mapping.java

Ideal Flow Machine For Data Plot

            g.setColor(Color.yellow);
            g.fillOval(xI-2,yI-2,4,4);
            g.setColor(Color.black);
            g.drawOval(xI-2,yI-2,4,4);
            }
        }


        for(int i=0;i<root.root.drawing.nst;i++) drawStreamline(root.root.drawing.xstream[i],root.root.drawing.ystream[i]);

    }


    public boolean handleEvent(Event event) {
        if (event.id == Event.MOUSE_MOVE && event.target == this) {
                mouseMoveThis(event);
                return true;
        }
        else
        if (event.id == Event.MOUSE_DRAG && event.target == this) {
                mouseMoveThis(event);
                return true;
        }

        return super.handleEvent(event);
    }


    public void mouseMoveThis(Event ev) {
        int xIndex,yIndex;

        xIndex=ev.x;yIndex=ev.y;
        if(xIndex>=xImin && xIndex<=xImax && yIndex>=yImin && yIndex<=yImax) {
            x=(double)(xIndex-xImin)/50.0-x0;
            y=y0-(double)(yIndex-yImin)/50.0;
            root.xD.setText("x1 = "+format(x,3));
            root.yD.setText("y1 = "+format(y,3));
        }

    }


    void drawStreamline(double xx, double yy) {
        double u,v,vmag=0.0,vmag1=0.0,Uinf,xs,ys,xs0,ys0,xs1,ys1,u1,v1,streamStep=.02;
        double kuttag=0.0,xr,yr,r2;
        int xI,yI,xI1,yI1,uI,uI1,vI,vI1,step,maxStep=1000,SKIP=3;
        float hue;
        Velocity vel=new Velocity(0.0,0.0);
        Velocity dzdw=new Velocity(0.0,0.0);
        Velocity upiv=new Velocity(0.0,0.0);
        String s;
        Graphics gs;

        gs=this.getGraphics();

        s="";
        xs0=xs=xx;ys0=ys=yy;
        upiv=W(xs,ys);
        dzdw=D(xs,ys);
        gs.setColor(Color.gray);
        xI=(int)Math.round((upiv.u+x0)*50.0)+xImin;
        yI=(int)Math.round((y0-upiv.v)*50.0)+yImin;
        step=0;

        while(step++<maxStep) {

            vel=root.root.drawing.totalVk(xs,ys);
            u=vel.u;v=vel.v;
            if(vel.inf==true) break;

            vmag = Math.sqrt(Math.abs(u * u + v * v));  //Estimate next point in streamline
            if(vmag==0.0) break;
            xs1=xs+u/vmag*streamStep;
            ys1=ys+v/vmag*streamStep;

            vel=root.root.drawing.totalVk(xs1,ys1);
            u1=vel.u;v1=vel.v;
            if(vel.inf==true) break;

            vmag1 = Math.sqrt(Math.abs(u1 * u1 + v1 * v1));  //Re-estimate next point in streamline
            if(vmag1==0.0) break;
            xs1=xs+(u/vmag+u1/vmag1)*streamStep/2.0;
            ys1=ys+(v/vmag+v1/vmag1)*streamStep/2.0;

            if(step%SKIP==0) {
                upiv=W(xs1,ys1);
                xI1=(int)Math.round((upiv.u+x0)*50.0)+xImin;
                yI1=(int)Math.round((y0-upiv.v)*50.0)+yImin;

                if((xI<xImax && xI>xImin && yI<yImax && yI>yImin)&&(xI1<xImax && xI1>xImin && yI1<yImax && yI1>yImin)) {
                    dzdw=D(xs,ys);
                    if(dzdw.inf==false) {
                        hue=1.0f-(float)(vmag*Math.sqrt(Math.abs(dzdw.u * dzdw.u + dzdw.v * dzdw.v))/2.);
                        if(hue<0.0f) hue=0.0f;
                    }
                    else hue=0.0f;
                    gs.setColor(Color.getHSBColor(hue,1.0f,1.0f));
                    if(xs0+xs1<=0 || (ys0*ys1>0.0 || (ys0==0.0 && ys1==0.0))) {   //Look for branch cut
                        gs.drawLine(xI,yI,xI1,yI1);
                    }
                }


                xI=xI1;xs0=xs;
                yI=yI1;ys0=ys;
                if(record) s+=fformat(upiv.u)+"\t"+fformat(upiv.v)+"\t"+fformat(u*dzdw.u+v*dzdw.v)+"\t"+fformat(-u*dzdw.v+v*dzdw.u)+"\n";
            }

