Sigmoid Function 2

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  <title>Dynamic Annotations in a Visualization Stepper</title>
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.t {
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<body>
  <div id="container">
    <h1>Albany Tableau Users Group: Sigmoid Function</h1>
    <p>The sigmoid function is a type of mathematical equation that mimics an S-shape curve and is often used in visualizations such as Sankey Diagrams, Ranking Visualizations, Node-Link Diagrams, and many others.By creating additional data points within Tableau for each 'real' data point, math can be used to implement the sigmoid function using data to define the starting and ending point for the curve.  The following sequence of examples shows how the sigmoid curve can by implemented in tableau and a few examples of it in use. <div id="vis-nav">
    <a href="#" id="step0" class="step-link active">Sigmoid Function Animation</a><a href="#" id="step1" class="step-link">Tableau Implementation</a><a href="#" id="step2" class="step-link">State Rankings Dataset</a><a href="#" id="step3" class="step-link">Data + Science Ranking Visualization</a><a href="#" id="step4" class="step-link">Sankey Diagrams</a><a href="#" id="step5" class="step-link">Node Link Diagrams</a>
 </div>
	
    <div id="vis-container">
		<div id="tableauBezier1"></div>

<div class="annotation-step" id="step0-annotation" style="display:block;">
		  <div class="annotation" id="step0-left-annotation" >
				<p>The animation below shows a single sigmoid curve using a logistic function.  In the text below, the value of t is shown, a number from -6 to 6 representing how far through the curve the animation is.  This value is what is used to determine the coordinates for intermediary values in Tableau.<div id="vis-nav">
				<p>To build many visualizations using the sigmoid curve (such as the Sankey Diagram), the X or Y positions are held constant for multiple paths or polygons in the visualization.  For example, rankings can be shown on the Y axis for two years, with smooth curves showing the change in rank.  <b>Drag the control points to the right to see how changes in one dimension effect the curves</b><div id="vis-nav">
		  </div>
		</div>

</div>
  <script src="tableau-2.min.js"></script>
  <script src="tableau-2.2.1.min.js"></script>
  <script>
  
  SigmoidAnimation()
  var laststep = "step0";
  
	function tableauViz(url,htmlElement) {
	
		var placeholderDiv = document.getElementById("tableauBezier1");
			  
		var options = {
			width: placeholderDiv.offsetWidth,
			height: placeholderDiv.offsetHeight,
			hideTabs: true,
			hideToolbar: true,
			onFirstInteractive: function () {
			  workbook = viz.getWorkbook();
			  activeSheet = workbook.getActiveSheet();
			}
			
		  };
		  
		  viz = new tableau.Viz(placeholderDiv, url, options);
		  
	}
			
	
		
	function switchStep(newStep)
	{
	
	  d3.selectAll(".step-link").classed("active", false);
	  d3.select("#" + newStep).classed("active", true);
	 
	  if (newStep=="step0"){
		SigmoidAnimation()
	  ;}
	  else {
	  	d3.selectAll("#vis-bezier").remove();
			}
	  
	  
	  if (newStep=="step1"){  
			if (laststep!="step2"){
				d3.selectAll("#tableauBezier1").remove();
			    d3.selectAll("#vis-container").append("div").attr("id","tableauBezier1");

tableauViz("https://public.tableau.com/views/TableauUsersGroupSigmoidFunction/SimgoidDash")

;}
		else {

;}
	  }
	  
	  if (newStep=="step2"){
	  
	  
	    d3.selectAll("#tableauBezier1").remove();
		  d3.selectAll("#vis-container").append("div").attr("id","tableauBezier1");
		  tableauViz("https://public.tableau.com/views/TableauUsersGroupRankingsDataset/RawData")
			;}	
	 	  
	  if (newStep=="step3"){
	  
	  
	    d3.selectAll("#tableauBezier1").remove();
		  d3.selectAll("#vis-container").append("div").attr("id","tableauBezier1");
		  tableauViz("https://public.tableau.com/views/TableauUsersGroupDataScienceRankingsVisual/Dashboard2")
			;}

if (newStep=="step4"){
	  
	  
	    d3.selectAll("#tableauBezier1").remove();
		  d3.selectAll("#vis-container").append("div").attr("id","tableauBezier1");
		  tableauViz("https://public.tableau.com/views/SankeyDiagram_5/PolygonicSankey3Steps")
			;}	
			
			
			
			
	if (newStep=="step5"){
	  
	  
	    d3.selectAll("#tableauBezier1").remove();
		  d3.selectAll("#vis-container").append("div").attr("id","tableauBezier1");
		  tableauViz("https://public.tableau.com/views/TableauUsersGroupNode-Link/NodeLink3")
			;}	
		  
	laststep = newStep;
	
