Commit a1777793 authored by Oleg Dzhimiev's avatar Oleg Dzhimiev
Browse files

more derivatives

parent 0e3c7053

js/x3dom_deltas.js

+282 −31
Original line number Diff line number Diff line
@@ -53,27 +53,240 @@ function Av_f(mark,pars){ 


}



function A_f(mark,pars){

function get_JE1(mark,pars){



  var e1_world = get_e1_w(mark,pars);

  var e2_world = get_e2_w(mark,pars);

  var M2W = get_e1_M2W(mark,pars);

  var W2M = M2W.inverse();



  // e1 depends on distance

  var e1_d = x3dom_3d_distance(e1_world.x,e1_world.y,e1_world.z,false);

  var e1_k = 20;

  //var e1_k = 1;

  // multiplier for debugging

  var e1_k = 1;

  // less precise

  //var e1_abc = [e1_k*0.00038*e1_d, e1_k*0.00038*e1_d, e1_k*e1_d*e1_d/10000];

  // more precise

  var e1_abc = [e1_k*0.00038*e1_d, e1_k*0.00038*e1_d, e1_k*e1_d*e1_d/25000];

  var JE1 = x3dom_ellipsoid_inertia_tensor_v2(1,e1_abc[0],e1_abc[1],e1_abc[2]);



  return JE1;



}



function get_RE1(mark,pars){



  var e1_world = get_e1_w(mark,pars);



  // build a right basis

  var e1_dir = e1_world.normalize();

  var xa1 = e1_dir.cross(new x3dom.fields.SFVec3f(0,1,0));

  var ya1 = xa1.cross(e1_dir);

  var za1 = e1_dir.negate();

  //var za1 = e1_dir.negate();

  var za1 = e1_dir;



  // e1 ref system

  var RE1 = x3dom.fields.SFMatrix4f.identity();

  RE1.setValue(xa1,ya1,za1);



  return RE1;



}



function get_JE2(mark,pars){



  // e2 depens on the map

  var e2_k = 1;

  var e2_abc = [e2_k*1,e2_k*1,e2_k*30];



  var JE2 = x3dom_ellipsoid_inertia_tensor_v2(1,e2_abc[0],e2_abc[1],e2_abc[2]);



  return JE2;



}



function get_RE2(mark,pars){



  var RE2 = x3dom.fields.SFMatrix4f.identity();

  return RE2;



}



function get_C(mark,pars){



  var JE1 = get_JE1(mark,pars);

  var RE1 = get_RE1(mark,pars);



  var JE2 = get_JE2(mark,pars);

  var RE2 = get_RE2(mark,pars);



  // now let's get to covariance matrix

  var RE1xJE1 = RE1.mult(JE1);

  var RE2xJE2 = RE2.mult(JE2);



  var C1 = RE1xJE1.mult(RE1xJE1.transpose());

  var C2 = RE2xJE2.mult(RE2xJE2.transpose());

  var C = C1.add(C2);

  //var C = C1.add(C1);

  //var C = C2.add(C2);



  return C;



}



function get_dC(mark,pars){



  var M1 = get_dC1(mark,pars);

  var M2 = get_dC2(mark,pars);



  var dC = M1.add(M2);



  return dC;



}



function get_A(mark,pars){



  var  C =  get_C(mark,pars);

  var dC = get_dC(mark,pars);



  Cn = matrix_x3dom_to_numeric(C);

  Bn = numeric.eig(Cn);



  var a = Math.sqrt(Bn.lambda.x[0]);

  var b = Math.sqrt(Bn.lambda.x[1]);

  var c = Math.sqrt(Bn.lambda.x[2]);



  var sa = Math.sqrt(a);

  var sb = Math.sqrt(b);

  var sc = Math.sqrt(c);



  var vec0 = new x3dom.fields.SFVec3f(Bn.E.x[0][0],Bn.E.x[0][1],Bn.E.x[0][2]);

  var vec1 = new x3dom.fields.SFVec3f(Bn.E.x[1][0],Bn.E.x[1][1],Bn.E.x[1][2]);

  var vec2 = new x3dom.fields.SFVec3f(Bn.E.x[2][0],Bn.E.x[2][1],Bn.E.x[2][2]);



  var R = new x3dom.fields.SFMatrix4f(

               vec0.x, vec1.x, vec2.x, 0,

               vec0.y, vec1.y, vec2.y, 0,

               vec0.z, vec1.z, vec2.z, 0,

                    0,      0,      0, 1

             );



  var J = new x3dom.fields.SFMatrix4f(

               sa,  0,  0, 0,

                0, sb,  0, 0,

                0,  0, sc, 0,

                0,  0,  0, 1

             );



  var Ji = J.inverse();



  var JiR = Ji.mult(R);



  return JiR;



