Lifespan events using segmented bézier curves

This block demonstrates an alternative styling approach to gradient stops and clipping-paths for parametric bézier curves. Given an initial bézier curve, we splice it into segments rather than generating gradient stops or clipping-paths to style the segments differently. The main advantage of this approach is that it reduces the number of elements required for each conceptual curve and simplify the representation in the DOM -- especially when anticipating large numbers of curves and a non-uniform segmentation. Thanks to Tim Hall for code review, and to Jason Davies for his work on animated béziers. Lifespan design concept inspired by Periscopic's work on U.S. gun deaths. Related: Aaron Bycoffe's block on how to Split an SVG path into pieces.

<!DOCTYPE html>
<style>
  #chart {background-color: white;}
  .x-axis line, .x-axis path {stroke: #999;}
  .x-axis text {fill: #999;}
</style>
<html>
  <body>
    <div id="chart">
      <svg></svg>
    </div>
  </body>
</html>

const margin = {
    top: 10,
    right: 10,
    bottom: 30,
    left: 10
  };
  const width = 900;
  const height = 380;

// svg container
  var svg = d3.select('#chart svg')
    .attr("width", width + margin.left + margin.right)
    .attr("height", height + margin.top + margin.bottom)
  
  // Create scales
  const xScale = d3.scaleLinear()
    .domain([0, 100])
    .range([20, width]);

const yScale = d3.scaleLinear()
    .domain([0, 100])
    .range([height, 0]);

const xAxis = d3.axisBottom(xScale)
    .ticks(10, ",f")
    .tickPadding(10);

svg.append("g")
    .attr("class", "x-axis")
    .attr("transform", "translate(0," + (height) + ")")
    .call(xAxis);

// Convert to quadratic bezier (1 control points) to cubic (2 control points)
    var full = quadraticToCubic(fullq);
  
    // Split the path into multiple segments with an event between each segment
    // Generate a random number of events (cuts) at random spots on each curve
    const parts = splitCurveMultiple(full, generate_random_cuts());
    var cumulative_proportion = 0;
    const segments = parts.map((points, index) => {
      // Calculate proportion of segment length relative to total length
      // We use that to determine the transition duration/delays later
      const proportion = (points[points.length - 1].x - points[0].x)/age_at_death
      cumulative_proportion += proportion;
      return { 
        points,
        proportion: proportion,
        cumulative_proportion: cumulative_proportion-proportion,
        // can specify what happens at the start or end of a segment
        start: null, 
        end: dropBall(d => d.points[d.points.length - 1])}
    });

curveData.push({ 
      full,
      segments,
      color: colors[i%colors.length],
      age_at_death
    })
  }
  
  const curves = svg.append("g").attr('class', 'curves').selectAll(".curve")
    .data(curveData);

const entering = curves
    .enter()
    .append('g');

entering.transition()
    .duration(total_delay)
    .delay((d, i) => i * total_delay)
    .attr('class', 'person')
    .on('start', drawSegment);

if (d.start) d.start.call(this, d, i);
        })
        .on('end', function(d, i) {
          if (d.end) d.end.call(this, d, i);
        });
  }

function dropBall(getPosition) {
    return function(d, i) {
      const group = d3.select(this.parentNode);
      const position = getPosition.call(this, d, i);

group.append('circle')
        .attr("cx", xScale(position.x))
        .attr("cy", yScale(position.y))
        .attr("r", 3)
        .attr('stroke', 'transparent')
        .attr('fill', 'transparent')
        .transition()
          .duration(delay_between_segments)
          .attr('stroke', "orange")
          .attr('fill', 'orange')
        .transition()
          .duration(100)
          .attr('r', 8)
        .transition()
          .duration(300)
          .attr('r', 3)
        .transition()
          .duration(500)
          .attr("cy", yScale(0))
        .transition()
          .duration(200)
          .style("opacity", 0.0)
    }
  }

// Utilities
  // ---------

function generate_random_cuts() {
    // generates a random number of cuts at random points between [0,1]
    var cuts = [];
    for (var j=0; j<d3.randomUniform(1, max_cuts)(); j++) {
      cuts.push(r());
    }
    return cuts.sort();
  };

function quadraticToCubic(pts) {
    // Converts a quadratic bezier curve (with 1 control point) to the equivalent cubic (with 2 control)
    // Reference: https://fontforge.github.io/bezier.html
    return [
      pts[0],
      {x: pts[0].x + (2/3)*(pts[1].x-pts[0].x),
        y: pts[0].y + (2/3)*(pts[1].y-pts[0].y)},
      {x: pts[2].x + (2/3)*(pts[1].x-pts[2].x),
        y: pts[2].y + (2/3)*(pts[1].y-pts[2].y)},
      pts[2] 
    ]
  }
  
  function cubicBezier(p) {
    // generates a cubic SVG path (2 control points)
    return "M " + xScale(p[0].x) + "," + yScale(p[0].y) 
      + " C " + xScale(p[1].x) +"," + yScale(p[1].y) 
      + " " + xScale(p[2].x) + "," + yScale(p[2].y)
      + " " + xScale(p[3].x) + "," + yScale(p[3].y) 
  }

function splitCurveMultiple(pts, ts) {
    // Takes a bezier curve (pts) and an array of cuts (ts)
    // Returns an array of bezier segements

let remaining = pts;
    let currentT = 0;
    const segments = [];

for (const t of ts) {
      // Find t relative to remaining segment
      const relativeT = (t - currentT) / (1 - currentT);
      const parts = splitCurve(remaining, relativeT);

segments.push(parts.first);

remaining = parts.last;
      currentT = t;
    }

// Add last remaining segment
    segments.push(remaining);

return segments;
  }

function splitCurve(pts, t) {
    // Splits a cubic Bezier curve into two segments at t
    // Source: https://stackoverflow.com/a/26831216

function lerp(a, b, t) {
      var s = 1 - t;
      return {x:a.x*s + b.x*t,
              y:a.y*s + b.y*t};
    }

var p0 = pts[0], p1 = pts[1], p2 = pts[2], p3 = pts[3];
    var p4 = lerp(p0, p1, t);
    var p5 = lerp(p1, p2, t);
    var p6 = lerp(p2, p3, t);
    var p7 = lerp(p4, p5, t);
    var p8 = lerp(p5, p6, t);
    var p9 = lerp(p7, p8, t);

return {first: [p0, p4, p7, p9],
            last: [p9, p8, p6, p3]}
  }
</script>

https://d3js.org/d3.v4.min.js

https://unpkg.com/seedrandom@2.4.3/seedrandom.min.js