            xs=xs1;ys=ys1;
        }
        if(record) root.out.addData(s);
    }


    String format(double d,int fdigits) {
        String out="",buf;
        String[] zeros={"0.","0.0","0.00"};
        int mant,exp,sgn=1;

        int sdigits=4;         //number of digits to show in scientific format
        int sci=4;            //absolute magnitude of numbers below which to display floating-point format

        if(d>0.0) sgn=1;
        else if(d<0.0) sgn=-1;
        else return(" 0.00");

        d=Math.abs(d);
        exp=(int)(Math.log(d*1.0000001)/Math.log(10));
        if(d<1.0) exp--;

        if(exp<4 & exp>=0) {
            mant=(int)Math.round(d*Math.pow(10.,(double)(fdigits-1-exp)));
            buf=String.valueOf(mant);
            out=buf.substring(0,buf.length()-fdigits+exp+1)+"."+buf.substring(buf.length()-fdigits+exp+1); //insert point
            //while(out.lastIndexOf("0")==out.length()-1) out=out.substring(0,out.length()-1); //strip trailing zeros
            //if(out.lastIndexOf(".")==out.length()-1) out=out.substring(0,out.length()-1);   //strip trailing point if necessary
            if(sgn==-1) out="-"+out;
            else out=" "+out;
        }
        else if(exp<0 & exp>-4) {
            mant=(int)Math.round(d*Math.pow(10.,(double)(fdigits-1)));
            buf=String.valueOf(mant);
            out=zeros[-exp-1]+buf; //insert point
            //while(out.lastIndexOf("0")==out.length()-1) out=out.substring(0,out.length()-1); //strip trailing zeros
            if(sgn==-1) out="-"+out;
            else out=" "+out;
        }
        else {
            mant=(int)Math.round(d*Math.pow(10.,(double)(sdigits-1-exp)));
            buf=String.valueOf(mant);
            out=buf.substring(0,1)+"."+buf.substring(1); //insert point
            while(out.lastIndexOf("0")==out.length()-1) out=out.substring(0,out.length()-1); //strip trailing zeros
            if(out.lastIndexOf(".")==out.length()-1) out=out.substring(0,out.length()-1);   //strip trailing point if necessary
            if(sgn==-1) out="-"+out;
            if(exp>0) out=out+"e+"+String.valueOf(exp);
            else out=out+"e"+String.valueOf(exp);
        }
        return(out);

    }

    String fformat(double d) {  //fixed scientific format
        String out="",buf;
        String[] zeros={"0.","0.0","0.00"};
        int mant,exp,sgn=1,esgn=1;
        int sdigits=5;         //number of digits to show in scientific format

        if(d>0.0) sgn=1;
        else if(d<0.0) sgn=-1;
        else return("0.0000e+000");

        d=Math.abs(d);
        exp=(int)(Math.log(d*1.0000001)/Math.log(10));
        if(d<1.0) exp--;

        mant=(int)Math.round(d*Math.pow(10.,(double)(sdigits-1-exp)));
        buf=String.valueOf(mant);
        out=buf.substring(0,1)+"."+buf.substring(1); //insert point
        if(sgn==-1) out="-"+out;
        else out=" "+out;
        if(exp>=0) out=out+"e+";
        else out=out+"e-";
        if(Math.abs(exp)>99) out=out+String.valueOf(Math.abs(exp));
        else if(Math.abs(exp)>9) out=out+"0"+String.valueOf(Math.abs(exp));
        else out=out+"00"+String.valueOf(Math.abs(exp));

        return(out);

    }

    Velocity W(double x, double y) {
        Velocity upiv=new Velocity(0.0,0.0);
        double r,th;

        th=0.0;r=0.0;
        if(x!=0.0 || y!=0.0) {
            th=Math.atan2(y,x);
            if(th<0.0) th+=2.0*Math.PI;
            r=Math.sqrt(x*x+y*y);
        }

