phase_plane_shallow_water_small.html

<h3> Shallow water phase plane</h3>
Drag the left and right states in the first plot to change them.
Drag the circle in the second plot to adjust the time.
<div id="fig_el126431399601080516646740895419"></div>
<script>
function mpld3_load_lib(url, callback){
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if(typeof(mpld3) !== "undefined" && mpld3._mpld3IsLoaded){
   // already loaded: just create the figure
   !function(mpld3){
       
    // init custom PPLaneNL plugin
    mpld3.register_plugin("drag", PPlaneNLPlugin);
    PPlaneNLPlugin.prototype = Object.create(mpld3.Plugin.prototype);
    PPlaneNLPlugin.prototype.constructor = PPlaneNLPlugin;
    PPlaneNLPlugin.prototype.requiredProps = ["id", "idmpoint", 
                                              "idg", "iditer", "iditer_charac", "idtime", "idhmax", "idoffm",
                                              "idhugol", "idhugor", "idintcl", "idintcr",
                                              "idhugol2", "idhugor2", "idintcl2", "idintcr2", 
                                              "idqlm", "idqmm", "idqrm", 
                                              "idshock1", "idshock2", "idrar1", "idrar2",
                                              "idrar1a", "idrar2a", "idrar1b", "idrar2b",
                                              "idrar1c", "idrar2c", "idrar1d", "idrar2d",
                                              "idtimedot", "idtimeline",
                                              "idq1", "idq2"];
    PPlaneNLPlugin.prototype.defaultProps = {}
    function PPlaneNLPlugin(fig, props){
        mpld3.Plugin.call(this, fig, props);
        mpld3.insert_css("#" + fig.figid + " path.dragging",
                         {"fill-opacity": "1.0 !important",
                          "stroke-opacity": "1.0 !important"});
    };

    // Call draw function, this function is being looped all the time
    PPlaneNLPlugin.prototype.draw = function(){
        // Get elements into script variables
        var obj = mpld3.get_element(this.props.id);
        var midpoint = mpld3.get_element(this.props.idmpoint);
        var g = this.props.idg;
        var iter = this.props.iditer;
        var iter_charac = this.props.iditer_charac;
        var time = this.props.idtime;
        var hmax = this.props.idhmax;
        var offm = this.props.idoffm;
        var hugol = mpld3.get_element(this.props.idhugol);
        var hugor = mpld3.get_element(this.props.idhugor);
        var intcl = mpld3.get_element(this.props.idintcl);
        var intcr = mpld3.get_element(this.props.idintcr);
        var hugol2 = mpld3.get_element(this.props.idhugol2);
        var hugor2 = mpld3.get_element(this.props.idhugor2);
        var intcl2 = mpld3.get_element(this.props.idintcl2);
        var intcr2 = mpld3.get_element(this.props.idintcr2);
        var qlm = mpld3.get_element(this.props.idqlm);
        var qmm = mpld3.get_element(this.props.idqmm);
        var qrm = mpld3.get_element(this.props.idqrm);
        var shock1 = mpld3.get_element(this.props.idshock1);
        var shock2 = mpld3.get_element(this.props.idshock2);
        var rar1 = mpld3.get_element(this.props.idrar1);
        var rar2 = mpld3.get_element(this.props.idrar2);
        var rar1a = mpld3.get_element(this.props.idrar1a);
        var rar2a = mpld3.get_element(this.props.idrar2a);
        var rar1b = mpld3.get_element(this.props.idrar1b);
        var rar2b = mpld3.get_element(this.props.idrar2b);
        var rar1c = mpld3.get_element(this.props.idrar1c);
        var rar2c = mpld3.get_element(this.props.idrar2c);
        var rar1d = mpld3.get_element(this.props.idrar1d);
        var rar2d = mpld3.get_element(this.props.idrar2d);
        var timedot = mpld3.get_element(this.props.idtimedot);
        var timeline = mpld3.get_element(this.props.idtimeline);
        var q1 = mpld3.get_element(this.props.idq1);
        var q2 = mpld3.get_element(this.props.idq2);
        
        // Set initial conditions for javascript calculations
        //var qleft = obj.offsets[0];
        //var qright = obj.offsets[1];
        //var qmid = midpoint.offsets[0];
        var offx = obj.ax.x(offm);
        var offy = offx;
        // Define initial values of hl, hr, hul and hur
        var hl = obj.offsets[0][0];
        var hul = obj.offsets[0][1];
        var hr = obj.offsets[1][0];
        var hur = obj.offsets[1][1];
        hmfinal = 0;
        humfinal = 0;
        
        // Main d3 drag function
        var drag = d3.behavior.drag()
            .origin(function(d) { return {x:obj.ax.x(d[0]),
                                          y:obj.ax.y(d[1])}; }) 
            .on("dragstart", dragstarted)
            .on("drag", dragged)
            .on("dragend", dragended);
        
        // Dragtime function for draggable time-dot (analog to main)
        var dragtime = d3.behavior.drag()
            .origin(function(d) { return {x:timedot.ax.x(d[0]),
                                          y:timedot.ax.y(d[1])}; })                              
            .on("dragstart", dragstarted)
            .on("drag", dragged)
            .on("dragend", dragended);
    
        // Set elements of ql and qr draggable points and call main drag function
        obj.elements()
           .data(obj.offsets)
           .style("cursor", "default")
           .call(drag);
            
        // Set elements for timedot draggable point and call dragtime function  
        timedot.elements()
           .data(timedot.offsets)
           .style("cursor", "default")
           .call(dragtime);

        // Begin phi and phi prime function
        function phi(h,hl,hr,hul,hur) {
            var ul = hul/hl;
            var ur = hur/hr;
            if (h < hl) {
                var termIC1 = 2.0*Math.sqrt(g*hl);
                var termIC2 = 2.0*Math.sqrt(g*h);
                var phil = ul + termIC1 - termIC2;
                var philp = -Math.sqrt(g/h);
            }
            if (h >= hl) {
                var termHL1 = (h - hl);
                var termHL2 = Math.sqrt(0.5*g*(1.0/h + 1.0/hl));
                var termHL3 = termHL1*termHL2;
                var phil = ul - termHL3 ;
                var nume = termHL2*4*h*h;
                var philp = -termHL2 + termHL1*g/nume;
            }
            if (h < hr) {
                var termIC1 = 2.0*Math.sqrt(g*hr);
                var termIC2 = 2.0*Math.sqrt(g*h);
                var phir = ur - termIC1 + termIC2;
                var phirp = Math.sqrt(g/h);
            }
            if (h >= hr) {
                var termHL1 = (h - hr);
                var termHL2 = Math.sqrt(0.5*g*(1.0/h + 1.0/hr));
                var termHL3 = termHL1*termHL2;
                var phir = ur + termHL3 ;
                var nume = termHL2*4*h*h;
                var phirp = termHL2 - termHL1*g/nume;
            }
            var phi = phil-phir;
            var phiprime = philp - phirp
            var um = 0.5*(phil + phir);
            return [phi,phiprime,um];
        }
        
        // Begin Newton iteration
        function newton(hstar,hl,hr,hul,hur) {
            var hn = hstar;
            var error = 1;
            while (error > 0.005) {
                var hold = hn;
                var phin = phi(hn,hl,hr,hul,hur);
                var hn = hold - phin[0]/phin[1];
                var um = phin[2];
                error = Math.abs(hold - hn);
            }
            return [hn,um];
        }
        
        // Calculate hugoniot loci
        function hugoloci(hm,hside,huside,sign) {
                var termHL1 = hm*(hm - hside);
                if (hm == 0) {
                    var termHL2 = 1.0; }
                else {
                   var termHL2 = Math.sqrt(0.5*g*(1.0/hm + 1.0/hside));}
                   var termHL3 = termHL1*termHL2;
                   var hloci = hm*huside/hside + sign*termHL3;
            return hloci;} 
            
        // Calculate integral curve
        function integralcurve(hm,hside,huside,sign) {
                var termIC1 = 2.0*hm*Math.sqrt(g*hside);
                var termIC2 = 2.0*hm*Math.sqrt(g*hm);
                var intcurve = hm*huside/hside - sign*(termIC1 - termIC2);
            return intcurve;}
            
        // Calculate solution plot of h and hu as function of x
        function solplot(hl,hm,hr,hul,hum,hur) {
            var lam = [];
            lam.push([-1000000, 0,0])
            var ul = hul/hl;
            var um = hum/hm;
            var ur = hur/hr;
            var shock1 = false;
            var shock2 = false;
            var qsol1 = d3.range(iter);
            var qsol2 = d3.range(iter);
            if (hm >= hl) {
                var s1 = time*(hum - hul)/(hm - hl);
                shock1 = true;
            } else {
                var s1b = [0,0];
                s1b[0] = time*(ul - Math.sqrt(g*hl));
                s1b[1] = time*(um - Math.sqrt(g*hm));
                s1b.sort(d3.ascending);
            }
            if (hm >= hr) {
                var s2 = time*(hur - hum)/(hr - hm);
                shock2 = true;
            } else {
                var s2b = [0,0];
                s2b[0] = time*(um + Math.sqrt(g*hm));
                s2b[1] = time*(ur + Math.sqrt(g*hr));
                s2b.sort(d3.ascending);
            }
            
            for (var ii=0; ii <2*iter; ii++){
                var xx = q1.data[ii][0];
                // Calculate plot solution for 1 charactersitic (shock or rarefaction)
                if (shock1) {
                    if (xx <= s1){ qsol1[ii] = hl; qsol2[ii] = hul;}
                    else { qsol1[ii] = hm; qsol2[ii] = hum;}
                }
                else {
                    if (xx <= s1b[0]) { qsol1[ii] = hl; qsol2[ii] = hul;}
                    else if (xx <= s1b[1]) {
                        var m1 = (hm - hl)/(s1b[1] - s1b[0]);
                        var m2 = (hum - hul)/(s1b[1] - s1b[0]);
                        qsol1[ii] = m1*(xx - s1b[0]) + hl;
                        qsol2[ii] = m2*(xx - s1b[0]) + hul;}
                    else { qsol1[ii] = hm; qsol2[ii] = hum;}
                }
                // Calculate plot solution for 2 charactersitic (shock or rarefaction)
                if (shock2) {
                    if (xx > s2) {qsol1[ii] = hr; qsol2[ii] = hur;}
                }
                else{
                    if (xx > s2b[0] && xx < s2b[1]) {
                        var m1 = (hr - hm)/(s2b[1] - s2b[0]);
                        var m2 = (hur - hum)/(s2b[1] - s2b[0]);
                        qsol1[ii] = m1*(xx - s2b[0]) + hm;
                        qsol2[ii] = m2*(xx - s2b[0]) + hum;}
                    else if (xx > s2b[1]) { qsol1[ii] = hr; qsol2[ii] = hur;}
                }
            }
            var solution = [qsol1,qsol2];
            return solution;
        }

