Mesh clipping

Research for an equidecomposability (scissors congruence) implementation.

<!DOCTYPE html>
<style>

circle {
  cursor: move;
  fill: #fff;
  stroke: #000; 
  stroke-width: 1px;
}

circle.active {
  stroke: #000;
  stroke-width: 2px;
}

path.clip {
  fill: rgba(0, 0, 0, 0.3);
  stroke: #000;
  stroke-width: 1px;
}

path.subject {
  fill: rgba(0, 0, 0, 0);
  stroke: #000;
  stroke-width: 1px;
}

path.clipped {
  fill: rgba(240, 0, 0, 1);
  stroke: #000;
  stroke-width: 3px;
}

</style>
<svg width="960" height="960"></svg>
<script src="https://d3js.org/d3.v4.min.js"></script>
<script src="d3-polygon-clip.js"></script>
<script>

var svg = d3.select("svg"),
    width = svg.attr("width"),
    height = svg.attr("height");

var randomX = d3.randomNormal(width / 2, width * 0.1),
    randomY = d3.randomNormal(height / 2, height * 0.1);

var sites = d3.range(20).map(function(d) {
  return [randomX(), randomY()];
});

// Counter-clockwise orientation.
var clip = [[width / 2, height / 5],
            [width / 5, 3 * height / 5],
            [3 * width / 5, 3 * height / 5]];

var voronoi = d3.voronoi()
    .extent([[width / 4, height / 4], [3 * width / 4, 3* height / 4]]);

var subject = svg.append("g")
  .selectAll("path")
  .data(voronoi.polygons(sites))
  .enter().append("path")
    .attr("class", "subject")
    .attr("d", function(d) { return "M" + d.join("L") + "Z"; });

var clipPolygon = svg.append("path")
    .datum(clip)
    .attr("class", "clip");

// Control points for the clip polygon.
var circle = svg.selectAll("circle")
  .data(clip);

var origin = [0, 0];

circle.enter()
  .append("circle")
    .attr("r", 9)
    .attr("cx", function(d) { return d[0]; })
    .attr("cy", function(d) { return d[1]; })
    .call(d3.drag()
        .on("start", dragstarted)
        .on("drag", dragged)
        .on("end", dragended));

update();

// Redraw polygons in response to control point movement.
function update() {
  // Ensure clip polygon has counter-clockwise orientation.
  if (!ccw(clip)) clip.reverse();

clipPolygon.attr("d", function(d) { return "M" + d.join("L") + "Z"; });
  clipped = svg.selectAll(".clipped")
    .data(
      voronoi.polygons(sites)
        .map(function(d) {
          d3.polygonClip(clip, d);
          return d;
        })
        .filter(function(d) {
          return d.length > 2;
        })
    , function(d) { return d; }); // Key on Object reference.
  
  clipped.enter().insert("path")
      .attr("class", "clipped")
      .attr("d", function(d) { return "M" + d.join("L") + "Z"; });

clipped.exit().remove();

// Circles drawn on top of all other SVG elements.
  d3.selectAll("circle").raise();
}

function dragstarted(d) {
  d3.select(this).classed("active", true);
}

function dragged(d) {
  d3.select(this)
      .attr("cx", d[0] = d3.event.x)
      .attr("cy", d[1] = d3.event.y)
  update();
}

function dragended(d, i) {
  d3.select(this).classed("active", false);
}

function polygonClone(polygon) {
  var cloned = [],
      i,
      n;

for (i = 0, n = polygon.length; i < n; i++) {
    cloned.push([polygon[i][0], polygon[i][1]]);
  }

return cloned;
}

// Returns true of the given polygon has counter-clockwise orientation.
function ccw(polygon) {
  function polygonInside(p, a, b) {
    return (b[0] - a[0]) * (p[1] - a[1]) < (b[1] - a[1]) * (p[0] - a[0]);
  }

return polygonInside(d3.polygonCentroid(polygon), polygon[0], polygon[1]);
}

</script>

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