// Icos.java  Copyright 1998 David J. Anderson

// computes the chord lengths for an n-frequency icosahedral geodesic patch

// to compile:  javac Icos.java

// to execute:  java Icos n s
//   where n is the frequency and s is the length of a side of the icosahedron
//   outputs an html document containing the vertex and chord information

import java.lang.Math;
import java.util.Hashtable;

class Rounding
{
  public static String toString (double d, int place)
  {
    if (place <= 0)
      return ""+(int)d;
    String s = "";
    if (d < 0)
      {
	s += "-";
	d = -d;
      }
    d += 0.5*Math.pow(10,-place);
    if (d > 1)
      {
	int i = (int)d;
	s += i;
	d -= i;
      }
    else
      s += "0";
    if (d > 0)
      {
	d += 1.0;
	String f = ""+(int)(d*Math.pow(10,place));
	s += "."+f.substring(1);
      }
    return s;
  }
}

class SPoint  // Spherical coordinate point
{
  public double radius;
  public double theta;
  public double phi;

  public SPoint (double radius, double theta, double phi)
  {
    this.radius = radius;
    this.theta = theta;
    this.phi = phi;
  }

  public CPoint cPoint ()
  {
    double x;
    double y;
    double z;
    x = radius*Math.cos(theta)*Math.sin(phi);
    y = radius*Math.sin(theta)*Math.sin(phi);
    z = radius*Math.cos(phi);
    return new CPoint(x,y,z);
  }
}

class CPoint  // Cartesian coordinate point
{
  public double x;
  public double y;
  public double z;

  public CPoint (double x, double y, double z)
  {
    this.x = x;
    this.y = y;
    this.z = z;
  }

  public double distanceTo (CPoint cPoint)
  {
    double xdiff = cPoint.x-x;
    double ydiff = cPoint.y-y;
    double zdiff = cPoint.z-z;
    return Math.sqrt((xdiff*xdiff)+(ydiff*ydiff)+(zdiff*zdiff));
  }

  public SPoint sPoint ()
  {
    double radius;
    double theta;
    double phi;
    radius = distanceTo(Icos.origin);
    theta = (x == 0.0)? 0.0 : Math.atan2(y,x);
    phi = Math.acos(z/radius);
    return new SPoint(radius,theta,phi);
  }
}

public class Icos  // the icosahedron chord determiner
{
  private int n;
  private double s;
  private double d;
  private Hashtable cPoints = new Hashtable();

  public static final CPoint origin = new CPoint(0.0,0.0,0.0);

  public Icos (int n, double s)
  {
    this.n = n;
    this.s = s;
    d = s*0.9510565162951534;
  }

  public String getLabel (int row, int column)
  {
    return "("+row+","+column+")";
  }

  public void mesh ()
  {
    CPoint topCorner = (new SPoint(d,0.0,0.0)).cPoint();
    CPoint leftCorner =
      (new SPoint(d,-Math.PI/5.0,1.107148717940909)).cPoint();
    CPoint rightCorner = 
      (new SPoint(d,Math.PI/5.0,1.107148717940909)).cPoint();
    double incX = (leftCorner.x-topCorner.x)/n;
    double incY = (rightCorner.y-leftCorner.y)/n;
    double incZ = (leftCorner.z-topCorner.z)/n;
    double x;
    double y;
    double z;
    String label;
    for (int i = 0; i <= n; i++)
      {
	z = topCorner.z+(incZ*i);
	x = topCorner.x+(incX*i);
	for (int j = 0; j <= i; j++)
	  {
	    y = -((incY*i)/2.0)+(incY*j);
	    label = getLabel(j,i-j);
	    cPoints.put(label,new CPoint(x,y,z));
	  }
      }
  }

  public void project ()
  {
    String label;
    SPoint sPoint;
    CPoint cPoint;

    System.out.println();
    System.out.println("<H2>Circumscribed Spherical Projection</H2>");
    System.out.println
      ("<P><CENTER><TABLE BORDER=1 CELLPADDING=3 CELLSPACING=3 BGCOLOR=ffffdd>");
    System.out.println("<TR><TD><B>Vertex<TD><B>x<TD><B>y<TD><B>z");

    for (int i = 0; i <= n; i++)
      for (int j = 0; j <= i; j++)
	{
	  label = getLabel(j,i-j);
	  sPoint = ((CPoint)cPoints.get(label)).sPoint();
	  sPoint.radius = d;
	  cPoint = sPoint.cPoint();
	  cPoints.put(label,cPoint);

	  System.out.println
	    ("<TR><TD>"+label+"<TD>"+Rounding.toString(cPoint.x,5)+"<TD>"+
	     Rounding.toString(cPoint.y,5)+"<TD>"+Rounding.toString(cPoint.z,5));
	}

    System.out.println("</TABLE></CENTER>");
  }

  public String getBelowLeftLabel (int row, int column)
  {
    int destinationColumn = column+1;
    if (row+destinationColumn > n)
      return null;
    return getLabel(row,destinationColumn);
  }

  public String getBelowRightLabel (int row, int column)
  {
    int destinationRow = row+1;
    if (destinationRow+column > n)
      return null;
    return getLabel(destinationRow,column);
  }

  public String getRightLabel (int row, int column)
  {
    int destinationRow = row+1;
    int destinationColumn = column-1;
    if ((destinationRow > n)||(destinationColumn < 0))
      return null;
    return getLabel(destinationRow,destinationColumn);
  }

  public void chords ()
  {
    String label;
    String belowLeftLabel;
    String belowRightLabel;
    String rightLabel;
    CPoint cPoint;

    System.out.println();
    System.out.println("<H2>Chord Lengths</H2>");
    System.out.println
      ("<P><CENTER><TABLE BORDER=1 CELLPADDING=3 CELLSPACING=3 BGCOLOR=ffffdd>");
    System.out.println("<TR><TD><B>Vertex<TD><B>Vertex<TD><B>chord");

    for (int i = 0; i <= n; i++)
      for (int j = 0; j <= i; j++)
	{
	  label = getLabel(j,i-j);
	  cPoint = (CPoint)cPoints.get(label);
	  belowLeftLabel = getBelowLeftLabel(j,i-j);

	  if (belowLeftLabel != null)
	    System.out.println
	      ("<TR><TD>"+label+"<TD>"+belowLeftLabel+"<TD>"+
	       Rounding.toString
	       (cPoint.distanceTo((CPoint)cPoints.get(belowLeftLabel)),5));

	  belowRightLabel = getBelowRightLabel(j,i-j);

	  if (belowRightLabel != null)
	    System.out.println
	      ("<TR><TD>"+label+"<TD>"+belowRightLabel+"<TD>"+
	       Rounding.toString
	       (cPoint.distanceTo((CPoint)cPoints.get(belowRightLabel)),5));

	  rightLabel = getRightLabel(j,i-j);
	  
	  if (rightLabel != null)
	    System.out.println
	      ("<TR><TD>"+label+"<TD>"+rightLabel+"<TD>"+
	       Rounding.toString
	       (cPoint.distanceTo((CPoint)cPoints.get(rightLabel)),5));
	}

  System.out.println("</TABLE></CENTER>");
  }  

  public static void main (String[] arguments)
  {
    int n = Integer.valueOf(arguments[0]).intValue();
    double s = Double.valueOf(arguments[1]).doubleValue();
    System.out.println
      ("<TITLE>Calculations for a "+n+"-frequency Icosahedral Geodesic Patch</TITLE>");
    Icos icos = new Icos(n,s);
    icos.mesh();
    icos.project();
    icos.chords();
  }
}