diff --git a/benchmark/src/main/java/frc/robot/Main.java b/benchmark/src/main/java/frc/robot/Main.java
index bb7564a6c2..862a2f58b7 100644
--- a/benchmark/src/main/java/frc/robot/Main.java
+++ b/benchmark/src/main/java/frc/robot/Main.java
@@ -39,7 +39,7 @@ public class Main {
   private static final TravelingSalesman twistTraveler =
       new TravelingSalesman(
           (pose1, pose2) -> {
-            var twist = pose1.log(pose2);
+            var twist = pose2.minus(pose1).log();
             return Math.hypot(twist.dx, twist.dy);
           });
 
diff --git a/benchmark/src/main/native/cpp/Main.cpp b/benchmark/src/main/native/cpp/Main.cpp
index e332345a88..1a9c3262a4 100644
--- a/benchmark/src/main/native/cpp/Main.cpp
+++ b/benchmark/src/main/native/cpp/Main.cpp
@@ -30,7 +30,7 @@ BENCHMARK(BM_Transform);
 
 void BM_Twist(benchmark::State& state) {
   frc::TravelingSalesman traveler{[](auto pose1, auto pose2) {
-    auto twist = pose1.Log(pose2);
+    auto twist = (pose2 - pose1).Log();
     return units::math::hypot(twist.dx, twist.dy).value();
   }};
   for (auto _ : state) {
diff --git a/wpimath/CMakeLists.txt b/wpimath/CMakeLists.txt
index ef21f48c6c..c5be554abb 100644
--- a/wpimath/CMakeLists.txt
+++ b/wpimath/CMakeLists.txt
@@ -12,8 +12,9 @@ file(
     src/main/native/cpp/jni/EigenJNI.cpp
     src/main/native/cpp/jni/Ellipse2dJNI.cpp
     src/main/native/cpp/jni/Exceptions.cpp
-    src/main/native/cpp/jni/Pose3dJNI.cpp
     src/main/native/cpp/jni/StateSpaceUtilJNI.cpp
+    src/main/native/cpp/jni/Transform3dJNI.cpp
+    src/main/native/cpp/jni/Twist3dJNI.cpp
 )
 
 # Java bindings
diff --git a/wpimath/src/main/java/edu/wpi/first/math/estimator/PoseEstimator.java b/wpimath/src/main/java/edu/wpi/first/math/estimator/PoseEstimator.java
index c68b8f1d9f..09a43bf952 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/estimator/PoseEstimator.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/estimator/PoseEstimator.java
@@ -271,7 +271,7 @@ public class PoseEstimator<T> {
     }
 
     // Step 4: Measure the twist between the old pose estimate and the vision pose.
-    var twist = visionSample.get().log(visionRobotPose);
+    var twist = visionRobotPose.minus(visionSample.get()).log();
 
     // Step 5: We should not trust the twist entirely, so instead we scale this twist by a Kalman
     // gain matrix representing how much we trust vision measurements compared to our current pose.
@@ -282,7 +282,8 @@ public class PoseEstimator<T> {
         new Twist2d(k_times_twist.get(0, 0), k_times_twist.get(1, 0), k_times_twist.get(2, 0));
 
     // Step 7: Calculate and record the vision update.
-    var visionUpdate = new VisionUpdate(visionSample.get().exp(scaledTwist), odometrySample.get());
+    var visionUpdate =
+        new VisionUpdate(visionSample.get().plus(scaledTwist.exp()), odometrySample.get());
     m_visionUpdates.put(timestamp, visionUpdate);
 
     // Step 8: Remove later vision measurements. (Matches previous behavior)
diff --git a/wpimath/src/main/java/edu/wpi/first/math/estimator/PoseEstimator3d.java b/wpimath/src/main/java/edu/wpi/first/math/estimator/PoseEstimator3d.java
index b3844a2bde..124ca35105 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/estimator/PoseEstimator3d.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/estimator/PoseEstimator3d.java
@@ -284,7 +284,7 @@ public class PoseEstimator3d<T> {
     }
 
