ALL_Point.hpp

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/*
Copyright 2018-2020 Rene Halver, Forschungszentrum Juelich GmbH, Germany
Copyright 2018-2020 Godehard Sutmann, Forschungszentrum Juelich GmbH, Germany
 
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
 
1. Redistributions of source code must retain the above copyright notice, this
   list of conditions and the following disclaimer.
 
2. Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation and/or
   other materials provided with the distribution.
 
3. Neither the name of the copyright holder nor the names of its contributors
may be used to endorse or promote products derived from this software without
   specific prior written permission.
 
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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*/
 
#ifndef ALL_POINT_HEADER_INC
#define ALL_POINT_HEADER_INC
 
#include "ALL_CustomExceptions.hpp"
#include <algorithm>
#include <cmath>
#include <iostream>
#include <stdexcept>
#include <vector>
 
namespace ALL {
 
template <class T> class Point;
template <typename T>
std::ostream &operator<<(std::ostream &, const Point<T> &);

template <class T> class Point {
public:
  Point() : dimension(0) {}
  Point(const int d) : dimension(d) {
    coordinates.resize(d);
    weight = (T)1;
  }

  Point(const int d, const T *data) : Point<T>(d) {
    // copy each element of the array into the vector (insecure, no boundary
    // checks for data!)
    for (auto i = 0; i < d; ++i)
      coordinates.at(i) = data[i];
  }

  Point(const std::vector<T> &data) {
    // initialize the coordinates vector with the data vector
    coordinates.insert(coordinates.begin(), data.begin(), data.end());
    // update the dimension with the size of the data vector
    dimension = data.size();
  }

  Point(const int d, const T *data, const T w) : Point<T>(d, data) {
    weight = w;
  }

  Point(const int d, const T *data, const T w, const long i)
      : Point<T>(d, data, w) {
    id = i;
  }

  Point(const std::vector<T> &data, const T w) : Point<T>(data) {
    weight = w;
  }

  Point(const std::vector<T> &data, const T w, const long i)
      : Point<T>(data, w) {
    id = i;
  }

  ~Point(){};
 
  // TODO: return values to check if operation was successful?
  void setDimension(const int d) {
    dimension = d;
    coordinates.resize(d);
  }

  void set_weight(const T w) { weight = w; }

  void set_id(const long i) { id = i; }

  T &operator[](const std::size_t idx) { return coordinates.at(idx); }

  const T &operator[](const std::size_t idx) const {
    return coordinates.at(idx);
  }

  T getWeight() const { return weight; }

  long get_id() const { return id; }

  int getDimension() const { return dimension; }

  T norm(T nd = 2) {
    T res = 0;
    for (int d = 0; d < dimension; ++d)
      res += std::pow(coordinates.at(d), nd);
    return std::pow(res, 1.0 / nd);
  }

  T d(Point<T> p) {
    int d_p = p.getDimension();
    if (d_p != dimension)
      throw PointDimensionMissmatchException(__FILE__, __func__, __LINE__);
    return dist(p).norm();
  }

  T d_1(Point<T> p) {
    int d_p = p.getDimension();
    if (d_p != dimension)
      throw PointDimensionMissmatchException(__FILE__, __func__, __LINE__);
    return dist(p, 1).norm();
  }

  Point<T> dist(Point<T> &p) {
    int d_p = p.getDimension();
    if (d_p != dimension)
      throw PointDimensionMissmatchException(__FILE__, __func__, __LINE__);
    std::vector<T> d_v;
    for (int d = 0; d < dimension; ++d)
      d_v.push_back(p[d] - coordinates.at(d));
 
    return Point<T>(d_v);
  }

  T dist_plane(const Point<T> &A, const Point<T> &B,
               const Point<T> &C) {
 
    if (A.getDimension() != dimension || B.getDimension() != dimension ||
        C.getDimension() != dimension)
      throw PointDimensionMissmatchException(__FILE__, __func__, __LINE__);
 
    // vectors spanning the plane from vertex 'a'
    Point<T> vb = B - A;
    Point<T> vc = C - A;
 
