diff --git a/geo/CHANGES.md b/geo/CHANGES.md
index ad1f414b0..b9961991c 100644
--- a/geo/CHANGES.md
+++ b/geo/CHANGES.md
@@ -2,6 +2,7 @@
 
 ## Unreleased
 
+* Improve handling of InterploatePoint with collapsed Line
 
 ## 0.29.0 - 2024.10.30
 
diff --git a/geo/src/algorithm/line_measures/interpolate_point.rs b/geo/src/algorithm/line_measures/interpolate_point.rs
index d53bc226e..9f653b966 100644
--- a/geo/src/algorithm/line_measures/interpolate_point.rs
+++ b/geo/src/algorithm/line_measures/interpolate_point.rs
@@ -32,3 +32,159 @@ pub trait InterpolatePoint<F: CoordFloat> {
         include_ends: bool,
     ) -> impl Iterator<Item = Point<F>>;
 }
+
+#[cfg(test)]
+mod tests {
+    use crate::{Euclidean, Geodesic, Haversine, InterpolatePoint, Point, Rhumb};
+
+    #[test]
+    fn point_at_ratio_between_line_ends() {
+        let start = Point::new(0.0, 0.0);
+        let end = Point::new(1.0, 1.0);
+
+        let ratio = 0.0;
+        assert_eq!(Haversine::point_at_ratio_between(start, end, ratio), start);
+        assert_eq!(Euclidean::point_at_ratio_between(start, end, ratio), start);
+        assert_eq!(Geodesic::point_at_ratio_between(start, end, ratio), start);
+        assert_eq!(Rhumb::point_at_ratio_between(start, end, ratio), start);
+
+        let ratio = 1.0;
+        assert_eq!(Haversine::point_at_ratio_between(start, end, ratio), end);
+        assert_eq!(Euclidean::point_at_ratio_between(start, end, ratio), end);
+        assert_eq!(Geodesic::point_at_ratio_between(start, end, ratio), end);
+        assert_eq!(Rhumb::point_at_ratio_between(start, end, ratio), end);
+    }
+
+    mod degenerate {
+        use super::*;
+
+        #[test]
+        fn point_at_ratio_between_collapsed_line() {
+            let start = Point::new(1.0, 1.0);
+
+            let ratio = 0.0;
+            assert_eq!(
+                Haversine::point_at_ratio_between(start, start, ratio),
+                start
+            );
+            assert_eq!(
+                Euclidean::point_at_ratio_between(start, start, ratio),
+                start
+            );
+            assert_eq!(Geodesic::point_at_ratio_between(start, start, ratio), start);
+            assert_eq!(Rhumb::point_at_ratio_between(start, start, ratio), start);
+
+            let ratio = 0.5;
+            assert_eq!(
+                Haversine::point_at_ratio_between(start, start, ratio),
+                start
+            );
+            assert_eq!(
+                Euclidean::point_at_ratio_between(start, start, ratio),
+                start
+            );
+            assert_eq!(Geodesic::point_at_ratio_between(start, start, ratio), start);
+            assert_eq!(Rhumb::point_at_ratio_between(start, start, ratio), start);
+
+            let ratio = 1.0;
+            assert_eq!(
+                Haversine::point_at_ratio_between(start, start, ratio),
+                start
+            );
+            assert_eq!(
+                Euclidean::point_at_ratio_between(start, start, ratio),
+                start
+            );
+            assert_eq!(Geodesic::point_at_ratio_between(start, start, ratio), start);
+            assert_eq!(Rhumb::point_at_ratio_between(start, start, ratio), start);
+        }
+
+        #[test]
+        fn point_at_distance_between_collapsed_line() {
+            // This method just documents existing behavior. I don't think our current behavior
+            // is especially useful, but we might consider handling it uniformly one day.
+            let start: Point = Point::new(1.0, 1.0);
+
+            let distance = 0.0;
+            assert_eq!(
+                Haversine::point_at_distance_between(start, start, distance),
+                start
+            );
+
+            let euclidean_result = Euclidean::point_at_distance_between(start, start, distance);
+            assert!(euclidean_result.x().is_nan());
+            assert!(euclidean_result.y().is_nan());
+            assert_eq!(
+                Geodesic::point_at_distance_between(start, start, distance),
+                start
+            );
+            assert_eq!(
+                Rhumb::point_at_distance_between(start, start, distance),
+                start
+            );
+
+            let distance = 100000.0;
+            let due_north = Point::new(1.0, 1.9);
+            let due_south = Point::new(1.0, 0.1);
+            assert_relative_eq!(
+                Haversine::point_at_distance_between(start, start, distance),