        // Function to update middle state   
        function update_midstate(){
            var hstar = 0.05*(hl + hr);
            var solution = newton(hstar,hl,hr,hul,hur);
            hmfinal = solution[0];
            humfinal = solution[1]*hmfinal;
            var xx = obj.ax.x(hmfinal);
            var yy = obj.ax.y(humfinal);
            // Update middle state point and marker position
            midpoint.elements().transition().duration(5)
            .attr("transform", "translate(" + [xx, yy] + ")");
            // Move marker
            qmm.elements().transition().duration(1)
              .attr("transform", "translate(" + [xx + 0.7*offx, yy + 0.7*offy] + ")");
        }
        
        // Functon to update xt-plane
        function update_xtplane() {
         // Calculate shcok speeds from R-H conditions
         var lam1 = (humfinal - hul)/(hmfinal - hl);   
         var lam2 = (hur - humfinal)/(hr - hmfinal);   
         var lam1m = humfinal/hmfinal - Math.sqrt(g*hmfinal);
         var lam2m = humfinal/hmfinal + Math.sqrt(g*hmfinal);
         var lam1l = hul/hl - Math.sqrt(g*hl);
         var lam2r = hur/hr + Math.sqrt(g*hr);
         var color1 = "red";
         var color2 = "red";
         var thick1 = 4;
         var thick2 = 4;
         var fan = 0;
         for (var ii=0; ii<iter_charac; ii++) {
             if (hmfinal >= hl) {
                 shock1.data[ii][1] = shock1.data[ii][0]/lam1;
                 rar1.data[ii][1] = rar1.data[ii][0]/lam1;
                 rar1a.data[ii][1] = rar1a.data[ii][0]/lam1;
                 rar1b.data[ii][1] = rar1b.data[ii][0]/lam1;
                 rar1c.data[ii][1] = rar1c.data[ii][0]/lam1;
                 rar1d.data[ii][1] = rar1d.data[ii][0]/lam1;
                 console.log(rar2a.data);
                 color1 = "red";
                 thick1 = 4;
             } else {
                 shock1.data[ii][1] = shock1.data[ii][0]/lam1l;
                 rar1.data[ii][1] = rar1.data[ii][0]/lam1m;
                 fan = Math.abs(lam1m - lam1l)/5;
                 rar1a.data[ii][1] = rar1a.data[ii][0]/(lam1l + fan);
                 rar1b.data[ii][1] = rar1b.data[ii][0]/(lam1l + 2*fan);
                 rar1c.data[ii][1] = rar1c.data[ii][0]/(lam1l + 3*fan);
                 rar1d.data[ii][1] = rar1d.data[ii][0]/(lam1l + 4*fan);
                 color1 = "blue";
                 thick1 = 1;
             }
             if (hmfinal >= hr) {
                 shock2.data[ii][2] = shock2.data[ii][0]/lam2;
                 rar2.data[ii][2] = rar2.data[ii][0]/lam2;
                 rar2a.data[ii][2] = rar2a.data[ii][0]/lam2;
                 rar2b.data[ii][2] = rar2b.data[ii][0]/lam2;
                 rar2c.data[ii][2] = rar2c.data[ii][0]/lam2;
                 rar2d.data[ii][2] = rar2d.data[ii][0]/lam2;
                 color2 = "red";
                 thick2 = 4;
            } else {
                 shock2.data[ii][2] = shock2.data[ii][0]/lam2r;
                 rar2.data[ii][2] = rar2.data[ii][0]/lam2m;
                 fan = Math.abs(lam2r - lam2m)/5;
                 rar2a.data[ii][2] = rar2a.data[ii][0]/(lam2m + fan);
                 rar2b.data[ii][2] = rar2b.data[ii][0]/(lam2m + 2*fan);
                 rar2c.data[ii][2] = rar2c.data[ii][0]/(lam2m + 3*fan);
                 rar2d.data[ii][2] = rar2d.data[ii][0]/(lam2m + 4*fan);
                 color2 = "blue";
                 thick2 = 1;
            }                     
         }
         // Do transitions
         shock1.elements().transition().duration(5)
             .attr("d", shock1.datafunc(shock1.data))
             .style("stroke", color1)
             .style("stroke-width", thick1);
         shock2.elements().transition().duration(5)
             .attr("d", shock2.datafunc(shock2.data))
             .style("stroke", color2)
             .style("stroke-width", thick2);
         rar1.elements().transition().duration(5)
             .attr("d", rar1.datafunc(rar1.data))
             .style("stroke", color1)
             .style("stroke-width", thick1);
         rar2.elements().transition().duration(5)
             .attr("d", rar2.datafunc(rar2.data))
             .style("stroke", color2)
             .style("stroke-width", thick2);
         rar1a.elements().transition().duration(5)
             .attr("d", rar1a.datafunc(rar1a.data))
             .style("stroke", color1)
             .style("stroke-width", thick1);
         rar2a.elements().transition().duration(5)
             .attr("d", rar2a.datafunc(rar2a.data))
             .style("stroke", color2)
             .style("stroke-width", thick2);
         rar1b.elements().transition().duration(5)
             .attr("d", rar1b.datafunc(rar1b.data))
             .style("stroke", color1)
             .style("stroke-width", thick1);
         rar2b.elements().transition().duration(5)
             .attr("d", rar2b.datafunc(rar2b.data))
             .style("stroke", color2)
             .style("stroke-width", thick2);
         rar1c.elements().transition().duration(5)
             .attr("d", rar1c.datafunc(rar1c.data))
             .style("stroke", color1)
             .style("stroke-width", thick1);
         rar2c.elements().transition().duration(5)
             .attr("d", rar2c.datafunc(rar2c.data))
             .style("stroke", color2)
             .style("stroke-width", thick2);
         rar1d.elements().transition().duration(5)
             .attr("d", rar1d.datafunc(rar1d.data))
             .style("stroke", color1)
             .style("stroke-width", thick1);
         rar2d.elements().transition().duration(5)
             .attr("d", rar2d.datafunc(rar2d.data))
             .style("stroke", color2)
             .style("stroke-width", thick2);
        }
        
        // Function to update solution plots
        function update_solplots() {
            var qsol = solplot(hl,hmfinal,hr,hul,humfinal,hur);
                for (var ii=0; ii<2*iter; ii++){
                    q1.data[ii][1] = qsol[0][ii]; 
                    q2.data[ii][2] = qsol[1][ii]; 
                }
                // Do transitions
                 q1.elements().transition().duration(5)
                     .attr("d", q1.datafunc(q1.data));
                 q2.elements().transition().duration(5)
                     .attr("d", q2.datafunc(q2.data));
        }
        
        // Initialize solution with given initial states before interacting
        update_midstate();
        update_xtplane();
        update_solplots();
        
        // Begin drag function
        function dragstarted(d) {
          d3.event.sourceEvent.stopPropagation();
          d3.select(this).classed("dragging", true);
        }
   
        // The drag function called while dragging is happening (meat of code here)
        function dragged(d,i) {
          if (i == 0  || i ==1) {
              // Convert mouse coordinates in drag event (d3.event) to python coordinates d
              d[0] = obj.ax.x.invert(d3.event.x);
              d[1] = obj.ax.y.invert(d3.event.y);             
              // Move ql and qr stored in obj (they have been selected in drag)
              d3.select(this)
                .attr("transform", "translate(" + [d3.event.x,d3.event.y] + ")");
              // If obj corresponds to ql, move all the other left elements 
              }
          if (i==0){
              // Move marker
              qlm.elements().transition().duration(1)
                  .attr("transform", "translate(" + [d3.event.x + offx, d3.event.y + offy] + ")");     
              // Re-calculate inital left variables when dragging 
              hl = obj.offsets[0][0];
              hul = obj.offsets[0][1];
              
              // Draw Hugoniot loci through left state    
              for (var ii=0; ii<iter; ii++) {
                //Left from hl
                hugol.data[ii][0] = ii*d[0]/(1.0*iter);
                var hm = hugol.data[ii][0];
                hugol.data[ii][1] = hugoloci(hm,hl,hul,-1) ;
                //Right from hl
                hugol2.data[ii][0] = d[0] + ii*(hmax-d[0])/(1.0*iter);
                var hm2 = hugol2.data[ii][0];
                hugol2.data[ii][1] = hugoloci(hm2,hl,hul,-1) ;
                }
              // Do transitions      
              hugol.elements().transition().duration(5)
                  .attr("d", hugol.datafunc(hugol.data))
                  .style("stroke-dasharray", ("7,7"));
              hugol2.elements().transition().duration(5)
                  .attr("d", hugol2.datafunc(hugol2.data));
                               
                  
              // Draw integral curve through left state (note index bug for intcl.data[ii][j])
              // and intcl2 it should be j =0,1 not j=1,2. Arrays somehow grow of sixe in mpld3
              for (var ii=0; ii<iter; ii++) {
                //Left from hl
                intcl.data[ii][1] = ii*d[0]/(1.0*iter);
                var hm = intcl.data[ii][1];
                intcl.data[ii][2] = integralcurve(hm,hl,hul,-1);
                //Right from hl
                intcl2.data[ii][1] = d[0] + ii*(hmax-d[0])/(1.0*iter);
                var hm2 = intcl2.data[ii][1];
                intcl2.data[ii][2] = integralcurve(hm2,hl,hul,-1);
              }
              // Do transitions      
              intcl.elements().transition().duration(5)
                  .attr("d", intcl.datafunc(intcl.data));
              intcl2.elements().transition().duration(5)
                  .attr("d", intcl2.datafunc(intcl2.data))
                  .style("stroke-dasharray", ("7,7"));
                  
