diff --git a/Cargo.toml b/Cargo.toml
index f03c5d2..1aeb82c 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -10,6 +10,7 @@ resolver = "2"
 [workspace.dependencies]
 derive-getters = "0.5"
 derive_more = { version = "2.1", features = ["full"] }
+num-traits = "0.2"
 serde = { version = "1", features = ["derive", "rc"] }
 thiserror = "2.0"
 undoredo = { version = "0.10", features = ["derive", "bidimap", "stable-vec", "rstar"] }
diff --git a/topola-egui/src/display.rs b/topola-egui/src/display.rs
index 2c2347e..e6625b3 100644
--- a/topola-egui/src/display.rs
+++ b/topola-egui/src/display.rs
@@ -39,7 +39,11 @@ impl Display {
         let layout = board.layout();
 
         // Start from the bottom layer so that top layers are drawn on top.
-        for layer in (0..*layout.layer_count()).rev().map(LayerId::new) {
+        // The active layer is drawn last so it stays visible above the rest.
+        for layer in workspace
+            .appearance_panel
+            .layers_in_display_order(*layout.layer_count())
+        {
             if !workspace.appearance_panel.visible[layer.index()] {
                 continue;
             }
@@ -212,7 +216,10 @@ impl Display {
         let board = workspace.workspace.board();
         let layout = board.layout();
 
-        for layer in (0..*layout.layer_count()).rev().map(LayerId::new) {
+        for layer in workspace
+            .appearance_panel
+            .layers_in_display_order(*layout.layer_count())
+        {
             if !workspace.appearance_panel.visible[layer.index()] {
                 continue;
             }
@@ -294,7 +301,10 @@ impl Display {
         };
         let autorouter = &autorouter_workspace.autorouter;
 
-        for layer in (0..*workspace.workspace.board().layout().layer_count()).map(LayerId::new) {
+        for layer in workspace
+            .appearance_panel
+            .layers_in_display_order(*workspace.workspace.board().layout().layer_count())
+        {
             if workspace.appearance_panel.visible[layer.index()] {
                 for navmesh in autorouter
                     .router()
diff --git a/topola-egui/src/layers_panel.rs b/topola-egui/src/layers_panel.rs
index 3393d23..b1e5c40 100644
--- a/topola-egui/src/layers_panel.rs
+++ b/topola-egui/src/layers_panel.rs
@@ -146,7 +146,7 @@ impl LayersPanel {
         Self {
             dark_colors,
             light_colors,
-            active: LayerId::new(0),
+            active: board.layer_id("F.Cu").unwrap_or(LayerId::new(0)),
             visible,
         }
     }
@@ -207,4 +207,17 @@ impl LayersPanel {
             self.colors(ctx).layers.colors(layer_desc).normal
         }
     }
+
+    pub fn layers_in_display_order(&self, layer_count: usize) -> Vec<LayerId> {
+        let active = self.active.index();
+        let mut layers = (0..layer_count)
+            .rev()
+            .filter(|&layer| layer != active)
+            .map(LayerId::new)
+            .collect::<Vec<_>>();
+
+        // The active layer should be drawn on top.
+        layers.push(self.active);
+        layers
+    }
 }
diff --git a/topola/Cargo.toml b/topola/Cargo.toml
index fb40f4a..96a6597 100644
--- a/topola/Cargo.toml
+++ b/topola/Cargo.toml
@@ -14,6 +14,7 @@ dearcut = { version = "0.3", features = ["serde", "undoredo"] }
 derive-getters.workspace = true
 derive_more.workspace = true
 i_triangle = "0.40"
+num-traits.workspace = true
 polygon_unionfind = "0.7"
 rstar = "0.12"
 serde.workspace = true
diff --git a/topola/src/board/interactors/drag_selection.rs b/topola/src/board/interactors/drag_selection.rs
index d1f7b82..d805808 100644
--- a/topola/src/board/interactors/drag_selection.rs
+++ b/topola/src/board/interactors/drag_selection.rs
@@ -64,12 +64,12 @@ impl DragSelectionInteractor {
             SelectionContainMode::Crossing => {
                 self.selection
                     .components
-                    .add(board.locate_components_intersecting_rect(rect));
+                    .add(board.locate_components_prefer_layer_intersecting_rect(rect));
             }
             SelectionContainMode::Window => {
                 self.selection
                     .components
-                    .add(board.locate_components_inside_rect(rect));
+                    .add(board.locate_components_prefer_layer_inside_rect(rect));
             }
         }
 
@@ -77,10 +77,12 @@ impl DragSelectionInteractor {
             SelectionContainMode::Crossing => {
                 self.selection
                     .nets
-                    .add(board.locate_nets_intersecting_rect(rect));
+                    .add(board.locate_nets_prefer_layer_intersecting_rect(rect));
             }
             SelectionContainMode::Window => {
-                self.selection.nets.add(board.locate_nets_inside_rect(rect));
+                self.selection
+                    .nets
+                    .add(board.locate_nets_prefer_layer_inside_rect(rect));
             }
         }
 
@@ -88,10 +90,12 @@ impl DragSelectionInteractor {
             SelectionContainMode::Crossing => {
                 self.selection
                     .pins
-                    .add(board.locate_pins_intersecting_rect(rect));
+                    .add(board.locate_pins_prefer_layer_intersecting_rect(rect));
             }
             SelectionContainMode::Window => {
-                self.selection.pins.add(board.locate_pins_inside_rect(rect));
+                self.selection
+                    .pins
+                    .add(board.locate_pins_prefer_layer_inside_rect(rect));
             }
         }
 
diff --git a/topola/src/board/interactors/selection.rs b/topola/src/board/interactors/selection.rs
index 20cc315..30d8daa 100644
--- a/topola/src/board/interactors/selection.rs
+++ b/topola/src/board/interactors/selection.rs
@@ -47,25 +47,16 @@ impl SelectionInteractor {
 
         if input.release && input.pointer == self.origin {
             let mut selection = self.original_selection.clone();
+            let point = Vector3::new(input.pointer.x, input.pointer.y, layer.index() as i64);
 
