Add Tensor-based implementation of FarthestPointDownSample (#6948)

* Add Tensor-based implementation of FarthestPointDownSample

* Use tensor-based version also for CPU Pointclouds

cpp/open3d/t/geometry/PointCloud.cpp

@@ -384,11 +384,37 @@ PointCloud PointCloud::RandomDownSample(double sampling_ratio) const {
 }
 
 PointCloud PointCloud::FarthestPointDownSample(size_t num_samples) const {
-    // We want the sampled points has the attributes of the original point
-    // cloud, so full copy is needed.
-    const open3d::geometry::PointCloud lpcd = ToLegacy();
-    return FromLegacy(*lpcd.FarthestPointDownSample(num_samples),
-                      GetPointPositions().GetDtype(), GetDevice());
+    const core::Dtype dtype = GetPointPositions().GetDtype();
+    const int64_t num_points = GetPointPositions().GetLength();
+    if (num_samples == 0) {
+        return PointCloud(GetDevice());
+    } else if (num_samples == size_t(num_points)) {
+        return Clone();
+    } else if (num_samples > size_t(num_points)) {
+        utility::LogError(
+                "Illegal number of samples: {}, must <= point size: {}",
+                num_samples, num_points);
+    }
+    core::Tensor selection_mask =
+            core::Tensor::Zeros({num_points}, core::Bool, GetDevice());
+    core::Tensor smallest_distances = core::Tensor::Full(
+            {num_points}, std::numeric_limits<double>::infinity(), dtype,
+            GetDevice());
+
+    int64_t farthest_index = 0;
+
+    for (size_t i = 0; i < num_samples; i++) {
+        selection_mask[farthest_index] = true;
+        core::Tensor selected = GetPointPositions()[farthest_index];
+
+        core::Tensor diff = GetPointPositions() - selected;
+        core::Tensor distances_to_selected = (diff * diff).Sum({1});
+        smallest_distances = open3d::core::Minimum(distances_to_selected,
+                                                   smallest_distances);
+
+        farthest_index = smallest_distances.ArgMax({0}).Item<int64_t>();
+    }
+    return SelectByMask(selection_mask);
 }
 
 std::tuple<PointCloud, core::Tensor> PointCloud::RemoveRadiusOutliers(