diff --git a/geo/Cargo.toml b/geo/Cargo.toml
index cf5dfc626a..6873e6b5c2 100644
--- a/geo/Cargo.toml
+++ b/geo/Cargo.toml
@@ -32,6 +32,7 @@ robust = "1.1.0"
 rstar = "0.12.0"
 serde = { version = "1.0", optional = true, features = ["derive"] }
 i_overlay = { version = "2.0.0, < 2.1.0", default-features = false }
+geo-traits = ">=0.3.0"
 
 [dev-dependencies]
 approx = ">= 0.4.0, < 0.6.0"
diff --git a/geo/src/algorithm/kernels/mod.rs b/geo/src/algorithm/kernels/mod.rs
index 814c45752b..2828a7224c 100644
--- a/geo/src/algorithm/kernels/mod.rs
+++ b/geo/src/algorithm/kernels/mod.rs
@@ -1,7 +1,8 @@
 use num_traits::Zero;
 use std::cmp::Ordering;
 
-use crate::{coord, Coord, CoordNum};
+use crate::CoordNum;
+use geo_traits::CoordTrait;
 
 #[derive(Debug, PartialEq, Eq, PartialOrd, Ord, Clone, Copy)]
 pub enum Orientation {
@@ -24,11 +25,14 @@ impl Orientation {
 
 /// Kernel trait to provide predicates to operate on
 /// different scalar types.
-pub trait Kernel<T: CoordNum> {
+pub trait Kernel<T: CoordTrait>
+where
+    T::T: CoordNum,
+{
     /// Gives the orientation of 3 2-dimensional points:
     /// ccw, cw or collinear (None)
-    fn orient2d(p: Coord<T>, q: Coord<T>, r: Coord<T>) -> Orientation {
-        let res = (q.x - p.x) * (r.y - q.y) - (q.y - p.y) * (r.x - q.x);
+    fn orient2d(p: T, q: T, r: T) -> Orientation {
+        let res = (q.x() - p.x()) * (r.y() - q.y()) - (q.y() - p.y()) * (r.x() - q.x());
         if res > Zero::zero() {
             Orientation::CounterClockwise
         } else if res < Zero::zero() {
@@ -38,21 +42,23 @@ pub trait Kernel<T: CoordNum> {
         }
     }
 
-    fn square_euclidean_distance(p: Coord<T>, q: Coord<T>) -> T {
-        (p.x - q.x) * (p.x - q.x) + (p.y - q.y) * (p.y - q.y)
+    fn square_euclidean_distance(p: T, q: T) -> T::T {
+        (p.x() - q.x()) * (p.x() - q.x()) + (p.y() - q.y()) * (p.y() - q.y())
     }
 
     /// Compute the sign of the dot product of `u` and `v` using
     /// robust predicates. The output is `CounterClockwise` if
     /// the sign is positive, `Clockwise` if negative, and
     /// `Collinear` if zero.
-    fn dot_product_sign(u: Coord<T>, v: Coord<T>) -> Orientation {
-        let zero = Coord::zero();
-        let vdash = coord! {
-            x: T::zero() - v.y,
-            y: v.x,
-        };
-        Self::orient2d(zero, u, vdash)
+    fn dot_product_sign(u: T, v: T) -> Orientation {
+        let dot_product = u.x() * v.x() + u.y() * v.y();
+        if dot_product > T::T::zero() {
+            Orientation::CounterClockwise
+        } else if dot_product < T::T::zero() {
+            Orientation::Clockwise
+        } else {
+            Orientation::Collinear
+        }
     }
 }
 
diff --git a/geo/src/algorithm/kernels/robust.rs b/geo/src/algorithm/kernels/robust.rs
index b41df55ab3..f965afea8d 100644
--- a/geo/src/algorithm/kernels/robust.rs
+++ b/geo/src/algorithm/kernels/robust.rs
@@ -1,5 +1,5 @@
 use super::{CoordNum, Kernel, Orientation};
-use crate::Coord;
+use geo_traits::CoordTrait;
 
 use num_traits::{Float, NumCast};
 
@@ -11,25 +11,26 @@ use num_traits::{Float, NumCast};
 #[derive(Default, Debug)]
 pub struct RobustKernel;
 
-impl<T> Kernel<T> for RobustKernel
+impl<P> Kernel<P> for RobustKernel
 where
-    T: CoordNum + Float,
+    P: CoordTrait,
+    P::T: CoordNum + Float,
 {
-    fn orient2d(p: Coord<T>, q: Coord<T>, r: Coord<T>) -> Orientation {
+    fn orient2d(p: P, q: P, r: P) -> Orientation {
         use robust::{orient2d, Coord};
 
         let orientation = orient2d(
             Coord {
-                x: <f64 as NumCast>::from(p.x).unwrap(),
-                y: <f64 as NumCast>::from(p.y).unwrap(),
+                x: <f64 as NumCast>::from(p.x()).unwrap(),
+                y: <f64 as NumCast>::from(p.y()).unwrap(),
             },
             Coord {
-                x: <f64 as NumCast>::from(q.x).unwrap(),
-                y: <f64 as NumCast>::from(q.y).unwrap(),
+                x: <f64 as NumCast>::from(q.x()).unwrap(),
+                y: <f64 as NumCast>::from(q.y()).unwrap(),
             },
             Coord {
-                x: <f64 as NumCast>::from(r.x).unwrap(),
-                y: <f64 as NumCast>::from(r.y).unwrap(),
+                x: <f64 as NumCast>::from(r.x()).unwrap(),
+                y: <f64 as NumCast>::from(r.y()).unwrap(),
             },
         );
 
diff --git a/geo/src/algorithm/kernels/simple.rs b/geo/src/algorithm/kernels/simple.rs
index 9bb75ed82c..c054b6df8b 100644
--- a/geo/src/algorithm/kernels/simple.rs
+++ b/geo/src/algorithm/kernels/simple.rs
@@ -1,5 +1,6 @@
 use super::Kernel;
 use crate::CoordNum;
+use geo_traits::CoordTrait;
 