             // Pins have intentional precedence over nets and components.
-            if let Some(pin_selector) = board.locate_pin_at_point(Vector3::new(
-                input.pointer.x,
-                input.pointer.y,
-                layer.index() as i64,
-            )) {
+            if let Some(pin_selector) = board.locate_pins_prefer_layer_at_point(point).next() {
                 selection.pins.xor(std::iter::once(pin_selector));
-            } else if let Some(net_selector) = board.locate_net_at_point(Vector3::new(
-                input.pointer.x,
-                input.pointer.y,
-                layer.index() as i64,
-            )) {
+            } else if let Some(net_selector) = board.locate_nets_prefer_layer_at_point(point).next() {
                 selection.nets.xor(std::iter::once(net_selector));
-            } else if let Some(component_selector) = board.locate_component_at_point(Vector3::new(
-                input.pointer.x,
-                input.pointer.y,
-                layer.index() as i64,
-            )) {
+            } else if let Some(component_selector) =
+                board.locate_components_prefer_layer_at_point(point).next()
+            {
                 selection
                     .components
                     .xor(std::iter::once(component_selector));
diff --git a/topola/src/board/locate.rs b/topola/src/board/locate.rs
index 47104b1..c426741 100644
--- a/topola/src/board/locate.rs
+++ b/topola/src/board/locate.rs
@@ -11,24 +11,76 @@ use crate::{
 };
 
 impl Board {
-    pub fn locate_component_at_point(&self, point: Vector3<i64>) -> Option<ComponentSelector> {
-        if let Some(joint_id) = self.layout.locate_joints_at_point(point).next() {
-            return self.joint_component_selector(joint_id);
-        }
+    pub fn locate_components_prefer_layer_at_point(
+        &self,
+        point: Vector3<i64>,
+    ) -> impl Iterator<Item = ComponentSelector> + '_ {
+        self.layout
+            .locate_joints_prefer_layer_at_point(point)
+            .filter_map(|joint_id| self.joint_component_selector(joint_id))
+            .chain(
+                self.layout
+                    .locate_segments_prefer_layer_at_point(point)
+                    .filter_map(|segment_id| self.segment_component_selector(segment_id)),
+            )
+            .chain(
+                self.layout
+                    .locate_vias_prefer_layer_at_point(point)
+                    .filter_map(|via_id| self.via_component_selector(via_id)),
+            )
+            .chain(
+                self.layout
+                    .locate_polygons_prefer_layer_at_point(point)
+                    .filter_map(|polygon_id| self.polygon_component_selector(polygon_id)),
+            )
+    }
 
-        if let Some(segment_id) = self.layout.locate_segments_at_point(point).next() {
-            return self.segment_component_selector(segment_id);
-        }
+    pub fn locate_components_at_point(
+        &self,
+        point: Vector3<i64>,
+    ) -> impl Iterator<Item = ComponentSelector> + '_ {
+        self.layout
+            .locate_joints_at_point(point)
+            .filter_map(|joint_id| self.joint_component_selector(joint_id))
+            .chain(
+                self.layout
+                    .locate_segments_at_point(point)
+                    .filter_map(|segment_id| self.segment_component_selector(segment_id)),
+            )
+            .chain(
+                self.layout
+                    .locate_vias_at_point(point)
+                    .filter_map(|via_id| self.via_component_selector(via_id)),
+            )
+            .chain(
+                self.layout
+                    .locate_polygons_at_point(point)
+                    .filter_map(|polygon_id| self.polygon_component_selector(polygon_id)),
+            )
+    }
 
-        if let Some(via_id) = self.layout.locate_vias_at_point(point).next() {
-            return self.via_component_selector(via_id);
-        }
-
-        if let Some(polygon_id) = self.layout.locate_polygons_at_point(point).next() {
-            return self.polygon_component_selector(polygon_id);
-        }
-
-        None
+    pub fn locate_components_prefer_layer_intersecting_rect(
+        &self,
+        rect: Rect3<i64>,
+    ) -> impl Iterator<Item = ComponentSelector> + '_ {
+        self.layout
+            .locate_joints_prefer_layer_intersecting_rect(rect)
+            .filter_map(|joint_id| self.joint_component_selector(joint_id))
+            .chain(
+                self.layout
+                    .locate_segments_prefer_layer_intersecting_rect(rect)
+                    .filter_map(|segment_id| self.segment_component_selector(segment_id)),
+            )
+            .chain(
+                self.layout
+                    .locate_vias_prefer_layer_intersecting_rect(rect)
+                    .filter_map(|via_id| self.via_component_selector(via_id)),
+            )
+            .chain(
+                self.layout
+                    .locate_polygons_prefer_layer_intersecting_rect(rect)
+                    .filter_map(|polygon_id| self.polygon_component_selector(polygon_id)),
+            )
     }
 
     pub fn locate_components_intersecting_rect(
@@ -55,48 +107,117 @@ impl Board {
             )
     }
 
+    pub fn locate_components_prefer_layer_inside_rect(
+        &self,
+        rect: Rect3<i64>,
+    ) -> impl Iterator<Item = ComponentSelector> + '_ {
+        self.layout
+            .locate_joints_prefer_layer_inside_rect(rect)
+            .filter_map(|joint_id| self.joint_component_selector(joint_id))
+            .chain(
+                self.layout
+                    .locate_segments_prefer_layer_inside_rect(rect)
+                    .filter_map(|segment_id| self.segment_component_selector(segment_id)),
+            )
+            .chain(
+                self.layout
+                    .locate_vias_prefer_layer_inside_rect(rect)
+                    .filter_map(|via_id| self.via_component_selector(via_id)),
+            )
+            .chain(
+                self.layout
+                    .locate_polygons_prefer_layer_inside_rect(rect)
+                    .filter_map(|polygon_id| self.polygon_component_selector(polygon_id)),
+            )
+    }
+
     pub fn locate_components_inside_rect(
         &self,
         rect: Rect3<i64>,
     ) -> impl Iterator<Item = ComponentSelector> + '_ {
         self.layout
-            .locate_joints_inside_rect(rect)
+            .locate_joints_prefer_layer_inside_rect(rect)
             .filter_map(|joint_id| self.joint_component_selector(joint_id))
             .chain(
                 self.layout
-                    .locate_segments_inside_rect(rect)
+                    .locate_segments_prefer_layer_inside_rect(rect)
                     .filter_map(|segment_id| self.segment_component_selector(segment_id)),
             )
             .chain(
                 self.layout
-                    .locate_vias_inside_rect(rect)
+                    .locate_vias_prefer_layer_inside_rect(rect)
                     .filter_map(|via_id| self.via_component_selector(via_id)),
             )
             .chain(
                 self.layout
-                    .locate_polygons_inside_rect(rect)
+                    .locate_polygons_prefer_layer_inside_rect(rect)
                     .filter_map(|polygon_id| self.polygon_component_selector(polygon_id)),
             )
     }
 