     // Step 4: Measure the twist between the old pose estimate and the vision pose.
-    var twist = visionSample.get().log(visionRobotPose);
+    var twist = visionRobotPose.minus(visionSample.get()).log();
 
     // Step 5: We should not trust the twist entirely, so instead we scale this twist by a Kalman
     // gain matrix representing how much we trust vision measurements compared to our current pose.
@@ -303,7 +303,8 @@ public class PoseEstimator3d<T> {
             k_times_twist.get(5, 0));
 
     // Step 7: Calculate and record the vision update.
-    var visionUpdate = new VisionUpdate(visionSample.get().exp(scaledTwist), odometrySample.get());
+    var visionUpdate =
+        new VisionUpdate(visionSample.get().plus(scaledTwist.exp()), odometrySample.get());
     m_visionUpdates.put(timestamp, visionUpdate);
 
     // Step 8: Remove later vision measurements. (Matches previous behavior)
diff --git a/wpimath/src/main/java/edu/wpi/first/math/geometry/Pose2d.java b/wpimath/src/main/java/edu/wpi/first/math/geometry/Pose2d.java
index 4a84ef6543..7ee7fc6fc7 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/geometry/Pose2d.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/geometry/Pose2d.java
@@ -249,81 +249,6 @@ public class Pose2d implements Interpolatable<Pose2d>, ProtobufSerializable, Str
     return new Pose2d(m_translation.rotateAround(point, rot), m_rotation.rotateBy(rot));
   }
 
-  /**
-   * Obtain a new Pose2d from a (constant curvature) velocity.
-   *
-   * <p>See <a href="https://file.tavsys.net/control/controls-engineering-in-frc.pdf">Controls
-   * Engineering in the FIRST Robotics Competition</a> section 10.2 "Pose exponential" for a
-   * derivation.
-   *
-   * <p>The twist is a change in pose in the robot's coordinate frame since the previous pose
-   * update. When the user runs exp() on the previous known field-relative pose with the argument
-   * being the twist, the user will receive the new field-relative pose.
-   *
-   * <p>"Exp" represents the pose exponential, which is solving a differential equation moving the
-   * pose forward in time.
-   *
-   * @param twist The change in pose in the robot's coordinate frame since the previous pose update.
-   *     For example, if a non-holonomic robot moves forward 0.01 meters and changes angle by 0.5
-   *     degrees since the previous pose update, the twist would be Twist2d(0.01, 0.0,
-   *     Units.degreesToRadians(0.5)).
-   * @return The new pose of the robot.
-   */
-  public Pose2d exp(Twist2d twist) {
-    double dx = twist.dx;
-    double dy = twist.dy;
-    double dtheta = twist.dtheta;
-
-    double sinTheta = Math.sin(dtheta);
-    double cosTheta = Math.cos(dtheta);
-
-    double s;
-    double c;
-    if (Math.abs(dtheta) < 1E-9) {
-      s = 1.0 - 1.0 / 6.0 * dtheta * dtheta;
-      c = 0.5 * dtheta;
-    } else {
-      s = sinTheta / dtheta;
-      c = (1 - cosTheta) / dtheta;
-    }
-    var transform =
-        new Transform2d(
-            new Translation2d(dx * s - dy * c, dx * c + dy * s),
-            new Rotation2d(cosTheta, sinTheta));
-
-    return this.plus(transform);
-  }
-
-  /**
-   * Returns a Twist2d that maps this pose to the end pose. If c is the output of {@code a.Log(b)},
-   * then {@code a.Exp(c)} would yield b.
-   *
-   * @param end The end pose for the transformation.
-   * @return The twist that maps this to end.
-   */
-  public Twist2d log(Pose2d end) {
-    final var transform = end.relativeTo(this);
-    final var dtheta = transform.getRotation().getRadians();
-    final var halfDtheta = dtheta / 2.0;
-
-    final var cosMinusOne = transform.getRotation().getCos() - 1;
-
-    double halfThetaByTanOfHalfDtheta;
-    if (Math.abs(cosMinusOne) < 1E-9) {
-      halfThetaByTanOfHalfDtheta = 1.0 - 1.0 / 12.0 * dtheta * dtheta;
-    } else {
-      halfThetaByTanOfHalfDtheta = -(halfDtheta * transform.getRotation().getSin()) / cosMinusOne;
-    }
-
-    Translation2d translationPart =
-        transform
-            .getTranslation()
-            .rotateBy(new Rotation2d(halfThetaByTanOfHalfDtheta, -halfDtheta))
-            .times(Math.hypot(halfThetaByTanOfHalfDtheta, halfDtheta));
-
-    return new Twist2d(translationPart.getX(), translationPart.getY(), dtheta);
-  }
-
   /**
    * Returns an affine transformation matrix representation of this pose.
    *
@@ -393,9 +318,9 @@ public class Pose2d implements Interpolatable<Pose2d>, ProtobufSerializable, Str
     } else if (t >= 1) {
       return endValue;
     } else {
-      var twist = this.log(endValue);
+      var twist = endValue.minus(this).log();
       var scaledTwist = new Twist2d(twist.dx * t, twist.dy * t, twist.dtheta * t);
-      return this.exp(scaledTwist);
+      return this.plus(scaledTwist.exp());
     }
   }
 
