githubmirror/omim

geometry/point2d.hpp
316 строк8 KB
Maxim Pimenov
Review fixes.
09 сен 2019, 13:52
09 сен 2019, 13:52d205599
#pragma once

#include "base/assert.hpp"
#include "base/base.hpp"
#include "base/math.hpp"
#include "base/matrix.hpp"

#include <array>
#include <cmath>
#include <functional>
#include <limits>
#include <sstream>
#include <typeinfo>

namespace m2
{
template <typename T>
class Point
{
public:
  using value_type = T;

  T x, y;

  constexpr Point() : x(T()), y(T()) {}

  constexpr Point(T x_, T y_) : x(x_), y(y_) {}

  template <typename U>
  explicit constexpr Point(Point<U> const & u) : x(u.x), y(u.y)
  {
  }

  static Point<T> Zero() { return Point<T>(0, 0); }
  static Point<T> Max() { return Point<T>(std::numeric_limits<T>::max(), std::numeric_limits<T>::max());}

  bool EqualDxDy(Point<T> const & p, T eps) const
  {
    return ((fabs(x - p.x) < eps) && (fabs(y - p.y) < eps));
  }

  T SquaredLength(Point<T> const & p) const { return pow(x - p.x, 2.0) + pow(y - p.y, 2.0); }

  T SquaredLength() const { return x * x + y * y; }

  double Length(Point<T> const & p) const { return std::sqrt(SquaredLength(p)); }

  bool IsAlmostZero() const { return AlmostEqualULPs(*this, Point<T>(0, 0)); }

  Point<T> Move(T len, T ang) const { return Point<T>(x + len * cos(ang), y + len * sin(ang)); }

  Point<T> Move(T len, T angSin, T angCos) const
  {
    return m2::Point<T>(x + len * angCos, y + len * angSin);
  }

  Point<T> const & operator-=(Point<T> const & a)
  {
    x -= a.x;
    y -= a.y;
    return *this;
  }

  Point<T> const & operator+=(Point<T> const & a)
  {
    x += a.x;
    y += a.y;
    return *this;
  }

  template <typename U>
  Point<T> const & operator*=(U const & k)
  {
    x = static_cast<T>(x * k);
    y = static_cast<T>(y * k);
    return *this;
  }

  template <typename U>
  Point<T> const & operator=(Point<U> const & a)
  {
    x = static_cast<T>(a.x);
    y = static_cast<T>(a.y);
    return *this;
  }

  bool operator==(m2::Point<T> const & p) const { return x == p.x && y == p.y; }

  bool operator!=(m2::Point<T> const & p) const { return !(*this == p); }

  m2::Point<T> operator+(m2::Point<T> const & pt) const { return m2::Point<T>(x + pt.x, y + pt.y); }

  m2::Point<T> operator-(m2::Point<T> const & pt) const { return m2::Point<T>(x - pt.x, y - pt.y); }

  m2::Point<T> operator-() const { return m2::Point<T>(-x, -y); }

  m2::Point<T> operator*(T scale) const { return m2::Point<T>(x * scale, y * scale); }

  m2::Point<T> const operator*(math::Matrix<T, 3, 3> const & m) const
  {
    m2::Point<T> res;
    res.x = x * m(0, 0) + y * m(1, 0) + m(2, 0);
    res.y = x * m(0, 1) + y * m(1, 1) + m(2, 1);
    return res;
  }

  m2::Point<T> operator/(T scale) const { return m2::Point<T>(x / scale, y / scale); }

  m2::Point<T> Mid(m2::Point<T> const & p) const
  {
    return m2::Point<T>((x + p.x) * 0.5, (y + p.y) * 0.5);
  }

  /// @name VectorOperationsOnPoint
  double Length() const { return std::sqrt(SquaredLength()); }

  Point<T> Normalize() const
  {
    if (IsAlmostZero())
      return Zero();

    double const length = this->Length();
    return Point<T>(x / length, y / length);
  }

  std::pair<Point<T>, Point<T>> Normals(T prolongationFactor = 1) const
  {
    T const prolongatedX = prolongationFactor * x;
    T const prolongatedY = prolongationFactor * y;
    return std::pair<Point<T>, Point<T>>(
        Point<T>(static_cast<T>(-prolongatedY), static_cast<T>(prolongatedX)),
        Point<T>(static_cast<T>(prolongatedY), static_cast<T>(-prolongatedX)));
  }

  m2::Point<T> const & operator*=(math::Matrix<T, 3, 3> const & m)
  {
    T tempX = x;
    x = tempX * m(0, 0) + y * m(1, 0) + m(2, 0);
    y = tempX * m(0, 1) + y * m(1, 1) + m(2, 1);
    return *this;
  }

  void Rotate(double angle)
  {
    T cosAngle = cos(angle);
    T sinAngle = sin(angle);
    T oldX = x;
    x = cosAngle * oldX - sinAngle * y;
    y = sinAngle * oldX + cosAngle * y;
  }