-    pub fn locate_net_at_point(&self, point: Vector3<i64>) -> Option<NetSelector> {
-        if let Some(joint_id) = self.layout.locate_joints_at_point(point).next() {
-            return self.joint_net_selector(joint_id);
+    pub fn locate_nets_prefer_layer_at_point(
+        &self,
+        point: Vector3<i64>,
+    ) -> impl Iterator<Item = NetSelector> + '_ {
+        self.layout
+            .locate_joints_prefer_layer_at_point(point)
+            .filter_map(|joint_id| self.joint_net_selector(joint_id))
+            .chain(
+                self.layout
+                    .locate_segments_prefer_layer_at_point(point)
+                    .filter_map(|segment_id| self.segment_net_selector(segment_id)),
+            )
+            .chain(
+                self.layout
+                    .locate_vias_prefer_layer_at_point(point)
+                    .filter_map(|via_id| self.via_net_selector(via_id)),
+            )
+            .chain(
+                self.layout
+                    .locate_polygons_prefer_layer_at_point(point)
+                    .filter_map(|polygon_id| self.polygon_net_selector(polygon_id)),
+            )
+    }
+
+    pub fn locate_nets_at_point(
+        &self,
+        point: Vector3<i64>,
+    ) -> impl Iterator<Item = NetSelector> + '_ {
+        self.layout
+            .locate_joints_at_point(point)
+            .filter_map(|joint_id| self.joint_net_selector(joint_id))
+            .chain(
+                self.layout
+                    .locate_segments_at_point(point)
+                    .filter_map(|segment_id| self.segment_net_selector(segment_id)),
+            )
+            .chain(
+                self.layout
+                    .locate_vias_at_point(point)
+                    .filter_map(|via_id| self.via_net_selector(via_id)),
+            )
+            .chain(
+                self.layout
+                    .locate_polygons_at_point(point)
+                    .filter_map(|polygon_id| self.polygon_net_selector(polygon_id)),
+            )
+    }
+
+    pub fn locate_nets_prefer_layer_intersecting_rect(
+        &self,
+        rect: Rect3<i64>,
+    ) -> impl Iterator<Item = NetSelector> + '_ {
+        let mut selectors = BTreeSet::new();
+
+        for net_id in self.layout.locate_nets_prefer_layer_intersecting_rect(rect) {
+            let Some(net_name) = self.net_name(net_id) else {
+                continue;
+            };
+
+            selectors.insert(NetSelector::new(net_name.to_string()));
         }
 
-        if let Some(segment_id) = self.layout.locate_segments_at_point(point).next() {
-            return self.segment_net_selector(segment_id);
-        }
-
-        if let Some(via_id) = self.layout.locate_vias_at_point(point).next() {
-            return self.via_net_selector(via_id);
-        }
-
-        if let Some(polygon_id) = self.layout.locate_polygons_at_point(point).next() {
-            return self.polygon_net_selector(polygon_id);
-        }
-
-        None
+        selectors.into_iter()
     }
 
     pub fn locate_nets_intersecting_rect(
@@ -116,6 +237,23 @@ impl Board {
         selectors.into_iter()
     }
 
+    pub fn locate_nets_prefer_layer_inside_rect(
+        &self,
+        rect: Rect3<i64>,
+    ) -> impl Iterator<Item = NetSelector> + '_ {
+        let mut selectors = BTreeSet::new();
+
+        for net_id in self.layout.locate_nets_prefer_layer_inside_rect(rect) {
+            let Some(net_name) = self.net_name(net_id) else {
+                continue;
+            };
+
+            selectors.insert(NetSelector::new(net_name.to_string()));
+        }
+
+        selectors.into_iter()
+    }
+
     pub fn locate_nets_inside_rect(
         &self,
         rect: Rect3<i64>,
@@ -133,25 +271,76 @@ impl Board {
         selectors.into_iter()
     }
 
-    pub fn locate_pin_at_point(&self, point: Vector3<i64>) -> Option<PinSelector> {
-        // Polygons have intentional precedence for pins.
-        if let Some(polygon_id) = self.layout.locate_polygons_at_point(point).next() {
-            return self.polygon_pin_selector(polygon_id);
-        }
+    pub fn locate_pins_prefer_layer_at_point(
+        &self,
+        point: Vector3<i64>,
+    ) -> impl Iterator<Item = PinSelector> + '_ {
+        self.layout
+            .locate_polygons_prefer_layer_at_point(point)
+            .filter_map(|polygon_id| self.polygon_pin_selector(polygon_id))
+            .chain(
+                self.layout
+                    .locate_joints_prefer_layer_at_point(point)
+                    .filter_map(|joint_id| self.joint_pin_selector(joint_id)),
+            )
+            .chain(
+                self.layout
+                    .locate_segments_prefer_layer_at_point(point)
+                    .filter_map(|segment_id| self.segment_pin_selector(segment_id)),
+            )
+            .chain(
+                self.layout
+                    .locate_vias_prefer_layer_at_point(point)
+                    .filter_map(|via_id| self.via_pin_selector(via_id)),
+            )
+    }
 
-        if let Some(joint_id) = self.layout.locate_joints_at_point(point).next() {
-            return self.joint_pin_selector(joint_id);
-        }
+    pub fn locate_pins_at_point(
+        &self,
+        point: Vector3<i64>,
+    ) -> impl Iterator<Item = PinSelector> + '_ {
+        self.layout
+            .locate_polygons_at_point(point)
+            .filter_map(|polygon_id| self.polygon_pin_selector(polygon_id))
+            .chain(
+                self.layout
+                    .locate_joints_at_point(point)
+                    .filter_map(|joint_id| self.joint_pin_selector(joint_id)),
+            )
+            .chain(
+                self.layout
+                    .locate_segments_at_point(point)
+                    .filter_map(|segment_id| self.segment_pin_selector(segment_id)),
+            )
+            .chain(
+                self.layout
+                    .locate_vias_at_point(point)
+                    .filter_map(|via_id| self.via_pin_selector(via_id)),
+            )
+    }
 
-        if let Some(segment_id) = self.layout.locate_segments_at_point(point).next() {
-            return self.segment_pin_selector(segment_id);
-        }
-
-        if let Some(via_id) = self.layout.locate_vias_at_point(point).next() {
-            return self.via_pin_selector(via_id);
-        }
-
-        None
+    pub fn locate_pins_prefer_layer_intersecting_rect(
+        &self,
+        rect: Rect3<i64>,
+    ) -> impl Iterator<Item = PinSelector> + '_ {
+        self.layout
+            .locate_polygons_prefer_layer_intersecting_rect(rect)
+            .filter_map(|polygon_id| self.polygon_pin_selector(polygon_id))
+            .chain(
+                self.layout
+                    .locate_joints_prefer_layer_intersecting_rect(rect)
+                    .filter_map(|joint_id| self.joint_pin_selector(joint_id)),
+            )
+            .chain(
+                self.layout
+                    .locate_segments_prefer_layer_intersecting_rect(rect)
+                    .filter_map(|segment_id| self.segment_pin_selector(segment_id)),
+            )
+            .chain(
+                self.layout
+                    .locate_vias_prefer_layer_intersecting_rect(rect)
+                    .filter_map(|via_id| self.via_pin_selector(via_id)),
+            )
     }
 