diff --git a/wpimath/src/main/java/edu/wpi/first/math/geometry/Pose3d.java b/wpimath/src/main/java/edu/wpi/first/math/geometry/Pose3d.java
index 20204235bc..a723d63e10 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/geometry/Pose3d.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/geometry/Pose3d.java
@@ -16,7 +16,6 @@ import edu.wpi.first.math.Nat;
 import edu.wpi.first.math.geometry.proto.Pose3dProto;
 import edu.wpi.first.math.geometry.struct.Pose3dStruct;
 import edu.wpi.first.math.interpolation.Interpolatable;
-import edu.wpi.first.math.jni.Pose3dJNI;
 import edu.wpi.first.math.numbers.N4;
 import edu.wpi.first.units.measure.Distance;
 import edu.wpi.first.util.protobuf.ProtobufSerializable;
@@ -285,82 +284,6 @@ public class Pose3d implements Interpolatable<Pose3d>, ProtobufSerializable, Str
     return new Pose3d(m_translation.rotateAround(point, rot), m_rotation.rotateBy(rot));
   }
 
-  /**
-   * Obtain a new Pose3d from a (constant curvature) velocity.
-   *
-   * <p>The twist is a change in pose in the robot's coordinate frame since the previous pose
-   * update. When the user runs exp() on the previous known field-relative pose with the argument
-   * being the twist, the user will receive the new field-relative pose.
-   *
-   * <p>"Exp" represents the pose exponential, which is solving a differential equation moving the
-   * pose forward in time.
-   *
-   * @param twist The change in pose in the robot's coordinate frame since the previous pose update.
-   *     For example, if a non-holonomic robot moves forward 0.01 meters and changes angle by 0.5
-   *     degrees since the previous pose update, the twist would be Twist3d(0.01, 0.0, 0.0, new new
-   *     Rotation3d(0.0, 0.0, Units.degreesToRadians(0.5))).
-   * @return The new pose of the robot.
-   */
-  public Pose3d exp(Twist3d twist) {
-    var quaternion = this.getRotation().getQuaternion();
-    double[] resultArray =
-        Pose3dJNI.exp(
-            this.getX(),
-            this.getY(),
-            this.getZ(),
-            quaternion.getW(),
-            quaternion.getX(),
-            quaternion.getY(),
-            quaternion.getZ(),
-            twist.dx,
-            twist.dy,
-            twist.dz,
-            twist.rx,
-            twist.ry,
-            twist.rz);
-    return new Pose3d(
-        resultArray[0],
-        resultArray[1],
-        resultArray[2],
-        new Rotation3d(
-            new Quaternion(resultArray[3], resultArray[4], resultArray[5], resultArray[6])));
-  }
-
-  /**
-   * Returns a Twist3d that maps this pose to the end pose. If c is the output of {@code a.Log(b)},
-   * then {@code a.Exp(c)} would yield b.
-   *
-   * @param end The end pose for the transformation.
-   * @return The twist that maps this to end.
-   */
-  public Twist3d log(Pose3d end) {
-    var thisQuaternion = this.getRotation().getQuaternion();
-    var endQuaternion = end.getRotation().getQuaternion();
-    double[] resultArray =
-        Pose3dJNI.log(
-            this.getX(),
-            this.getY(),
-            this.getZ(),
-            thisQuaternion.getW(),
-            thisQuaternion.getX(),
-            thisQuaternion.getY(),
-            thisQuaternion.getZ(),
-            end.getX(),
-            end.getY(),
-            end.getZ(),