          }      
          // if element corresponds to qr
          else if (i==1) {
              // Move marker
              qrm.elements().transition().duration(1)
                  .attr("transform", "translate(" + [d3.event.x + offx, d3.event.y + offy] + ")");
              // Re-calculate inital right variables when dragging
              hr = obj.offsets[1][0];
              hur = obj.offsets[1][1];
              
              // Draw Hugoniot loci through right state    
              for (var ii=0; ii<iter; ii++) {
                //Left from hr
                hugor.data[ii][0] = ii*d[0]/(1.0*iter);
                var hm = hugor.data[ii][0];
                hugor.data[ii][1] = hugoloci(hm,hr,hur,1) ;
                //Right from hr
                hugor2.data[ii][0] = d[0] + ii*(hmax-d[0])/(1.0*iter);
                var hm2 = hugor2.data[ii][0];
                hugor2.data[ii][1] = hugoloci(hm2,hr,hur,1) ;
                }
              // Do transitions      
              hugor.elements().transition().duration(5)
                  .attr("d", hugor.datafunc(hugor.data))
                  .style("stroke-dasharray", ("7,7"));
              hugor2.elements().transition().duration(5)
                  .attr("d", hugor2.datafunc(hugor2.data));
                    
              // Draw integral curve through right state (note index bug for intcr.data[ii][j])
              // and intcr2 it should be j =0,1 not j=1,2. Arrays somehow grow of sixe in mpld3   
              for (var ii=0; ii<iter; ii++) {
                //Left from hr
                intcr.data[ii][1] = ii*d[0]/(1.0*iter);
                var hm = intcr.data[ii][1];
                intcr.data[ii][2] = integralcurve(hm,hr,hur,1);
                //Right from hr
                intcr2.data[ii][1] = d[0] + ii*(hmax-d[0])/(1.0*iter);
                var hm2 = intcr2.data[ii][1];
                intcr2.data[ii][2] = integralcurve(hm2,hr,hur,1);
              }
              // Do transitions      
              intcr.elements().transition().duration(5)
                  .attr("d", intcl.datafunc(intcr.data));
              intcr2.elements().transition().duration(5)
                  .attr("d", intcr2.datafunc(intcr2.data))
                  .style("stroke-dasharray", ("7,7"));
            }
            // If time marker is moved
            else if (i==2) {
                // Convert mouse coordinates in drag event (d3.event) to python coordinates d
                d[0] = timedot.ax.x.invert(d3.event.x);
                d[1] = timedot.ax.y.invert(d3.event.y);      
                d3.select(this)
                    .attr("transform", "translate(" + [d3.event.x,d3.event.y] + ")");
                // Calculate timedot position and assign it
                var ty = timedot.ax.y.invert(d3.event.y);
                if (ty >=0) {
                    timeline.data[0][1] = ty;
                    timeline.data[1][1] = ty;
                    timeline.data[2][1] = ty;
                    time = ty;
                }
                // Do transitions
                timeline.elements().transition().duration(5)
                    .attr("d", timeline.datafunc(timeline.data));
            }
            
            // Calculate middle state    
            update_midstate();
                  
            // Calculate solution plots of h and hu
            update_solplots();
            
            // Update characteristic in x-t plane
            update_xtplane();
             
        }
        // End dragging
        function dragended(d) {
          d3.select(this).classed("dragging", false);
        }
    }
    mpld3.register_plugin("drag", PPlaneNLPlugin); 
    
       mpld3.draw_figure("fig_el126431399601080516646740895419", {"axes": [{"xlim": [0.0, 10.0], "yscale": "linear", "axesbg": "#FFFFFF", "texts": [{"v_baseline": "hanging", "h_anchor": "middle", "color": "#000000", "text": "h", "coordinates": "axes", "zorder": 3, "alpha": 1, "fontsize": 17.0, "position": [0.5, -0.08625000000000016], "rotation": -0.0, "id": "el12643139960686845520"}, {"v_baseline": "auto", "h_anchor": "middle", "color": "#000000", "text": "hu", "coordinates": "axes", "zorder": 3, "alpha": 1, "fontsize": 17.0, "position": [-0.084034276589423668, 0.49999999999999978], "rotation": -90.0, "id": "el12643139959698296976"}, {"v_baseline": "auto", "h_anchor": "middle", "color": "#000000", "text": "Phase plane", "coordinates": "axes", "zorder": 3, "alpha": 1, "fontsize": 18.0, "position": [0.5, 1.0199652777777777], "rotation": -0.0, "id": "el12643139959698346896"}, {"v_baseline": "auto", "h_anchor": "start", "color": "#000000", "text": "", "coordinates": "axes", "zorder": 1000003.0, "alpha": 1, "fontsize": 12.0, "position": [-0.12647058823529414, -1.5874999999999997], "rotation": -0.0, "id": "el12643139959601033104"}, {"v_baseline": "auto", "h_anchor": "start", "color": "#000000", "text": "Hugoniot Loci", "coordinates": "axes", "zorder": 1000003.0, "alpha": 1, "fontsize": 10.0, "position": [0.11816696375519908, 0.93531249999999999], "rotation": -0.0, "id": "el12643139959600945424"}, {"v_baseline": "auto", "h_anchor": "start", "color": "#000000", "text": "Hugoniot Loci (unphysical)", "coordinates": "axes", "zorder": 1000003.0, "alpha": 1, "fontsize": 10.0, "position": [0.11816696375519908, 0.87940972222222213], "rotation": -0.0, "id": "el12643139959601017360"}, {"v_baseline": "auto", "h_anchor": "start", "color": "#000000", "text": "Integral Curves", "coordinates": "axes", "zorder": 1000003.0, "alpha": 1, "fontsize": 10.0, "position": [0.11816696375519908, 0.82350694444444428], "rotation": -0.0, "id": "el12643139959600943760"}, {"v_baseline": "auto", "h_anchor": "start", "color": "#000000", "text": "Integral Curves (unphysical)", "coordinates": "axes", "zorder": 1000003.0, "alpha": 1, "fontsize": 10.0, "position": [0.11816696375519908, 0.76760416666666687], "rotation": -0.0, "id": "el12643139959601030160"}], "zoomable": true, "images": [], "xdomain": [0.0, 10.0], "ylim": [-15.0, 15.0], "paths": [{"edgecolor": "#000000", "facecolor": "#FFFFFF", "edgewidth": 1.0, "pathcodes": ["M", "L", "L", "L", "Z"], "yindex": 1, "coordinates": "axes", "dasharray": "10,0", "zorder": 1000001.0, "alpha": 1, "xindex": 0, "data": "data10", "id": "el12643139959600944080"}], "sharey": [], "sharex": [], "axesbgalpha": null, "axes": [{"scale": "linear", "tickformat": null, "grid": {"color": "#000000", "alpha": 0.1, "dasharray": "6,6", "gridOn": true}, "fontsize": 12.0, "position": "bottom", "nticks": 6, "tickvalues": null}, {"scale": "linear", "tickformat": null, "grid": {"color": "#000000", "alpha": 0.1, "dasharray": "6,6", "gridOn": true}, "fontsize": 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[11.1, 169.76593783806587, -169.76593783806587]], "data01": [[-1.0, -1.0]]}, "id": "el12643139960108051664"});
   }(mpld3);
}else if(typeof define === "function" && define.amd){
   // require.js is available: use it to load d3/mpld3
   require.config({paths: {d3: "https://mpld3.github.io/js/d3.v3.min"}});
   require(["d3"], function(d3){
      window.d3 = d3;
      mpld3_load_lib("https://mpld3.github.io/js/mpld3.v0.2.js", function(){
         
    // init custom PPLaneNL plugin
    mpld3.register_plugin("drag", PPlaneNLPlugin);
    PPlaneNLPlugin.prototype = Object.create(mpld3.Plugin.prototype);
    PPlaneNLPlugin.prototype.constructor = PPlaneNLPlugin;
    PPlaneNLPlugin.prototype.requiredProps = ["id", "idmpoint", 
                                              "idg", "iditer", "iditer_charac", "idtime", "idhmax", "idoffm",
                                              "idhugol", "idhugor", "idintcl", "idintcr",
                                              "idhugol2", "idhugor2", "idintcl2", "idintcr2", 
                                              "idqlm", "idqmm", "idqrm", 
                                              "idshock1", "idshock2", "idrar1", "idrar2",
                                              "idrar1a", "idrar2a", "idrar1b", "idrar2b",
                                              "idrar1c", "idrar2c", "idrar1d", "idrar2d",
                                              "idtimedot", "idtimeline",
                                              "idq1", "idq2"];
    PPlaneNLPlugin.prototype.defaultProps = {}
    function PPlaneNLPlugin(fig, props){
        mpld3.Plugin.call(this, fig, props);
        mpld3.insert_css("#" + fig.figid + " path.dragging",
                         {"fill-opacity": "1.0 !important",
                          "stroke-opacity": "1.0 !important"});
    };

