testing eigenthings

js/x3dom_deltas.js

@@ -9,31 +9,300 @@ function x3dom_delta_markers(){
 
   var marker = Data.markers[index];
 
-  //console.log(marker.latitude+", "+marker.longitude);
-
   var Camera = Map.marker;
 
   var p_mark_ll = new L.LatLng(marker.latitude, marker.longitude);
-  var p_cam_ll  = Camera._latlng;
+  //var p_cam_ll  = Camera._latlng;
+  var p_cam_ll  = new L.LatLng(Data.camera.kml.latitude,Data.camera.kml.longitude);
 
   var p_w = x3dom_delta_map2scene(p_cam_ll, p_mark_ll);
+  //p_w = x3dom_scene_to_real(p_w.x,p_w.y,p_w.z);
+
+
+  // vertical ellipse's center
+  var e2_c = p_w;
+  // depth ellipse's center
+  var e1_c = new x3dom.fields.SFVec3f(marker.x,marker.y,marker.z);
+
+
+  // E2: draw vertical ellipsoid
+
+  // just a coefficient
+  var e2_k = 1/2;
+  var e2_abc = [e2_k*1,e2_k*30,e2_k*1];
+  var e2_scale = e2_abc.join(",");
+  //x3dom_draw_ellipsoid("e2","green",e2_c.toString(),"",e2_scale);
+
+  // draw ellipsoid axes
+  //var xa = new x3dom.fields.SFVec3f(1,0,0);
+  //var ya = new x3dom.fields.SFVec3f(0,1,0);
+  //var za = new x3dom.fields.SFVec3f(0,0,1);
+
+  //x3dom_draw_line("xa","red",  e2_c, e2_c.add(xa.multiply(e2_abc[0])));
+  //x3dom_draw_line("ya","green",e2_c, e2_c.add(ya.multiply(e2_abc[1])));
+  //x3dom_draw_line("za","blue", e2_c, e2_c.add(za.multiply(e2_abc[2])));
+
+  // to 0,0,0
+  //x3dom_draw_line("test0","white", e2_c, new x3dom.fields.SFVec3f(0,0,0));
+
+  //x3dom_draw_line("test1","tomato", new x3dom.fields.SFVec3f(0,0,0), new x3dom.fields.SFVec3f(100,0,0));
+  //x3dom_draw_line("test2","seagreen", new x3dom.fields.SFVec3f(0,0,0), new x3dom.fields.SFVec3f(0,100,0));
+  //x3dom_draw_line("test3","royalblue", new x3dom.fields.SFVec3f(0,0,0), new x3dom.fields.SFVec3f(0,0,100));
+  //x3dom_draw_line("test4","royalblue", e2_c.add(za.multiply(e2_abc[2])), new x3dom.fields.SFVec3f(0,0,100));
+
+
+  // e1 direction
+  x3dom_draw_line("helper_line0","white", e1_c, new x3dom.fields.SFVec3f(0,0,0));
+  // e1 direction from e2_c
+  x3dom_draw_line("helper_line1","white", e2_c.add(e1_c), e2_c.subtract(e1_c));
+
+
+  // E1: draw tilted ellipsoid
+
+  var e1_d = x3dom_3d_distance(e1_c.x,e1_c.y,e1_c.z,false);
+  var e1_k = 20;
+  var e1_abc = [e1_k*0.00038*e1_d,e1_k*0.00038*e1_d,2*e1_k*e1_d*e1_d/10000];
+  var e1_scale = e1_abc.join(",");
+  console.log("e1 scale: "+e1_scale);
+
+  // draw ellipsoid axes
+  var e1_dir  = e1_c;
+  e1_dir = e1_dir.normalize();
+
+  var xa = e1_dir.cross(new x3dom.fields.SFVec3f(0,1,0));
+  var ya = xa.cross(e1_dir);
+  var za = e1_dir.negate();
+
+  x3dom_draw_line("xa","red",  e2_c, e2_c.add(xa.multiply(e1_abc[0])));
+  x3dom_draw_line("ya","green",e2_c, e2_c.add(ya.multiply(e1_abc[1])));
+  x3dom_draw_line("za","blue", e2_c, e2_c.add(za.multiply(e1_abc[2])));
+
+  //console.log(xa.toString());
+  //console.log(ya.toString());
+  //console.log(za.toString());
+
+  // next construct rotation matrix
+  var RE1 = x3dom.fields.SFMatrix4f.identity();
+  RE1.setValue(xa,ya,za);
+
+  console.log(RE1.toString());
+
+  var translation = new x3dom.fields.SFVec3f(0,0,0);
+  var scaleFactor = new x3dom.fields.SFVec3f(1,1,1);
+  var rotation = new x3dom.fields.Quaternion(0,0,1,0);
+  var scaleOrientation = new x3dom.fields.Quaternion(0,0,1,0);
+  RE1.getTransform(translation, rotation, scaleFactor, scaleOrientation);
+
+  var q = rotation.toAxisAngle();
+  var q_str = q[0].toString()+" "+q[1];
+
+  x3dom_draw_ellipsoid("e1b","green",e2_c,q_str,e1_scale);
+
+  // now let's get to covariance matrix
+  var JE1 = x3dom_ellipsoid_inertia_tensor(1,e1_abc[0],e1_abc[1],e1_abc[2]);
+  var RE1i = RE1.inverse();
+  var RE1iJE1 = RE1i.mult(JE1);
+
+  var C = RE1iJE1.mult(RE1iJE1.transpose());
+
+  Cn = matrix_x3dom_to_numeric(C);
+  Bn = numeric.eig(Cn);
+
+  console.log(Bn);
+
+  var m = 1/5;
+
+  var jxx = Math.sqrt(Bn.lambda.x[0]);
+  var jyy = Math.sqrt(Bn.lambda.x[1]);
+  var jzz = Math.sqrt(Bn.lambda.x[2]);
+
+  var ee_a = Math.sqrt(1/2/m*(jyy+jzz-jxx));
+  var ee_b = Math.sqrt(1/2/m*(jxx+jzz-jyy));
+  var ee_c = Math.sqrt(1/2/m*(jxx+jyy-jzz));
+
+  console.log("e1 restored scale: "+[ee_a,ee_b,ee_c].join(" "));
+
+  var RE1n = new x3dom.fields.SFMatrix4f(
+               Bn.E.x[0][0], Bn.E.x[1][0], Bn.E.x[2][0], 0,
+               Bn.E.x[0][1], Bn.E.x[1][1], Bn.E.x[2][1], 0,
+               Bn.E.x[0][2], Bn.E.x[1][2], Bn.E.x[2][2], 0,
+                          0,             0,           0, 1
+             );
 