-            endQuaternion.getW(),
-            endQuaternion.getX(),
-            endQuaternion.getY(),
-            endQuaternion.getZ());
-    return new Twist3d(
-        resultArray[0],
-        resultArray[1],
-        resultArray[2],
-        resultArray[3],
-        resultArray[4],
-        resultArray[5]);
-  }
-
   /**
    * Returns an affine transformation matrix representation of this pose.
    *
@@ -445,11 +368,11 @@ public class Pose3d implements Interpolatable<Pose3d>, ProtobufSerializable, Str
     } else if (t >= 1) {
       return endValue;
     } else {
-      var twist = this.log(endValue);
+      var twist = endValue.minus(this).log();
       var scaledTwist =
           new Twist3d(
               twist.dx * t, twist.dy * t, twist.dz * t, twist.rx * t, twist.ry * t, twist.rz * t);
-      return this.exp(scaledTwist);
+      return this.plus(scaledTwist.exp());
     }
   }
 
diff --git a/wpimath/src/main/java/edu/wpi/first/math/geometry/Transform2d.java b/wpimath/src/main/java/edu/wpi/first/math/geometry/Transform2d.java
index 7a4cf8f4f9..475f037b1a 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/geometry/Transform2d.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/geometry/Transform2d.java
@@ -209,6 +209,33 @@ public class Transform2d implements ProtobufSerializable, StructSerializable {
     return m_rotation;
   }
 
+  /**
+   * Returns a Twist2d of the current transform (pose delta). If b is the output of {@code a.log()},
+   * then {@code b.exp()} would yield a.
+   *
+   * @return The twist that maps the current transform.
+   */
+  public Twist2d log() {
+    final double dtheta = m_rotation.getRadians();
+    final double halfDtheta = dtheta / 2.0;
+
+    final double cosMinusOne = m_rotation.getCos() - 1;
+
+    double halfThetaByTanOfHalfDtheta;
+    if (Math.abs(cosMinusOne) < 1E-9) {
+      halfThetaByTanOfHalfDtheta = 1.0 - 1.0 / 12.0 * dtheta * dtheta;
+    } else {
+      halfThetaByTanOfHalfDtheta = -(halfDtheta * m_rotation.getSin()) / cosMinusOne;
+    }
+
+    Translation2d translationPart =
+        m_translation
+            .rotateBy(new Rotation2d(halfThetaByTanOfHalfDtheta, -halfDtheta))
+            .times(Math.hypot(halfThetaByTanOfHalfDtheta, halfDtheta));
+
+    return new Twist2d(translationPart.getX(), translationPart.getY(), dtheta);
+  }
+
   /**
    * Invert the transformation. This is useful for undoing a transformation.
    *
diff --git a/wpimath/src/main/java/edu/wpi/first/math/geometry/Transform3d.java b/wpimath/src/main/java/edu/wpi/first/math/geometry/Transform3d.java
index d993d86100..dc893d1279 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/geometry/Transform3d.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/geometry/Transform3d.java
@@ -11,6 +11,7 @@ import edu.wpi.first.math.Matrix;
 import edu.wpi.first.math.Nat;
 import edu.wpi.first.math.geometry.proto.Transform3dProto;
 import edu.wpi.first.math.geometry.struct.Transform3dStruct;
+import edu.wpi.first.math.jni.Transform3dJNI;
 import edu.wpi.first.math.numbers.N4;
 import edu.wpi.first.units.measure.Distance;
 import edu.wpi.first.util.protobuf.ProtobufSerializable;
@@ -251,6 +252,32 @@ public class Transform3d implements ProtobufSerializable, StructSerializable {
     return m_rotation;
   }
 
