diff --git a/topola/src/compass.rs b/topola/src/compass.rs
index e5d5b96..75b396d 100644
--- a/topola/src/compass.rs
+++ b/topola/src/compass.rs
@@ -13,6 +13,55 @@ pub trait CompassDirection<T>: Copy + PartialEq + Into<Vector2<T>> {
     fn nearest_from_vector(vector: Vector2<T>) -> Self;
     fn turn_clockwise(self) -> Self;
     fn turn_counterclockwise(self) -> Self;
+
+    fn cast_vector(self, vector: Vector2<T>) -> Vector2<T>
+    where
+        T: Copy + Neg<Output = T> + PartialOrd + Signed + Zero,
+    {
+        let axis = self.into();
+        let zero = T::zero();
+
+        if axis.y.is_zero() {
+            let x = if axis.x < zero {
+                -vector.x
+            } else {
+                vector.x
+            };
+            return Vector2::new(x, zero);
+        }
+
+        if axis.x.is_zero() {
+            let y = if axis.y < zero {
+                -vector.y
+            } else {
+                vector.y
+            };
+            return Vector2::new(zero, y);
+        }
+
+        let magnitude = if vector.x.abs() < vector.y.abs() {
+            vector.x.abs()
+        } else {
+            vector.y.abs()
+        };
+
+        Vector2::new(
+            if axis.x > zero {
+                magnitude
+            } else if axis.x < zero {
+                -magnitude
+            } else {
+                zero
+            },
+            if axis.y > zero {
+                magnitude
+            } else if axis.y < zero {
+                -magnitude
+            } else {
+                zero
+            },
+        )
+    }
 }
 
 #[derive(Clone, Copy, Debug, Deserialize, Eq, Ord, PartialEq, PartialOrd, Serialize)]
diff --git a/topola/src/layout/compounds/component.rs b/topola/src/layout/compounds/component.rs
index 39e92ed..186b810 100644
--- a/topola/src/layout/compounds/component.rs
+++ b/topola/src/layout/compounds/component.rs
@@ -5,7 +5,10 @@
 use derive_more::{Constructor, From};
 use serde::{Deserialize, Serialize};
 
-use crate::layout::primitives::{JointId, PolygonId, SegmentId, ViaId};
+use crate::{
+    layout::primitives::{JointId, PolygonId, SegmentId, ViaId},
+    primitives::PrimitiveId,
+};
 
 #[derive(
     Clone,
@@ -42,4 +45,21 @@ impl Component {
     pub fn new() -> Self {
         Default::default()
     }
+
+    pub fn primitives(&self) -> impl Iterator<Item = PrimitiveId> + '_ {
+        self.joints
+            .iter()
+            .map(|&joint_id| PrimitiveId::Joint(joint_id))
+            .chain(
+                self.segments
+                    .iter()
+                    .map(|&segment_id| PrimitiveId::Segment(segment_id)),
+            )
+            .chain(self.vias.iter().map(|&via_id| PrimitiveId::Via(via_id)))
+            .chain(
+                self.polygons
+                    .iter()
+                    .map(|&polygon_id| PrimitiveId::Polygon(polygon_id)),
+            )
+    }
 }
diff --git a/topola/src/layout/mod.rs b/topola/src/layout/mod.rs
index 539305b..c9a6235 100644
--- a/topola/src/layout/mod.rs
+++ b/topola/src/layout/mod.rs
@@ -11,6 +11,7 @@ mod locate;
 mod modify;
 mod overlap;
 pub mod primitives;
+mod repulsion;
 mod transforms;
 
 use derive_getters::Getters;
diff --git a/topola/src/layout/repulsion.rs b/topola/src/layout/repulsion.rs
new file mode 100644
index 0000000..d6aecfe
--- /dev/null
+++ b/topola/src/layout/repulsion.rs
@@ -0,0 +1,392 @@
+// SPDX-FileCopyrightText: 2026 Topola contributors
+//
+// SPDX-License-Identifier: MIT OR Apache-2.0
+
+use crate::{
+    Board, Rect2, Vector2,
+    compass::CompassDirection,
+    layout::compounds::ComponentId,
+    orientation::Orientation,
+    primitives::{JointId, PolygonId, PrimitiveId, SegmentId, ViaId},
+};
+
+impl Board {
+    pub fn component_component_repulsion(
+        &self,
+        infringer: ComponentId,
+        infringee: ComponentId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        let mut max_repulsion = Vector2::new(0, 0);
+        let mut max_repulsion_magnitude = 0;
+
+        for infringer_primitive in self.layout().component(infringer).primitives() {
+            for infringee_primitive in self.layout().component(infringee).primitives() {
+                let repulsion = self.primitive_primitive_repulsion(
+                    infringer_primitive,
+                    infringee_primitive,
+                    orientation,
+                );
+                let repulsion_magnitude = repulsion.x.abs() + repulsion.y.abs();
+
+                if repulsion_magnitude > max_repulsion_magnitude {
+                    max_repulsion = repulsion;
+                    max_repulsion_magnitude = repulsion_magnitude;
+                }
+            }
+        }