    // normal vector of plane
    Point<T> n = vb.cross(vc);
    n = n/n.norm();
 
    // return r.n - A.n = (r-A).n as distance from plane to r
    return std::abs( (coordinates.at(0) - A[0]) * n[0] +
         (coordinates.at(1) - A[1]) * n[1] +
         (coordinates.at(2) - A[2]) * n[2] );
  }

  Point<T> operator+(const Point<T> &rhs) const {
    if (rhs.getDimension() != dimension) {
      throw PointDimensionMissmatchException(__FILE__, __func__, __LINE__);
    }
    Point<T> result(dimension);
    for (int d = 0; d < dimension; ++d) {
      result[d] = coordinates.at(d) + rhs[d];
    }
    return result;
  }

  Point<T> operator-(const Point<T> &rhs) const {
    if (rhs.getDimension() != dimension) {
      throw PointDimensionMissmatchException(__FILE__, __func__, __LINE__);
    }
    Point<T> result(dimension);
    for (int d = 0; d < dimension; ++d) {
      result[d] = coordinates.at(d) - rhs[d];
    }
    return result;
  }

  T operator*(const Point<T> &rhs) const {
    if (rhs.getDimension() != dimension) {
      throw PointDimensionMissmatchException(__FILE__, __func__, __LINE__);
    }
    T result = (T)0.0;
    for (int d = 0; d < dimension; ++d) {
      result += coordinates.at(d) * rhs[d];
    }
    return result;
  }

  Point<T> operator*(const T &rhs) const {
    Point<T> result(dimension);
    for (int d = 0; d < dimension; ++d) {
      result[d] = coordinates.at(d) * rhs;
    }
    return result;
  }

  Point<T> operator/(const T &rhs) const {
    Point<T> result(dimension);
    for (int d = 0; d < dimension; ++d) {
      result[d] = coordinates.at(d) / rhs;
    }
    return result;
  }

  Point<T> cross(const Point<T> &rhs) const {
    if (rhs.getDimension() != dimension && dimension != 3) {
      throw PointDimensionMissmatchException(__FILE__, __func__, __LINE__);
    }
    Point<T> result(dimension);
    for (int d = 0; d < dimension; ++d) {
      result[d] = coordinates.at((d + 1) % 3) * rhs[(d + 2) % 3] -
                  coordinates.at((d + 2) % 3) * rhs[(d + 1) % 3];
    }
    return result;
  }

  bool same_side_plane(const Point<T> &A, const Point<T> &B,
                       const Point<T> &C, const Point<T> &P) {
    // compute difference vectors:
    Point<T> BA = B - A;
    Point<T> CA = C - A;
    Point<T> PA = P - A;
    Point<T> tA = *(this) - A;
 
    // compute normal vector of plane
    Point<T> n = CA.cross(BA);
 
    // compute scalar product of distance
    // vectors with normal vector
    T PAn = PA * n;
    T tAn = tA * n;
 
    return ((PAn * tAn) > 0);
  }

  bool inTetrahedron(const Point<T> &A, const Point<T> &B,
                     const Point<T> &C, const Point<T> &D) {
    return (same_side_plane(A, B, C, D) && same_side_plane(B, C, D, A) &&
            same_side_plane(C, D, A, B) && same_side_plane(A, D, B, C));
  };
 
private:
  int dimension;
  long id;
  // array containg the coordinates
  std::vector<T> coordinates;
  T weight;
};

template <class T>
std::ostream &operator<<(std::ostream &os, const Point<T> &p) {
  for (int i = 0; i < p.getDimension(); ++i)
    os << p[i] << " ";
  os << p.getWeight();
  return os;
}

template <class T>
Point<T> operator*(const T &lhs, const Point<T> &rhs) {
  return rhs * lhs;
}
 
// template <class T>
// Point<T> operator/(const T &lhs, const Point<T> &rhs) {
//   return rhs * ((T)1 / lhs);
// }
 
}//namespace ALL
 
#endif