+  /**
+   * Returns a Twist3d of the current transform (pose delta). If b is the output of {@code a.log()},
+   * then {@code b.exp()} would yield a.
+   *
+   * @return The twist that maps the current transform.
+   */
+  public Twist3d log() {
+    var thisQuaternion = m_rotation.getQuaternion();
+    double[] resultArray =
+        Transform3dJNI.log(
+            this.getX(),
+            this.getY(),
+            this.getZ(),
+            thisQuaternion.getW(),
+            thisQuaternion.getX(),
+            thisQuaternion.getY(),
+            thisQuaternion.getZ());
+    return new Twist3d(
+        resultArray[0],
+        resultArray[1],
+        resultArray[2],
+        resultArray[3],
+        resultArray[4],
+        resultArray[5]);
+  }
+
   /**
    * Invert the transformation. This is useful for undoing a transformation.
    *
diff --git a/wpimath/src/main/java/edu/wpi/first/math/geometry/Twist2d.java b/wpimath/src/main/java/edu/wpi/first/math/geometry/Twist2d.java
index 0867d05062..36edd569c6 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/geometry/Twist2d.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/geometry/Twist2d.java
@@ -42,6 +42,39 @@ public class Twist2d implements ProtobufSerializable, StructSerializable {
     this.dtheta = dtheta;
   }
 
+  /**
+   * Obtain a new Transform2d from a (constant curvature) velocity.
+   *
+   * <p>See <a href="https://file.tavsys.net/control/controls-engineering-in-frc.pdf">Controls
+   * Engineering in the FIRST Robotics Competition</a> section 10.2 "Pose exponential" for a
+   * derivation.
+   *
+   * <p>The twist is a change in pose in the robot's coordinate frame since the previous pose
+   * update. When the user runs exp() on the twist, the user will receive the pose delta.
+   *
+   * <p>"Exp" represents the pose exponential, which is solving a differential equation moving the
+   * pose forward in time.
+   *
+   * @return The pose delta of the robot.
+   */
+  public Transform2d exp() {
+    double sinTheta = Math.sin(dtheta);
+    double cosTheta = Math.cos(dtheta);
+
+    double s;
+    double c;
+    if (Math.abs(dtheta) < 1E-9) {
+      s = 1.0 - 1.0 / 6.0 * dtheta * dtheta;
+      c = 0.5 * dtheta;
+    } else {
+      s = sinTheta / dtheta;
+      c = (1 - cosTheta) / dtheta;
+    }
+
+    return new Transform2d(
+        new Translation2d(dx * s - dy * c, dx * c + dy * s), new Rotation2d(cosTheta, sinTheta));
+  }
+
   @Override
   public String toString() {
     return String.format("Twist2d(dX: %.2f, dY: %.2f, dTheta: %.2f)", dx, dy, dtheta);
diff --git a/wpimath/src/main/java/edu/wpi/first/math/geometry/Twist3d.java b/wpimath/src/main/java/edu/wpi/first/math/geometry/Twist3d.java
index a03a035adf..64274dfb24 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/geometry/Twist3d.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/geometry/Twist3d.java
@@ -6,6 +6,7 @@ package edu.wpi.first.math.geometry;
 
 import edu.wpi.first.math.geometry.proto.Twist3dProto;
 import edu.wpi.first.math.geometry.struct.Twist3dStruct;
+import edu.wpi.first.math.jni.Twist3dJNI;
 import edu.wpi.first.util.protobuf.ProtobufSerializable;
 import edu.wpi.first.util.struct.StructSerializable;
 import java.util.Objects;
@@ -57,6 +58,31 @@ public class Twist3d implements ProtobufSerializable, StructSerializable {
     this.rz = rz;
   }
 