     pub fn locate_pins_intersecting_rect(
@@ -159,8 +348,13 @@ impl Board {
         rect: Rect3<i64>,
     ) -> impl Iterator<Item = PinSelector> + '_ {
         self.layout
-            .locate_joints_intersecting_rect(rect)
-            .filter_map(|joint_id| self.joint_pin_selector(joint_id))
+            .locate_polygons_intersecting_rect(rect)
+            .filter_map(|polygon_id| self.polygon_pin_selector(polygon_id))
+            .chain(
+                self.layout
+                    .locate_joints_intersecting_rect(rect)
+                    .filter_map(|joint_id| self.joint_pin_selector(joint_id)),
+            )
             .chain(
                 self.layout
                     .locate_segments_intersecting_rect(rect)
@@ -171,10 +365,29 @@ impl Board {
                     .locate_vias_intersecting_rect(rect)
                     .filter_map(|via_id| self.via_pin_selector(via_id)),
             )
+    }
+
+    pub fn locate_pins_prefer_layer_inside_rect(
+        &self,
+        rect: Rect3<i64>,
+    ) -> impl Iterator<Item = PinSelector> + '_ {
+        self.layout
+            .locate_polygons_prefer_layer_inside_rect(rect)
+            .filter_map(|polygon_id| self.polygon_pin_selector(polygon_id))
             .chain(
                 self.layout
-                    .locate_polygons_intersecting_rect(rect)
-                    .filter_map(|polygon_id| self.polygon_pin_selector(polygon_id)),
+                    .locate_joints_prefer_layer_inside_rect(rect)
+                    .filter_map(|joint_id| self.joint_pin_selector(joint_id)),
+            )
+            .chain(
+                self.layout
+                    .locate_segments_prefer_layer_inside_rect(rect)
+                    .filter_map(|segment_id| self.segment_pin_selector(segment_id)),
+            )
+            .chain(
+                self.layout
+                    .locate_vias_prefer_layer_inside_rect(rect)
+                    .filter_map(|via_id| self.via_pin_selector(via_id)),
             )
     }
 
@@ -183,8 +396,13 @@ impl Board {
         rect: Rect3<i64>,
     ) -> impl Iterator<Item = PinSelector> + '_ {
         self.layout
-            .locate_joints_inside_rect(rect)
-            .filter_map(|joint_id| self.joint_pin_selector(joint_id))
+            .locate_polygons_inside_rect(rect)
+            .filter_map(|polygon_id| self.polygon_pin_selector(polygon_id))
+            .chain(
+                self.layout
+                    .locate_joints_inside_rect(rect)
+                    .filter_map(|joint_id| self.joint_pin_selector(joint_id)),
+            )
             .chain(
                 self.layout
                     .locate_segments_inside_rect(rect)
@@ -195,10 +413,5 @@ impl Board {
                     .locate_vias_inside_rect(rect)
                     .filter_map(|via_id| self.via_pin_selector(via_id)),
             )
-            .chain(
-                self.layout
-                    .locate_polygons_inside_rect(rect)
-                    .filter_map(|polygon_id| self.polygon_pin_selector(polygon_id)),
-            )
     }
 }
diff --git a/topola/src/layout/locate.rs b/topola/src/layout/locate.rs
index 8e53736..3a922af 100644
--- a/topola/src/layout/locate.rs
+++ b/topola/src/layout/locate.rs
@@ -5,19 +5,64 @@
 use std::collections::BTreeSet;
 
 use crate::{
-    Rect3, Vector3,
-    layout::{LayerId, Layout, compounds::NetId},
+    Rect2, Rect3, Vector2, Vector3,
+    layout::{Layout, compounds::NetId},
     primitives::{JointId, PolygonId, SegmentId, ViaId},
 };
 
 impl Layout {
+    pub fn locate_joints_prefer_layer_at_point(
+        &self,
+        point: Vector3<i64>,
+    ) -> impl Iterator<Item = JointId> {
+        let at_point = self.locate_joints_at_point(point).collect::<Vec<_>>();
+
+        let joints = if at_point.is_empty() {
+            self.locate_joints_any_layer_at_point(point.xy()).collect()
+        } else {
+            at_point
+        };
+
+        joints.into_iter()
+    }
+
     pub fn locate_joints_at_point(&self, point: Vector3<i64>) -> impl Iterator<Item = JointId> {
-        let point2 = point.xy();
         self.joints_rtree
             .as_ref()
             .locate_all_at_point(&[point.x, point.y, point.z])
             .map(|geom_with_data| geom_with_data.data)
-            .filter(move |&joint_id| self.joints[joint_id.index()].contains_point(point2))
+            .filter(move |&joint_id| self.joints[joint_id.index()].contains_point2(point.xy()))
+    }
+
+    pub fn locate_joints_any_layer_at_point(
+        &self,
+        point: Vector2<i64>,
+    ) -> impl Iterator<Item = JointId> {
+        let envelope = point.z_extruded_infinitely().aabb();
+
+        self.joints_rtree
+            .as_ref()
+            .locate_in_envelope_intersecting(&envelope)
+            .map(|geom_with_data| geom_with_data.data)
+            .filter(move |&joint_id| self.joints[joint_id.index()].contains_point2(point))
+    }
+
+    pub fn locate_joints_prefer_layer_intersecting_rect(
+        &self,
+        rect: Rect3<i64>,
+    ) -> impl Iterator<Item = JointId> {
+        let at_rect = self
+            .locate_joints_intersecting_rect(rect)
+            .collect::<Vec<_>>();
+
+        let joints = if at_rect.is_empty() {
+            self.locate_joints_any_layer_intersecting_rect(rect.xy())
+                .collect()
+        } else {
+            at_rect
+        };
+
+        joints.into_iter()
     }
 
     pub fn locate_joints_intersecting_rect(
@@ -26,33 +71,128 @@ impl Layout {
     ) -> impl Iterator<Item = JointId> {
         self.joints_rtree
             .as_ref()
-            .locate_in_envelope_intersecting(&rect.aabb3())
+            .locate_in_envelope_intersecting(&rect.aabb())
             .map(|geom_with_data| geom_with_data.data)
             .filter(move |&joint_id| {
                 let joint = self.joint(joint_id);
-                rect.rect2()
+                rect.xy()
                     .intersects_circle(joint.spec.position, joint.spec.radius as i64)
             })
     }
 
+    pub fn locate_joints_any_layer_intersecting_rect(
+        &self,
+        rect: Rect2<i64>,
+    ) -> impl Iterator<Item = JointId> {
+        let envelope = rect.z_extruded_infinitely().aabb();
+
+        self.joints_rtree
+            .as_ref()
+            .locate_in_envelope_intersecting(&envelope)
+            .map(|geom_with_data| geom_with_data.data)
+            .filter(move |&joint_id| {
+                let joint = self.joint(joint_id);
+                rect.intersects_circle(joint.spec.position, joint.spec.radius as i64)
+            })
+    }
+
+    pub fn locate_joints_prefer_layer_inside_rect(
+        &self,
+        rect: Rect3<i64>,
+    ) -> impl Iterator<Item = JointId> {
+        let at_rect = self.locate_joints_inside_rect(rect).collect::<Vec<_>>();
+
+        let joints = if at_rect.is_empty() {
+            self.locate_joints_any_layer_inside_rect(rect.xy())
+                .collect()
+        } else {
+            at_rect
+        };
+
+        joints.into_iter()
+    }
+
     pub fn locate_joints_inside_rect(&self, rect: Rect3<i64>) -> impl Iterator<Item = JointId> {
         self.joints_rtree
             .as_ref()
-            .locate_in_envelope(&rect.aabb3())
+            .locate_in_envelope(&rect.aabb())
             .map(|geom_with_data| geom_with_data.data)
             .filter(move |&joint_id| {
                 let joint = self.joint(joint_id);
-                rect.rect2()
+                rect.xy()
                     .contains_circle(joint.spec.position, joint.spec.radius as i64)
             })
     }
 
