csv - c++ explore a dataset stored in a std::vector with bilinear interpolation -

i have vector std::vector <int> density; stores set of values imported input.csv file.

the values varying between 0 , 2^16, , ordered on regular grid of int c columns , int l lines.

now, want use bilinear interpolation compute new set of values std::vector <float> d

these new values arranged in regular grid of int x columns , int y lines.

.

my problem:

to perform bilinear interpolation based on squared grid of data have know each position (x,y) local 4 surrounding density values for:

d1 (c,l), d2 (c,l), d3 (c,l), d4 (c,l)

in other words, each interpolated point of d position (dx,dy) - dx , dy being inferior or equal 1 - located within squared "cell" of original dataset defined 4 density values relative position (c,l) original grid.

how can define, arbitrary position (dx,dy) within range of c , l (not outside grid!) 4 surrounding density values d1, d2, d3, d4?

and how can define, within (d1, d2, d3, d4) cell, positions (u,v) defined point d (see code understanding point d) within cell

if please me improve code... :) thanks!

//

to make easier conceptualize, here's example numerical values:

• input.csv

  200; 300; 400

  100; 100; 100

  0; 100; 200

• number of columns: c = 3

• number of lines : l = 3

• after pushing these, vector contains following:

  200, 300, 400, 100, 100, 100, 0, 100, 200

• number of columns of new file: x = 4

• number of lines of new file : y = 4

• the algorithm should following:

for position (dx, dy) = (0, 0)

(u, v) = (0, 0) 

we in 1st cell so

(d1, d2, d3, d4) = (200, 300, 100, 100) 

and since (u, v) = (0, 0)

the density equal d1 = 200

so b = 200

now, pass next xalue of dx > dx = x+1 (returns 1)

• c equal 3, x equal 4, , dx * c / x = 1 * 2 / 3 = 0.666666667 or 2/3

• 2/3 < 1 still in first cell

for position (dx, dy) = (2/3, 0)

(u, v) = (2/3, 0) 

since u > 0 , v = 0 density between d1 , d2

d = u * d2 + (1-u) * d1   (returns 266.666666667) 

lets imagine file output.csv containing 4 col , 4 lines, result, should contain: (spaces here reading...)

200;          266.6666667;  333.3333333;  400 133.3333333;  155.5555556;  177.7777778;  200 66.66666667;  66.88888889;  111.1111111;  133,3333333 0;            66.66666667;  133,3333333;  200 

• input 3 x 3 was:

  200; 300; 400

  100; 100; 100

  0; 100; 200

//

code:

#include <iostream> #include <fstream> #include <vector>  using namespace std;  //_____________________________________________________________________________  int main() {  /// original grid  int c = 0;                  // amount of columns in .csv int l = 0;                  // amount of lines   in .csv int = 0;                  // variable temporarily stores .csv value std::vector <int> density;  // stores dataset .csv  //_____________________________________________________________________________      ifstream ifs ("input.csv");                 // importing .csv      cout << "number of columns?" << endl;       // specifying number of columns     cin  >> c;     cout << endl;     cout << "number of lines?" << endl;         // specifying number of lines     cin  >> l;     cout << endl;       char dummy;          (int = 0; < l; ++i){            // pushing values of .csv vector             (int = 0; < c; ++i){                 ifs >> a;                 density.push_back(a);                      if (i < (c - 1))                         ifs >> dummy;             }  //_______________________________________________________________________________  /// output grid  int x = 0;                  // coordinate x int y = 0;                  // coordiante y int dx = 0;                 // horizontal position  int dy = 0;                 // vertical position int b = 0;                  // interpolated density std::vector <float> d;      // stores interpolated values       cout << "number of columns of new file?" << endl;       // specifying number of columns     cin  >> x;     cout << endl;     cout << "number of lines of new file?" << endl;         // specifying number of lines     cin  >> y;     cout << endl;  }  /// diagram of cell position of: b (u,v)  //__________________________________________________ // //      d1 ---u--- d2 //       |    |     | //       v----b     | //       |          | //      d3 ------- d4 // //__________________________________________________   int d1 = 0;         // densities of 4 points of cell containing (x,y) int d2 = 0; int d3 = 0; int d4 = 0;  float u = 0;        // horizontal , vertical positions of b within cell float v = 0;    //_______________________________________________________________________ /// part missing here: how d1, d2, d3, d4, u, v ??? //_______________________________________________________________________           while (x<c, y<l)    {                                                 // formulae bilinear interpolation         double dl = d1 - d1 * v + d3 * v;       // vertical linear interpolation right side         double dr = d2 - d2 * v + d4 * v;       // vertical linear interpolation left side         double d  = dl - dl * u + dr * u;       // horizontal linear interpolation          d.push_back (b);          x++;                // next interpolation              if (x>c) {                  y = y++;             }         }  }