 /// Simple kernel provides the direct implementation of the
 /// predicates. These are meant to be used with exact
@@ -7,4 +8,9 @@ use crate::CoordNum;
 #[derive(Default, Debug)]
 pub struct SimpleKernel;
 
-impl<T: CoordNum> Kernel<T> for SimpleKernel {}
+impl<T> Kernel<T> for SimpleKernel
+where
+    T: CoordTrait,
+    T::T: CoordNum,
+{
+}
diff --git a/geo/src/algorithm/old_sweep/line_or_point.rs b/geo/src/algorithm/old_sweep/line_or_point.rs
index 594b907cb9..0c8b3ac2e8 100644
--- a/geo/src/algorithm/old_sweep/line_or_point.rs
+++ b/geo/src/algorithm/old_sweep/line_or_point.rs
@@ -333,7 +333,10 @@ mod tests {
     use geo_types::{Coord, LineString};
     use wkt::ToWkt;
 
-    use crate::{GeoFloat, GeoNum, Kernel};
+    use crate::{
+        kernels::{RobustKernel, SimpleKernel},
+        GeoFloat, GeoNum, Kernel,
+    };
 
     use super::LineOrPoint;
 
@@ -385,13 +388,7 @@ mod tests {
         eprintln!("l1: {}", l87.to_wkt());
         eprintln!("lo: {}", lo.to_wkt());
 
-        eprintln!(
-            "pred: {:?}",
-            <f64 as GeoNum>::Ker::orient2d(pt_8, pt_7, pt_17)
-        );
-        eprintln!(
-            "pred: {:?}",
-            <f64 as GeoNum>::Ker::orient2d(pt_8, pt_14, pt_16)
-        );
+        eprintln!("pred: {:?}", SimpleKernel::orient2d(pt_8, pt_7, pt_17));
+        eprintln!("pred: {:?}", RobustKernel::orient2d(pt_8, pt_14, pt_16));
     }
 }
diff --git a/geo/src/algorithm/winding_order.rs b/geo/src/algorithm/winding_order.rs
index 8f85fe69a3..f065a4e87e 100644
--- a/geo/src/algorithm/winding_order.rs
+++ b/geo/src/algorithm/winding_order.rs
@@ -1,7 +1,7 @@
 use super::kernels::*;
 use crate::coords_iter::CoordsIter;
 use crate::utils::EitherIter;
-use crate::{CoordNum, GeoFloat, GeoNum, LineString, Point};
+use crate::{Coord, CoordNum, GeoFloat, GeoNum, LineString, Point};
 use geo_types::{PointsIter, Triangle};
 use std::iter::Rev;
 
@@ -117,8 +117,8 @@ pub trait Winding {
 
 impl<T, K> Winding for LineString<T>
 where
-    T: GeoNum<Ker = K>,
-    K: Kernel<T>,
+    T: GeoNum<Ker<Coord<T>> = K>,
+    K: Kernel<Coord<T>>,
 {
     type Scalar = T;
 
diff --git a/geo/src/lib.rs b/geo/src/lib.rs
index 4f8447ee65..1fa3cd1fdf 100644
--- a/geo/src/lib.rs
+++ b/geo/src/lib.rs
@@ -255,6 +255,7 @@ use std::cmp::Ordering;
 
 pub use crate::algorithm::sweep::Intersections;
 pub use crate::relate::PreparedGeometry;
+use geo_traits::CoordTrait;
 pub use geo_types::{coord, line_string, point, polygon, wkt, CoordFloat, CoordNum};
 
 pub mod geometry;
@@ -345,7 +346,7 @@ impl<T> GeoFloat for T where
 
 /// A trait for methods which work for both integers **and** floating point
 pub trait GeoNum: CoordNum {
-    type Ker: Kernel<Self>;
+    type Ker<C: CoordTrait<T = Self>>: Kernel<C>;
 
     /// Return the ordering between self and other.
     ///
@@ -361,7 +362,7 @@ pub trait GeoNum: CoordNum {
 macro_rules! impl_geo_num_for_float {
     ($t: ident) => {
         impl GeoNum for $t {
-            type Ker = RobustKernel;
+            type Ker<C: CoordTrait<T = Self>> = RobustKernel;
             fn total_cmp(&self, other: &Self) -> Ordering {
                 self.total_cmp(other)
             }
@@ -371,7 +372,7 @@ macro_rules! impl_geo_num_for_float {
 macro_rules! impl_geo_num_for_int {
     ($t: ident) => {
         impl GeoNum for $t {
-            type Ker = SimpleKernel;
+            type Ker<C: CoordTrait<T = Self>> = SimpleKernel;
             fn total_cmp(&self, other: &Self) -> Ordering {
                 self.cmp(other)
             }