Tetrahedral Gnomonic projection Antarctic

The Tetrahedral Gnomonic projection, published by A. J. Potter in The Geographical Teacher, Vol. 13, No. 1 (SPRING, 1925), pp. 52-56.

Using d3.geoPolyhedral on the tetrahedron
Gnomonic projection on each face
This is the Antarctic-centered aspect. See Potter’s North Pole aspect

Research by Philippe Rivière for d3-geo-projection issue 107.

[

](https://github.com/Fil/) Questions and comments welcome on [gitter.im/d3](https://gitter.im/d3/d3), [twitter](https://twitter.com/@recifs) or [slack](https://d3js.slack.com).

<!DOCTYPE html>
<canvas width="960" height="600"></canvas>
<script src="https://d3js.org/d3.v4.js"></script>
<script src="https://d3js.org/d3-geo-projection.v2.min.js"></script>
<script src="https://d3js.org/topojson.v2.min.js"></script>
<script src="versor.js"></script>

// retina display
  var devicePixelRatio = window.devicePixelRatio || 1;
  canvas.style('width', canvas.attr('width')+'px');
  canvas.style('height', canvas.attr('height')+'px');
  canvas.attr('width', canvas.attr('width') * devicePixelRatio);
  canvas.attr('height', canvas.attr('height') * devicePixelRatio);
  context.scale(devicePixelRatio,devicePixelRatio);

var pi = Math.PI, degrees = 180 / pi, asin1_3 = Math.asin(1 / 3);

var centers = [
  [0, 90],
  [-180, -asin1_3 * degrees],
  [-60, -asin1_3 * degrees],
  [60, -asin1_3 * degrees]
];

d3.geoTetrahedralGnomonic = function(faceProjection) {
  var tetrahedron = [[1, 2, 3], [0, 2, 1], [0, 3, 2], [0, 1, 3]].map(function(
    face
  ) {
    return face.map(function(i) {
      return centers[i];
    });
  });

faceProjection =
    faceProjection ||
    function(face) {
      var c = d3.geoCentroid({ type: "MultiPoint", coordinates: face });
      return d3
        .geoGnomonic()
        .scale(1)
        .translate([0, 0])
        .rotate([-c[0] * (Math.abs(c[1]) != 90), -c[1]]);
    };

var faces = tetrahedron.map(function(face) {
    return { face: face, project: faceProjection(face) };
  });

[-1, 0, 0, 0].forEach(function(d, i) {
    var node = faces[d];
    node && (node.children || (node.children = [])).push(faces[i]);
  });

return d3
    .geoPolyhedral(
      faces[0],
      function(lambda, phi) {
        lambda *= degrees;
        phi *= degrees;
        for (var i = 0; i < faces.length; i++) {
          if (
            d3.geoContains(
              {
                type: "Polygon",
                coordinates: [[...tetrahedron[i], tetrahedron[i][0]]]
              },
              [lambda, phi]
            )
          ) {
            return faces[i];
          }
        }
      },
      pi / 3
    )
    .clipAngle(180)
    .rotate([-30, 0])
    .fitExtent([[0, 0], [width, height]], { type: "Sphere" });
};

projection = d3.geoTetrahedralGnomonic();

var init_scale = projection.scale(),
  path = d3.geoPath().projection(projection).context(context);

d3.json("https://unpkg.com/world-atlas@1/world/110m.json", function(
  error,
  world
) {
  if (error) throw error;

var land = topojson.feature(world, world.objects.countries);

render = function() {
    context.fillStyle = "#fff";
    context.fillRect(0, 0, width, height);

context.beginPath();
    path({type:"Sphere"});
    context.strokeStyle = "black";
    context.stroke(), context.clip(), context.closePath();

context.beginPath();
    path(land);
    context.fillStyle = "#000";
    context.fill(), context.closePath();

context.beginPath();
    path(d3.geoGraticule()());
    context.strokeStyle = "#777";
    context.stroke(), context.closePath();

};

render();
});

canvas.call(d3.drag().on("start", dragstarted).on("drag", dragged));

var render = function() {},
  v0, // Mouse position in Cartesian coordinates at start of drag gesture.
  r0, // Projection rotation as Euler angles at start.
  q0; // Projection rotation as versor at start.

function dragstarted() {
  v0 = versor.cartesian(projection.invert(d3.mouse(this)));
  r0 = projection.rotate();
  console.log("r0", r0);
  q0 = versor(r0);
}

function dragged() {
  var v1 = versor.cartesian(projection.rotate(r0).invert(d3.mouse(this))),
    q1 = versor.multiply(q0, versor.delta(v0, v1)),
    r1 = versor.rotation(q1);
  projection.rotate(r1);
  render();
}
</script>

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

https://d3js.org/d3-geo-projection.v2.min.js

https://d3js.org/topojson.v2.min.js