// sailors_area.java     compile    javac -cp . sailors_area.java
//                       execute    java  -cp . sailors_area
// poly_area1 for 2 dimensional, n points of a closed polygon
//           each point  x,y   last point goes to first point all stuff
// poly_area for 2 dimensional, n points of a closed polygon
//           each point  x,y   last point goes to first point optimized
//
// area 0f volume 3 dimensional, n points for each enclosing surface of volume
//           each point  x,y,z  size of array/n is number of surface
// volume of 3 dimensional object, n points for each enclosing area
//           each point  x,y,z  size of array/n is number of surface
// 4D volume for 4 dimensional,
//

public class sailors_area
{
  public sailors_area()
  {
     double tri[][] = {{3.0,1.0},{1.0,1.0},{1.0,3.0}};
     double pa4[][] = {{0.0, -1.0},
                      {1.0, 0.0},
                      {0.0, 1.0},
                      {-1.0, 0.0}};

    double pa[][] = {{2.0, 3.0},
                     {4.0, 3.0},
                     {4.0, 1.0},
                     {5.0, 1.0},
                     {5.0, 4.0},
                     {1.0, 4.0},
                     {1.0, 1.0},
                     {3.0, 1.0},
                     {3.0, 2.0},
                     {2.0, 2.0}};

    double pastar[][] = {{0.00000, 5.00000},  // star
                         {1.12257, 1.54508},
                         {4.75528, 1.54508},
                         {1.81636, -0.59017},
                         {2.93893, -4.04508},
                         {-0.00000, -1.90983}, 
                         {-2.93893, -4.04508},
                         {-1.81636, -0.59017},
                         {-4.75528, 1.54508},
                         {-1.12257, 1.54508}};

    double area = 0.0;
    
    System.out.println("sailors_area.java running");
    System.out.println("test poly_area1 tri");
    area = poly_area1(3, tri);
    System.out.println("poly_area1(3,tri)="+area);
    System.out.println(" ");
    System.out.println(" ");
    System.out.println("test poly_area1 pa4");
    area = poly_area1(4, pa4);
    System.out.println("poly_area1(4,pa4)="+area);
    System.out.println(" ");
    System.out.println(" ");
    System.out.println("test poly_area1 pa");
    area = poly_area1(10, pa);
    System.out.println("poly_area1(10,pa)="+area);
    System.out.println(" ");
    System.out.println(" ");
    System.out.println("test poly_area1 pastar");
    area = poly_area1(10, pastar);
    System.out.println("poly_area1(10,pastar)="+area);
    System.out.println(" ");
    System.out.println(" ");
    
    System.out.println("test poly_area tri");
    area = poly_area(3, tri);
    System.out.println("poly_area(3,tri)="+area);
    System.out.println(" ");
    System.out.println(" ");
    System.out.println("test poly_area pa4");
    area = poly_area(4, pa4);
    System.out.println("poly_area(4,pa4)="+area);
    System.out.println(" ");
    System.out.println(" ");
    System.out.println("test poly_area pa");
    area = poly_area(10, pa);
    System.out.println("poly_area(10,pa)="+area);
    System.out.println(" ");
    System.out.println(" ");
    System.out.println("test poly_area pastar");
    area = poly_area(10, pastar);
    System.out.println("poly_area(10,pastar)="+area);
    System.out.println(" ");
    System.out.println(" ");
    
    System.out.println("test area of 3D volume");

    System.out.println("test 3D object volume");

    System.out.println("test 4D object area");

    System.out.println("test 4D object 3D volume");

    System.out.println("test 4D object 4D volume");

  } // end sailors_area

  double poly_area1(int n, double pa0[][])
  {
    double area = 0.0;
    double maxarea = 0.0;
    int k, len1, len2;
    // poly_area.c  compute area of a closed polygon
    //              sailors algorithm
    //              sum signed areas of trapezoids
    double x1, y1, x2, y2;  // read points
    double x0=0.0, y0=0.0;  // first point for close
    double dx; // difference x2-x1
    double da;
    double pa[][] = new double[pa0.length][pa0[0].length];
    double xmin, xmax, ymin, ymax;