+    pub fn locate_joints_any_layer_inside_rect(
+        &self,
+        rect: Rect2<i64>,
+    ) -> impl Iterator<Item = JointId> {
+        let envelope = rect.z_extruded_infinitely().aabb();
+
+        self.joints_rtree
+            .as_ref()
+            .locate_in_envelope(&envelope)
+            .map(|geom_with_data| geom_with_data.data)
+            .filter(move |&joint_id| {
+                let joint = self.joint(joint_id);
+                rect.intersects_circle(joint.spec.position, joint.spec.radius as i64)
+            })
+    }
+
+    pub fn locate_segments_prefer_layer_at_point(
+        &self,
+        point: Vector3<i64>,
+    ) -> impl Iterator<Item = SegmentId> {
+        let at_point = self.locate_segments_at_point(point).collect::<Vec<_>>();
+
+        let segments = if at_point.is_empty() {
+            self.locate_segments_any_layer_at_point(point.xy())
+                .collect()
+        } else {
+            at_point
+        };
+
+        segments.into_iter()
+    }
+
     pub fn locate_segments_at_point(&self, point: Vector3<i64>) -> impl Iterator<Item = SegmentId> {
         self.segments_rtree
             .as_ref()
             .locate_all_at_point(&[point.x, point.y, point.z])
             .map(|geom_with_data| geom_with_data.data)
-            .filter(move |&segment_id| self.segment(segment_id).contains_point(point.xy()))
+            .filter(move |&segment_id| self.segment(segment_id).contains_point2(point.xy()))
+    }
+
+    pub fn locate_segments_any_layer_at_point(
+        &self,
+        point: Vector2<i64>,
+    ) -> impl Iterator<Item = SegmentId> {
+        let envelope = point.z_extruded_infinitely().aabb();
+
+        self.segments_rtree
+            .as_ref()
+            .locate_in_envelope_intersecting(&envelope)
+            .map(|geom_with_data| geom_with_data.data)
+            .filter(move |&segment_id| self.segments[segment_id.index()].contains_point2(point))
+    }
+
+    pub fn locate_segments_prefer_layer_intersecting_rect(
+        &self,
+        rect: Rect3<i64>,
+    ) -> impl Iterator<Item = SegmentId> {
+        let at_point = self
+            .locate_segments_intersecting_rect(rect)
+            .collect::<Vec<_>>();
+
+        let joints = if at_point.is_empty() {
+            self.locate_segments_any_layer_intersecting_rect(rect.xy())
+                .collect()
+        } else {
+            at_point
+        };
+
+        joints.into_iter()
     }
 
     pub fn locate_segments_intersecting_rect(
@@ -61,66 +201,251 @@ impl Layout {
     ) -> impl Iterator<Item = SegmentId> {
         self.segments_rtree
             .as_ref()
-            .locate_in_envelope_intersecting(&rect.aabb3())
+            .locate_in_envelope_intersecting(&rect.aabb())
             .map(|geom_with_data| geom_with_data.data)
             .filter(move |&segment_id| {
                 let segment = self.segment(segment_id);
-                rect.rect2()
-                    .intersects_polygon(&segment.bounding_rectangle())
+                rect.xy().intersects_polygon(&segment.bounding_rectangle())
             })
     }
 
+    pub fn locate_segments_any_layer_intersecting_rect(
+        &self,
+        rect: Rect2<i64>,
+    ) -> impl Iterator<Item = SegmentId> {
+        let envelope = rect.z_extruded_infinitely().aabb();
+
+        self.segments_rtree
+            .as_ref()
+            .locate_in_envelope_intersecting(&envelope)
+            .map(|geom_with_data| geom_with_data.data)
+            .filter(move |&segment_id| {
+                let segment = self.segment(segment_id);
+                rect.intersects_polygon(&segment.bounding_rectangle())
+            })
+    }
+
+    pub fn locate_segments_prefer_layer_inside_rect(
+        &self,
+        rect: Rect3<i64>,
+    ) -> impl Iterator<Item = SegmentId> {
+        let at_point = self.locate_segments_inside_rect(rect).collect::<Vec<_>>();
+
+        let joints = if at_point.is_empty() {
+            self.locate_segments_any_layer_inside_rect(rect.xy())
+                .collect()
+        } else {
+            at_point
+        };
+
+        joints.into_iter()
+    }
+
     pub fn locate_segments_inside_rect(&self, rect: Rect3<i64>) -> impl Iterator<Item = SegmentId> {
         self.segments_rtree
             .as_ref()
-            .locate_in_envelope(&rect.aabb3())
+            .locate_in_envelope(&rect.aabb())
             .map(|geom_with_data| geom_with_data.data)
             .filter(move |&segment_id| {
                 let segment = self.segment(segment_id);
-                rect.rect2().contains_polygon(&segment.bounding_rectangle())
+                rect.xy().contains_polygon(&segment.bounding_rectangle())
             })
     }
 
+    pub fn locate_segments_any_layer_inside_rect(
+        &self,
+        rect: Rect2<i64>,
+    ) -> impl Iterator<Item = SegmentId> {
+        let envelope = rect.z_extruded_infinitely().aabb();
+
+        self.segments_rtree
+            .as_ref()
+            .locate_in_envelope(&envelope)
+            .map(|geom_with_data| geom_with_data.data)
+            .filter(move |&segment_id| {
+                let segment = self.segment(segment_id);
+                rect.contains_polygon(&segment.bounding_rectangle())
+            })
+    }
+
+    pub fn locate_vias_prefer_layer_at_point(
+        &self,
+        point: Vector3<i64>,
+    ) -> impl Iterator<Item = ViaId> {
+        let at_point = self.locate_vias_at_point(point).collect::<Vec<_>>();
+
+        let vias = if at_point.is_empty() {
+            self.locate_vias_any_layer_at_point(point.xy()).collect()
+        } else {
+            at_point
+        };
+
+        vias.into_iter()
+    }
+
     pub fn locate_vias_at_point(&self, point: Vector3<i64>) -> impl Iterator<Item = ViaId> {
-        let layer = LayerId::new(point.z as usize);
         self.vias_rtree
             .as_ref()
             .locate_all_at_point(&[point.x, point.y, point.z])
             .map(|geom_with_data| geom_with_data.data)
-            .filter(move |&via_id| self.vias[via_id.index()].contains_point(layer, point.xy()))
+            .filter(move |&via_id| self.vias[via_id.index()].contains_point2(point.xy()))
+    }
+
+    pub fn locate_vias_any_layer_at_point(
+        &self,
+        point: Vector2<i64>,
+    ) -> impl Iterator<Item = ViaId> {
+        let envelope = point.z_extruded_infinitely().aabb();
+
+        self.vias_rtree
+            .as_ref()
+            .locate_in_envelope_intersecting(&envelope)
+            .map(|geom_with_data| geom_with_data.data)
+            .filter(move |&via_id| self.vias[via_id.index()].contains_point2(point))
+    }
+
+    pub fn locate_vias_prefer_layer_intersecting_rect(
+        &self,
+        rect: Rect3<i64>,
+    ) -> impl Iterator<Item = ViaId> {
+        let at_point = self.locate_vias_intersecting_rect(rect).collect::<Vec<_>>();
+
+        let vias = if at_point.is_empty() {
+            self.locate_vias_any_layer_intersecting_rect(rect.xy())
+                .collect()
+        } else {
+            at_point
+        };
+
+        vias.into_iter()
     }
 
