function point2ball (xmouse, ymouse, m) { // compute intersection with
vtb, no need to normalize, 1 sqrt/call
	var factor; var inout; dir=new Array(3);
	// change xconv, yconv to *, make this vector?
	xm = (xmouse-xcenter)*oneoverxconv; ym =
-(ymouse-ycenter)*oneoveryconv;// convert to image plane coordinates
	for (i=0; i<3; i++) m[i] = xm*i1[i]+ym*i2[i]; // convert to R^3
	normpmsq = normsq3(m); // =0 for center
	if (normpmsq>grazsq) { // normalize to radius of grazing circle in
image plane
		inout=1;
		factor = 1.0/Math.sqrt(normpmsq);
		for (i=0; i<3; i++) m[i] *= factor;
	} else { // normpmsq <= grazsq, quadratic for parameter of
viewline intersection with ball
		inout=0;
		for (i=0;i<3;i++) dir[i]=vp[i]-m[i];
		a=normsq3(dir);
		//a = focsq+normpmsq;  // a>normpmsq>0 since focsq >0
		// either form screws up because they assume (vp,m)=0 in b
		// which is really -2dot3(m,dir) so use that.
		//b = -2.0*normpmsq;   // b=0 for centerpoint, else b<0
		b=2.0*dot3(m,dir); // if not gradual instability loss of
orthogonality feedback!
		c = normpmsq-1.0; // 0<c<(grazsq-rballsq) defines two
positive solution annulus
		srdisc=Math.sqrt(b*b-4.0*a*c); // =
4*((rballsq-focsq)*normpmsq+ (rballsq*focsq))
		q=-0.5*(b-srdisc); //q=-0.5*(b+sgn*disc); // q>0
		t =q/a; // r1=q/a;// r2=c/q;  // a>0 gives one positive
solution always
		for (i=0; i<3; i++) m[i] += t*dir[i]; } // end else
(inside ball)
		return inout;
	 }

	function transvect () {// rotate vd,i2 by e2 to e1 transvection, 4
dot products, 1 division
	bb = new Array(3); w = new Array(3); // 4 scalar multiplies, 4
scalar ax+y, 1 vector +, 1 scalar ax
	for (i=0; i<3; i++)	bb[i] = e1[i]+e2[i];
	nsbb=normsq3(bb);
	if (nsbb > tol){ // do nothing if bb is numerically zero, identity
rotation anyway
	twoovernormsqbb = 2.0/nsbb; // reflect v1 in bb then in e1, then
do same for v2
	twov1dotbb = dot3(vd, bb)*twoovernormsqbb;
	for (i=0; i<3; i++) w[i] = twov1dotbb*bb[i]-vd[i];
	twowdote1 = 2.0*dot3(w, e1);
	for (i=0; i<3; i++) vd[i] = twowdote1*e1[i]-w[i];
	twov2dotbb = dot3(i2, bb)*twoovernormsqbb;
	for (i=0; i<3; i++) w[i] = twov2dotbb*bb[i]-i2[i];
	twowdote1 = 2.0*dot3(w, e1);
	for (i=0; i<3; i++) i2[i] = twowdote1*e1[i]-w[i];
	cross(vd, i2, i1);
	for (i=0; i<3; i++) vp[i] = -foc*vd[i];	} }

function persp (dp, p) { // compute perspective projection of data point
into viewplane
	// (vp+t(dp-vp),vd)=0 so t=-(vd,vp)/(vd,dp-vp) // doesn't require
basis for that plane
	// so it can be used to set i2 in initialization!
	var t; dir = new Array(3); centerv = new Array(3);
	for (i=0; i<3; i++) dir[i] = dp[i]-vp[i];
	t = -dot3(vd, vp)/dot3(vd, dir);
	for (i=0; i<3; i++) p[i] = vp[i]+t*dir[i]; }

// the main loop:
	if (mouseisdown == 0) { // mouseisup
		transvect();
		mousewasdown=0; }
	else {
		mousewasout=mouseisout;
		mouseisout=point2ball(_xmouse, _ymouse,  e2);// gets new
point on ball and mouse in/out state
		if ((mousewasdown==1)&&(mousewasout==mouseisout))
transvect();//mouse was down, didn't cross horizon
		else for (i=0; i<3; i++) e1[i]=e2[i]; //just down/crossed
horizon, initialize identity
		mousewasdown=1; } // end if isdown

someListener.onMouseDown = function () { // the event, not the state
	mousewasdown=0; mouseisdown=1;
	name1 = "circle"; attachMovie("circle", name1, 1); //attached so
not cleared each frame
	_root[name1]._x = xcenter;_root[name1]._y = ycenter;
	_root[name1]._xscale = xconv*graz; _root[name1]._yscale =
yconv*graz; }

someListener.onMouseUp = function () { // the event, not the state
	mousewasdown=1; mouseisdown=0;
	_root[name1].removeMovieClip(); }