+                due_north,
+                epsilon = 1.0e-1
+            );
+            let euclidean_result = Euclidean::point_at_distance_between(start, start, distance);
+            assert!(euclidean_result.x().is_nan());
+            assert!(euclidean_result.y().is_nan());
+            assert_relative_eq!(
+                Geodesic::point_at_distance_between(start, start, distance),
+                due_south,
+                epsilon = 1.0e-1
+            );
+            assert_relative_eq!(
+                Rhumb::point_at_distance_between(start, start, distance),
+                due_north,
+                epsilon = 1.0e-1
+            );
+        }
+
+        #[test]
+        fn points_along_collapsed_line() {
+            let start = Point::new(1.0, 1.0);
+
+            let max_distance = 1.0;
+
+            let include_ends = true;
+            let points: Vec<_> =
+                Haversine::points_along_line(start, start, max_distance, include_ends).collect();
+            assert_eq!(points, vec![start, start]);
+
+            let points: Vec<_> =
+                Euclidean::points_along_line(start, start, max_distance, include_ends).collect();
+            assert_eq!(points, vec![start, start]);
+
+            let points: Vec<_> =
+                Geodesic::points_along_line(start, start, max_distance, include_ends).collect();
+            assert_eq!(points, vec![start, start]);
+
+            let points: Vec<_> =
+                Rhumb::points_along_line(start, start, max_distance, include_ends).collect();
+            assert_eq!(points, vec![start, start]);
+
+            let include_ends = false;
+            let points: Vec<_> =
+                Haversine::points_along_line(start, start, max_distance, include_ends).collect();
+            assert_eq!(points, vec![]);
+
+            let points: Vec<_> =
+                Euclidean::points_along_line(start, start, max_distance, include_ends).collect();
+            assert_eq!(points, vec![]);
+
+            let points: Vec<_> =
+                Geodesic::points_along_line(start, start, max_distance, include_ends).collect();
+            assert_eq!(points, vec![]);
+
+            let points: Vec<_> =
+                Rhumb::points_along_line(start, start, max_distance, include_ends).collect();
+            assert_eq!(points, vec![]);
+        }
+    }
+}
diff --git a/geo/src/algorithm/line_measures/metric_spaces/geodesic.rs b/geo/src/algorithm/line_measures/metric_spaces/geodesic.rs
index 6e9ccb874..89335ca87 100644
--- a/geo/src/algorithm/line_measures/metric_spaces/geodesic.rs
+++ b/geo/src/algorithm/line_measures/metric_spaces/geodesic.rs
@@ -168,6 +168,9 @@ impl InterpolatePoint<f64> for Geodesic {
         end: Point<f64>,
         meters_from_start: f64,
     ) -> Point<f64> {
+        if meters_from_start == 0.0 {
+            return start;
+        }
         let bearing = Self::bearing(start, end);
         Self::destination(start, bearing, meters_from_start)
     }
@@ -205,6 +208,13 @@ impl InterpolatePoint<f64> for Geodesic {
         end: Point<f64>,
         ratio_from_start: f64,
     ) -> Point<f64> {
+        if start == end || ratio_from_start == 0.0 {
+            return start;
+        }
+        if ratio_from_start == 1.0 {
+            return end;
+        }
+
         let g = geographiclib_rs::Geodesic::wgs84();
         let (total_distance, azi1, _azi2, _a12) = g.inverse(start.y(), start.x(), end.y(), end.x());
         let distance = total_distance * ratio_from_start;
diff --git a/geo/src/algorithm/line_measures/metric_spaces/haversine.rs b/geo/src/algorithm/line_measures/metric_spaces/haversine.rs
index 971e7504e..ac4b02479 100644
--- a/geo/src/algorithm/line_measures/metric_spaces/haversine.rs
+++ b/geo/src/algorithm/line_measures/metric_spaces/haversine.rs
@@ -204,6 +204,12 @@ impl<F: CoordFloat + FromPrimitive> InterpolatePoint<F> for Haversine {
     ///
     /// [great circle]: https://en.wikipedia.org/wiki/Great_circle
     fn point_at_ratio_between(start: Point<F>, end: Point<F>, ratio_from_start: F) -> Point<F> {
+        if start == end || ratio_from_start == F::zero() {
+            return start;
+        }
+        if ratio_from_start == F::one() {
+            return end;
+        }
         let calculation = HaversineIntermediateFillCalculation::new(start, end);
         calculation.point_at_ratio(ratio_from_start)
     }