     pub fn locate_vias_intersecting_rect(&self, rect: Rect3<i64>) -> impl Iterator<Item = ViaId> {
         self.vias_rtree
             .as_ref()
-            .locate_in_envelope_intersecting(&rect.aabb3())
+            .locate_in_envelope_intersecting(&rect.aabb())
             .map(|geom_with_data| geom_with_data.data)
             .filter(move |&via_id| {
                 let via = self.via(via_id);
-                rect.rect2()
+                rect.xy()
                     .intersects_circle(via.position, via.spec.radius as i64)
             })
     }
 
+    pub fn locate_vias_any_layer_intersecting_rect(
+        &self,
+        rect: Rect2<i64>,
+    ) -> impl Iterator<Item = ViaId> {
+        let envelope = rect.z_extruded_infinitely().aabb();
+
+        self.vias_rtree
+            .as_ref()
+            .locate_in_envelope_intersecting(&envelope)
+            .map(|geom_with_data| geom_with_data.data)
+            .filter(move |&via_id| {
+                let via = self.via(via_id);
+                rect.intersects_circle(via.position, via.spec.radius as i64)
+            })
+    }
+
+    pub fn locate_vias_prefer_layer_inside_rect(
+        &self,
+        rect: Rect3<i64>,
+    ) -> impl Iterator<Item = ViaId> {
+        let at_rect = self.locate_vias_inside_rect(rect).collect::<Vec<_>>();
+
+        let vias = if at_rect.is_empty() {
+            self.locate_vias_any_layer_inside_rect(rect.xy()).collect()
+        } else {
+            at_rect
+        };
+
+        vias.into_iter()
+    }
+
     pub fn locate_vias_inside_rect(&self, rect: Rect3<i64>) -> impl Iterator<Item = ViaId> {
         self.vias_rtree
             .as_ref()
-            .locate_in_envelope(&rect.aabb3())
+            .locate_in_envelope(&rect.aabb())
             .map(|geom_with_data| geom_with_data.data)
             .filter(move |&via_id| {
                 let via = self.via(via_id);
-                rect.rect2()
+                rect.xy()
                     .contains_circle(via.position, via.spec.radius as i64)
             })
     }
 
+    pub fn locate_vias_any_layer_inside_rect(
+        &self,
+        rect: Rect2<i64>,
+    ) -> impl Iterator<Item = ViaId> {
+        let envelope = rect.z_extruded_infinitely().aabb();
+
+        self.vias_rtree
+            .as_ref()
+            .locate_in_envelope(&envelope)
+            .map(|geom_with_data| geom_with_data.data)
+            .filter(move |&via_id| {
+                let via = self.via(via_id);
+                rect.contains_circle(via.position, via.spec.radius as i64)
+            })
+    }
+
+    pub fn locate_polygons_prefer_layer_at_point(
+        &self,
+        point: Vector3<i64>,
+    ) -> impl Iterator<Item = PolygonId> {
+        let at_point = self.locate_polygons_at_point(point).collect::<Vec<_>>();
+
+        let polygons = if at_point.is_empty() {
+            self.locate_polygons_any_layer_at_point(point.xy())
+                .collect()
+        } else {
+            at_point
+        };
+
+        polygons.into_iter()
+    }
+
     pub fn locate_polygons_at_point(&self, point: Vector3<i64>) -> impl Iterator<Item = PolygonId> {
-        let point2 = point.xy();
         self.polygons_rtree
             .as_ref()
             .locate_all_at_point(&[point.x, point.y, point.z])
             .map(|geom_with_data| geom_with_data.data)
-            .filter(move |&polygon_id| self.polygons[polygon_id.index()].contains_point(point2))
+            .filter(move |&polygon_id| {
+                self.polygons[polygon_id.index()].contains_point2(point.xy())
+            })
+    }
+
+    pub fn locate_polygons_any_layer_at_point(
+        &self,
+        point: Vector2<i64>,
+    ) -> impl Iterator<Item = PolygonId> {
+        let envelope = point.z_extruded_infinitely().aabb();
+
+        self.polygons_rtree
+            .as_ref()
+            .locate_in_envelope_intersecting(&envelope)
+            .map(|geom_with_data| geom_with_data.data)
+            .filter(move |&polygon_id| self.polygons[polygon_id.index()].contains_point2(point))
+    }
+
+    pub fn locate_polygons_prefer_layer_intersecting_rect(
+        &self,
+        rect: Rect3<i64>,
+    ) -> impl Iterator<Item = PolygonId> {
+        let at_rect = self
+            .locate_polygons_intersecting_rect(rect)
+            .collect::<Vec<_>>();
+
+        let polygons = if at_rect.is_empty() {
+            self.locate_polygons_any_layer_intersecting_rect(rect.xy())
+                .collect()
+        } else {
+            at_rect
+        };
+
+        polygons.into_iter()
     }
 
     pub fn locate_polygons_intersecting_rect(
@@ -129,25 +454,98 @@ impl Layout {
     ) -> impl Iterator<Item = PolygonId> {
         self.polygons_rtree
             .as_ref()
-            .locate_in_envelope_intersecting(&rect.aabb3())
+            .locate_in_envelope_intersecting(&rect.aabb())
             .map(|geom_with_data| geom_with_data.data)
             .filter(move |&polygon_id| {
                 let polygon = self.polygon(polygon_id);
-                rect.rect2().intersects_polygon(&polygon.vertices)
+                rect.xy().intersects_polygon(&polygon.vertices)
             })
     }
 
