re #41: initial port of pj_cass

/*******************************************************************************

NAME                            CASSINI

PURPOSE:	Transforms input longitude and latitude to Easting and

		Northing for the Cassini projection.  The

		longitude and latitude must be in radians.  The Easting

		and Northing values will be returned in meters.

    Ported from PROJ.4.

ALGORITHM REFERENCES

1.  Snyder, John P., "Map Projections--A Working Manual", U.S. Geological

    Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United

    State Government Printing Office, Washington D.C., 1987.

2.  Snyder, John P. and Voxland, Philip M., "An Album of Map Projections",

    U.S. Geological Survey Professional Paper 1453 , United State Government

*******************************************************************************/

//Proj4js.defs["EPSG:28191"] = "+proj=cass +lat_0=31.73409694444445 +lon_0=35.21208055555556 +x_0=170251.555 +y_0=126867.909 +a=6378300.789 +b=6356566.435 +towgs84=-275.722,94.7824,340.894,-8.001,-4.42,-11.821,1 +units=m +no_defs";

// Initialize the Cassini projection

// -----------------------------------------------------------------

Proj4js.Proj.cass = {

  init : function() {

    if (!this.sphere) {

      this.en = this.pj_enfn(this.es)

      this.m0 = this.pj_mlfn(this.lat0, Math.sin(this.lat0), Math.cos(this.lat0), this.en);

    }

  },

  C1:	.16666666666666666666,

  C2:	.00833333333333333333,

  C3:	.04166666666666666666,

  C4:	.33333333333333333333,

  C5:	.06666666666666666666,

/* Cassini forward equations--mapping lat,long to x,y

  -----------------------------------------------------------------------*/

  forward: function(p) {

    /* Forward equations

      -----------------*/

    var x,y;

    var lam=p.x;

    var phi=p.y;

    lam = Proj4js.common.adjust_lon(lam - this.long0);

    if (this.sphere) {

      x = Math.asin(Math.cos(phi) * Math.sin(lam));

      y = Math.atan2(Math.tan(phi) , Math.cos(lam)) - this.phi0;

    } else {

        //ellipsoid

      this.n = Math.sin(phi);

      this.c = Math.cos(phi);

      y = this.pj_mlfn(phi, this.n, this.c, this.en);

      this.n = 1./Math.sqrt(1. - this.es * this.n * this.n);

      this.tn = Math.tan(phi); 

      this.t = this.tn * this.tn;

      this.a1 = lam * this.c;

      this.c *= this.es * this.c / (1 - this.es);

      this.a2 = this.a1 * this.a1;

      x = this.n * this.a1 * (1. - this.a2 * this.t * (this.C1 - (8. - this.t + 8. * this.c) * this.a2 * this.C2));

      y -= this.m0 - this.n * this.tn * this.a2 * (.5 + (5. - this.t + 6. * this.c) * this.a2 * this.C3);

    }

    p.x = this.a*x + this.x0;

    p.y = this.a*y + this.y0;

    return p;

  },//cassFwd()

/* Inverse equations

  -----------------*/

  inverse: function(p) {

    p.x -= this.x0;

    p.y -= this.y0;

    var x = p.x/this.a;

    var y = p.y/this.a;

    if (this.sphere) {

      this.dd = y + this.lat0;

      phi = Math.asin(Math.sin(this.dd) * Math.cos(x));

      lam = Math.atan2(Math.tan(x), Math.cos(this.dd));

    } else {

      /* ellipsoid */

      ph1 = this.pj_inv_mlfn(this.m0 + y, this.es, this.en);

      this.tn = Math.tan(ph1); 

      this.t = this.tn * this.tn;

      this.n = Math.sin(ph1);

      this.r = 1. / (1. - this.es * this.n * this.n);

      this.n = Math.sqrt(this.r);

      this.r *= (1. - this.es) * this.n;

      this.dd = x / this.n;

      this.d2 = this.dd * this.dd;

      phi = ph1 - (this.n * this.tn / this.r) * this.d2 * (.5 - (1. + 3. * this.t) * this.d2 * this.C3);

      lam = this.dd * (1. + this.t * this.d2 * (-this.C4 + (1. + 3. * this.t) * this.d2 * this.C5)) / Math.cos(ph1);

    }

    p.x = Proj4js.common.adjust_lon(this.long0+lam);

    p.y = phi;

    return p;

  },//lamazInv()

  //code from the PROJ.4 pj_mlfn.c file;  this may be useful for other projections

  pj_enfn: function(es) {

    en = new Array();

    en[0] = this.C00 - es * (this.C02 + es * (this.C04 + es * (this.C06 + es * this.C08)));

    en[1] = es * (this.C22 - es * (this.C04 + es * (this.C06 + es * this.C08)));

    var t = es * es;

    en[2] = t * (this.C44 - es * (this.C46 + es * this.C48));

    t *= es;

    en[3] = t * (this.C66 - es * this.C68);

    en[4] = t * es * this.C88;

    return en;

  },

  pj_mlfn: function(phi, sphi, cphi, en) {

    cphi *= sphi;

    sphi *= sphi;

    return(en[0] * phi - cphi * (en[1] + sphi*(en[2]+ sphi*(en[3] + sphi*en[4]))));

  },

  pj_inv_mlfn: function(arg, es, en) {

    k = 1./(1.-es);

    phi = arg;

    for (i = Proj4js.common.MAX_ITER; i ; --i) { /* rarely goes over 2 iterations */

      s = Math.sin(phi);

      t = 1. - es * s * s;

      //t = this.pj_mlfn(phi, s, Math.cos(phi), en) - arg;

      //phi -= t * (t * Math.sqrt(t)) * k;

      t = (this.pj_mlfn(phi, s, Math.cos(phi), en) - arg) * (t * Math.sqrt(t)) * k;

      phi -= t;

      if (Math.abs(t) < Proj4js.common.EPSLN)

        return phi;

    }

    Proj4js.reportError("cass:pj_inv_mlfn: Convergence error");

    return phi;

  },

/* meridinal distance for ellipsoid and inverse

**	8th degree - accurate to < 1e-5 meters when used in conjuction

**		with typical major axis values.

**	Inverse determines phi to EPS (1e-11) radians, about 1e-6 seconds.

*/

  C00: 1.0,

  C02: .25,

  C04: .046875,

  C06: .01953125,

  C08: .01068115234375,

  C22: .75,

  C44: .46875,

  C46: .01302083333333333333,

  C48: .00712076822916666666,

  C66: .36458333333333333333,

  C68: .00569661458333333333,

  C88: .3076171875

}