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Algoritmo cuadrado de diamante

Question

Estoy intentando escribir el algoritmo Diamond-Square en Java para generar un mapa aleatorio pero no puedo entender la implementación ...

¡Cualquier persona con algún código Java (u otro idioma) para que pueda verificar cómo se hace el bucle sería muy apreciado!

¡Gracias!

Answer 1

Echa un vistazo a esta demostración hecha con Processing :

http://www.intelegance.net/code/diamondsquare.shtml

Además, aquí hay otra página con algo escrito:

http://www.javaworld.com/javaworld/jw-08-1998/jw-08-step.html?page=2

Por último, un papel un poco más formal:

http://www.student.math.uwaterloo.ca/~pmat370/PROJECTS/2006/Keith_Stanger_Fractal_Landscapes.pdf

¡Disfrutar!

Answer 2

Este es un interesante algoritmo para generar valores. Aquí hay una implementación que he creado basada en la explicación dada en esta página en las referencias del artículo de wikipedia . Creará "valores esféricos" (envueltos en todos los bordes). Hay notas en los comentarios sobre cómo cambiarlo para generar nuevos valores en los bordes en lugar de ajuste (aunque el significado de promedio para los bordes no es realmente correcto en estos casos).

//size of grid to generate, note this must be a
//value 2^n+1
final int DATA_SIZE = 9;
//an initial seed value for the corners of the data
final double SEED = 1000.0;
double[][] data = new double[DATA_SIZE][DATA_SIZE];
//seed the data
data[0][0] = data[0][DATA_SIZE-1] = data[DATA_SIZE-1][0] = 
  data[DATA_SIZE-1][DATA_SIZE-1] = SEED;

double h = 500.0;//the range (-h -> +h) for the average offset
Random r = new Random();//for the new value in range of h
//side length is distance of a single square side
//or distance of diagonal in diamond
for(int sideLength = DATA_SIZE-1;
    //side length must be >= 2 so we always have
    //a new value (if its 1 we overwrite existing values
    //on the last iteration)
    sideLength >= 2;
    //each iteration we are looking at smaller squares
    //diamonds, and we decrease the variation of the offset
    sideLength /=2, h/= 2.0){
  //half the length of the side of a square
  //or distance from diamond center to one corner
  //(just to make calcs below a little clearer)
  int halfSide = sideLength/2;

  //generate the new square values
  for(int x=0;x<DATA_SIZE-1;x+=sideLength){
    for(int y=0;y<DATA_SIZE-1;y+=sideLength){
      //x, y is upper left corner of square
      //calculate average of existing corners
      double avg = data[x][y] + //top left
      data[x+sideLength][y] +//top right
      data[x][y+sideLength] + //lower left
      data[x+sideLength][y+sideLength];//lower right
      avg /= 4.0;

      //center is average plus random offset
      data[x+halfSide][y+halfSide] = 
    //We calculate random value in range of 2h
    //and then subtract h so the end value is
    //in the range (-h, +h)
    avg + (r.nextDouble()*2*h) - h;
    }
  }

  //generate the diamond values
  //since the diamonds are staggered we only move x
  //by half side
  //NOTE: if the data shouldn''t wrap then x < DATA_SIZE
  //to generate the far edge values
  for(int x=0;x<DATA_SIZE-1;x+=halfSide){
    //and y is x offset by half a side, but moved by
    //the full side length
    //NOTE: if the data shouldn''t wrap then y < DATA_SIZE
    //to generate the far edge values
    for(int y=(x+halfSide)%sideLength;y<DATA_SIZE-1;y+=sideLength){
      //x, y is center of diamond
      //note we must use mod  and add DATA_SIZE for subtraction 
      //so that we can wrap around the array to find the corners
      double avg = 
        data[(x-halfSide+DATA_SIZE)%DATA_SIZE][y] + //left of center
        data[(x+halfSide)%DATA_SIZE][y] + //right of center
        data[x][(y+halfSide)%DATA_SIZE] + //below center
        data[x][(y-halfSide+DATA_SIZE)%DATA_SIZE]; //above center
      avg /= 4.0;

      //new value = average plus random offset
      //We calculate random value in range of 2h
      //and then subtract h so the end value is
      //in the range (-h, +h)
      avg = avg + (r.nextDouble()*2*h) - h;
      //update value for center of diamond
      data[x][y] = avg;

      //wrap values on the edges, remove
      //this and adjust loop condition above
      //for non-wrapping values.
      if(x == 0)  data[DATA_SIZE-1][y] = avg;
      if(y == 0)  data[x][DATA_SIZE-1] = avg;
    }
  }
}

//print out the data
for(double[] row : data){
  for(double d : row){
    System.out.printf("%8.3f ", d);
  }
  System.out.println();
}

Answer 3

La respuesta de M. Jessup parece estar un poco molesta. Donde tenia

      double avg =         data[(x-halfSide+DATA_SIZE)%DATA_SIZE][y] + //left of center         data[(x+halfSide)%DATA_SIZE][y] + //right of center         data[x][(y+halfSide)%DATA_SIZE] + //below center         data[x][(y-halfSide+DATA_SIZE)%DATA_SIZE]; //above center

En su lugar debería leer:

      double avg =         data[(x-halfSide+DATA_SIZE-1)%(DATA_SIZE-1)][y] + //left of center         data[(x+halfSide)%(DATA_SIZE-1)][y] + //right of center         data[x][(y+halfSide)%(DATA_SIZE-1)] + //below center         data[x][(y-halfSide+DATA_SIZE-1)%(DATA_SIZE-1)]; //above center

De lo contrario, se lee desde ubicaciones equivocadas (que pueden estar sin inicializar).

