Question

I’m doing a program for a recursive Sierpinski triangle and do not know how to change the points in arrays xm[] and ym[] in order to do this. to be more specific, when i run this program, only one outlined triangle with one blue inner triangle is drawn. any help would be greatly appreciated!

public class recursiveSierpinski {
   public static void draw(int n, double x0, double y0, double x1,
      double y1, double x2, double y2) {
      // if reach base case, method return
      if (n==0) return;
      // define array xm, ym to store x and y values of midpoints
      double [] xm = new double[3];
      double [] ym = new double[3];

      // assign midpoints’ values to xm and ym
      xm[0]= (x0+x1)/2;
      xm[1]= (x1+x2)/2;
      xm[2]= (x2+x0)/2;
      ym[0]= (y0+y1)/2;
      ym[1]= (y1+y2)/2;
      ym[2]= (y2+y0)/2;

      StdDraw.setPenColor(StdDraw.BLUE);
      StdDraw.filledPolygon(xm, ym); //this makes triangle
      xm[0]=xm[0]/2.0;
      ym[0]=ym[0]/2.0;
      xm[1]=xm[1]/2.0;
      ym[1]=ym[1]/2.0;
      xm[2]=xm[2]/2.0;
      ym[2]=ym[2]/2.0;

      draw(n,xm[0],ym[0],xm[1],ym[1],xm[2],ym[2]);
      draw(n,xm[1],ym[1],xm[2],ym[2],xm[0],ym[0]);
      draw(n,xm[2],ym[2],xm[0],ym[0],xm[1],ym[1]);

      // recursively draw the sub triangles (?)


     }
     public static void main(String[] args) {
     // N levels of recursion
     int N = Integer.parseInt(args[0]);
     // outline the triangle
     double t = Math.sqrt(3.0) / 2.0;
     StdDraw.line(0.0, 0.0, 1.0, 0.0);
     StdDraw.line(1.0, 0.0, 0.5, t);
     StdDraw.line(0.5, t, 0.0, 0.0);
     draw(N, 0.0, 0.0, 0.5, t, 1.0, 0.0);
     }
}

Answer 1

Try this:

public class recursiveSierpinski {
   public static void draw(int n, double x0, double y0, double x1,
      double y1, double x2, double y2) {
      // if reach base case, method return
      if (n==0) return;
      // define array xm, ym to store x and y values of midpoints
      double [] xm = new double[3];
      double [] ym = new double[3];

      // assign midpoints’ values to xm and ym
      xm[0]= (x0+x1)/2;
      xm[1]= (x1+x2)/2;
      xm[2]= (x2+x0)/2;
      ym[0]= (y0+y1)/2;
      ym[1]= (y1+y2)/2;
      ym[2]= (y2+y0)/2;

      StdDraw.filledPolygon(xm, ym); //this makes triangle

      draw(n-1,xm[0],ym[0],xm[1],ym[1],x1,y1);
      draw(n-1,xm[1],ym[1],xm[2],ym[2],x2,y2);
      draw(n-1,xm[2],ym[2],xm[0],ym[0],x0,y0);


     }
     public static void main(String[] args) {
     // N levels of recursion
     int N = Integer.parseInt(args[0]);
     // outline the triangle

     double t = Math.sqrt(3.0) / 2.0;


     StdDraw.setPenColor(StdDraw.BLACK);
     // fill arrays initially to draw black solid TRIANGLE xm, ym = 0.0, 0.0, 0.5, t, 1.0, 0.0
     StdDraw.filledPolygon(xm, ym);

     StdDraw.setPenColor(StdDraw.WHITE);
     draw(N, 0.0, 0.0, 0.5, t, 1.0, 0.0);
     }
}