Australia↔Austria

Trying to figure out if there’s a problem with Australia↔Austria spherical linear interpolation in the World Countries example, as hinted at by Hadley Wickham.

Note how the geodesic is always a straight line under the orthographic projection, since it is always going through the centre. (Except for the initial view centred at (0°, 0°), which is not on the geodesic). This is true for all azimuthal projections.

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

.country {
  fill: #b8b8b8;
  stroke: #fff;
  stroke-width: .5px;
  stroke-linejoin: round;
}

.graticule {
  fill: none;
  stroke: #000;
  stroke-opacity: .3;
  stroke-width: .5px;
}

.graticule-outline {
  fill: none;
  stroke: #333;
  stroke-width: 1.5px;
}

text {
  font-family: "Helvetica Neue", Helvetica, Arial, sans-serif;
  font-size: 18px;
  font-weight: bold;
  text-anchor: middle;
}

.arc {
  stroke: #000;
  fill: none;
}

.point {
  fill: #000;
}

</style>
<body>
<script src="https://d3js.org/d3.v3.min.js"></script>
<script src="https://d3js.org/topojson.v0.min.js"></script>
<script>

var width = 960,
    height = 500;

var centroid = d3.geo.path()
    .projection(function(d) { return d; })
    .centroid;

var projection = d3.geo.orthographic()
    .scale(248)
    .clipAngle(90);

var path = d3.geo.path()
    .pointRadius(1.5)
    .projection(projection);

var graticule = d3.geo.graticule()
    .extent([[-180, -90], [180 - .1, 90 - .1]]);

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

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

svg.append("circle")
    .attr("class", "graticule-outline")
    .attr("cx", width / 2)
    .attr("cy", height / 2)
    .attr("r", projection.scale());

var title = svg.append("text")
    .attr("x", width / 2)
    .attr("y", height * 3 / 5);

var rotate = d3_geo_greatArcInterpolator();

d3.json("readme-world-110m.json", function(error, world) {
  var countries = topojson.object(world, world.objects.countries).geometries,
      i = -1,
      n = countries.length;

var country = svg.selectAll(".country")
      .data(countries)
    .enter().insert("path", ".graticule")
      .attr("class", "country")
      .attr("d", path);

var au0, au1;
  countries.forEach(function(d, i) {
    if (d.id === "Australia") au0 = i;
    if (d.id === "Austria") au1 = i;
  });

var arc = d3.geo.greatArc()
      .precision(1)
      .source(centroid(countries[au0]))
      .target(centroid(countries[au1]));

var arcPoints = svg.selectAll("path.point")
      .data(arc().coordinates.map(function(d) { return {type: "Point", coordinates: d}; }))
    .enter().append("path")
      .attr("class", "point")
      .attr("d", path);

step();

function step() {
    //if (++i >= n) i = 0;
    i = i === au0 ? au1 : au0;

title.text(countries[i].id);

country.transition()
        .style("fill", function(d, j) { return j === i ? "red" : "#b8b8b8"; });

d3.transition()
        .delay(250)
        .duration(1250)
        .tween("rotate", function() {
          var point = centroid(countries[i]);
          rotate.source(projection.rotate()).target([-point[0], -point[1]]).distance();
          return function(t) {
            projection.rotate(rotate(t));
            arcPoints.attr("d", path);
            country.attr("d", path);
            line.attr("d", path);
          };
        })
      .transition()
        .each("end", step);
  }
});

var d3_radians = Math.PI / 180;

function d3_geo_greatArcInterpolator() {
  var x0, y0, cy0, sy0, kx0, ky0,
      x1, y1, cy1, sy1, kx1, ky1,
      d,
      k;

function interpolate(t) {
    var B = Math.sin(t *= d) * k,
        A = Math.sin(d - t) * k,
        x = A * kx0 + B * kx1,
        y = A * ky0 + B * ky1,
        z = A * sy0 + B * sy1;
    return [
      Math.atan2(y, x) / d3_radians,
      Math.atan2(z, Math.sqrt(x * x + y * y)) / d3_radians
    ];
  }

interpolate.distance = function() {
    if (d == null) k = 1 / Math.sin(d = Math.acos(Math.max(-1, Math.min(1, sy0 * sy1 + cy0 * cy1 * Math.cos(x1 - x0)))));
    return d;
  };

interpolate.source = function(_) {
    var cx0 = Math.cos(x0 = _[0] * d3_radians),
        sx0 = Math.sin(x0);
    cy0 = Math.cos(y0 = _[1] * d3_radians);
    sy0 = Math.sin(y0);
    kx0 = cy0 * cx0;
    ky0 = cy0 * sx0;
    d = null;
    return interpolate;
  };

interpolate.target = function(_) {
    var cx1 = Math.cos(x1 = _[0] * d3_radians),
        sx1 = Math.sin(x1);
    cy1 = Math.cos(y1 = _[1] * d3_radians);
    sy1 = Math.sin(y1);
    kx1 = cy1 * cx1;
    ky1 = cy1 * sx1;
    d = null;
    return interpolate;
  };

return interpolate;
}

</script>

Modified http://d3js.org/d3.v3.min.js to a secure url

Modified http://d3js.org/topojson.v0.min.js to a secure url

https://d3js.org/d3.v3.min.js

https://d3js.org/topojson.v0.min.js