	}

function switchAnnotation(newStep)
	{
	
	  d3.selectAll(".annotation-step")
		.style("display", "none")
		.style("opacity", 0.0);

console.log(newStep + "-annotation")
		
	  d3.select("#" + newStep + "-annotation")
		.style("display", "block")
		.transition().delay(300).duration(2000)
		  .style("opacity", 1);
	}

d3.selectAll("a.step-link").on("click", function(d) {
	  var clickedStep = d3.select(this).attr("id");
	  switchStep(clickedStep);
	  switchAnnotation(clickedStep);
	  return false;
	});
  
  
 function SigmoidAnimation() {
 			
		var w = 900,
			h = 650,
			t = .5,
			delta = .01,
			padding = 0,
			bezier = {},
			n = 4,
			line = d3.line().x(function(d){return d.x;}).y(function(d){return d.y;});
				
		var lineGenerator = d3.line();

var points = [
		  {x: 350, y: 300},
		  {x: 750,y: 100}
		];

var svgBezier = d3.select("#vis-canvas").append("div").attr("id","vis-bezier")
			.append("svg")
			.attr("width", w + 2 * padding)
			.attr("height", h + 2 * padding)

svgBezier.append("rect").attr("width",w).attr("height",h).attr("fill","white")	
		var vis = svgBezier.attr("transform", "translate(" + padding + "," + padding + ")")
		var curve = svgBezier.append("g").append("path").attr("class", "curve");
		var controlPath = svgBezier.append("g");
		var circles = svgBezier.append("g");
	
		var PathData = [];
		
		var lineGenerator = d3.line();

controlPath.append("line").attr("id","controlPath1").attr("x1",points[0].x).attr("x2",points[0].x).attr("y1",20).attr("y2",400).attr("stroke","black").attr("stroke-width",.5)
		controlPath.append("line").attr("id","controlPath1").attr("x1",points[1].x).attr("x2",points[1].x).attr("y1",20).attr("y2",400).attr("stroke","black").attr("stroke-width",.5)
		
		circles.selectAll("circle.control")
			.data(points)
			.enter()
			.append("circle")
			.attr("class", "control")
			.attr("z-index",10)
			.attr("r", 7)
			.attr("cx", x)
			.attr("cy", y)
			.call(d3.drag()
			  .on("start", function(d) {
				this.__origin__ = [d.x, d.y];
						d3.select(this).classed("drag", true);
			  })
			  .on("drag", function(d) {
				getSigmoid();				
				//d.x = Math.min(w, Math.max(0, this.__origin__[0] += d3.event.dx));
				d.y = Math.min(400, Math.max(15, this.__origin__[1] += d3.event.dy));
				bezier = {};
				update();
				vis.selectAll("circle.control")
				 // .attr("cx", x)
				  .attr("cy", y);
			  })
			  .on("end", function() {
				delete this.__origin__;
						d3.select(this).classed("drag", false);
			  }));

vis.append("text")
		  .attr("class", "t")
		  .attr("x", 100)
		  .attr("y", 350)
		  .attr("text-anchor", "middle");

vis.selectAll("text.controltext")
			.data(points)
			.enter()
			.append("text")
			.attr("class", "controltext")
			.attr("x", x)
			.attr("y", y)
			.attr("dx", "10px")
			.attr("dy", "15px")
			.text(function(d, i) { return "P" + i });
	
		getSigmoid();
		update();	
						
		var last = 0;
		d3.timer(function(elapsed) {
			t = (t + (elapsed - last) / 5000) % 1;
			last = elapsed;
	  		update();
		});
		
		function update() {
		  curve.attr("d", lineGenerator(PathData.slice(0,PathData.length*t)));
		  vis.selectAll("text.controltext").attr("x", x).attr("y", y);		
		  
		  t1 = t*12-6;
			if (t1<0){color = "red";}
			else { color = "green";}
		  vis.selectAll("text.t").attr("fill",color)
		  .text("t=" + t1.toFixed(1));
		  
		  vis.selectAll(".controlPath1")
		  
		  
		}

controlPath1 = [];
		controlPath2 = [];

//function to recreate an array of points for curve path.  Run with drag events to update array. 
		function getSigmoid(){
				
			x1 = points[0].x;
			x2 = points[1].x;
			y1 = points[0].y;
			y2 = points[1].y;
			
			controlPath1 = [[x1,100],[x1,500]]
			controlPath2 = [[x2,100],[x2,500]]
			
			PathData = [];
			
			for (z=-6; z<=6; z+=.05) {
			
				sigmoid = 1/(1+ Math.pow(Math.exp(1),-z ))
				
				sigmoidX = x1+(x2-x1)*((z+6)/12); 
				sigmoidY = y1 + (y2-y1)*sigmoid;
				
				PathData.push([sigmoidX,sigmoidY]);	
				;}
			;}

function getLevels(d, t_) {
		  if (arguments.length < 2) t_ = t;
		  var x = [points.slice(0, d)];
		  for (var i=1; i<d; i++) {
			x.push(interpolate(x[x.length-1], t_));
		  }
		  return x;
		}

function x(d) {return d.x; }
		function y(d) {return d.y; }
 
 ;}
  
  
  
  
  
  
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