    // Call draw function, this function is being looped all the time
    PPlaneNLPlugin.prototype.draw = function(){
        // Get elements into script variables
        var obj = mpld3.get_element(this.props.id);
        var midpoint = mpld3.get_element(this.props.idmpoint);
        var g = this.props.idg;
        var iter = this.props.iditer;
        var iter_charac = this.props.iditer_charac;
        var time = this.props.idtime;
        var hmax = this.props.idhmax;
        var offm = this.props.idoffm;
        var hugol = mpld3.get_element(this.props.idhugol);
        var hugor = mpld3.get_element(this.props.idhugor);
        var intcl = mpld3.get_element(this.props.idintcl);
        var intcr = mpld3.get_element(this.props.idintcr);
        var hugol2 = mpld3.get_element(this.props.idhugol2);
        var hugor2 = mpld3.get_element(this.props.idhugor2);
        var intcl2 = mpld3.get_element(this.props.idintcl2);
        var intcr2 = mpld3.get_element(this.props.idintcr2);
        var qlm = mpld3.get_element(this.props.idqlm);
        var qmm = mpld3.get_element(this.props.idqmm);
        var qrm = mpld3.get_element(this.props.idqrm);
        var shock1 = mpld3.get_element(this.props.idshock1);
        var shock2 = mpld3.get_element(this.props.idshock2);
        var rar1 = mpld3.get_element(this.props.idrar1);
        var rar2 = mpld3.get_element(this.props.idrar2);
        var rar1a = mpld3.get_element(this.props.idrar1a);
        var rar2a = mpld3.get_element(this.props.idrar2a);
        var rar1b = mpld3.get_element(this.props.idrar1b);
        var rar2b = mpld3.get_element(this.props.idrar2b);
        var rar1c = mpld3.get_element(this.props.idrar1c);
        var rar2c = mpld3.get_element(this.props.idrar2c);
        var rar1d = mpld3.get_element(this.props.idrar1d);
        var rar2d = mpld3.get_element(this.props.idrar2d);
        var timedot = mpld3.get_element(this.props.idtimedot);
        var timeline = mpld3.get_element(this.props.idtimeline);
        var q1 = mpld3.get_element(this.props.idq1);
        var q2 = mpld3.get_element(this.props.idq2);
        
        // Set initial conditions for javascript calculations
        //var qleft = obj.offsets[0];
        //var qright = obj.offsets[1];
        //var qmid = midpoint.offsets[0];
        var offx = obj.ax.x(offm);
        var offy = offx;
        // Define initial values of hl, hr, hul and hur
        var hl = obj.offsets[0][0];
        var hul = obj.offsets[0][1];
        var hr = obj.offsets[1][0];
        var hur = obj.offsets[1][1];
        hmfinal = 0;
        humfinal = 0;
        
        // Main d3 drag function
        var drag = d3.behavior.drag()
            .origin(function(d) { return {x:obj.ax.x(d[0]),
                                          y:obj.ax.y(d[1])}; }) 
            .on("dragstart", dragstarted)
            .on("drag", dragged)
            .on("dragend", dragended);
        
        // Dragtime function for draggable time-dot (analog to main)
        var dragtime = d3.behavior.drag()
            .origin(function(d) { return {x:timedot.ax.x(d[0]),
                                          y:timedot.ax.y(d[1])}; })                              
            .on("dragstart", dragstarted)
            .on("drag", dragged)
            .on("dragend", dragended);
    
        // Set elements of ql and qr draggable points and call main drag function
        obj.elements()
           .data(obj.offsets)
           .style("cursor", "default")
           .call(drag);
            
        // Set elements for timedot draggable point and call dragtime function  
        timedot.elements()
           .data(timedot.offsets)
           .style("cursor", "default")
           .call(dragtime);

        // Begin phi and phi prime function
        function phi(h,hl,hr,hul,hur) {
            var ul = hul/hl;
            var ur = hur/hr;
            if (h < hl) {
                var termIC1 = 2.0*Math.sqrt(g*hl);
                var termIC2 = 2.0*Math.sqrt(g*h);
                var phil = ul + termIC1 - termIC2;
                var philp = -Math.sqrt(g/h);
            }
            if (h >= hl) {
                var termHL1 = (h - hl);
                var termHL2 = Math.sqrt(0.5*g*(1.0/h + 1.0/hl));
                var termHL3 = termHL1*termHL2;
                var phil = ul - termHL3 ;
                var nume = termHL2*4*h*h;
                var philp = -termHL2 + termHL1*g/nume;
            }
            if (h < hr) {
                var termIC1 = 2.0*Math.sqrt(g*hr);
                var termIC2 = 2.0*Math.sqrt(g*h);
                var phir = ur - termIC1 + termIC2;
                var phirp = Math.sqrt(g/h);
            }
            if (h >= hr) {
                var termHL1 = (h - hr);
                var termHL2 = Math.sqrt(0.5*g*(1.0/h + 1.0/hr));
                var termHL3 = termHL1*termHL2;
                var phir = ur + termHL3 ;
                var nume = termHL2*4*h*h;
                var phirp = termHL2 - termHL1*g/nume;
            }
            var phi = phil-phir;
            var phiprime = philp - phirp
            var um = 0.5*(phil + phir);
            return [phi,phiprime,um];
        }
        
        // Begin Newton iteration
        function newton(hstar,hl,hr,hul,hur) {
            var hn = hstar;
            var error = 1;
            while (error > 0.005) {
                var hold = hn;
                var phin = phi(hn,hl,hr,hul,hur);
                var hn = hold - phin[0]/phin[1];
                var um = phin[2];
                error = Math.abs(hold - hn);
            }
            return [hn,um];
        }
        
        // Calculate hugoniot loci
        function hugoloci(hm,hside,huside,sign) {
                var termHL1 = hm*(hm - hside);
                if (hm == 0) {
                    var termHL2 = 1.0; }
                else {
                   var termHL2 = Math.sqrt(0.5*g*(1.0/hm + 1.0/hside));}
                   var termHL3 = termHL1*termHL2;
                   var hloci = hm*huside/hside + sign*termHL3;
            return hloci;} 
            
        // Calculate integral curve
        function integralcurve(hm,hside,huside,sign) {
                var termIC1 = 2.0*hm*Math.sqrt(g*hside);
                var termIC2 = 2.0*hm*Math.sqrt(g*hm);
                var intcurve = hm*huside/hside - sign*(termIC1 - termIC2);
            return intcurve;}
            
        // Calculate solution plot of h and hu as function of x
        function solplot(hl,hm,hr,hul,hum,hur) {
            var lam = [];
            lam.push([-1000000, 0,0])
            var ul = hul/hl;
            var um = hum/hm;
            var ur = hur/hr;
            var shock1 = false;
            var shock2 = false;
            var qsol1 = d3.range(iter);
            var qsol2 = d3.range(iter);
            if (hm >= hl) {
                var s1 = time*(hum - hul)/(hm - hl);
                shock1 = true;
            } else {
                var s1b = [0,0];
                s1b[0] = time*(ul - Math.sqrt(g*hl));
                s1b[1] = time*(um - Math.sqrt(g*hm));
                s1b.sort(d3.ascending);
            }
            if (hm >= hr) {
                var s2 = time*(hur - hum)/(hr - hm);
                shock2 = true;
            } else {
                var s2b = [0,0];
                s2b[0] = time*(um + Math.sqrt(g*hm));
                s2b[1] = time*(ur + Math.sqrt(g*hr));
                s2b.sort(d3.ascending);
            }
            
            for (var ii=0; ii <2*iter; ii++){
                var xx = q1.data[ii][0];
                // Calculate plot solution for 1 charactersitic (shock or rarefaction)
                if (shock1) {
                    if (xx <= s1){ qsol1[ii] = hl; qsol2[ii] = hul;}
                    else { qsol1[ii] = hm; qsol2[ii] = hum;}
                }
                else {
                    if (xx <= s1b[0]) { qsol1[ii] = hl; qsol2[ii] = hul;}
                    else if (xx <= s1b[1]) {
                        var m1 = (hm - hl)/(s1b[1] - s1b[0]);
                        var m2 = (hum - hul)/(s1b[1] - s1b[0]);
                        qsol1[ii] = m1*(xx - s1b[0]) + hl;
                        qsol2[ii] = m2*(xx - s1b[0]) + hul;}
                    else { qsol1[ii] = hm; qsol2[ii] = hum;}
                }
                // Calculate plot solution for 2 charactersitic (shock or rarefaction)
                if (shock2) {
                    if (xx > s2) {qsol1[ii] = hr; qsol2[ii] = hur;}
                }
                else{
                    if (xx > s2b[0] && xx < s2b[1]) {
                        var m1 = (hr - hm)/(s2b[1] - s2b[0]);
                        var m2 = (hur - hum)/(s2b[1] - s2b[0]);
                        qsol1[ii] = m1*(xx - s2b[0]) + hm;
                        qsol2[ii] = m2*(xx - s2b[0]) + hum;}
                    else if (xx > s2b[1]) { qsol1[ii] = hr; qsol2[ii] = hur;}
                }
            }
            var solution = [qsol1,qsol2];
            return solution;
        }

        // Function to update middle state   
        function update_midstate(){
            var hstar = 0.05*(hl + hr);
            var solution = newton(hstar,hl,hr,hul,hur);
            hmfinal = solution[0];
            humfinal = solution[1]*hmfinal;
            var xx = obj.ax.x(hmfinal);
            var yy = obj.ax.y(humfinal);
            // Update middle state point and marker position
            midpoint.elements().transition().duration(5)
            .attr("transform", "translate(" + [xx, yy] + ")");
            // Move marker
            qmm.elements().transition().duration(1)
              .attr("transform", "translate(" + [xx + 0.7*offx, yy + 0.7*offy] + ")");
        }
        