  // Returns vector rotated 90 degrees counterclockwise.
  Point Ort() const { return Point(-y, x); }

  void Transform(m2::Point<T> const & org, m2::Point<T> const & dx, m2::Point<T> const & dy)
  {
    T oldX = x;
    x = org.x + oldX * dx.x + y * dy.x;
    y = org.y + oldX * dx.y + y * dy.y;
  }

  struct Hash
  {
    size_t operator()(m2::Point<T> const & p) const { return base::Hash(p.x, p.y); }
  };
};

using PointF = Point<float>;
using PointD = Point<double>;
using PointU = Point<uint32_t>;
using PointU64 = Point<uint64_t>;
using PointI = Point<int32_t>;
using PointI64 = Point<int64_t>;

template <typename T>
Point<T> const operator-(Point<T> const & a, Point<T> const & b)
{
  return Point<T>(a.x - b.x, a.y - b.y);
}

template <typename T>
Point<T> const operator+(Point<T> const & a, Point<T> const & b)
{
  return Point<T>(a.x + b.x, a.y + b.y);
}

template <typename T>
T const DotProduct(Point<T> const & a, Point<T> const & b)
{
  return a.x * b.x + a.y * b.y;
}

template <typename T>
T const CrossProduct(Point<T> const & a, Point<T> const & b)
{
  return a.x * b.y - a.y * b.x;
}

template <typename T>
Point<T> const Rotate(Point<T> const & pt, T a)
{
  Point<T> res(pt);
  res.Rotate(a);
  return res;
}

template <typename T, typename U>
Point<T> const Shift(Point<T> const & pt, U const & dx, U const & dy)
{
  return Point<T>(pt.x + dx, pt.y + dy);
}

template <typename T, typename U>
Point<T> const Shift(Point<T> const & pt, Point<U> const & offset)
{
  return Shift(pt, offset.x, offset.y);
}

template <typename T>
Point<T> const Floor(Point<T> const & pt)
{
  Point<T> res;
  res.x = floor(pt.x);
  res.y = floor(pt.y);
  return res;
}

template <typename T>
std::string DebugPrint(m2::Point<T> const & p)
{
  std::ostringstream out;
  out.precision(20);
  out << "m2::Point<" << typeid(T).name() << ">(" << p.x << ", " << p.y << ")";
  return out.str();
}

template <typename T>
bool AlmostEqualAbs(m2::Point<T> const & a, m2::Point<T> const & b, double const eps)
{
  return base::AlmostEqualAbs(a.x, b.x, eps) && base::AlmostEqualAbs(a.y, b.y, eps);
}

template <typename T>
bool AlmostEqualULPs(m2::Point<T> const & a, m2::Point<T> const & b, unsigned int maxULPs = 256)
{
  return base::AlmostEqualULPs(a.x, b.x, maxULPs) && base::AlmostEqualULPs(a.y, b.y, maxULPs);
}

/// Calculate three points of a triangle (p1, p2 and p3) which give an arrow that
/// presents an equilateral triangle with the median
/// starting at point b and having direction b,e.
/// The height of the equilateral triangle is l and the base of the triangle is 2 * w
template <typename T, typename TT, typename PointT = Point<T>>
void GetArrowPoints(PointT const & b, PointT const & e, T w, T l, std::array<Point<TT>, 3> & arr)
{
  ASSERT(!m2::AlmostEqualULPs(b, e), ());

  PointT const beVec = e - b;
  PointT beNormalizedVec = beVec.Normalize();
  std::pair<PointT, PointT> beNormVecs = beNormalizedVec.Normals(w);

  arr[0] = e + beNormVecs.first;
  arr[1] = e + beNormalizedVec * l;
  arr[2] = e + beNormVecs.second;
}

/// Returns a point which is belonged to the segment p1, p2 with respet the indent shiftFromP1 from
/// p1. If shiftFromP1 is more the distance between (p1, p2) it returns p2. If shiftFromP1 is less
/// or equal zero it returns p1.
template <typename T>
Point<T> PointAtSegment(Point<T> const & p1, Point<T> const & p2, T shiftFromP1)
{
  Point<T> p12 = p2 - p1;
  shiftFromP1 = base::Clamp(shiftFromP1, static_cast<T>(0.0), static_cast<T>(p12.Length()));
  return p1 + p12.Normalize() * shiftFromP1;
}

template <class TArchive, class PointT>
TArchive & operator>>(TArchive & ar, m2::Point<PointT> & pt)
{
  ar >> pt.x;
  ar >> pt.y;
  return ar;
}

template <class TArchive, class PointT>
TArchive & operator<<(TArchive & ar, m2::Point<PointT> const & pt)
{
  ar << pt.x;
  ar << pt.y;
  return ar;
}

template <typename T>
bool operator<(Point<T> const & l, Point<T> const & r)
{
  if (l.x != r.x)
    return l.x < r.x;
  return l.y < r.y;
}
}  // namespace m2

namespace base
{
template <typename T>
bool AlmostEqualULPs(m2::Point<T> const & p1, m2::Point<T> const & p2, unsigned int maxULPs = 256)
{
  return m2::AlmostEqualULPs(p1, p2, maxULPs);
}

template <typename T>
bool AlmostEqualAbs(m2::Point<T> const & p1, m2::Point<T> const & p2, double const & eps)
{
  return m2::AlmostEqualAbs(p1, p2, eps);
}
}  // namespace base