-  $("#deltasphere").remove();
-  $("#deltalink").remove();
+  console.log(RE1n.toString());
 
-  var transl = [p_w.x,p_w.y,p_w.z].join(",");
+  return 0;
+
+  //$(".my-markers").find("material").attr("transparency","0.5");
+
+  //$("#deltalink").remove();
+
+  var coords = [
+    "0 0 0",
+    p_w.x+" "+p_w.y+" "+p_w.z,
+    marker.x+" "+marker.y+" "+marker.z,
+    "0 0 0",
+  ].join(" ");
 
   var html = [
-    '<group id="deltasphere" class="deltasphere">',
+    '<group id="deltalink" class="deltalink">',
+    '  <switch whichChoice="0">',
+    '    <transform>',
+    '      <shape>',
+    '        <appearance>',
+    '          <material emissiveColor="white" transparency="0.0"></material>',
+    '        </appearance>',
+    '        <lineset vertexCount="4" solid="true" ccw="true" lit="true">',
+    '          <coordinate point="'+coords+'"></coordinate>',
+    '        </lineset>',
+    '      </shape>',
+    '    </transform>',
+    '  </switch>',
+    '</group>'
+  ].join('\n');
+
+  var sphere_element = $(html);
+  $('scene',Scene.element).append(sphere_element);
+
+  //var d = x3dom_3d_distance(p_w.x,p_w.y,p_w.z,false);
+  var d = x3dom_3d_distance(marker.x,marker.y,marker.z,false);
+  //console.log("Distance to pointe is "+d);
+
+  // z-axis
+  var mark_dir  = new x3dom.fields.SFVec3f(marker.x,marker.y,marker.z);
+  mark_dir = mark_dir.normalize();
+
+  var world_y = new x3dom.fields.SFVec3f(0,1,0);
+
+  var mark_x = mark_dir.cross(world_y);
+  var mark_y = mark_x.cross(mark_dir);
+  var mark_z = mark_dir.negate();
+
+  var M = x3dom.fields.SFMatrix4f.lookAt(new x3dom.fields.SFVec3f(0,0,0), mark_dir, mark_y);
+
+  var translation = new x3dom.fields.SFVec3f(0,0,0);
+  var scaleFactor = new x3dom.fields.SFVec3f(1,1,1);
+  var rotation = new x3dom.fields.Quaternion(0,0,1,0);
+  var scaleOrientation = new x3dom.fields.Quaternion(0,0,1,0);
+  M.getTransform(translation, rotation, scaleFactor, scaleOrientation);
+
+  console.log("Rotation matrix");
+  console.log(M.toString());
+
+  // draw vectors?!
+
+  var aa = rotation.toAxisAngle();
+  var aa_string = aa[0].toString()+" "+aa[1];
+
+  //
+  // now draw the 1st ellipse
+  //
+  mark_dir  = new x3dom.fields.SFVec3f(marker.x,marker.y,marker.z);
+  var k = 20;
+  var e1_abc = [k*0.00038*d,k*0.00038*d,2*k*d*d/10000];
+  var model_scale = e1_abc.join(",");
+
+  // at marker
+  //x3dom_draw_ellipsoid("e2a","gold",mark_dir.toString(),aa_string,model_scale);
+  // overlayed
+  //x3dom_draw_ellipsoid("e1b","green",transl,aa_string,model_scale);
+
+  // now Covariance
+
+  // E1 (model, tilted):
+  var J1 = x3dom_ellipsoid_inertia_tensor(1,e1_abc[0],e1_abc[1],e1_abc[2]);
+  var R1 = M;
+  var R1i = R1.inverse();
+  var R1iJ1 = R1i.mult(J1);
+
+  // E2 (map, vertical):
+  var J2 = x3dom_ellipsoid_inertia_tensor(1,e2_abc[0],e2_abc[1],e2_abc[2]);
+  var R2 = new x3dom.fields.SFMatrix4f(
+              1, 0, 0, 0,
+              0, 1, 0, 0,
+              0, 0, 1, 0,
+              0, 0, 0, 1
+           );
+  var R2i = R2.inverse();
+  var R2iJ2 = R2i.mult(J2);
+
+  var   C = R1iJ1.mult(R1iJ1.transpose());