        // Functon to update xt-plane
        function update_xtplane() {
         // Calculate shcok speeds from R-H conditions
         var lam1 = (humfinal - hul)/(hmfinal - hl);   
         var lam2 = (hur - humfinal)/(hr - hmfinal);   
         var lam1m = humfinal/hmfinal - Math.sqrt(g*hmfinal);
         var lam2m = humfinal/hmfinal + Math.sqrt(g*hmfinal);
         var lam1l = hul/hl - Math.sqrt(g*hl);
         var lam2r = hur/hr + Math.sqrt(g*hr);
         var color1 = "red";
         var color2 = "red";
         var thick1 = 4;
         var thick2 = 4;
         var fan = 0;
         for (var ii=0; ii<iter_charac; ii++) {
             if (hmfinal >= hl) {
                 shock1.data[ii][1] = shock1.data[ii][0]/lam1;
                 rar1.data[ii][1] = rar1.data[ii][0]/lam1;
                 rar1a.data[ii][1] = rar1a.data[ii][0]/lam1;
                 rar1b.data[ii][1] = rar1b.data[ii][0]/lam1;
                 rar1c.data[ii][1] = rar1c.data[ii][0]/lam1;
                 rar1d.data[ii][1] = rar1d.data[ii][0]/lam1;
                 console.log(rar2a.data);
                 color1 = "red";
                 thick1 = 4;
             } else {
                 shock1.data[ii][1] = shock1.data[ii][0]/lam1l;
                 rar1.data[ii][1] = rar1.data[ii][0]/lam1m;
                 fan = Math.abs(lam1m - lam1l)/5;
                 rar1a.data[ii][1] = rar1a.data[ii][0]/(lam1l + fan);
                 rar1b.data[ii][1] = rar1b.data[ii][0]/(lam1l + 2*fan);
                 rar1c.data[ii][1] = rar1c.data[ii][0]/(lam1l + 3*fan);
                 rar1d.data[ii][1] = rar1d.data[ii][0]/(lam1l + 4*fan);
                 color1 = "blue";
                 thick1 = 1;
             }
             if (hmfinal >= hr) {
                 shock2.data[ii][2] = shock2.data[ii][0]/lam2;
                 rar2.data[ii][2] = rar2.data[ii][0]/lam2;
                 rar2a.data[ii][2] = rar2a.data[ii][0]/lam2;
                 rar2b.data[ii][2] = rar2b.data[ii][0]/lam2;
                 rar2c.data[ii][2] = rar2c.data[ii][0]/lam2;
                 rar2d.data[ii][2] = rar2d.data[ii][0]/lam2;
                 color2 = "red";
                 thick2 = 4;
            } else {
                 shock2.data[ii][2] = shock2.data[ii][0]/lam2r;
                 rar2.data[ii][2] = rar2.data[ii][0]/lam2m;
                 fan = Math.abs(lam2r - lam2m)/5;
                 rar2a.data[ii][2] = rar2a.data[ii][0]/(lam2m + fan);
                 rar2b.data[ii][2] = rar2b.data[ii][0]/(lam2m + 2*fan);
                 rar2c.data[ii][2] = rar2c.data[ii][0]/(lam2m + 3*fan);
                 rar2d.data[ii][2] = rar2d.data[ii][0]/(lam2m + 4*fan);
                 color2 = "blue";
                 thick2 = 1;
            }                     
         }
         // Do transitions
         shock1.elements().transition().duration(5)
             .attr("d", shock1.datafunc(shock1.data))
             .style("stroke", color1)
             .style("stroke-width", thick1);
         shock2.elements().transition().duration(5)
             .attr("d", shock2.datafunc(shock2.data))
             .style("stroke", color2)
             .style("stroke-width", thick2);
         rar1.elements().transition().duration(5)
             .attr("d", rar1.datafunc(rar1.data))
             .style("stroke", color1)
             .style("stroke-width", thick1);
         rar2.elements().transition().duration(5)
             .attr("d", rar2.datafunc(rar2.data))
             .style("stroke", color2)
             .style("stroke-width", thick2);
         rar1a.elements().transition().duration(5)
             .attr("d", rar1a.datafunc(rar1a.data))
             .style("stroke", color1)
             .style("stroke-width", thick1);
         rar2a.elements().transition().duration(5)
             .attr("d", rar2a.datafunc(rar2a.data))
             .style("stroke", color2)
             .style("stroke-width", thick2);
         rar1b.elements().transition().duration(5)
             .attr("d", rar1b.datafunc(rar1b.data))
             .style("stroke", color1)
             .style("stroke-width", thick1);
         rar2b.elements().transition().duration(5)
             .attr("d", rar2b.datafunc(rar2b.data))
             .style("stroke", color2)
             .style("stroke-width", thick2);
         rar1c.elements().transition().duration(5)
             .attr("d", rar1c.datafunc(rar1c.data))
             .style("stroke", color1)
             .style("stroke-width", thick1);
         rar2c.elements().transition().duration(5)
             .attr("d", rar2c.datafunc(rar2c.data))
             .style("stroke", color2)
             .style("stroke-width", thick2);
         rar1d.elements().transition().duration(5)
             .attr("d", rar1d.datafunc(rar1d.data))
             .style("stroke", color1)
             .style("stroke-width", thick1);
         rar2d.elements().transition().duration(5)
             .attr("d", rar2d.datafunc(rar2d.data))
             .style("stroke", color2)
             .style("stroke-width", thick2);
        }
        
        // Function to update solution plots
        function update_solplots() {
            var qsol = solplot(hl,hmfinal,hr,hul,humfinal,hur);
                for (var ii=0; ii<2*iter; ii++){
                    q1.data[ii][1] = qsol[0][ii]; 
                    q2.data[ii][2] = qsol[1][ii]; 
                }
                // Do transitions
                 q1.elements().transition().duration(5)
                     .attr("d", q1.datafunc(q1.data));
                 q2.elements().transition().duration(5)
                     .attr("d", q2.datafunc(q2.data));
        }
        
        // Initialize solution with given initial states before interacting
        update_midstate();
        update_xtplane();
        update_solplots();
        
        // Begin drag function
        function dragstarted(d) {
          d3.event.sourceEvent.stopPropagation();
          d3.select(this).classed("dragging", true);
        }
   
        // The drag function called while dragging is happening (meat of code here)
        function dragged(d,i) {
          if (i == 0  || i ==1) {
              // Convert mouse coordinates in drag event (d3.event) to python coordinates d
              d[0] = obj.ax.x.invert(d3.event.x);
              d[1] = obj.ax.y.invert(d3.event.y);             
              // Move ql and qr stored in obj (they have been selected in drag)
              d3.select(this)
                .attr("transform", "translate(" + [d3.event.x,d3.event.y] + ")");
              // If obj corresponds to ql, move all the other left elements 
              }
          if (i==0){
              // Move marker
              qlm.elements().transition().duration(1)
                  .attr("transform", "translate(" + [d3.event.x + offx, d3.event.y + offy] + ")");     
              // Re-calculate inital left variables when dragging 
              hl = obj.offsets[0][0];
              hul = obj.offsets[0][1];
              
              // Draw Hugoniot loci through left state    
              for (var ii=0; ii<iter; ii++) {
                //Left from hl
                hugol.data[ii][0] = ii*d[0]/(1.0*iter);
                var hm = hugol.data[ii][0];
                hugol.data[ii][1] = hugoloci(hm,hl,hul,-1) ;
                //Right from hl
                hugol2.data[ii][0] = d[0] + ii*(hmax-d[0])/(1.0*iter);
                var hm2 = hugol2.data[ii][0];
                hugol2.data[ii][1] = hugoloci(hm2,hl,hul,-1) ;
                }
              // Do transitions      
              hugol.elements().transition().duration(5)
                  .attr("d", hugol.datafunc(hugol.data))
                  .style("stroke-dasharray", ("7,7"));
              hugol2.elements().transition().duration(5)
                  .attr("d", hugol2.datafunc(hugol2.data));
                               
                  
              // Draw integral curve through left state (note index bug for intcl.data[ii][j])
              // and intcl2 it should be j =0,1 not j=1,2. Arrays somehow grow of sixe in mpld3
              for (var ii=0; ii<iter; ii++) {
                //Left from hl
                intcl.data[ii][1] = ii*d[0]/(1.0*iter);
                var hm = intcl.data[ii][1];
                intcl.data[ii][2] = integralcurve(hm,hl,hul,-1);
                //Right from hl
                intcl2.data[ii][1] = d[0] + ii*(hmax-d[0])/(1.0*iter);
                var hm2 = intcl2.data[ii][1];
                intcl2.data[ii][2] = integralcurve(hm2,hl,hul,-1);
              }
              // Do transitions      
              intcl.elements().transition().duration(5)
                  .attr("d", intcl.datafunc(intcl.data));
              intcl2.elements().transition().duration(5)
                  .attr("d", intcl2.datafunc(intcl2.data))
                  .style("stroke-dasharray", ("7,7"));
                  
          }      
          // if element corresponds to qr
          else if (i==1) {
              // Move marker
              qrm.elements().transition().duration(1)
                  .attr("transform", "translate(" + [d3.event.x + offx, d3.event.y + offy] + ")");
              // Re-calculate inital right variables when dragging
              hr = obj.offsets[1][0];
              hur = obj.offsets[1][1];
              
              // Draw Hugoniot loci through right state    
              for (var ii=0; ii<iter; ii++) {
                //Left from hr
                hugor.data[ii][0] = ii*d[0]/(1.0*iter);
                var hm = hugor.data[ii][0];
                hugor.data[ii][1] = hugoloci(hm,hr,hur,1) ;
                //Right from hr
                hugor2.data[ii][0] = d[0] + ii*(hmax-d[0])/(1.0*iter);
                var hm2 = hugor2.data[ii][0];
                hugor2.data[ii][1] = hugoloci(hm2,hr,hur,1) ;
                }
              // Do transitions      
              hugor.elements().transition().duration(5)
                  .attr("d", hugor.datafunc(hugor.data))
                  .style("stroke-dasharray", ("7,7"));
              hugor2.elements().transition().duration(5)
                  .attr("d", hugor2.datafunc(hugor2.data));
                    
              // Draw integral curve through right state (note index bug for intcr.data[ii][j])
              // and intcr2 it should be j =0,1 not j=1,2. Arrays somehow grow of sixe in mpld3   
              for (var ii=0; ii<iter; ii++) {
                //Left from hr
                intcr.data[ii][1] = ii*d[0]/(1.0*iter);
                var hm = intcr.data[ii][1];
                intcr.data[ii][2] = integralcurve(hm,hr,hur,1);
                //Right from hr
                intcr2.data[ii][1] = d[0] + ii*(hmax-d[0])/(1.0*iter);
                var hm2 = intcr2.data[ii][1];
                intcr2.data[ii][2] = integralcurve(hm2,hr,hur,1);
              }
              // Do transitions      
              intcr.elements().transition().duration(5)
                  .attr("d", intcl.datafunc(intcr.data));
              intcr2.elements().transition().duration(5)
                  .attr("d", intcr2.datafunc(intcr2.data))
                  .style("stroke-dasharray", ("7,7"));
            }
            // If time marker is moved
            else if (i==2) {
                // Convert mouse coordinates in drag event (d3.event) to python coordinates d
                d[0] = timedot.ax.x.invert(d3.event.x);
                d[1] = timedot.ax.y.invert(d3.event.y);      
                d3.select(this)
                    .attr("transform", "translate(" + [d3.event.x,d3.event.y] + ")");
                // Calculate timedot position and assign it
                var ty = timedot.ax.y.invert(d3.event.y);
                if (ty >=0) {
                    timeline.data[0][1] = ty;
                    timeline.data[1][1] = ty;
                    timeline.data[2][1] = ty;
                    time = ty;
                }
                // Do transitions
                timeline.elements().transition().duration(5)
                    .attr("d", timeline.datafunc(timeline.data));
            }
            
