diff --git a/geom/sample.hpp b/geom/sample.hpp
index f88fb1b5..c0c9e61e 100644
--- a/geom/sample.hpp
+++ b/geom/sample.hpp
@@ -103,6 +103,8 @@ namespace util::geom {
 
         {
             using point_type = decltype (target (gen));
+            using value_type = typename point_type::value_type;
+
             std::vector<point_type> selected;
             std::vector<point_type> candidates;
 
@@ -125,28 +127,28 @@ namespace util::geom {
                 // find the point whose minimum distance to the existing
                 // points is the greatest (while also being greater than the
                 // required minimum distance);
-                float best_distance = -INFINITY;
+                auto best_distance2 = std::numeric_limits<value_type>::lowest ();
                 size_t best_index;
 
                 for (size_t i = 0; i < candidates.size (); ++i) {
                     auto const p = candidates[i];
-                    float d = INFINITY;
+                    auto d2 = std::numeric_limits<value_type>::max ();
 
                     // find the minimum distance from this candidate to the
                     // selected points
                     for (auto q: selected)
-                        d = util::min (d, distance (p, q));
+                        d2 = util::min (d2, util::distance2 (p, q));
 
                     // record if it's the furthest away
-                    if (d > best_distance && d > minimum_distance (p)) {
-                        best_distance = d;
+                    if (d2 > best_distance2 && d2 > util::pow (minimum_distance (p), 2)) {
+                        best_distance2 = d2;
                         best_index = i;
                     }
                 }
 
                 // if we didn't find a suitable point then we give up and
                 // return the points we found, otherwise record the best point
-                if (best_distance <= 0)
+                if (best_distance2 <= 0)
                     break;
 
                 selected.push_back (candidates[best_index]);