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jasondaviesjasondavies
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Workaround for lack of symmetry in Math.sin.
Chrome 33 included some sin/cos optimisations, which unfortunately broke our assumption that sin(-x) + sin(x) = 0 for all x. More details here: https://code.google.com/p/v8/issues/detail?id=3006 This fix uses: sin(x) = sgn(x) * sin(abs(x)) and: cos(x) = cos(abs(x)) where it matters, which fixes area calculations for degenerate polygons such as: {"type":"Polygon", "coordinates":[[[-0.0002,0.0001],[0.0002,0.0001],[-0.0002,0.0001]]]} Fixes d3#1753.
1 parent 04fa5dd commit bef5de7

4 files changed

Lines changed: 16 additions & 12 deletions

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‎d3.js‎

Lines changed: 4 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -2877,7 +2877,7 @@
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function nextPoint(λ, φ) {
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λ *= d3_radians;
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φ = φ * d3_radians / 2 + π / 4;
2880-
var dλ = λ - λ0, cosφ = Math.cos(φ), sinφ = Math.sin(φ), k = sinφ0 * sinφ, u = cosφ0 * cosφ + k * Math.cos(dλ), v = k * Math.sin(dλ);
2880+
var dλ = λ - λ0, sdλ = dλ >= 0 ? 1 : -1, adλ = sdλ * dλ, cosφ = Math.cos(φ), sinφ = Math.sin(φ), k = sinφ0 * sinφ, u = cosφ0 * cosφ + k * Math.cos(adλ), v = k * sdλ * Math.sin(adλ);
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d3_geo_areaRingSum.add(Math.atan2(v, u));
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λ0 = λ, cosφ0 = cosφ, sinφ0 = sinφ;
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}
@@ -3339,9 +3339,9 @@
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while (true) {
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if (j === m) j = 0;
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point = ring[j];
3342-
var λ = point[0], φ = point[1] / 2 + π / 4, sinφ = Math.sin(φ), cosφ = Math.cos(φ), dλ = λ - λ0, antimeridian = abs(dλ) > π, k = sinφ0 * sinφ;
3343-
d3_geo_areaRingSum.add(Math.atan2(k * Math.sin(dλ), cosφ0 * cosφ + k * Math.cos(dλ)));
3344-
polarAngle += antimeridian ? dλ + (dλ >= 0 ? τ : -τ) : dλ;
3342+
var λ = point[0], φ = point[1] / 2 + π / 4, sinφ = Math.sin(φ), cosφ = Math.cos(φ), dλ = λ - λ0, sdλ = dλ >= 0 ? 1 : -1, adλ = sdλ * dλ, antimeridian = adλ > π, k = sinφ0 * sinφ;
3343+
d3_geo_areaRingSum.add(Math.atan2(k * sdλ * Math.sin(adλ), cosφ0 * cosφ + k * Math.cos(adλ)));
3344+
polarAngle += antimeridian ? dλ + sdλ * τ : dλ;
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if (antimeridian ^ λ0 >= meridian ^ λ >= meridian) {
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var arc = d3_geo_cartesianCross(d3_geo_cartesian(point0), d3_geo_cartesian(point));
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d3_geo_cartesianNormalize(arc);

‎d3.min.js‎

Lines changed: 3 additions & 3 deletions
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‎src/geo/area.js‎

Lines changed: 4 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -49,11 +49,13 @@ function d3_geo_areaRingStart() {
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// previous point, current point. Uses a formula derived from Cagnoli’s
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// theorem. See Todhunter, Spherical Trig. (1871), Sec. 103, Eq. (2).
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var dλ = λ - λ0,
52+
sdλ = dλ >= 0 ? 1 : -1,
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adλ = sdλ * dλ,
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cosφ = Math.cos(φ),
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sinφ = Math.sin(φ),
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k = sinφ0 * sinφ,
55-
u = cosφ0 * cosφ + k * Math.cos(dλ),
56-
v = k * Math.sin(dλ);
57+
u = cosφ0 * cosφ + k * Math.cos(adλ),
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v = k * sdλ * Math.sin(adλ);
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d3_geo_areaRingSum.add(Math.atan2(v, u));
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// Advance the previous points.

‎src/geo/point-in-polygon.js‎

Lines changed: 5 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -31,11 +31,13 @@ function d3_geo_pointInPolygon(point, polygon) {
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sinφ = Math.sin(φ),
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cosφ = Math.cos(φ),
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dλ = λ - λ0,
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antimeridian = abs(dλ) > π,
34+
sdλ = dλ >= 0 ? 1 : -1,
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adλ = sdλ * dλ,
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antimeridian = adλ > π,
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k = sinφ0 * sinφ;
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d3_geo_areaRingSum.add(Math.atan2(k * Math.sin(dλ), cosφ0 * cosφ + k * Math.cos(dλ)));
38+
d3_geo_areaRingSum.add(Math.atan2(k * sdλ * Math.sin(adλ), cosφ0 * cosφ + k * Math.cos(adλ)));
3739

38-
polarAngle += antimeridian ? dλ + (dλ >= 0 ? τ : -τ): dλ;
40+
polarAngle += antimeridian ? dλ + sdλ * τ : dλ;
3941

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// Are the longitudes either side of the point's meridian, and are the
4143
// latitudes smaller than the parallel?

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