+    pub fn locate_polygons_any_layer_intersecting_rect(
+        &self,
+        rect: Rect2<i64>,
+    ) -> impl Iterator<Item = PolygonId> {
+        let envelope = rect.z_extruded_infinitely().aabb();
+
+        self.polygons_rtree
+            .as_ref()
+            .locate_in_envelope_intersecting(&envelope)
+            .map(|geom_with_data| geom_with_data.data)
+            .filter(move |&polygon_id| {
+                let polygon = self.polygon(polygon_id);
+                rect.intersects_polygon(&polygon.vertices)
+            })
+    }
+
+    pub fn locate_polygons_prefer_layer_inside_rect(
+        &self,
+        rect: Rect3<i64>,
+    ) -> impl Iterator<Item = PolygonId> {
+        let at_rect = self.locate_polygons_inside_rect(rect).collect::<Vec<_>>();
+
+        let polygons = if at_rect.is_empty() {
+            self.locate_polygons_any_layer_inside_rect(rect.xy())
+                .collect()
+        } else {
+            at_rect
+        };
+
+        polygons.into_iter()
+    }
+
     pub fn locate_polygons_inside_rect(&self, rect: Rect3<i64>) -> impl Iterator<Item = PolygonId> {
         self.polygons_rtree
             .as_ref()
-            .locate_in_envelope(&rect.aabb3())
+            .locate_in_envelope(&rect.aabb())
             .map(|geom_with_data| geom_with_data.data)
             .filter(move |&polygon_id| {
                 let polygon = self.polygon(polygon_id);
-                rect.rect2().contains_polygon(&polygon.vertices)
+                rect.xy().contains_polygon(&polygon.vertices)
             })
     }
 
+    pub fn locate_polygons_any_layer_inside_rect(
+        &self,
+        rect: Rect2<i64>,
+    ) -> impl Iterator<Item = PolygonId> {
+        let envelope = rect.z_extruded_infinitely().aabb();
+
+        self.polygons_rtree
+            .as_ref()
+            .locate_in_envelope(&envelope)
+            .map(|geom_with_data| geom_with_data.data)
+            .filter(move |&polygon_id| {
+                let polygon = self.polygon(polygon_id);
+                rect.contains_polygon(&polygon.vertices)
+            })
+    }
+
+    pub fn locate_nets_prefer_layer_intersecting_rect(
+        &self,
+        rect: Rect3<i64>,
+    ) -> impl Iterator<Item = NetId> {
+        let mut nets = BTreeSet::new();
+
+        for joint_id in self.locate_joints_prefer_layer_intersecting_rect(rect) {
+            nets.insert(self.joint(joint_id).spec.net);
+        }
+
+        for segment_id in self.locate_segments_prefer_layer_intersecting_rect(rect) {
+            nets.insert(self.segment(segment_id).net);
+        }
+
+        for via_id in self.locate_vias_prefer_layer_intersecting_rect(rect) {
+            nets.insert(self.via(via_id).net);
+        }
+
+        for polygon_id in self.locate_polygons_prefer_layer_intersecting_rect(rect) {
+            nets.insert(self.polygon(polygon_id).net);
+        }
+
+        nets.into_iter()
+    }
+
     pub fn locate_nets_intersecting_rect(&self, rect: Rect3<i64>) -> impl Iterator<Item = NetId> {
         let mut nets = BTreeSet::new();
 
@@ -170,6 +568,31 @@ impl Layout {
         nets.into_iter()
     }
 
+    pub fn locate_nets_prefer_layer_inside_rect(
+        &self,
+        rect: Rect3<i64>,
+    ) -> impl Iterator<Item = NetId> {
+        let mut nets = BTreeSet::new();
+
+        for joint_id in self.locate_joints_prefer_layer_inside_rect(rect) {
+            nets.insert(self.joint(joint_id).spec.net);
+        }
+
+        for segment_id in self.locate_segments_prefer_layer_inside_rect(rect) {
+            nets.insert(self.segment(segment_id).net);
+        }
+
+        for via_id in self.locate_vias_prefer_layer_inside_rect(rect) {
+            nets.insert(self.via(via_id).net);
+        }
+
+        for polygon_id in self.locate_polygons_prefer_layer_inside_rect(rect) {
+            nets.insert(self.polygon(polygon_id).net);
+        }
+
+        nets.into_iter()
+    }
+
     pub fn locate_nets_inside_rect(&self, rect: Rect3<i64>) -> impl Iterator<Item = NetId> {
         let mut nets = BTreeSet::new();
 
diff --git a/topola/src/layout/primitives/joint.rs b/topola/src/layout/primitives/joint.rs
index 41b4890..1cb22d0 100644
--- a/topola/src/layout/primitives/joint.rs
+++ b/topola/src/layout/primitives/joint.rs
@@ -72,7 +72,7 @@ impl Joint {
         ))
     }
 
-    pub fn contains_point(&self, point: Vector2<i64>) -> bool {
+    pub fn contains_point2(&self, point: Vector2<i64>) -> bool {
         (point.x - self.spec.position.x).pow(2) as u64
             + (point.y - self.spec.position.y).pow(2) as u64
             <= self.spec.radius.pow(2)
diff --git a/topola/src/layout/primitives/polygon.rs b/topola/src/layout/primitives/polygon.rs
index 3c498e6..05db7fe 100644
--- a/topola/src/layout/primitives/polygon.rs
+++ b/topola/src/layout/primitives/polygon.rs
@@ -61,7 +61,7 @@ impl Polygon {
         Vector2::<i64>::polygon_centroid(&self.vertices)
     }
 
-    pub fn contains_point(&self, point: Vector2<i64>) -> bool {
+    pub fn contains_point2(&self, point: Vector2<i64>) -> bool {
         point.inside_polygon(&self.vertices)
     }
 }
diff --git a/topola/src/layout/primitives/segment.rs b/topola/src/layout/primitives/segment.rs
index beac50a..a9ee387 100644
--- a/topola/src/layout/primitives/segment.rs
+++ b/topola/src/layout/primitives/segment.rs
@@ -57,7 +57,7 @@ impl Segment {
         (self.endpoints[0] + self.endpoints[1]) / 2
     }
 
-    pub fn contains_point(&self, point: Vector2<i64>) -> bool {
+    pub fn contains_point2(&self, point: Vector2<i64>) -> bool {
         let vertices = crate::math::inflated_segment(
             self.endpoints[0].x,
             self.endpoints[0].y,
diff --git a/topola/src/layout/primitives/via.rs b/topola/src/layout/primitives/via.rs
index 1782316..f8b5c63 100644
--- a/topola/src/layout/primitives/via.rs
+++ b/topola/src/layout/primitives/via.rs
@@ -54,11 +54,7 @@ pub struct Via {
 }
 
 impl Via {
-    pub fn contains_point(&self, layer: LayerId, point: Vector2<i64>) -> bool {
-        if layer < self.min_layer || layer > self.max_layer {
-            return false;
-        }
-
+    pub fn contains_point2(&self, point: Vector2<i64>) -> bool {
         (point.x - self.position.x).pow(2) as u64 + (point.y - self.position.y).pow(2) as u64
             <= self.spec.radius.pow(2)
     }
diff --git a/topola/src/rect.rs b/topola/src/rect.rs
index 326baeb..66aaf65 100644
--- a/topola/src/rect.rs
+++ b/topola/src/rect.rs
@@ -3,15 +3,37 @@
 // SPDX-License-Identifier: MIT OR Apache-2.0
 
 use derive_getters::Getters;
+use derive_more::Constructor;
+use num_traits::Bounded;
 use rstar::{AABB, RTreeNum};
 use serde::{Deserialize, Serialize};
 
 use crate::{Vector2, Vector3};
 