+  /**
+   * Obtain a new Transform3d from a (constant curvature) velocity.
+   *
+   * <p>See <a href="https://file.tavsys.net/control/controls-engineering-in-frc.pdf">Controls
+   * Engineering in the FIRST Robotics Competition</a> section 10.2 "Pose exponential" for a
+   * derivation.
+   *
+   * <p>The twist is a change in pose in the robot's coordinate frame since the previous pose
+   * update. When the user runs exp() on the twist, the user will receive the pose delta.
+   *
+   * <p>"Exp" represents the pose exponential, which is solving a differential equation moving the
+   * pose forward in time.
+   *
+   * @return The pose delta of the robot.
+   */
+  public Transform3d exp() {
+    double[] resultArray = Twist3dJNI.exp(dx, dy, dz, rx, ry, rz);
+    return new Transform3d(
+        resultArray[0],
+        resultArray[1],
+        resultArray[2],
+        new Rotation3d(
+            new Quaternion(resultArray[3], resultArray[4], resultArray[5], resultArray[6])));
+  }
+
   @Override
   public String toString() {
     return String.format(
diff --git a/wpimath/src/main/java/edu/wpi/first/math/jni/Pose3dJNI.java b/wpimath/src/main/java/edu/wpi/first/math/jni/Pose3dJNI.java
deleted file mode 100644
index f32d58e0b1..0000000000
--- a/wpimath/src/main/java/edu/wpi/first/math/jni/Pose3dJNI.java
+++ /dev/null
@@ -1,83 +0,0 @@
-// Copyright (c) FIRST and other WPILib contributors.
-// Open Source Software; you can modify and/or share it under the terms of
-// the WPILib BSD license file in the root directory of this project.
-
-package edu.wpi.first.math.jni;
-
-/** Pose3d JNI. */
-public final class Pose3dJNI extends WPIMathJNI {
-  /**
-   * Obtain a Pose3d from a (constant curvature) velocity.
-   *
-   * <p>The double array returned is of the form [dx, dy, dz, qx, qy, qz].
-   *
-   * @param poseX The pose's translational X component.
-   * @param poseY The pose's translational Y component.
-   * @param poseZ The pose's translational Z component.
-   * @param poseQw The pose quaternion's W component.
-   * @param poseQx The pose quaternion's X component.
-   * @param poseQy The pose quaternion's Y component.
-   * @param poseQz The pose quaternion's Z component.
-   * @param twistDx The twist's dx value.
-   * @param twistDy The twist's dy value.
-   * @param twistDz The twist's dz value.
-   * @param twistRx The twist's rx value.
-   * @param twistRy The twist's ry value.
-   * @param twistRz The twist's rz value.
-   * @return The new pose as a double array.
-   */
-  public static native double[] exp(
-      double poseX,
-      double poseY,
-      double poseZ,
-      double poseQw,
-      double poseQx,
-      double poseQy,
-      double poseQz,
-      double twistDx,
-      double twistDy,
-      double twistDz,
-      double twistRx,
-      double twistRy,
-      double twistRz);
-
-  /**
-   * Returns a Twist3d that maps the starting pose to the end pose.
-   *
-   * <p>The double array returned is of the form [dx, dy, dz, rx, ry, rz].
-   *
-   * @param startX The starting pose's translational X component.
-   * @param startY The starting pose's translational Y component.
-   * @param startZ The starting pose's translational Z component.
-   * @param startQw The starting pose quaternion's W component.
-   * @param startQx The starting pose quaternion's X component.
-   * @param startQy The starting pose quaternion's Y component.
-   * @param startQz The starting pose quaternion's Z component.
-   * @param endX The ending pose's translational X component.
-   * @param endY The ending pose's translational Y component.
-   * @param endZ The ending pose's translational Z component.
-   * @param endQw The ending pose quaternion's W component.
-   * @param endQx The ending pose quaternion's X component.
-   * @param endQy The ending pose quaternion's Y component.