    System.out.println("poly_area1 len="+n);
    len1 = pa.length;
    len2 = pa[0].length;
    System.out.println("size pa["+len1+"]["+len2+"]");
    xmin = pa0[0][0];
    xmax = xmin;
    ymin = pa0[0][1];
    ymax = ymin;
    for(int i=0; i<len1; i++)
    {
      for(int j=0; j<len2; j++)
      {
	pa[i][j] = pa0[i][j];
	if(j==0)
	{
	  xmin = Math.min(xmin, pa[i][j]);
	  xmax = Math.max(xmax, pa[i][j]);
        }
	if(j==1)
	{
	  ymin = Math.min(ymin, pa[i][j]);
	  ymax = Math.max(ymax, pa[i][j]);
	}
      }
    }
    System.out.println("xmin="+xmin+", xmax="+xmax); 
    System.out.println("ymin="+ymin+", ymax="+ymax);
    maxarea = (xmax-xmin)*(ymax-ymin);
    System.out.println("maxarea="+maxarea);
    
    // read data, closed polygon, last point is first point */
    x1 = pa[0][0];
    y1 = pa[0][1];
    y1 = y1-ymin; // y's must be zero or positive
    x0 = x1;
    y0 = y1;
    k = 0;
    while(k<n-1)
    {
      k++;
      x2 = pa[k][0];
      y2 = pa[k][1];
      System.out.println("data x1="+x1+", y1="+y1);
      System.out.println("data x2="+x2+", y2="+y2);
      y2 = y2 - ymin; // y's must be zero or positive 
      // compute area
      dx = x2-x1; // determines sign of da
      da = dx*(y1+y2)/2.0; // area of trapezoid 
      area = area + da;
      System.out.println("dx="+dx+", da="+da+", area="+area);
      x1 = x2;
      y1 = y2;
    } // end while, close
    x2 = x0;
    y2 = y0;
    // compute area
    System.out.println("data x1="+x1+", y1="+y1);
    System.out.println("data x2="+x2+", y2="+y2);
    dx = x2-x1; // determines sign of da
    da = dx*(y1+y2)/2.0; // area of trapezoid 
    area = area + da;
    System.out.println("dx="+dx+", da="+da+", area="+area);    
    System.out.println(" ");
    return Math.abs(area);
  } // end poly_area1

  double poly_area(int len, double pa[][]) // optimized
  {
    Boolean debug = true;
    double area = 0.0;
    int k;
    // compute area of a closed polygon, no segments may cross
    // sum signed areas of trapezoids, y made positive if ymax<0
    double x1, y1, x2, y2;  // read points
    double x0=0.0, y0=0.0;  // first point for close
    double dx; // difference x2-x1
    double da;
    double ymin;

    ymin = pa[0][1];
    for(int i=1; i<len; i++)
    {
      ymin = Math.min(ymin, pa[i][1]);
    }
    if(debug) System.out.println("ymin="+ymin);
    x1 = pa[0][0];
    y1 = pa[0][1];
    if(ymin<0.0) {y1 = y1-ymin;} // y's must be zero or positive
    x0 = x1;
    y0 = y1;
    k = 0;
    while(k<len-1) // not first or last
    {
      k++;
      x2 = pa[k][0];
      y2 = pa[k][1];
      if(debug) System.out.println("data x1="+x1+", y1="+y1);
      if(debug) System.out.println("data x2="+x2+", y2="+y2);
      if(ymin<0.0) {y2 = y2 - ymin;} // y's must be zero or positive 
      // compute area
      dx = x2-x1; // determines sign of da
      da = dx*(y1+y2)/2.0; // area of trapezoid 
      area = area + da;
      if(debug) System.out.println("dx="+dx+", da="+da+", area="+area);
      x1 = x2;
      y1 = y2;
    } // end while, close
    x2 = x0;
    y2 = y0;
    // compute area
    if(debug) System.out.println("data x1="+x1+", y1="+y1);
    if(debug) System.out.println("data x2="+x2+", y2="+y2);
    dx = x2-x1; // determines sign of da
    da = dx*(y1+y2)/2.0; // area of trapezoid 
    area = area + da;
    if(debug) System.out.println("dx="+dx+", da="+da+", area="+area);    
    return Math.abs(area);
  } // end poly_area optimized
    

  double volume_area(int n, double pv[])
  {
    double area = 0.0;
    return area;
  } // end volume_area

  double volume(int n, double pv[])
  {
    double volume = 0.0;
    return volume;
  } // end volume

  double object4D_area(int n, double pv4[])
  {
    double area = 0.0;
    return area;
  } // end object4D_area

  double object4D_volume3(int n, double pv4[])
  {
    double volume3 = 0.0;
    return volume3;
  } // end object4D_volume3

  double object4D_volume(int n, double pv4[])
  {
    double volume = 0.0;
    return volume;
  } // end object4D_volume
    
  public static void main (String[] args)
  {
    new sailors_area();
  }
} // end sailors_area.java