}



//E = Av

function get_dA(mark,pars){



  var  C =  get_C(mark,pars);

  var dC = get_dC(mark,pars);



  Cn = matrix_x3dom_to_numeric(C);

  Bn = numeric.eig(Cn);



  var a = Math.sqrt(Bn.lambda.x[0]);

  var b = Math.sqrt(Bn.lambda.x[1]);

  var c = Math.sqrt(Bn.lambda.x[2]);



  var sa = Math.sqrt(a);

  var sb = Math.sqrt(b);

  var sc = Math.sqrt(c);



  var vec0 = new x3dom.fields.SFVec3f(Bn.E.x[0][0],Bn.E.x[0][1],Bn.E.x[0][2]);

  var vec1 = new x3dom.fields.SFVec3f(Bn.E.x[1][0],Bn.E.x[1][1],Bn.E.x[1][2]);

  var vec2 = new x3dom.fields.SFVec3f(Bn.E.x[2][0],Bn.E.x[2][1],Bn.E.x[2][2]);



  var R = new x3dom.fields.SFMatrix4f(

               vec0.x, vec1.x, vec2.x, 0,

               vec0.y, vec1.y, vec2.y, 0,

               vec0.z, vec1.z, vec2.z, 0,

                    0,      0,      0, 1

             );



  var J = new x3dom.fields.SFMatrix4f(

               sa,  0,  0, 0,

                0, sb,  0, 0,

                0,  0, sc, 0,

                0,  0,  0, 1

             );



  var Ji = J.inverse();





  var da = vec0.dot(dC.multMatrixVec(vec0));

  var db = vec1.dot(dC.multMatrixVec(vec1));

  var dc = vec2.dot(dC.multMatrixVec(vec2));



  var dJi = new x3dom.fields.SFMatrix4f(

               0.5/sa*da,         0,         0, 0,

                       0, 0.5/sb*db,         0, 0,

                       0,         0, 0.5/sc*dc, 0,

                       0,         0,         0, 1

             );



  var dvec0 = get_dvec(C,dC,a,da);

  var dvec1 = get_dvec(C,dC,b,db);

  var dvec2 = get_dvec(C,dC,c,dc);



  var dR = new x3dom.fields.SFMatrix4f(

               dvec0.x, dvec1.x, dvec2.x, 0,

               dvec0.y, dvec1.y, dvec2.y, 0,

               dvec0.z, dvec1.z, dvec2.z, 0,

                     0,       0,       0, 1

             );



  // Q = JiR

  // dQ = dJi x R + Ji x dR



  var dA = dJi.mult(R).add(Ji.mult(dR));



  // ok

  return dA;



}



function get_dvec(A,dA,lambda,dlambda,vec){



  var I = x3dom.fields.SFMatrix4f.identity();

  var M1 = A.subtract(I.multiply(lambda)).inverse();

  var M2 = I.multiply(dlambda).subtract(dA);

  var dvec = M1.mult(M2).multMatrixVec(vec);

  return dvec;



}



function get_dE(mark,pars){



  var A  = get_A(mark,pars);

  var dA = get_dA(mark,pars);



  var v  = v_f(mark,pars);

  var dv = dv_f(mark,pars);



  var p1 =  A.multMatrixVec(dv);

  var p2 = dA.multMatrixVec(v);



  var de = p1.add(p2);

  return de;



}



function A_f(mark,pars){



  /*

  var e1_world = get_e1_w(mark,pars);

  var e2_world = get_e2_w(mark,pars);

  var M2W = get_e1_M2W(mark,pars);

  var W2M = M2W.inverse();

