Cylindrical Stereographic

The cylindrical stereographic projection is available as d3.geoCylindricalStereographic in d3-geo-projection. With a parallel of 45°, also known as Gall’s stereographic.

<!DOCTYPE html>
<meta charset="utf-8">
<style>

.graticule {
  fill: none;
  stroke: #777;
  stroke-width: 0.5px;
  stroke-opacity: 0.5;
}

.land {
  fill: #222;
}

.boundary {
  fill: none;
  stroke: #fff;
  stroke-width: 0.5px;
}

</style>
<svg width="960" height="611"></svg>
<script src="//d3js.org/d3.v4.min.js"></script>
<script src="//d3js.org/topojson.v1.min.js"></script>
<script src="d3-geo-projection.min.js"></script>
<script>

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

var projection = d3.geoCylindricalStereographic()
    .scale(153)
    .translate([width / 2, height / 2])
    .precision(0.1);

var path = d3.geoPath()
    .projection(projection);

var graticule = d3.geoGraticule();

svg.append("path")
    .datum(graticule)
    .attr("class", "graticule")
    .attr("d", path);

svg.append("path")
    .datum({type: "Sphere"})
    .attr("class", "sphere")
    .attr("d", path)
    .attr("fill", "none")
    .attr("stroke", "black");

d3.json("/../../data/world-50m.json", function(error, world) {
  if (error) throw error;

svg.insert("path", ".graticule")
      .datum(topojson.feature(world, world.objects.land))
      .attr("class", "land")
      .attr("d", path);

svg.insert("path", ".graticule")
      .datum(topojson.mesh(world, world.objects.countries, function(a, b) { return a !== b; }))
      .attr("class", "boundary")
      .attr("d", path);
});

</script>

Changed /mbostock/raw/4090846/world-50m.json to a local referenece

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

https://d3js.org/topojson.v1.min.js