        switch (root.mapno) {
            case 0:   //s=z
            upiv.u=x;
            upiv.v=y;
            upiv.inf=false;
            break;
            case 1:   //s=az^b
            if(r>0.0) {
                upiv.u=root.aconst*Math.pow(r,root.bconst)*Math.cos(root.bconst*th);
                upiv.v=root.aconst*Math.pow(r,root.bconst)*Math.sin(root.bconst*th);
                upiv.inf=false;
            }
            else if(root.bconst>0.0) {upiv.u=0.0;upiv.v=0.0;upiv.inf=false;}
            else {upiv.u=0.0;upiv.v=0.0;upiv.inf=true;}
            break;
            case 2:   //s=a(z+b/z)
            if(r>0.0) {
                upiv.u=root.aconst*x+root.aconst*root.bconst*x/r/r;
                upiv.v=root.aconst*y-root.aconst*root.bconst*y/r/r;
                upiv.inf=false;
            }
            else {upiv.u=0.0;upiv.v=0.0;upiv.inf=true;}
            break;
            case 3:   //s=alog(z) - ib
            if(r>0.0) {
                upiv.u=root.aconst*Math.log(r);
                upiv.v=root.aconst*th-root.bconst;
                upiv.inf=false;
            }
            else {upiv.u=0.0;upiv.v=0.0;upiv.inf=true;}
            break;
            case 4:   //s=a(exp(bz)+bz)
            upiv.u=root.aconst*Math.exp(root.bconst*x)*Math.cos(root.bconst*y)+root.aconst*root.bconst*x;
            upiv.v=root.aconst*Math.exp(root.bconst*x)*Math.sin(root.bconst*y)+root.aconst*root.bconst*y;
            upiv.inf=false;
            break;
            case 5:   //s=(z-a)/(az-1) + b
            upiv.u=(root.aconst*(r*r-root.aconst*x+1)-x)/((root.aconst*x-1.)*(root.aconst*x-1.)+root.aconst*root.aconst*y*y)+root.bconst;
            upiv.v=(root.aconst*root.aconst-1.)*y/((root.aconst*x-1.)*(root.aconst*x-1.)+root.aconst*root.aconst*y*y);
            upiv.inf=false;
            break;
        }

        return upiv;
    }

    Velocity D(double x, double y) {
        Velocity dzdw=new Velocity(0.0,0.0);
        double r,th,p1,p2;

        th=0.0;r=0.0;
        if(x!=0.0 || y!=0.0) {
            th=Math.atan2(y,x);
            if(th<0.0) th+=2.0*Math.PI;
            r=Math.sqrt(x*x+y*y);
        }

        switch (root.mapno) {
            case 0:   //s=z
            dzdw.u=1.0;
            dzdw.inf=false;
            break;
            case 1:   //s=az^b
            if(r>0.0) {
                dzdw.u=1.0/root.aconst/root.bconst*Math.pow(r,1.0-root.bconst);
                dzdw.inf=false;
            }
            else if(root.bconst>1.0) {
                dzdw.u=0.0;
                dzdw.inf=true;
            }
            else {
                dzdw.u=0.0;
                dzdw.inf=false;
            }
            break;
            case 2:   //s=a(z+b/z)
            dzdw.u=Math.pow(root.aconst*r*r*r*r-root.aconst*root.bconst*(x*x-y*y),2.0)+4.0*x*x*y*y*root.aconst*root.aconst*root.bconst*root.bconst;
            if(dzdw.u>0.0) {
                dzdw.u=r*r*r*r/Math.sqrt(dzdw.u);
                dzdw.inf=false;
            }
            else {
                dzdw.u=0.0;
                dzdw.inf=true;
            }
            break;
            case 3:   //s=alog(z) - ib
            dzdw.u=r/root.aconst;
            dzdw.inf=false;
            break;
            case 4:   //s=a(exp(bz)+bz)
            p1=Math.exp(root.bconst*x)*Math.cos(root.bconst*y)+1;
            p2=Math.exp(root.bconst*x)*Math.sin(root.bconst*y);
            p1=p1*p1+p2*p2;
            if(p1>0.0) {
                dzdw.u=1.0/root.aconst/root.bconst/Math.sqrt(p1);
                dzdw.inf=false;
            }
            else {
                dzdw.u=0.0;
                dzdw.inf=true;
            }
            break;
            case 5:   //s=(z-a)/(az-1) + b
            p1=root.aconst*(root.aconst*x*x-root.aconst*y*y-2.*x)+1.;
            p2=root.aconst*(root.aconst*2*x*y-2.*y);
            dzdw.u=Math.sqrt(p1*p1+p2*p2)/(root.aconst*root.aconst-1);
            break;
        }

        return dzdw;
    }
}