+  //var   C = R2iJ2.mult(R2iJ2.transpose());
+  //C = C.add(R2iJ2.mult(R2iJ2.transpose()));
+
+  Cnum = matrix_x3dom_to_numeric(C);
+  Bnum = numeric.eig(Cnum);
+
+  var point = new x3dom.fields.SFVec3f(p_w.x,p_w.y,p_w.z);
+
+  var RNEW = new x3dom.fields.SFMatrix4f(
+              Bnum.E.x[0][0], Bnum.E.x[1][0], Bnum.E.x[2][0], 0,
+              Bnum.E.x[0][1], Bnum.E.x[1][1], Bnum.E.x[2][1], 0,
+              Bnum.E.x[0][2], Bnum.E.x[1][2], Bnum.E.x[2][2], 0,
+                           0,              0,              0, 1
+           );
+
+  console.log("R new");
+  console.log(Rnew.toString());
+
+  var xnew = new x3dom.fields.SFVec3f(Bnum.E.x[0][0],Bnum.E.x[1][0],Bnum.E.x[2][0]);
+  var ynew = new x3dom.fields.SFVec3f(Bnum.E.x[0][1],Bnum.E.x[1][1],Bnum.E.x[2][1]);
+  var znew = new x3dom.fields.SFVec3f(Bnum.E.x[0][2],Bnum.E.x[1][2],Bnum.E.x[2][2]);
+
+  var m = 1/5;
+
+  var jxx = Math.sqrt(Bnum.lambda.x[0]);
+  var jyy = Math.sqrt(Bnum.lambda.x[1]);
+  var jzz = Math.sqrt(Bnum.lambda.x[2]);
+
+  var ee_a = Math.sqrt(1/2/m*(jyy+jzz-jxx));
+  var ee_b = Math.sqrt(1/2/m*(jxx+jzz-jyy));
+  var ee_c = Math.sqrt(1/2/m*(jxx+jyy-jzz));
+
+  //x3dom_draw_line("yaxis","green",point, point.add(ynew.multiply(ee_b)));
+
+  x3dom_draw_line("xaxis","red",  point, point.add(xnew.multiply(ee_a)));
+  x3dom_draw_line("yaxis","green",point, point.add(ynew.multiply(ee_b)));
+  x3dom_draw_line("zaxis","blue", point, point.add(znew.multiply(ee_c)));
+
+  console.log("Covariance matrix");
+  console.log(C.toString());
+
+  // now what if I get transform from this?
+  var translation = new x3dom.fields.SFVec3f(0,0,0);
+  var scaleFactor = new x3dom.fields.SFVec3f(1,1,1);
+  var rotation = new x3dom.fields.Quaternion(0,0,1,0);
+  var scaleOrientation = new x3dom.fields.Quaternion(0,0,1,0);
+  C.getTransform(translation, rotation, scaleFactor, scaleOrientation);
+
+  console.log("Covariance decomposition");
+  console.log(translation.toString());
+  console.log(rotation.toString());
+  console.log(scaleFactor.toString());
+  console.log(scaleOrientation.toString());
+
+
+}
+
+function x3dom_draw_ellipsoid(id,color,transl,rotat,scale){
+
+  $("#"+id).remove();
+
+  var html = [
+    '<group id="'+id+'">',
     '  <switch whichChoice="0">',
     '    <transform translation="'+transl+'" >',
+    '      <transform rotation="'+rotat+'" >',
+    '        <transform scale="'+scale+'" >',
     '          <shape>',
     '            <appearance>',
-    '          <material diffuseColor="green" transparency="0.5"></material>',
+    '               <material diffuseColor="'+color+'" transparency="0.5"></material>',
     '            </appearance>',
-    '        <sphere radius="'+(x3dom_markersize()/2)+'"></sphere>',
+    '            <sphere radius="1"></sphere>',
     '          </shape>',
     '        </transform>',
+    '      </transform>',
+    '    </transform>',
     '  </switch>',
     '</group>'
   ].join('\n');
@@ -41,20 +310,22 @@ function x3dom_delta_markers(){
   var sphere_element = $(html);
   $('scene',Scene.element).append(sphere_element);
 
