From: Earl F. Glynn
Subject: Re: Von koch kurve...
Newsgroups: sci.fractals
View complete thread (3 articles)
Date: 1997/02/19

Anders Öhrt wrote:
>
> Tjaba!
>
> Could someone show me how to get the point of the middle triangle if the
> line streches from x1,y1 to x2,y2...? I need the math behind x1,y1...
> Can't get mine to work...
>
>          /\<= x3, y3
>         /  \
> -------/    \--------
> x1,y1             x2,y2
>
> // Anders
>
> Ps. C++ syntax could be nice... Ds.

Will you take Pascal code?  I'll bet you can figure it out:


 PROCEDURE CreateKochSnowflake;

    TYPE
      Point =
        RECORD
          x:  DOUBLE;
          y:  DOUBLE
        END;

    VAR
      a,b,c :  Point;
      draw  :  INTEGER;
      loop  :  WORD;
      w     :  GraphicsWindow;

    {                     s




            a        r         t        b
    }
    PROCEDURE NextSegments (a,b:  Point; n:  WORD);
      CONST
        factor = 0.288675135;  { SQRT(3) / 6 }
      VAR
        middle:  Point;
        xDelta:  DOUBLE;
        yDelta:  DOUBLE;
        r,s,t:  Point;
    BEGIN
      IF   n > 0
      THEN BEGIN
        r.x :=      (2.0*a.x +     b.x) / 3.0;
        r.y :=      (2.0*a.y +     b.y) / 3.0;

        t.x :=      (    a.x + 2.0*b.x) / 3.0;
        t.y :=      (    a.y + 2.0*b.y) / 3.0;

        middle.x := (    a.x +     b.x) / 2.0;
        middle.y := (    a.y +     b.y) / 2.0;

        xDelta := b.x - a.x;
        yDelta := b.y - a.y;

        s.x := middle.x + factor*yDelta;
        s.y := middle.y - factor*xDelta;

        SetColor (LightBlue);
        w.MoveTo2D (a.x,a.y);    {blank this line}
        w.LineTo2D (b.x,b.y);

        SetColor (draw);
        w.MoveTo2D (a.x,a.y);    {add new lines}
        w.LineTo2D (r.x,r.y);
        w.LineTo2D (s.x,s.y);
        w.LineTo2D (t.x,t.y);
        w.LineTo2D (b.x,b.y);

        NextSegments (a,r, n-1);
        NextSegments (r,s, n-1);
        NextSegments (s,t, n-1);
        NextSegments (t,b, n-1);
      END
    END {NextSegments};

    PROCEDURE KochSnowflake (a,b,c:  Point; n:  WORD);
    BEGIN
      SetLineStyle (SolidLn, 0, NormWidth);
      SetColor (Draw);
      w.MoveTo2D (a.x,a.y);
      w.LineTo2D (b.x,b.y);
      NextSegments (a,b, n);

      w.MoveTo2D (b.x,b.y);
      w.LineTo2D (c.x,c.y);
      NextSegments (b,c, n);

      w.MoveTo2D (c.x,c.y);
      w.LineTo2D (a.x,a.y);
      NextSegments (c,a, n);
    END {KochSnowflake};

  BEGIN
    w.init;
    w.viewport (0.0, 0.0, 1.0, 1.0);
    w.WorldCoordinatesRange (-12,12, -10,8);

    SetFillStyle (SolidFill, LightBlue);
    BARIJ (0,GetMaxX, 0,GetMaxY);

    a.x := -6.0;
    a.y := -3*SQRT(3.0);

    b.x :=  6.0;
    b.y := -3*SQRT(3.0);

    c.x :=  0.0;
    c.y :=  3*SQRT(3.0);

    FOR loop := 0 TO 6 DO BEGIN

{     SetFillStyle (SolidFill, LightBlue);
      BARIJ (0,GetMaxX, 0,GetMaxY);
}
      IF   loop MOD 2 = 0
      THEN draw := white
      ELSE draw := black;
      KochSnowflake (a,b,c, loop);
      SetFillStyle (SolidFill, draw);
      FloodFillIJ (GetMaxX DIV 2, GetMaxY DIV 2, draw);
      DELAY (3000);
    END

  END {CreateKochSnowflake};


--
Earl F. Glynn
EFG Software