The equatorial aspect of the Peirce quincuncial projection, which is available in d3-geo-projection. By setting the clip angle to 90°, you can produce the Adams hemisphere-in-a-square projection.
forked from mbostock's block: Peirce Equatorial — I removed one rotation.
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<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="960"></svg>
<script src="//d3js.org/d3.v4.min.js"></script>
<script src="//d3js.org/d3-geo-projection.v1.min.js"></script>
<script src="//d3js.org/topojson.v1.min.js"></script>
<script>
var svg = d3.select("svg"),
width = +svg.attr("width"),
height = +svg.attr("height"),
g = svg.append("g");
var projection = d3.geoPierceQuincuncial() // N.B. geoPeirceQuincuncial in 1.1+
.scale(214)
.translate([width / 2, height / 2])
.rotate([0, 0, -45])
// .clipAngle(90)
.precision(0.1);
var path = d3.geoPath()
.projection(projection);
var graticule = d3.geoGraticule();
g.append("path")
.datum(graticule)
.attr("class", "graticule")
.attr("d", path);
g.append("path")
.datum({type: "Sphere"})
.attr("class", "sphere")
.attr("d", path)
.attr("fill", "none")
.attr("stroke", "black");
d3.json("https://gist.githubusercontent.com/mbostock/4090846/raw/d534aba169207548a8a3d670c9c2cc719ff05c47/world-50m.json", function(error, world) {
if (error) throw error;
g.insert("path", ".graticule")
.datum(topojson.feature(world, world.objects.land))
.attr("class", "land")
.attr("d", path);
g.insert("path", ".graticule")
.datum(topojson.mesh(world, world.objects.countries, function(a, b) { return a !== b; }))
.attr("class", "boundary")
.attr("d", path);
});
</script>
https://d3js.org/d3.v4.min.js
https://d3js.org/d3-geo-projection.v1.min.js
https://d3js.org/topojson.v1.min.js