-  //$(".my-markers").find("material").attr("transparency","0.5");
+}
+
+function x3dom_draw_line(id,color,p1,p2){
 
   var coords = [
-    p_w.x+" "+p_w.y+" "+p_w.z,
-    marker.x+" "+marker.y+" "+marker.z,
+    p1.x+" "+p1.y+" "+p1.z,
+    p2.x+" "+p2.y+" "+p2.z
   ].join(" ");
 
   var html = [
-    '<group id="deltalink" class="deltalink">',
+    '<group id="'+id+'">',
     '  <switch whichChoice="0">',
     '    <transform>',
     '      <shape>',
     '        <appearance>',
-    '          <material emissiveColor="white" transparency="0.0"></material>',
+    '          <material emissiveColor="'+color+'" transparency="0.0"></material>',
     '        </appearance>',
     '        <lineset vertexCount="2" solid="true" ccw="true" lit="true">',
     '          <coordinate point="'+coords+'"></coordinate>',
@@ -68,5 +339,62 @@ function x3dom_delta_markers(){
   var sphere_element = $(html);
   $('scene',Scene.element).append(sphere_element);
 
+}
+
+// Ellipsoids parameters:
+
+// For map:
+//   m = 1,
+//   a = 0.1
+//   b = 0.1
+//   c = 30 or 50? or 100?
+
+// For model (depends on distance):
+//   m = 1
+//   a = 4.38*0.0001*d
+//   b = 4.38*0.0001*d
+//   c = d*d/10000 or d*d/25000
+
+function x3dom_ellipsoid_inertia_tensor(m,a,b,c){
+
+    var Jxx = 1/5*m*(b*b+c*c);
+    var Jyy = 1/5*m*(a*a+c*c);
+    var Jzz = 1/5*m*(a*a+b*b);
+
+    return new x3dom.fields.SFMatrix4f(
+        Jxx,   0,   0, 0,
+          0, Jyy,   0, 0,
+          0,   0, Jzz, 0,
+          0,   0,   0, 1
+    );
+
+}
+
+// also from 4x4 to 3x3
+function matrix_x3dom_to_numeric(m){
+
+  return [
+    [m._00, m._01, m._02],
+    [m._10, m._11, m._12],
+    [m._20, m._21, m._22]
+  ];
 
 }
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+

viewer.html

@@ -25,6 +25,8 @@
     <script type='text/javascript' src='js/leaflet/leaflet.camera-view-marker.js'></script>
     <script type='text/javascript' src='js/leaflet/leaflet.camera-view-marker.measure.js'></script>
 
+    <script type='text/javascript' src='js/numeric/numeric.js'></script>
+
     <script type='text/javascript' src='js/numbers/numbers.js'></script>
     <script type='text/javascript' src='js/numbers/numbers.matrix.extra.js'></script>
     <script type='text/javascript' src='js/numbers/numbers.calculus.extra.js'></script>