diff --git a/topola/src/layout/mod.rs b/topola/src/layout/mod.rs
index a9b3cc8..539305b 100644
--- a/topola/src/layout/mod.rs
+++ b/topola/src/layout/mod.rs
@@ -9,6 +9,7 @@ mod infringement;
 mod insert;
 mod locate;
 mod modify;
+mod overlap;
 pub mod primitives;
 mod transforms;
 
diff --git a/topola/src/layout/overlap.rs b/topola/src/layout/overlap.rs
new file mode 100644
index 0000000..2c640eb
--- /dev/null
+++ b/topola/src/layout/overlap.rs
@@ -0,0 +1,187 @@
+// SPDX-FileCopyrightText: 2026 Topola contributors
+//
+// SPDX-License-Identifier: MIT OR Apache-2.0
+
+use crate::{
+    Rect2,
+    board::Board,
+    primitives::{JointId, PolygonId, SegmentId, ViaId},
+};
+
+impl Board {
+    pub fn joint_joint_rect_overlap(
+        &self,
+        infringer: JointId,
+        infringee: JointId,
+    ) -> Option<Rect2<i64>> {
+        let infringer_bbox = self.layout().joint(infringer).bbox().xy();
+        let infringee_bbox = self.layout().joint(infringee).bbox().xy();
+
+        infringer_bbox.intersection(infringee_bbox)
+    }
+
+    pub fn joint_segment_rect_overlap(
+        &self,
+        infringer: JointId,
+        infringee: SegmentId,
+    ) -> Option<Rect2<i64>> {
+        let infringer_bbox = self.layout().joint(infringer).bbox().xy();
+        let infringee_bbox = self.layout().segment(infringee).bbox().xy();
+
+        infringer_bbox.intersection(infringee_bbox)
+    }
+
+    pub fn joint_via_rect_overlap(
+        &self,
+        infringer: JointId,
+        infringee: ViaId,
+    ) -> Option<Rect2<i64>> {
+        let infringer_bbox = self.layout().joint(infringer).bbox().xy();
+        let infringee_bbox = self.layout().via(infringee).bbox().xy();
+
+        infringer_bbox.intersection(infringee_bbox)
+    }
+
+    pub fn joint_polygon_rect_overlap(
+        &self,
+        infringer: JointId,
+        infringee: PolygonId,
+    ) -> Option<Rect2<i64>> {
+        let infringer_bbox = self.layout().joint(infringer).bbox().xy();
+        let infringee_bbox = self.layout().polygon(infringee).bbox().xy();
+
+        infringer_bbox.intersection(infringee_bbox)
+    }
+
+    pub fn segment_joint_rect_overlap(
+        &self,
+        infringer: SegmentId,
+        infringee: JointId,
+    ) -> Option<Rect2<i64>> {
+        let infringer_bbox = self.layout().segment(infringer).bbox().xy();
+        let infringee_bbox = self.layout().joint(infringee).bbox().xy();
+
+        infringer_bbox.intersection(infringee_bbox)
+    }
+
+    pub fn segment_segment_rect_overlap(
+        &self,
+        infringer: SegmentId,
+        infringee: SegmentId,
+    ) -> Option<Rect2<i64>> {
+        let infringer_bbox = self.layout().segment(infringer).bbox().xy();
+        let infringee_bbox = self.layout().segment(infringee).bbox().xy();
+
+        infringer_bbox.intersection(infringee_bbox)
+    }
+
+    pub fn segment_via_rect_overlap(
+        &self,
+        infringer: SegmentId,
+        infringee: ViaId,
+    ) -> Option<Rect2<i64>> {
+        let infringer_bbox = self.layout().segment(infringer).bbox().xy();
+        let infringee_bbox = self.layout().via(infringee).bbox().xy();
+
+        infringer_bbox.intersection(infringee_bbox)
+    }
+
+    pub fn segment_polygon_rect_overlap(
+        &self,
+        infringer: SegmentId,
+        infringee: PolygonId,
+    ) -> Option<Rect2<i64>> {
+        let infringer_bbox = self.layout().segment(infringer).bbox().xy();
+        let infringee_bbox = self.layout().polygon(infringee).bbox().xy();
+
+        infringer_bbox.intersection(infringee_bbox)
+    }
+
+    pub fn via_joint_rect_overlap(
+        &self,
+        infringer: ViaId,
+        infringee: JointId,
+    ) -> Option<Rect2<i64>> {
+        let infringer_bbox = self.layout().via(infringer).bbox().xy();
+        let infringee_bbox = self.layout().joint(infringee).bbox().xy();
+
+        infringer_bbox.intersection(infringee_bbox)
+    }
+
+    pub fn via_segment_rect_overlap(
+        &self,
+        infringer: ViaId,
+        infringee: SegmentId,
+    ) -> Option<Rect2<i64>> {
+        let infringer_bbox = self.layout().via(infringer).bbox().xy();
+        let infringee_bbox = self.layout().segment(infringee).bbox().xy();
+
+        infringer_bbox.intersection(infringee_bbox)
+    }
+
+    pub fn via_via_rect_overlap(
+        &self,
+        infringer: ViaId,
+        infringee: ViaId,
+    ) -> Option<Rect2<i64>> {
+        let infringer_bbox = self.layout().via(infringer).bbox().xy();
+        let infringee_bbox = self.layout().via(infringee).bbox().xy();
+
+        infringer_bbox.intersection(infringee_bbox)
+    }
+
+    pub fn via_polygon_rect_overlap(
+        &self,
+        infringer: ViaId,
+        infringee: PolygonId,
+    ) -> Option<Rect2<i64>> {
+        let infringer_bbox = self.layout().via(infringer).bbox().xy();
+        let infringee_bbox = self.layout().polygon(infringee).bbox().xy();
+
+        infringer_bbox.intersection(infringee_bbox)
+    }
+
+    pub fn polygon_joint_rect_overlap(
+        &self,
+        infringer: PolygonId,
+        infringee: JointId,
+    ) -> Option<Rect2<i64>> {
+        let infringer_bbox = self.layout().polygon(infringer).bbox().xy();
+        let infringee_bbox = self.layout().joint(infringee).bbox().xy();
+
+        infringer_bbox.intersection(infringee_bbox)
+    }
+
+    pub fn polygon_segment_rect_overlap(
+        &self,
+        infringer: PolygonId,
+        infringee: SegmentId,
+    ) -> Option<Rect2<i64>> {
+        let infringer_bbox = self.layout().polygon(infringer).bbox().xy();
+        let infringee_bbox = self.layout().segment(infringee).bbox().xy();
+
+        infringer_bbox.intersection(infringee_bbox)
+    }
+
+    pub fn polygon_via_rect_overlap(
+        &self,
+        infringer: PolygonId,
+        infringee: ViaId,
+    ) -> Option<Rect2<i64>> {
+        let infringer_bbox = self.layout().polygon(infringer).bbox().xy();
+        let infringee_bbox = self.layout().via(infringee).bbox().xy();
+
+        infringer_bbox.intersection(infringee_bbox)
+    }
+
+    pub fn polygon_polygon_rect_overlap(
+        &self,
+        infringer: PolygonId,
+        infringee: PolygonId,
+    ) -> Option<Rect2<i64>> {
+        let infringer_bbox = self.layout().polygon(infringer).bbox().xy();
+        let infringee_bbox = self.layout().polygon(infringee).bbox().xy();
+
+        infringer_bbox.intersection(infringee_bbox)
+    }
+}