-   * @param endQz The ending pose quaternion's Z component.
-   * @return The twist that maps start to end as a double array.
-   */
-  public static native double[] log(
-      double startX,
-      double startY,
-      double startZ,
-      double startQw,
-      double startQx,
-      double startQy,
-      double startQz,
-      double endX,
-      double endY,
-      double endZ,
-      double endQw,
-      double endQx,
-      double endQy,
-      double endQz);
-
-  /** Utility class. */
-  private Pose3dJNI() {}
-}
diff --git a/wpimath/src/main/java/edu/wpi/first/math/jni/Transform3dJNI.java b/wpimath/src/main/java/edu/wpi/first/math/jni/Transform3dJNI.java
new file mode 100644
index 0000000000..22fff99fe8
--- /dev/null
+++ b/wpimath/src/main/java/edu/wpi/first/math/jni/Transform3dJNI.java
@@ -0,0 +1,34 @@
+// Copyright (c) FIRST and other WPILib contributors.
+// Open Source Software; you can modify and/or share it under the terms of
+// the WPILib BSD license file in the root directory of this project.
+
+package edu.wpi.first.math.jni;
+
+/** Transform3d JNI. */
+public final class Transform3dJNI extends WPIMathJNI {
+  /**
+   * Returns a Twist3d that maps the Transform3d (pose delta).
+   *
+   * <p>The double array returned is of the form [dx, dy, dz, rx, ry, rz].
+   *
+   * @param relX The transform's translational X component.
+   * @param relY The transform's translational Y component.
+   * @param relZ The transform's translational Z component.
+   * @param relQw The transform quaternion's W component.
+   * @param relQx The transform quaternion's X component.
+   * @param relQy The transform quaternion's Y component.
+   * @param relQz The transform quaternion's Z component.
+   * @return The twist that maps start to end as a double array.
+   */
+  public static native double[] log(
+      double relX,
+      double relY,
+      double relZ,
+      double relQw,
+      double relQx,
+      double relQy,
+      double relQz);
+
+  /** Utility class. */
+  private Transform3dJNI() {}
+}
diff --git a/wpimath/src/main/java/edu/wpi/first/math/jni/Twist3dJNI.java b/wpimath/src/main/java/edu/wpi/first/math/jni/Twist3dJNI.java
new file mode 100644
index 0000000000..d594c0cafc
--- /dev/null
+++ b/wpimath/src/main/java/edu/wpi/first/math/jni/Twist3dJNI.java
@@ -0,0 +1,32 @@
+// Copyright (c) FIRST and other WPILib contributors.
+// Open Source Software; you can modify and/or share it under the terms of
+// the WPILib BSD license file in the root directory of this project.
+
+package edu.wpi.first.math.jni;
+
+/** Twist3d JNI. */
+public final class Twist3dJNI extends WPIMathJNI {
+  /**
+   * Obtain a Transform3d from a (constant curvature) velocity.
+   *
+   * <p>The double array returned is of the form [dx, dy, dz, qw, qx, qy, qz].
+   *
+   * @param twistDx The twist's dx value.
+   * @param twistDy The twist's dy value.
+   * @param twistDz The twist's dz value.
+   * @param twistRx The twist's rx value.
+   * @param twistRy The twist's ry value.
+   * @param twistRz The twist's rz value.
+   * @return The new pose as a double array.
+   */
+  public static native double[] exp(
+      double twistDx,
+      double twistDy,
+      double twistDz,
+      double twistRx,
+      double twistRy,
+      double twistRz);
+
+  /** Utility class. */
+  private Twist3dJNI() {}
+}
diff --git a/wpimath/src/main/java/edu/wpi/first/math/kinematics/ChassisSpeeds.java b/wpimath/src/main/java/edu/wpi/first/math/kinematics/ChassisSpeeds.java
index 9de9d528f7..913a66a784 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/kinematics/ChassisSpeeds.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/kinematics/ChassisSpeeds.java
@@ -7,8 +7,8 @@ package edu.wpi.first.math.kinematics;
 import static edu.wpi.first.units.Units.MetersPerSecond;
 import static edu.wpi.first.units.Units.RadiansPerSecond;
 