  */



  /*

  x3dom_draw_ellipsoid_by_semiaxes_and_center("e1","green",{
@@ -84,19 +297,11 @@ function A_f(mark,pars){ 
  },transparency=0.5);

  */



  // e1 ref system

  var RE1 = x3dom.fields.SFMatrix4f.identity();

  RE1.setValue(xa1,ya1,za1);



  // e2 depens on the map

  var e2_k = 1;

  var e2_abc = [e2_k*1,e2_k*1,e2_k*30];



  /*

  var xa2 = new x3dom.fields.SFVec3f(e2_abc[0],         0,         0);

  var ya2 = new x3dom.fields.SFVec3f(        0, e2_abc[1],         0);

  var za2 = new x3dom.fields.SFVec3f(        0,         0, e2_abc[2]);



  /*

  x3dom_draw_ellipsoid_by_semiaxes_and_center("e2","green",{

    O:  W2M.multMatrixVec(e2_world),

    Ox: W2M.multMatrixVec(xa2),
@@ -107,21 +312,8 @@ function A_f(mark,pars){ 


  // e2 ref system

  // it's vertical in the WORLD

  var RE2 = x3dom.fields.SFMatrix4f.identity();





  // now let's get to covariance matrix

  var JE1 = x3dom_ellipsoid_inertia_tensor_v2(1,e1_abc[0],e1_abc[1],e1_abc[2]);

  var RE1xJE1 = RE1.mult(JE1);



  var JE2 = x3dom_ellipsoid_inertia_tensor_v2(1,e2_abc[0],e2_abc[1],e2_abc[2]);

  var RE2xJE2 = RE2.mult(JE2);



  var C1 = RE1xJE1.mult(RE1xJE1.transpose());

  var C2 = RE2xJE2.mult(RE2xJE2.transpose());

  var C = C1.add(C2);

  //var C = C1.add(C1);

  //var C = C2.add(C2);

  var C = get_C(mark,pars);



  Cn = matrix_x3dom_to_numeric(C);

  Bn = numeric.eig(Cn);
@@ -174,6 +366,9 @@ function v_f(mark,pars){ 
// rads per degree

var RPD = Math.PI/180;



// C derivatives





// v derivatives



function dv_lat(mark,pars){
@@ -250,7 +445,63 @@ function dv_roll(mark,pars){ 
}





function get_dRE1(mark,pars){



  // a'

  var e1_model = new x3dom.fields.SFVec3f(mark.model.x,mark.model.y,mark.model.z);

  var e1_world = get_e1_w(mark,pars);

  var a = e1_world;



  var heading = pars.heading*RPD;

  var tilt    = (pars.tilt-90)*RPD;

  var roll    = pars.roll*RPD;



  var T = x3dom_toYawPitchRoll();



  var M = x3dom.fields.SFMatrix4f.zeroMatrix();

  M.add(dHTR(heading,tilt,roll));

  M.add(HdTR(heading,tilt,roll));

  M.add(HTdR(heading,tilt,roll));



  var d_e1_world = M.mult(T).multMatrixVec(e1_model).multiply(RPD);



  var da = d_e1_world;



  var dR1 = new x3dom.fields.SFMatrix4f(

          -da.z,    -da.x*a.z-a.x*da.z, da.x, 0,

              0, 2*a.x*da.x+2*a.z*da.z, da.y, 0,

           da.x,    -da.y*a.z-a.y*da.z, da.z, 0,

              0,                     0,    0, 1

  );



  return dR1;



}



function get_dC1(mark,pars){



  var RE1  = get_RE1(mark,pars);

  var dRE1 = get_dRE1(mark,pars);

  var JE1  = get_JE1(mark,pars);



  var JE1xJE1t = JE1.mult(JE1.transpose());



  var P1 = dRE1.mult(JE1xJE1t).mult(RE1);

  var P2 = RE1.mult(JE1xJE1t).mult(dRE1);



  var RES = P1.add(P2);



  return RES;



}



function get_dC2(mark,pars){



  var M = x3dom.fields.SFMatrix4f.zeroMatrix();



  return M;



}



// BASIC FUNCTIONS and DERIVATIVES