matrix: rotations

Matrix: rotations

Extending http://ncase.me/matrix/ with SVG and d3.js, with a focus on 2D Rotation matrices.

I want to illustrate the relationship between angles and the matrix representation of a rotational transformation.

I'm still working on porting all of the original interactions, but I'm quite pleased with the work in progress.

Additional inspiration for Matrix UI (namely the coloring) comes from Max Goldstein's excellent Invitation to Another Dimension

forked from enjalot's block: matrix: reboot

<!DOCTYPE html>
<head>
  <meta charset="utf-8">
  <script src="https://cdnjs.cloudflare.com/ajax/libs/d3/3.5.5/d3.min.js"></script>
  <link rel="stylesheet" type="text/css" href="style.css">
  <script src="scrubbing.js"></script>
  <style>
    .sin {
background-color: #bdeae8 !important;
}
.cos {
background-color: #bbb9de !important;
}
  </style>
</head>

<body>
  <svg width=960 height=250></svg>
  <div id="math">
    <div class="angle-container unselectable">
      <div>Angle:</div> <input class="angle" value="0"/>
      
      <span class="unit sin">sin(<span class="angle-in">0</span>) = <span class="sin-out">0</span></span>
      <span class="unit cos">cos(<span class="angle-in">0</span>) = <span class="cos-out">1</span></span>
      
    </div>
		<div id="mtx_transform" class="matrix unselectable" style="width:180px"> 
      <div class="transforms cos"></div><div class="transforms sin"></div> <input value="0.0"/>
  <div class="transforms sin"></div><div class="transforms cos"/></div> <input value="0.0"/>
			<div plain style="position: absolute; top: 120px;">0</div>
			<div plain style="position: absolute; top: 120px; left:70px">0</div>
			<div plain style="position: absolute; top: 120px; left:130px">1</div>
			<div class="label">
			the transformation matrix
			<br>
			<span>(adjust the numbers!)</span>
			</div>
		</div>
		<div id="mtx_input"  class="matrix unselectable" style="width:60px">
			<div plain style="position: absolute; top: 0px;">x</div>
			<div plain style="position: absolute; top: 60px;">y</div>
			<div plain style="position: absolute; top: 120px;">1</div>
			<div class="label">
			a vector
			<br>
			<span>(hover over the dots)</span>
			</div>
		</div>
		
		<div class="equals"></div>
		<div id="mtx_output"  class="matrix" style="width:60px">
			<div>x'</div>
			<div>y'</div>
			<div>1</div>
			<div class="label">
			new vector
			<br>
			<span>(hover over the dots)</span>
			</div>
		</div>
    
  </div>
  <script>
    var transform = {}; // global transform
    var t = transform;  // convenience
    var bullets = []; // global data
    
    var mtx_inputs = document.querySelectorAll("#mtx_input div");
    var mtx_outputs = document.querySelectorAll("#mtx_output div");
    var mtx_transforms = document.querySelectorAll("#mtx_transform input");
    
    var transforms = d3.selectAll("div.transforms");
    var angle = d3.select("input.angle").node();
    var angleIn = d3.selectAll("span.angle-in");
    var sinOut = d3.select("span.sin-out")
    var cosOut = d3.select("span.cos-out")
    
    function calculate(x,y){
      x = x || 0;
      y = y || 0;
      var x2 = t.a*x + t.b*y + t.tx;
      var y2 = t.c*x + t.d*y + t.ty;
      return {x:x2, y:y2};
    }
    
    function render() {
      var xscale = d3.scale.linear()
        .domain([-1, 1])
        .range([350, 510]);
      var yscale = d3.scale.linear()
      .domain([-1, 1])
      .range([200, 50])
      
      var transformed = bullets.map(function(d) {
        return calculate(d.x, d.y)
      })
      
      var svg = d3.select("svg");
      
      function hover(d,i) {
        mtx_inputs[0].innerHTML = bullets[i].x.toFixed(1);
        mtx_inputs[1].innerHTML = bullets[i].y.toFixed(1);
        d3.select(mtx_inputs[0]).style("border", "3px solid red");
        d3.select(mtx_inputs[1]).style("border", "3px solid red");
        function filter(f,j) { return j === i }
        d3.selectAll("line")
          .filter(filter).style("stroke", "red")
        d3.selectAll("circle.bullet")
          .filter(filter).style("stroke", "red")
        d3.selectAll("circle.transformed")
          .filter(filter).style({stroke:"red", fill:"red"})
      }
      function mouseout(d,i) {
        mtx_inputs[0].innerHTML = "x";
        mtx_inputs[1].innerHTML = "y";
        d3.select(mtx_inputs[0]).style("border", "3px solid #eee");
        d3.select(mtx_inputs[1]).style("border", "3px solid #eee");
        d3.selectAll("line").style("stroke", "#111");
        d3.selectAll("circle.bullet").style("stroke", "#111")
        d3.selectAll("circle.transformed").style({stroke:"#111", fill:"#111"})
      }
      
      var lines = svg.selectAll("line")
        .data(bullets)
      lines.enter().append("line")
        .on("mouseover", hover)
        .on("mouseout", mouseout)
      lines
        .transition()
        .duration(170)
        .ease("linear")
        .attr({
          x1: function(d,i) { return xscale(d.x) },
          y1: function(d,i) { return yscale(d.y) },
          x2: function(d,i) { return xscale(transformed[i].x)},
          y2: function(d,i) { return yscale(transformed[i].y)},
          stroke: "#111"
        })

transform.a = parseFloat(mtx_transforms[0].value) || 0;
      transform.b = parseFloat(mtx_transforms[1].value) || 0;
      transform.tx = parseFloat(mtx_transforms[2].value) || 0;
      transform.c = parseFloat(mtx_transforms[3].value) || 0;
      transform.d = parseFloat(mtx_transforms[4].value) || 0;
      transform.ty = parseFloat(mtx_transforms[5].value) || 0;
      */
      var tvalues = [
        transform.a, transform.b, transform.c, transform.d
      ]
      transforms.text(function(d,i) { return tvalues[i] })
      
      angleIn.text(theta);
      sinOut.text(sin);
      cosOut.text(cos);
      render();
    }
    
    setupScrubbing(updateMatrixLeft);
    for(var i=0;i<mtx_transforms.length;i++){
      var input = mtx_transforms[i];
      input.onchange = updateMatrixLeft;
      makeScrubbable(input);
    }
    makeScrubbable(angle, 5);
    
    
    
    // get the data and trigger the initial rendering
    d3.json("bullets.json", function(err, data) {
      bullets = data.map(function(d) {
        return {x: d.x, y: d.y};
      });
      updateMatrixLeft();
    })
    
  </script>
</body>

https://cdnjs.cloudflare.com/ajax/libs/d3/3.5.5/d3.min.js