darkma773r commented on a change in pull request #97:
URL: https://github.com/apache/commons-geometry/pull/97#discussion_r454072077
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File path:
commons-geometry-spherical/src/main/java/org/apache/commons/geometry/spherical/twod/ConvexArea2S.java
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@@ -132,35 +139,167 @@ public Point2S getCentroid() {
return weighted == null ? null : Point2S.from(weighted);
}
- /** Returns the weighted vector for the centroid. This vector is computed
by scaling the
- * pole vector of the great circle of each boundary arc by the size of the
arc and summing
- * the results. By combining the weighted centroid vectors of multiple
areas, a single
- * centroid can be computed for the whole group.
+ /** Return the weighted centroid vector of the area. The returned vector
points in the direction of the
+ * centroid point on the surface of the unit sphere with the length of the
vector proportional to the
+ * effective mass of the area at the centroid. By adding the weighted
centroid vectors of multiple
+ * convex areas, a single centroid can be computed for the combined area.
* @return weighted centroid vector.
* @see <a href="https://archive.org/details/centroidinertiat00broc";>
* <em>The Centroid and Inertia Tensor for a Spherical Triangle</em> -
John E. Brock</a>
*/
Vector3D getWeightedCentroidVector() {
final List<GreatArc> arcs = getBoundaries();
- switch (arcs.size()) {
+ final int numBoundaries = arcs.size();
+
+ switch (numBoundaries) {
case 0:
// full space; no centroid
return null;
case 1:
- // hemisphere; centroid is the pole of the hemisphere
- final GreatArc singleArc = arcs.get(0);
- return
singleArc.getCircle().getPole().withNorm(singleArc.getSize());
+ // hemisphere
+ return computeHemisphereWeightedCentroidVector(arcs.get(0));
+ case 2:
+ // lune
+ return computeLuneWeightedCentroidVector(arcs.get(0), arcs.get(1));
default:
- // 2 or more sides; use an extension of the approach outlined here:
- // https://archive.org/details/centroidinertiat00broc
- // In short, the centroid is the sum of the pole vectors of each
side
- // multiplied by their arc lengths.
- Vector3D centroid = Vector3D.ZERO;
- for (final GreatArc arc : getBoundaries()) {
- centroid =
centroid.add(arc.getCircle().getPole().withNorm(arc.getSize()));
+ // triangle or other convex polygon
+ final double arcLengthSum = arcs.stream()
+ .mapToDouble(GreatArc::getSize)
+ .sum();
+
+ if (arcLengthSum < TRIANGLE_FAN_CENTROID_COMPUTE_THRESHOLD) {
+ return computeTriangleFanWeightedCentroidVector(arcs);
+ }
+
+ return computeArcPoleWeightedCentroidVector(arcs);
+ }
+ }
+
+ /** Compute the weighted centroid vector for the hemisphere formed by the
given arc.
+ * @param arc arc defining the hemisphere
+ * @return the weighted centroid vector for the hemisphere
+ * @see #getWeightedCentroidVector()
+ */
+ private Vector3D computeHemisphereWeightedCentroidVector(final GreatArc
arc) {
Review comment:
Sounds good.
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