+
+        max_repulsion
+    }
+
+    pub fn primitive_primitive_repulsion(
+        &self,
+        infringer: PrimitiveId,
+        infringee: PrimitiveId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        match infringer {
+            PrimitiveId::Joint(infringer) => {
+                self.joint_primitive_repulsion(infringer, infringee, orientation)
+            }
+            PrimitiveId::Segment(infringer) => {
+                self.segment_primitive_repulsion(infringer, infringee, orientation)
+            }
+            PrimitiveId::Via(infringer) => {
+                self.via_primitive_repulsion(infringer, infringee, orientation)
+            }
+            PrimitiveId::Polygon(infringer) => {
+                self.polygon_primitive_repulsion(infringer, infringee, orientation)
+            }
+        }
+    }
+
+    pub fn joint_joint_repulsion(
+        &self,
+        infringer: JointId,
+        infringee: JointId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        Self::repulsion_from_rect_overlap(
+            self.joint_joint_rect_overlap(infringer, infringee),
+            self.layout().joint(infringer).center(),
+            self.layout().joint(infringee).center(),
+            orientation,
+        )
+    }
+
+    pub fn joint_segment_repulsion(
+        &self,
+        infringer: JointId,
+        infringee: SegmentId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        Self::repulsion_from_rect_overlap(
+            self.joint_segment_rect_overlap(infringer, infringee),
+            self.layout().joint(infringer).center(),
+            self.layout().segment(infringee).center(),
+            orientation,
+        )
+    }
+
+    pub fn joint_via_repulsion(
+        &self,
+        infringer: JointId,
+        infringee: ViaId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        Self::repulsion_from_rect_overlap(
+            self.joint_via_rect_overlap(infringer, infringee),
+            self.layout().joint(infringer).center(),
+            self.layout().via(infringee).position,
+            orientation,
+        )
+    }
+
+    pub fn joint_polygon_repulsion(
+        &self,
+        infringer: JointId,
+        infringee: PolygonId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        Self::repulsion_from_rect_overlap(
+            self.joint_polygon_rect_overlap(infringer, infringee),
+            self.layout().joint(infringer).center(),
+            self.layout().polygon(infringee).center(),
+            orientation,
+        )
+    }
+
+    pub fn joint_primitive_repulsion(
+        &self,
+        infringer: JointId,
+        infringee: PrimitiveId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        match infringee {
+            PrimitiveId::Joint(infringee) => {
+                self.joint_joint_repulsion(infringer, infringee, orientation)
+            }
+            PrimitiveId::Segment(infringee) => {
+                self.joint_segment_repulsion(infringer, infringee, orientation)
+            }
+            PrimitiveId::Via(infringee) => {
+                self.joint_via_repulsion(infringer, infringee, orientation)
+            }
+            PrimitiveId::Polygon(infringee) => {
+                self.joint_polygon_repulsion(infringer, infringee, orientation)
+            }
+        }
+    }
+
+    pub fn segment_joint_repulsion(
+        &self,
+        infringer: SegmentId,
+        infringee: JointId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        Self::repulsion_from_rect_overlap(
+            self.segment_joint_rect_overlap(infringer, infringee),
+            self.layout().segment(infringer).center(),
+            self.layout().joint(infringee).center(),
+            orientation,
+        )
+    }
+
+    pub fn segment_segment_repulsion(
+        &self,
+        infringer: SegmentId,
+        infringee: SegmentId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        Self::repulsion_from_rect_overlap(
+            self.segment_segment_rect_overlap(infringer, infringee),
+            self.layout().segment(infringer).center(),
+            self.layout().segment(infringee).center(),
+            orientation,
+        )
+    }
+
+    pub fn segment_via_repulsion(
+        &self,
+        infringer: SegmentId,
+        infringee: ViaId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        Self::repulsion_from_rect_overlap(
+            self.segment_via_rect_overlap(infringer, infringee),
+            self.layout().segment(infringer).center(),
+            self.layout().via(infringee).position,
+            orientation,
+        )
+    }
+
+    pub fn segment_polygon_repulsion(
+        &self,
+        infringer: SegmentId,
