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x3domlet
Commit a1777793 authored by Oleg Dzhimiev's avatar Oleg Dzhimiev
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more derivatives

parent 0e3c7053
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Showing with 282 additions and 31 deletions
js/x3dom_deltas.js
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......@@ -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
......
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