - point2.x;
    double diffY = point1.y - point2.y;
    return sqrt(diffX * diffX + diffY * diffY);
  }

  static double getDotProductOfVectors(Point point1, Point point2) {
    return point1.x * point2.x + point1.y * point2.y;
  }

  static Point getPerPendicularVector(Point vector) {
    return {-vector.y, vector.x};
  }

  static double getLengthOfVector(Point vector) {
    return sqrt(vector.x * vector.x + vector.y * vector.y);
  }

  /**
   * Discouraged, acos() function is slow.
   */
  static double getAngleBetweenVectors(Point vector1, Point vector2) {
    double dotProd = Point::getDotProductOfVectors(vector1, vector2);
    double lengthProduct =
        Point::getLengthOfVector(vector1) * Point::getLengthOfVector(vector2);
    return acos(dotProd / lengthProduct);
  }

  static double getCosineOfAngleBetweenVectors(Point vector1, Point vector2) {
    double dotProd = Point::getDotProductOfVectors(vector1, vector2);
    double lengthProduct =
        Point::getLengthOfVector(vector1) * Point::getLengthOfVector(vector2);
    return dotProd / lengthProduct;
  }

  static double getSlopeOfPoints(Point point1, Point point2) {
    return (point2.y - point1.y) / (point1.x - point2.x);
  }
};

struct PointHasher {
  std::size_t operator()(const Point &p) const;
};

#endif /* POINT_H_ */