+        infringee: PolygonId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        Self::repulsion_from_rect_overlap(
+            self.segment_polygon_rect_overlap(infringer, infringee),
+            self.layout().segment(infringer).center(),
+            self.layout().polygon(infringee).center(),
+            orientation,
+        )
+    }
+
+    pub fn segment_primitive_repulsion(
+        &self,
+        infringer: SegmentId,
+        infringee: PrimitiveId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        match infringee {
+            PrimitiveId::Joint(infringee) => {
+                self.segment_joint_repulsion(infringer, infringee, orientation)
+            }
+            PrimitiveId::Segment(infringee) => {
+                self.segment_segment_repulsion(infringer, infringee, orientation)
+            }
+            PrimitiveId::Via(infringee) => {
+                self.segment_via_repulsion(infringer, infringee, orientation)
+            }
+            PrimitiveId::Polygon(infringee) => {
+                self.segment_polygon_repulsion(infringer, infringee, orientation)
+            }
+        }
+    }
+
+    pub fn via_joint_repulsion(
+        &self,
+        infringer: ViaId,
+        infringee: JointId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        Self::repulsion_from_rect_overlap(
+            self.via_joint_rect_overlap(infringer, infringee),
+            self.layout().via(infringer).position,
+            self.layout().joint(infringee).center(),
+            orientation,
+        )
+    }
+
+    pub fn via_segment_repulsion(
+        &self,
+        infringer: ViaId,
+        infringee: SegmentId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        Self::repulsion_from_rect_overlap(
+            self.via_segment_rect_overlap(infringer, infringee),
+            self.layout().via(infringer).position,
+            self.layout().segment(infringee).center(),
+            orientation,
+        )
+    }
+
+    pub fn via_via_repulsion(
+        &self,
+        infringer: ViaId,
+        infringee: ViaId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        Self::repulsion_from_rect_overlap(
+            self.via_via_rect_overlap(infringer, infringee),
+            self.layout().via(infringer).position,
+            self.layout().via(infringee).position,
+            orientation,
+        )
+    }
+
+    pub fn via_polygon_repulsion(
+        &self,
+        infringer: ViaId,
+        infringee: PolygonId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        Self::repulsion_from_rect_overlap(
+            self.via_polygon_rect_overlap(infringer, infringee),
+            self.layout().via(infringer).position,
+            self.layout().polygon(infringee).center(),
+            orientation,
+        )
+    }
+
+    pub fn via_primitive_repulsion(
+        &self,
+        infringer: ViaId,
+        infringee: PrimitiveId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        match infringee {
+            PrimitiveId::Joint(infringee) => {
+                self.via_joint_repulsion(infringer, infringee, orientation)
+            }
+            PrimitiveId::Segment(infringee) => {
+                self.via_segment_repulsion(infringer, infringee, orientation)
+            }
+            PrimitiveId::Via(infringee) => {
+                self.via_via_repulsion(infringer, infringee, orientation)
+            }
+            PrimitiveId::Polygon(infringee) => {
+                self.via_polygon_repulsion(infringer, infringee, orientation)
+            }
+        }
+    }
+
+    pub fn polygon_joint_repulsion(
+        &self,
+        infringer: PolygonId,
+        infringee: JointId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        Self::repulsion_from_rect_overlap(
+            self.polygon_joint_rect_overlap(infringer, infringee),
+            self.layout().polygon(infringer).center(),
+            self.layout().joint(infringee).center(),
+            orientation,
+        )
+    }
+
+    pub fn polygon_segment_repulsion(
+        &self,
+        infringer: PolygonId,
+        infringee: SegmentId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        Self::repulsion_from_rect_overlap(
+            self.polygon_segment_rect_overlap(infringer, infringee),
+            self.layout().polygon(infringer).center(),
+            self.layout().segment(infringee).center(),
+            orientation,
+        )
+    }
+
+    pub fn polygon_via_repulsion(
+        &self,
+        infringer: PolygonId,
+        infringee: ViaId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        Self::repulsion_from_rect_overlap(
+            self.polygon_via_rect_overlap(infringer, infringee),