            // Calculate middle state    
            update_midstate();
                  
            // Calculate solution plots of h and hu
            update_solplots();
            
            // Update characteristic in x-t plane
            update_xtplane();
             
        }
        // End dragging
        function dragended(d) {
          d3.select(this).classed("dragging", false);
        }
    }
    mpld3.register_plugin("drag", PPlaneNLPlugin); 
    
         mpld3.draw_figure("fig_el126431399601080516646740895419", {"axes": [{"xlim": [0.0, 10.0], "yscale": "linear", "axesbg": "#FFFFFF", "texts": [{"v_baseline": "hanging", "h_anchor": "middle", "color": "#000000", "text": "h", "coordinates": "axes", "zorder": 3, "alpha": 1, "fontsize": 17.0, "position": [0.5, -0.08625000000000016], "rotation": -0.0, "id": "el12643139960686845520"}, {"v_baseline": "auto", "h_anchor": "middle", "color": "#000000", "text": "hu", "coordinates": "axes", "zorder": 3, "alpha": 1, "fontsize": 17.0, "position": [-0.084034276589423668, 0.49999999999999978], "rotation": -90.0, "id": "el12643139959698296976"}, {"v_baseline": "auto", "h_anchor": "middle", "color": "#000000", "text": "Phase plane", "coordinates": "axes", "zorder": 3, "alpha": 1, "fontsize": 18.0, "position": [0.5, 1.0199652777777777], "rotation": -0.0, "id": "el12643139959698346896"}, {"v_baseline": "auto", "h_anchor": "start", "color": "#000000", "text": "", "coordinates": "axes", "zorder": 1000003.0, "alpha": 1, "fontsize": 12.0, "position": [-0.12647058823529414, -1.5874999999999997], "rotation": -0.0, "id": "el12643139959601033104"}, {"v_baseline": "auto", "h_anchor": "start", "color": "#000000", "text": "Hugoniot Loci", "coordinates": "axes", "zorder": 1000003.0, "alpha": 1, "fontsize": 10.0, "position": [0.11816696375519908, 0.93531249999999999], "rotation": -0.0, "id": "el12643139959600945424"}, {"v_baseline": "auto", "h_anchor": "start", "color": "#000000", "text": "Hugoniot Loci (unphysical)", "coordinates": "axes", "zorder": 1000003.0, "alpha": 1, "fontsize": 10.0, "position": [0.11816696375519908, 0.87940972222222213], "rotation": -0.0, "id": "el12643139959601017360"}, {"v_baseline": "auto", "h_anchor": "start", "color": "#000000", "text": "Integral Curves", "coordinates": "axes", "zorder": 1000003.0, "alpha": 1, "fontsize": 10.0, "position": [0.11816696375519908, 0.82350694444444428], "rotation": -0.0, "id": "el12643139959600943760"}, {"v_baseline": "auto", 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-7.589505878615411], [9.01010101010101, -10.50690462161472, -7.862194115260785], [9.08080808080808, -10.866670779690198, -8.137380704851152], [9.151515151515152, -11.230536350514056, -8.415055901605596], [9.222222222222221, -11.598500988185139, -8.695210072913062], [9.292929292929292, -11.970564355982784, -8.977833697159028], [9.363636363636363, -12.34672612606271, -9.26291736160997], [9.434343434343434, -12.72698597916509, -9.550451760353951], [9.505050505050505, -13.111343604334126, -9.840427692295288], [9.575757575757574, -13.499798698648544, -10.132836059201566], [9.646464646464647, -13.892350966962642, -10.427667863801204], [9.717171717171716, -14.289000121657185, -10.724914207929864], [9.787878787878787, -14.689745882400086, -11.024566290724305], [9.858585858585858, -15.094587975915953, -11.32661540686179], [9.929292929292929, -15.503526135764563, -11.631052944843955], [10.0, -15.91656010212753, -11.937870385323382]], "data13": [[-11.1, -169.76593783806587, 169.76593783806587], [11.1, 169.76593783806587, -169.76593783806587]], "data01": [[-1.0, -1.0]]}, "id": "el12643139960108051664"});
      });
    });
}else{
    // require.js not available: dynamically load d3 & mpld3
    mpld3_load_lib("https://mpld3.github.io/js/d3.v3.min.js", function(){
         mpld3_load_lib("https://mpld3.github.io/js/mpld3.v0.2.js", function(){
                 
    // init custom PPLaneNL plugin
    mpld3.register_plugin("drag", PPlaneNLPlugin);
    PPlaneNLPlugin.prototype = Object.create(mpld3.Plugin.prototype);
    PPlaneNLPlugin.prototype.constructor = PPlaneNLPlugin;
    PPlaneNLPlugin.prototype.requiredProps = ["id", "idmpoint", 
                                              "idg", "iditer", "iditer_charac", "idtime", "idhmax", "idoffm",
                                              "idhugol", "idhugor", "idintcl", "idintcr",
                                              "idhugol2", "idhugor2", "idintcl2", "idintcr2", 
                                              "idqlm", "idqmm", "idqrm", 
                                              "idshock1", "idshock2", "idrar1", "idrar2",
                                              "idrar1a", "idrar2a", "idrar1b", "idrar2b",
                                              "idrar1c", "idrar2c", "idrar1d", "idrar2d",
                                              "idtimedot", "idtimeline",
                                              "idq1", "idq2"];
    PPlaneNLPlugin.prototype.defaultProps = {}
    function PPlaneNLPlugin(fig, props){
        mpld3.Plugin.call(this, fig, props);
        mpld3.insert_css("#" + fig.figid + " path.dragging",
                         {"fill-opacity": "1.0 !important",
                          "stroke-opacity": "1.0 !important"});
    };

    // Call draw function, this function is being looped all the time
    PPlaneNLPlugin.prototype.draw = function(){
        // Get elements into script variables
        var obj = mpld3.get_element(this.props.id);
        var midpoint = mpld3.get_element(this.props.idmpoint);
        var g = this.props.idg;
        var iter = this.props.iditer;
        var iter_charac = this.props.iditer_charac;
        var time = this.props.idtime;
        var hmax = this.props.idhmax;
        var offm = this.props.idoffm;
        var hugol = mpld3.get_element(this.props.idhugol);
        var hugor = mpld3.get_element(this.props.idhugor);
        var intcl = mpld3.get_element(this.props.idintcl);
        var intcr = mpld3.get_element(this.props.idintcr);
        var hugol2 = mpld3.get_element(this.props.idhugol2);
        var hugor2 = mpld3.get_element(this.props.idhugor2);
        var intcl2 = mpld3.get_element(this.props.idintcl2);
        var intcr2 = mpld3.get_element(this.props.idintcr2);
        var qlm = mpld3.get_element(this.props.idqlm);
        var qmm = mpld3.get_element(this.props.idqmm);
        var qrm = mpld3.get_element(this.props.idqrm);
        var shock1 = mpld3.get_element(this.props.idshock1);
        var shock2 = mpld3.get_element(this.props.idshock2);
        var rar1 = mpld3.get_element(this.props.idrar1);
        var rar2 = mpld3.get_element(this.props.idrar2);
        var rar1a = mpld3.get_element(this.props.idrar1a);
        var rar2a = mpld3.get_element(this.props.idrar2a);
        var rar1b = mpld3.get_element(this.props.idrar1b);
        var rar2b = mpld3.get_element(this.props.idrar2b);
        var rar1c = mpld3.get_element(this.props.idrar1c);
        var rar2c = mpld3.get_element(this.props.idrar2c);
        var rar1d = mpld3.get_element(this.props.idrar1d);
        var rar2d = mpld3.get_element(this.props.idrar2d);
        var timedot = mpld3.get_element(this.props.idtimedot);
        var timeline = mpld3.get_element(this.props.idtimeline);
        var q1 = mpld3.get_element(this.props.idq1);
        var q2 = mpld3.get_element(this.props.idq2);
        
        // Set initial conditions for javascript calculations
        //var qleft = obj.offsets[0];
        //var qright = obj.offsets[1];
        //var qmid = midpoint.offsets[0];
        var offx = obj.ax.x(offm);
        var offy = offx;
        // Define initial values of hl, hr, hul and hur
        var hl = obj.offsets[0][0];
        var hul = obj.offsets[0][1];
        var hr = obj.offsets[1][0];
        var hur = obj.offsets[1][1];
        hmfinal = 0;
        humfinal = 0;
        
        // Main d3 drag function
        var drag = d3.behavior.drag()
            .origin(function(d) { return {x:obj.ax.x(d[0]),
                                          y:obj.ax.y(d[1])}; }) 
            .on("dragstart", dragstarted)
            .on("drag", dragged)
            .on("dragend", dragended);
        
        // Dragtime function for draggable time-dot (analog to main)
        var dragtime = d3.behavior.drag()
            .origin(function(d) { return {x:timedot.ax.x(d[0]),
                                          y:timedot.ax.y(d[1])}; })                              
            .on("dragstart", dragstarted)
            .on("drag", dragged)
            .on("dragend", dragended);
    
        // Set elements of ql and qr draggable points and call main drag function
        obj.elements()
           .data(obj.offsets)
           .style("cursor", "default")
           .call(drag);
            
        // Set elements for timedot draggable point and call dragtime function  
        timedot.elements()
           .data(timedot.offsets)
           .style("cursor", "default")
           .call(dragtime);