Answer 4

Para cualquiera que busque, aquí está el algoritmo proporcionado por M. Jessup envuelto en una clase que toma una semilla (para permitir la reproducción de los resultados), un valor para n para especificar dimensiones (las dimensiones son 2 ^ n + 1), y expone el resultados como una serie normalizada de flotadores. También tiene la solución para la segunda parte del algoritmo aplicado.

import java.util.Random;

public class DiamondSquare {

public float[][] data;
public int width;
public int height;

public DiamondSquare(long mseed, int n) {
    //size of grid to generate, note this must be a
    //value 2^n+1
    int DATA_SIZE = (1 << n) + 1;
    width = DATA_SIZE;
    height = DATA_SIZE;
    //an initial seed value for the corners of the data
    final float SEED = 1000.0f;
    data = new float[DATA_SIZE][DATA_SIZE];
    //seed the data
    data[0][0] = data[0][DATA_SIZE-1] = data[DATA_SIZE-1][0] = 
            data[DATA_SIZE-1][DATA_SIZE-1] = SEED;

    float valmin = Float.MAX_VALUE;
    float valmax = Float.MIN_VALUE;

    float h = 500.0f;//the range (-h -> +h) for the average offset
    Random r = new Random(mseed);//for the new value in range of h
    //side length is distance of a single square side
    //or distance of diagonal in diamond
    for(int sideLength = DATA_SIZE-1;
            //side length must be >= 2 so we always have
            //a new value (if its 1 we overwrite existing values
            //on the last iteration)
            sideLength >= 2;
            //each iteration we are looking at smaller squares
            //diamonds, and we decrease the variation of the offset
            sideLength /=2, h/= 2.0){
        //half the length of the side of a square
        //or distance from diamond center to one corner
        //(just to make calcs below a little clearer)
        int halfSide = sideLength/2;

        //generate the new square values
        for(int x=0;x<DATA_SIZE-1;x+=sideLength){
            for(int y=0;y<DATA_SIZE-1;y+=sideLength){
                //x, y is upper left corner of square
                //calculate average of existing corners
                float avg = data[x][y] + //top left
                        data[x+sideLength][y] +//top right
                        data[x][y+sideLength] + //lower left
                        data[x+sideLength][y+sideLength];//lower right
                avg /= 4.0;

                //center is average plus random offset
                data[x+halfSide][y+halfSide] = 
                        //We calculate random value in range of 2h
                        //and then subtract h so the end value is
                        //in the range (-h, +h)
                        avg + (r.nextFloat()*2*h) - h;

                valmax = Math.max(valmax, data[x+halfSide][y+halfSide]);
                valmin = Math.min(valmin, data[x+halfSide][y+halfSide]);
            }
        }

        //generate the diamond values
        //since the diamonds are staggered we only move x
        //by half side
        //NOTE: if the data shouldn''t wrap then x < DATA_SIZE
        //to generate the far edge values
        for(int x=0;x<DATA_SIZE-1;x+=halfSide){
            //and y is x offset by half a side, but moved by
            //the full side length
            //NOTE: if the data shouldn''t wrap then y < DATA_SIZE
            //to generate the far edge values
            for(int y=(x+halfSide)%sideLength;y<DATA_SIZE-1;y+=sideLength){
                //x, y is center of diamond
                //note we must use mod  and add DATA_SIZE for subtraction 
                //so that we can wrap around the array to find the corners
                float avg = 
                        data[(x-halfSide+DATA_SIZE-1)%(DATA_SIZE-1)][y] + //left of center
                        data[(x+halfSide)%(DATA_SIZE-1)][y] + //right of center
                        data[x][(y+halfSide)%(DATA_SIZE-1)] + //below center
                        data[x][(y-halfSide+DATA_SIZE-1)%(DATA_SIZE-1)]; //above center
                avg /= 4.0;

                //new value = average plus random offset
                //We calculate random value in range of 2h
                //and then subtract h so the end value is
                //in the range (-h, +h)
                avg = avg + (r.nextFloat()*2*h) - h;
                //update value for center of diamond
                data[x][y] = avg;

                valmax = Math.max(valmax, avg);
                valmin = Math.min(valmin, avg);


                //wrap values on the edges, remove
                //this and adjust loop condition above
                //for non-wrapping values.
                if(x == 0)  data[DATA_SIZE-1][y] = avg;
                if(y == 0)  data[x][DATA_SIZE-1] = avg;
            }
        }
    }


    for(int i=0; i<width; i++) {
        for(int j=0; j<height; j++) { 
            data[i][j] = (data[i][j] - valmin) / (valmax - valmin); 
        } 
    }

}
}