+            self.layout().polygon(infringer).center(),
+            self.layout().via(infringee).position,
+            orientation,
+        )
+    }
+
+    pub fn polygon_polygon_repulsion(
+        &self,
+        infringer: PolygonId,
+        infringee: PolygonId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        Self::repulsion_from_rect_overlap(
+            self.polygon_polygon_rect_overlap(infringer, infringee),
+            self.layout().polygon(infringer).center(),
+            self.layout().polygon(infringee).center(),
+            orientation,
+        )
+    }
+
+    pub fn polygon_primitive_repulsion(
+        &self,
+        infringer: PolygonId,
+        infringee: PrimitiveId,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        match infringee {
+            PrimitiveId::Joint(infringee) => {
+                self.polygon_joint_repulsion(infringer, infringee, orientation)
+            }
+            PrimitiveId::Segment(infringee) => {
+                self.polygon_segment_repulsion(infringer, infringee, orientation)
+            }
+            PrimitiveId::Via(infringee) => {
+                self.polygon_via_repulsion(infringer, infringee, orientation)
+            }
+            PrimitiveId::Polygon(infringee) => {
+                self.polygon_polygon_repulsion(infringer, infringee, orientation)
+            }
+        }
+    }
+
+    fn repulsion_from_rect_overlap(
+        overlap: Option<Rect2<i64>>,
+        infringer_pos: Vector2<i64>,
+        infringee_pos: Vector2<i64>,
+        orientation: Orientation,
+    ) -> Vector2<i64> {
+        let Some(overlap) = overlap else {
+            return Vector2::new(0, 0);
+        };
+
+        let Some(wind) = orientation.principal_wind(infringer_pos - infringee_pos) else {
+            return Vector2::new(0, 0);
+        };
+
+        wind.cast_vector(overlap.size())
+    }
+}
diff --git a/topola/src/lib.rs b/topola/src/lib.rs
index 4897ab2..d6557a7 100644
--- a/topola/src/lib.rs
+++ b/topola/src/lib.rs
@@ -9,6 +9,7 @@ mod drawer;
 mod layout;
 mod math;
 mod navmesher;
+mod orientation;
 mod pathfinder;
 mod ratsnest;
 mod rect;
diff --git a/topola/src/orientation.rs b/topola/src/orientation.rs
new file mode 100644
index 0000000..0f58c3c
--- /dev/null
+++ b/topola/src/orientation.rs
@@ -0,0 +1,62 @@
+// SPDX-FileCopyrightText: 2026 Topola contributors
+//
+// SPDX-License-Identifier: MIT OR Apache-2.0
+
+use std::ops::Add;
+
+use derive_more::From;
+use num_traits::{Signed, Zero};
+use serde::{Deserialize, Serialize};
+
+use crate::{
+    Vector2,
+    compass::{CompassDirection, PrincipalWind},
+};
+
+#[derive(Clone, Copy, Debug, Deserialize, Eq, From, Ord, PartialEq, PartialOrd, Serialize)]
+pub enum OrthogonalOrientation {
+    Horizontal,
+    Vertical,
+}
+
+#[derive(Clone, Copy, Debug, Deserialize, Eq, From, Ord, PartialEq, PartialOrd, Serialize)]
+pub enum Orientation {
+    Horizontal,
+    Vertical,
+    Oblique,
+}
+
+impl Orientation {
+    pub fn principal_wind<T>(self, vector: Vector2<T>) -> Option<PrincipalWind>
+    where
+        T: Copy + Add<Output = T> + PartialOrd + Signed + Zero,
+    {
+        match self {
+            Self::Horizontal => {
+                if vector.x.is_zero() {
+                    None
+                } else if vector.x > T::zero() {
+                    Some(PrincipalWind::East)
+                } else {
+                    Some(PrincipalWind::West)
+                }
+            }
+            Self::Vertical => {
+                if vector.y.is_zero() {
+                    None
+                } else if vector.y < T::zero() {
+                    Some(PrincipalWind::North)
+                } else {
+                    Some(PrincipalWind::South)
+                }
+            }
+            Self::Oblique => {
+                if vector.x.is_zero() && vector.y.is_zero() {
+                    None
+                } else {
+                    Some(PrincipalWind::nearest_from_vector(vector))
+                }
+            }
+        }
+    }
+}
diff --git a/topola/src/rect.rs b/topola/src/rect.rs
index 18845fd..1ca9ea0 100644
--- a/topola/src/rect.rs
+++ b/topola/src/rect.rs
@@ -2,6 +2,8 @@
 //
 // SPDX-License-Identifier: MIT OR Apache-2.0
 
+use std::ops::Sub;
+
 use derive_getters::Getters;
 use derive_more::Constructor;
 use num_traits::Bounded;
@@ -66,6 +68,12 @@ impl<T: Bounded + Copy> Rect2<T> {
     }
 }
 
+impl<T: Copy + Sub<Output = T>> Rect2<T> {
+    pub fn size(&self) -> Vector2<T> {
+        Vector2::new(self.max.x - self.min.x, self.max.y - self.min.y)
+    }
+}
+
 impl<T: Copy> Rect2<T> {
     pub fn corners(&self) -> [Vector2<T>; 4] {
         [