        // Begin phi and phi prime function
        function phi(h,hl,hr,hul,hur) {
            var ul = hul/hl;
            var ur = hur/hr;
            if (h < hl) {
                var termIC1 = 2.0*Math.sqrt(g*hl);
                var termIC2 = 2.0*Math.sqrt(g*h);
                var phil = ul + termIC1 - termIC2;
                var philp = -Math.sqrt(g/h);
            }
            if (h >= hl) {
                var termHL1 = (h - hl);
                var termHL2 = Math.sqrt(0.5*g*(1.0/h + 1.0/hl));
                var termHL3 = termHL1*termHL2;
                var phil = ul - termHL3 ;
                var nume = termHL2*4*h*h;
                var philp = -termHL2 + termHL1*g/nume;
            }
            if (h < hr) {
                var termIC1 = 2.0*Math.sqrt(g*hr);
                var termIC2 = 2.0*Math.sqrt(g*h);
                var phir = ur - termIC1 + termIC2;
                var phirp = Math.sqrt(g/h);
            }
            if (h >= hr) {
                var termHL1 = (h - hr);
                var termHL2 = Math.sqrt(0.5*g*(1.0/h + 1.0/hr));
                var termHL3 = termHL1*termHL2;
                var phir = ur + termHL3 ;
                var nume = termHL2*4*h*h;
                var phirp = termHL2 - termHL1*g/nume;
            }
            var phi = phil-phir;
            var phiprime = philp - phirp
            var um = 0.5*(phil + phir);
            return [phi,phiprime,um];
        }
        
        // Begin Newton iteration
        function newton(hstar,hl,hr,hul,hur) {
            var hn = hstar;
            var error = 1;
            while (error > 0.005) {
                var hold = hn;
                var phin = phi(hn,hl,hr,hul,hur);
                var hn = hold - phin[0]/phin[1];
                var um = phin[2];
                error = Math.abs(hold - hn);
            }
            return [hn,um];
        }
        
        // Calculate hugoniot loci
        function hugoloci(hm,hside,huside,sign) {
                var termHL1 = hm*(hm - hside);
                if (hm == 0) {
                    var termHL2 = 1.0; }
                else {
                   var termHL2 = Math.sqrt(0.5*g*(1.0/hm + 1.0/hside));}
                   var termHL3 = termHL1*termHL2;
                   var hloci = hm*huside/hside + sign*termHL3;
            return hloci;} 
            
        // Calculate integral curve
        function integralcurve(hm,hside,huside,sign) {
                var termIC1 = 2.0*hm*Math.sqrt(g*hside);
                var termIC2 = 2.0*hm*Math.sqrt(g*hm);
                var intcurve = hm*huside/hside - sign*(termIC1 - termIC2);
            return intcurve;}
            
        // Calculate solution plot of h and hu as function of x
        function solplot(hl,hm,hr,hul,hum,hur) {
            var lam = [];
            lam.push([-1000000, 0,0])
            var ul = hul/hl;
            var um = hum/hm;
            var ur = hur/hr;
            var shock1 = false;
            var shock2 = false;
            var qsol1 = d3.range(iter);
            var qsol2 = d3.range(iter);
            if (hm >= hl) {
                var s1 = time*(hum - hul)/(hm - hl);
                shock1 = true;
            } else {
                var s1b = [0,0];
                s1b[0] = time*(ul - Math.sqrt(g*hl));
                s1b[1] = time*(um - Math.sqrt(g*hm));
                s1b.sort(d3.ascending);
            }
            if (hm >= hr) {
                var s2 = time*(hur - hum)/(hr - hm);
                shock2 = true;
            } else {
                var s2b = [0,0];
                s2b[0] = time*(um + Math.sqrt(g*hm));
                s2b[1] = time*(ur + Math.sqrt(g*hr));
                s2b.sort(d3.ascending);
            }
            
            for (var ii=0; ii <2*iter; ii++){
                var xx = q1.data[ii][0];
                // Calculate plot solution for 1 charactersitic (shock or rarefaction)
                if (shock1) {
                    if (xx <= s1){ qsol1[ii] = hl; qsol2[ii] = hul;}
                    else { qsol1[ii] = hm; qsol2[ii] = hum;}
                }
                else {
                    if (xx <= s1b[0]) { qsol1[ii] = hl; qsol2[ii] = hul;}
                    else if (xx <= s1b[1]) {
                        var m1 = (hm - hl)/(s1b[1] - s1b[0]);
                        var m2 = (hum - hul)/(s1b[1] - s1b[0]);
                        qsol1[ii] = m1*(xx - s1b[0]) + hl;
                        qsol2[ii] = m2*(xx - s1b[0]) + hul;}
                    else { qsol1[ii] = hm; qsol2[ii] = hum;}
                }
                // Calculate plot solution for 2 charactersitic (shock or rarefaction)
                if (shock2) {
                    if (xx > s2) {qsol1[ii] = hr; qsol2[ii] = hur;}
                }
                else{
                    if (xx > s2b[0] && xx < s2b[1]) {
                        var m1 = (hr - hm)/(s2b[1] - s2b[0]);
                        var m2 = (hur - hum)/(s2b[1] - s2b[0]);
                        qsol1[ii] = m1*(xx - s2b[0]) + hm;
                        qsol2[ii] = m2*(xx - s2b[0]) + hum;}
                    else if (xx > s2b[1]) { qsol1[ii] = hr; qsol2[ii] = hur;}
                }
            }
            var solution = [qsol1,qsol2];
            return solution;
        }

        // Function to update middle state   
        function update_midstate(){
            var hstar = 0.05*(hl + hr);
            var solution = newton(hstar,hl,hr,hul,hur);
            hmfinal = solution[0];
            humfinal = solution[1]*hmfinal;
            var xx = obj.ax.x(hmfinal);
            var yy = obj.ax.y(humfinal);
            // Update middle state point and marker position
            midpoint.elements().transition().duration(5)
            .attr("transform", "translate(" + [xx, yy] + ")");
            // Move marker
            qmm.elements().transition().duration(1)
              .attr("transform", "translate(" + [xx + 0.7*offx, yy + 0.7*offy] + ")");
        }
        
        // Functon to update xt-plane
        function update_xtplane() {
         // Calculate shcok speeds from R-H conditions
         var lam1 = (humfinal - hul)/(hmfinal - hl);   
         var lam2 = (hur - humfinal)/(hr - hmfinal);   
         var lam1m = humfinal/hmfinal - Math.sqrt(g*hmfinal);
         var lam2m = humfinal/hmfinal + Math.sqrt(g*hmfinal);
         var lam1l = hul/hl - Math.sqrt(g*hl);
         var lam2r = hur/hr + Math.sqrt(g*hr);
         var color1 = "red";
         var color2 = "red";
         var thick1 = 4;
         var thick2 = 4;
         var fan = 0;
         for (var ii=0; ii<iter_charac; ii++) {
             if (hmfinal >= hl) {
                 shock1.data[ii][1] = shock1.data[ii][0]/lam1;
                 rar1.data[ii][1] = rar1.data[ii][0]/lam1;
                 rar1a.data[ii][1] = rar1a.data[ii][0]/lam1;
                 rar1b.data[ii][1] = rar1b.data[ii][0]/lam1;
                 rar1c.data[ii][1] = rar1c.data[ii][0]/lam1;
                 rar1d.data[ii][1] = rar1d.data[ii][0]/lam1;
                 console.log(rar2a.data);
                 color1 = "red";
                 thick1 = 4;
             } else {
                 shock1.data[ii][1] = shock1.data[ii][0]/lam1l;
                 rar1.data[ii][1] = rar1.data[ii][0]/lam1m;
                 fan = Math.abs(lam1m - lam1l)/5;
                 rar1a.data[ii][1] = rar1a.data[ii][0]/(lam1l + fan);
                 rar1b.data[ii][1] = rar1b.data[ii][0]/(lam1l + 2*fan);
                 rar1c.data[ii][1] = rar1c.data[ii][0]/(lam1l + 3*fan);
                 rar1d.data[ii][1] = rar1d.data[ii][0]/(lam1l + 4*fan);
                 color1 = "blue";
                 thick1 = 1;
             }
             if (hmfinal >= hr) {
                 shock2.data[ii][2] = shock2.data[ii][0]/lam2;
                 rar2.data[ii][2] = rar2.data[ii][0]/lam2;
                 rar2a.data[ii][2] = rar2a.data[ii][0]/lam2;
                 rar2b.data[ii][2] = rar2b.data[ii][0]/lam2;
                 rar2c.data[ii][2] = rar2c.data[ii][0]/lam2;
                 rar2d.data[ii][2] = rar2d.data[ii][0]/lam2;
                 color2 = "red";
                 thick2 = 4;
            } else {
                 shock2.data[ii][2] = shock2.data[ii][0]/lam2r;
                 rar2.data[ii][2] = rar2.data[ii][0]/lam2m;
                 fan = Math.abs(lam2r - lam2m)/5;
                 rar2a.data[ii][2] = rar2a.data[ii][0]/(lam2m + fan);
                 rar2b.data[ii][2] = rar2b.data[ii][0]/(lam2m + 2*fan);
                 rar2c.data[ii][2] = rar2c.data[ii][0]/(lam2m + 3*fan);
                 rar2d.data[ii][2] = rar2d.data[ii][0]/(lam2m + 4*fan);
                 color2 = "blue";
                 thick2 = 1;
            }                     
         }
         // Do transitions
         shock1.elements().transition().duration(5)
             .attr("d", shock1.datafunc(shock1.data))
             .style("stroke", color1)
             .style("stroke-width", thick1);
         shock2.elements().transition().duration(5)
             .attr("d", shock2.datafunc(shock2.data))
             .style("stroke", color2)
             .style("stroke-width", thick2);
         rar1.elements().transition().duration(5)
             .attr("d", rar1.datafunc(rar1.data))
             .style("stroke", color1)
             .style("stroke-width", thick1);
         rar2.elements().transition().duration(5)
             .attr("d", rar2.datafunc(rar2.data))
             .style("stroke", color2)
             .style("stroke-width", thick2);
         rar1a.elements().transition().duration(5)
             .attr("d", rar1a.datafunc(rar1a.data))
             .style("stroke", color1)
             .style("stroke-width", thick1);
         rar2a.elements().transition().duration(5)
             .attr("d", rar2a.datafunc(rar2a.data))
             .style("stroke", color2)
             .style("stroke-width", thick2);
         rar1b.elements().transition().duration(5)
             .attr("d", rar1b.datafunc(rar1b.data))
             .style("stroke", color1)
             .style("stroke-width", thick1);
         rar2b.elements().transition().duration(5)
             .attr("d", rar2b.datafunc(rar2b.data))
             .style("stroke", color2)
             .style("stroke-width", thick2);
         rar1c.elements().transition().duration(5)
             .attr("d", rar1c.datafunc(rar1c.data))
             .style("stroke", color1)
             .style("stroke-width", thick1);
         rar2c.elements().transition().duration(5)
             .attr("d", rar2c.datafunc(rar2c.data))
             .style("stroke", color2)
             .style("stroke-width", thick2);
         rar1d.elements().transition().duration(5)
             .attr("d", rar1d.datafunc(rar1d.data))
             .style("stroke", color1)
             .style("stroke-width", thick1);
         rar2d.elements().transition().duration(5)
             .attr("d", rar2d.datafunc(rar2d.data))
             .style("stroke", color2)
             .style("stroke-width", thick2);
        }
        