-#[derive(Clone, Copy, Debug, Deserialize, Eq, Getters, Ord, PartialEq, PartialOrd, Serialize)]
+#[derive(
+    Clone, Constructor, Copy, Debug, Deserialize, Eq, Getters, Ord, PartialEq, PartialOrd, Serialize,
+)]
 pub struct Rect2<T> {
-    min: Vector2<T>,
-    max: Vector2<T>,
+    pub min: Vector2<T>,
+    pub max: Vector2<T>,
+}
+
+impl<T: Copy + Ord> Rect2<T> {
+    pub fn z_extruded(self, from: T, to: T) -> Rect3<T> {
+        Rect3 {
+            min: Vector3::new(self.min.x, self.min.y, std::cmp::min(from, to)),
+            max: Vector3::new(self.max.x, self.max.y, std::cmp::max(from, to)),
+        }
+    }
+}
+
+impl<T: Bounded + Copy> Rect2<T> {
+    pub fn z_extruded_infinitely(self) -> Rect3<T> {
+        Rect3 {
+            min: Vector3::new(self.min.x, self.min.y, Bounded::min_value()),
+            max: Vector3::new(self.max.x, self.max.y, Bounded::max_value()),
+        }
+    }
 }
 
 impl<T: Copy> Rect2<T> {
@@ -25,18 +47,9 @@ impl<T: Copy> Rect2<T> {
     }
 }
 
-impl<T: Copy + Ord> Rect2<T> {
-    pub fn new(from: Vector2<T>, to: Vector2<T>) -> Self {
-        Self {
-            min: Vector2::new(std::cmp::min(from.x, to.x), std::cmp::min(from.y, to.y)),
-            max: Vector2::new(std::cmp::max(from.x, to.x), std::cmp::max(from.y, to.y)),
-        }
-    }
-}
-
 impl<T: RTreeNum> Rect2<T> {
-    pub fn aabb3(self, z: T) -> AABB<[T; 3]> {
-        AABB::from_corners([self.min.x, self.min.y, z], [self.max.x, self.max.y, z])
+    pub fn aabb(self) -> AABB<[T; 2]> {
+        AABB::from_corners([self.min.x, self.min.y], [self.max.x, self.max.y])
     }
 }
 
@@ -172,8 +185,8 @@ impl_rect2_intersects_polygon!(f64);
 
 #[derive(Clone, Copy, Debug, Deserialize, Eq, Getters, Ord, PartialEq, PartialOrd, Serialize)]
 pub struct Rect3<T> {
-    min: Vector3<T>,
-    max: Vector3<T>,
+    pub min: Vector3<T>,
+    pub max: Vector3<T>,
 }
 
 impl<T: Ord + Copy> Rect3<T> {
@@ -194,13 +207,13 @@ impl<T: Ord + Copy> Rect3<T> {
 }
 
 impl<T: Copy + Ord> Rect3<T> {
-    pub fn rect2(&self) -> Rect2<T> {
+    pub fn xy(self) -> Rect2<T> {
         Rect2::new(self.min.xy(), self.max.xy())
     }
 }
 
 impl<T: RTreeNum> Rect3<T> {
-    pub fn aabb3(&self) -> AABB<[T; 3]> {
+    pub fn aabb(self) -> AABB<[T; 3]> {
         AABB::from_corners(
             [self.min.x, self.min.y, self.min.z],
             [self.max.x, self.max.y, self.max.z],
diff --git a/topola/src/vector.rs b/topola/src/vector.rs
index aa5aa1c..801d2e5 100644
--- a/topola/src/vector.rs
+++ b/topola/src/vector.rs
@@ -5,8 +5,11 @@
 use derive_more::{
     Add, AddAssign, Constructor, Div, DivAssign, From, Into, Mul, MulAssign, Sub, SubAssign,
 };
+use num_traits::Bounded;
 use serde::{Deserialize, Serialize};
 
+use crate::Rect3;
+
 #[derive(
     Add,
     AddAssign,
@@ -34,40 +37,6 @@ pub struct Vector2<T> {
     pub y: T,
 }
 
-#[derive(
-    Add,
-    AddAssign,
-    Clone,
-    Constructor,
-    Copy,
-    Debug,
-    Deserialize,
-    Div,
-    DivAssign,
-    Eq,
-    From,
-    Into,
-    Mul,
-    MulAssign,
-    Ord,
-    PartialEq,
-    PartialOrd,
-    Serialize,
-    Sub,
-    SubAssign,
-)]
-pub struct Vector3<T> {
-    pub x: T,
-    pub y: T,
-    pub z: T,
-}
-
-impl<T: Copy> Vector3<T> {
-    pub fn xy(self) -> Vector2<T> {
-        Vector2::new(self.x, self.y)
-    }
-}
-
 impl<T: Copy> From<[T; 2]> for Vector2<T> {
     fn from(from: [T; 2]) -> Self {
         Self {
@@ -83,6 +52,24 @@ impl<T: Copy> From<Vector2<T>> for [T; 2] {
     }
 }
 
+impl<T: Copy + Ord> Vector2<T> {
+    pub fn z_extruded(self, from: T, to: T) -> Rect3<T> {
+        Rect3 {
+            min: Vector3::new(self.x, self.y, std::cmp::min(from, to)),
+            max: Vector3::new(self.x, self.y, std::cmp::max(from, to)),
+        }
+    }
+}
+
+impl<T: Bounded + Copy> Vector2<T> {
+    pub fn z_extruded_infinitely(self) -> Rect3<T> {
+        Rect3 {
+            min: Vector3::new(self.x, self.y, Bounded::min_value()),
+            max: Vector3::new(self.x, self.y, Bounded::max_value()),
+        }
+    }
+}
+
 macro_rules! impl_vector2_inside_polygon {
     ($type:ty) => {
         impl Vector2<$type> {
@@ -216,3 +203,37 @@ impl_polygon_centroid!(u32);
 impl_polygon_centroid!(u64);
 impl_polygon_centroid!(f32);
 impl_polygon_centroid!(f64);
+
+#[derive(
+    Add,
+    AddAssign,
+    Clone,
+    Constructor,
+    Copy,
+    Debug,
+    Deserialize,
+    Div,
+    DivAssign,
+    Eq,
+    From,
+    Into,
+    Mul,
+    MulAssign,
+    Ord,
+    PartialEq,
+    PartialOrd,
+    Serialize,
+    Sub,
+    SubAssign,
+)]
+pub struct Vector3<T> {
+    pub x: T,
+    pub y: T,
+    pub z: T,
+}
+
+impl<T: Copy> Vector3<T> {
+    pub fn xy(self) -> Vector2<T> {
+        Vector2::new(self.x, self.y)
+    }
+}