        // Function to update solution plots
        function update_solplots() {
            var qsol = solplot(hl,hmfinal,hr,hul,humfinal,hur);
                for (var ii=0; ii<2*iter; ii++){
                    q1.data[ii][1] = qsol[0][ii]; 
                    q2.data[ii][2] = qsol[1][ii]; 
                }
                // Do transitions
                 q1.elements().transition().duration(5)
                     .attr("d", q1.datafunc(q1.data));
                 q2.elements().transition().duration(5)
                     .attr("d", q2.datafunc(q2.data));
        }
        
        // Initialize solution with given initial states before interacting
        update_midstate();
        update_xtplane();
        update_solplots();
        
        // Begin drag function
        function dragstarted(d) {
          d3.event.sourceEvent.stopPropagation();
          d3.select(this).classed("dragging", true);
        }
   
        // The drag function called while dragging is happening (meat of code here)
        function dragged(d,i) {
          if (i == 0  || i ==1) {
              // Convert mouse coordinates in drag event (d3.event) to python coordinates d
              d[0] = obj.ax.x.invert(d3.event.x);
              d[1] = obj.ax.y.invert(d3.event.y);             
              // Move ql and qr stored in obj (they have been selected in drag)
              d3.select(this)
                .attr("transform", "translate(" + [d3.event.x,d3.event.y] + ")");
              // If obj corresponds to ql, move all the other left elements 
              }
          if (i==0){
              // Move marker
              qlm.elements().transition().duration(1)
                  .attr("transform", "translate(" + [d3.event.x + offx, d3.event.y + offy] + ")");     
              // Re-calculate inital left variables when dragging 
              hl = obj.offsets[0][0];
              hul = obj.offsets[0][1];
              
              // Draw Hugoniot loci through left state    
              for (var ii=0; ii<iter; ii++) {
                //Left from hl
                hugol.data[ii][0] = ii*d[0]/(1.0*iter);
                var hm = hugol.data[ii][0];
                hugol.data[ii][1] = hugoloci(hm,hl,hul,-1) ;
                //Right from hl
                hugol2.data[ii][0] = d[0] + ii*(hmax-d[0])/(1.0*iter);
                var hm2 = hugol2.data[ii][0];
                hugol2.data[ii][1] = hugoloci(hm2,hl,hul,-1) ;
                }
              // Do transitions      
              hugol.elements().transition().duration(5)
                  .attr("d", hugol.datafunc(hugol.data))
                  .style("stroke-dasharray", ("7,7"));
              hugol2.elements().transition().duration(5)
                  .attr("d", hugol2.datafunc(hugol2.data));
                               
                  
              // Draw integral curve through left state (note index bug for intcl.data[ii][j])
              // and intcl2 it should be j =0,1 not j=1,2. Arrays somehow grow of sixe in mpld3
              for (var ii=0; ii<iter; ii++) {
                //Left from hl
                intcl.data[ii][1] = ii*d[0]/(1.0*iter);
                var hm = intcl.data[ii][1];
                intcl.data[ii][2] = integralcurve(hm,hl,hul,-1);
                //Right from hl
                intcl2.data[ii][1] = d[0] + ii*(hmax-d[0])/(1.0*iter);
                var hm2 = intcl2.data[ii][1];
                intcl2.data[ii][2] = integralcurve(hm2,hl,hul,-1);
              }
              // Do transitions      
              intcl.elements().transition().duration(5)
                  .attr("d", intcl.datafunc(intcl.data));
              intcl2.elements().transition().duration(5)
                  .attr("d", intcl2.datafunc(intcl2.data))
                  .style("stroke-dasharray", ("7,7"));
                  
          }      
          // if element corresponds to qr
          else if (i==1) {
              // Move marker
              qrm.elements().transition().duration(1)
                  .attr("transform", "translate(" + [d3.event.x + offx, d3.event.y + offy] + ")");
              // Re-calculate inital right variables when dragging
              hr = obj.offsets[1][0];
              hur = obj.offsets[1][1];
              
              // Draw Hugoniot loci through right state    
              for (var ii=0; ii<iter; ii++) {
                //Left from hr
                hugor.data[ii][0] = ii*d[0]/(1.0*iter);
                var hm = hugor.data[ii][0];
                hugor.data[ii][1] = hugoloci(hm,hr,hur,1) ;
                //Right from hr
                hugor2.data[ii][0] = d[0] + ii*(hmax-d[0])/(1.0*iter);
                var hm2 = hugor2.data[ii][0];
                hugor2.data[ii][1] = hugoloci(hm2,hr,hur,1) ;
                }
              // Do transitions      
              hugor.elements().transition().duration(5)
                  .attr("d", hugor.datafunc(hugor.data))
                  .style("stroke-dasharray", ("7,7"));
              hugor2.elements().transition().duration(5)
                  .attr("d", hugor2.datafunc(hugor2.data));
                    
              // Draw integral curve through right state (note index bug for intcr.data[ii][j])
              // and intcr2 it should be j =0,1 not j=1,2. Arrays somehow grow of sixe in mpld3   
              for (var ii=0; ii<iter; ii++) {
                //Left from hr
                intcr.data[ii][1] = ii*d[0]/(1.0*iter);
                var hm = intcr.data[ii][1];
                intcr.data[ii][2] = integralcurve(hm,hr,hur,1);
                //Right from hr
                intcr2.data[ii][1] = d[0] + ii*(hmax-d[0])/(1.0*iter);
                var hm2 = intcr2.data[ii][1];
                intcr2.data[ii][2] = integralcurve(hm2,hr,hur,1);
              }
              // Do transitions      
              intcr.elements().transition().duration(5)
                  .attr("d", intcl.datafunc(intcr.data));
              intcr2.elements().transition().duration(5)
                  .attr("d", intcr2.datafunc(intcr2.data))
                  .style("stroke-dasharray", ("7,7"));
            }
            // If time marker is moved
            else if (i==2) {
                // Convert mouse coordinates in drag event (d3.event) to python coordinates d
                d[0] = timedot.ax.x.invert(d3.event.x);
                d[1] = timedot.ax.y.invert(d3.event.y);      
                d3.select(this)
                    .attr("transform", "translate(" + [d3.event.x,d3.event.y] + ")");
                // Calculate timedot position and assign it
                var ty = timedot.ax.y.invert(d3.event.y);
                if (ty >=0) {
                    timeline.data[0][1] = ty;
                    timeline.data[1][1] = ty;
                    timeline.data[2][1] = ty;
                    time = ty;
                }
                // Do transitions
                timeline.elements().transition().duration(5)
                    .attr("d", timeline.datafunc(timeline.data));
            }
            
            // Calculate middle state    
            update_midstate();
                  
            // Calculate solution plots of h and hu
            update_solplots();
            
            // Update characteristic in x-t plane
            update_xtplane();
             
        }
        // End dragging
        function dragended(d) {
          d3.select(this).classed("dragging", false);
        }
    }
    mpld3.register_plugin("drag", PPlaneNLPlugin); 
    
                 mpld3.draw_figure("fig_el126431399601080516646740895419", {"axes": [{"xlim": [0.0, 10.0], "yscale": "linear", "axesbg": "#FFFFFF", "texts": [{"v_baseline": "hanging", "h_anchor": "middle", "color": "#000000", "text": "h", "coordinates": "axes", "zorder": 3, "alpha": 1, "fontsize": 17.0, "position": [0.5, -0.08625000000000016], "rotation": -0.0, "id": "el12643139960686845520"}, {"v_baseline": "auto", "h_anchor": "middle", "color": "#000000", "text": "hu", "coordinates": "axes", "zorder": 3, "alpha": 1, "fontsize": 17.0, "position": [-0.084034276589423668, 0.49999999999999978], "rotation": -90.0, "id": "el12643139959698296976"}, {"v_baseline": "auto", "h_anchor": "middle", "color": "#000000", "text": "Phase plane", "coordinates": "axes", "zorder": 3, "alpha": 1, "fontsize": 18.0, "position": [0.5, 1.0199652777777777], "rotation": -0.0, "id": "el12643139959698346896"}, {"v_baseline": "auto", "h_anchor": "start", "color": "#000000", "text": "", "coordinates": "axes", "zorder": 1000003.0, "alpha": 1, "fontsize": 12.0, "position": [-0.12647058823529414, -1.5874999999999997], "rotation": -0.0, "id": "el12643139959601033104"}, {"v_baseline": "auto", "h_anchor": "start", "color": "#000000", "text": "Hugoniot Loci", "coordinates": "axes", "zorder": 1000003.0, "alpha": 1, "fontsize": 10.0, "position": [0.11816696375519908, 0.93531249999999999], "rotation": -0.0, "id": "el12643139959600945424"}, {"v_baseline": "auto", "h_anchor": "start", "color": "#000000", "text": "Hugoniot Loci (unphysical)", "coordinates": "axes", "zorder": 1000003.0, "alpha": 1, "fontsize": 10.0, "position": [0.11816696375519908, 0.87940972222222213], "rotation": -0.0, "id": "el12643139959601017360"}, {"v_baseline": "auto", "h_anchor": "start", "color": "#000000", "text": "Integral Curves", "coordinates": "axes", "zorder": 1000003.0, "alpha": 1, "fontsize": 10.0, "position": [0.11816696375519908, 0.82350694444444428], "rotation": -0.0, "id": "el12643139959600943760"}, {"v_baseline": 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