-import edu.wpi.first.math.geometry.Pose2d;
 import edu.wpi.first.math.geometry.Rotation2d;
+import edu.wpi.first.math.geometry.Transform2d;
 import edu.wpi.first.math.geometry.Translation2d;
 import edu.wpi.first.math.geometry.Twist2d;
 import edu.wpi.first.math.kinematics.proto.ChassisSpeedsProto;
@@ -101,11 +101,11 @@ public class ChassisSpeeds implements ProtobufSerializable, StructSerializable {
   public ChassisSpeeds discretize(double dt) {
     // Construct the desired pose after a timestep, relative to the current pose. The desired pose
     // has decoupled translation and rotation.
-    var desiredDeltaPose = new Pose2d(vx * dt, vy * dt, new Rotation2d(omega * dt));
+    var desiredTransform = new Transform2d(vx * dt, vy * dt, new Rotation2d(omega * dt));
 
     // Find the chassis translation/rotation deltas in the robot frame that move the robot from its
     // current pose to the desired pose
-    var twist = Pose2d.kZero.log(desiredDeltaPose);
+    var twist = desiredTransform.log();
 
     // Turn the chassis translation/rotation deltas into average velocities
     return new ChassisSpeeds(twist.dx / dt, twist.dy / dt, twist.dtheta / dt);
diff --git a/wpimath/src/main/java/edu/wpi/first/math/kinematics/Odometry.java b/wpimath/src/main/java/edu/wpi/first/math/kinematics/Odometry.java
index 9c99696590..c5fee7ebfc 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/kinematics/Odometry.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/kinematics/Odometry.java
@@ -117,7 +117,7 @@ public class Odometry<T> {
     var twist = m_kinematics.toTwist2d(m_previousWheelPositions, wheelPositions);
     twist.dtheta = angle.minus(m_previousAngle).getRadians();
 
-    var newPose = m_pose.exp(twist);
+    var newPose = m_pose.plus(twist.exp());
 
     m_kinematics.copyInto(wheelPositions, m_previousWheelPositions);
     m_previousAngle = angle;
diff --git a/wpimath/src/main/java/edu/wpi/first/math/kinematics/Odometry3d.java b/wpimath/src/main/java/edu/wpi/first/math/kinematics/Odometry3d.java
index a50a7f1d73..12211f721a 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/kinematics/Odometry3d.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/kinematics/Odometry3d.java
@@ -134,7 +134,7 @@ public class Odometry3d<T> {
             angle_difference.get(1),
             angle_difference.get(2));
 
-    var newPose = m_pose.exp(twist);
+    var newPose = m_pose.plus(twist.exp());
 
     m_kinematics.copyInto(wheelPositions, m_previousWheelPositions);
     m_previousAngle = angle;
diff --git a/wpimath/src/main/java/edu/wpi/first/math/spline/SplineParameterizer.java b/wpimath/src/main/java/edu/wpi/first/math/spline/SplineParameterizer.java
index bc63d1a672..35d526e8d0 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/spline/SplineParameterizer.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/spline/SplineParameterizer.java
@@ -126,7 +126,7 @@ public final class SplineParameterizer {
         throw new MalformedSplineException(kMalformedSplineExceptionMsg);
       }
 
-      final var twist = start.get().pose.log(end.get().pose);
+      final var twist = (end.get().pose.minus(start.get().pose)).log();
       if (Math.abs(twist.dy) > kMaxDy
           || Math.abs(twist.dx) > kMaxDx
           || Math.abs(twist.dtheta) > kMaxDtheta) {
diff --git a/wpimath/src/main/native/cpp/jni/Pose3dJNI.cpp b/wpimath/src/main/native/cpp/jni/Pose3dJNI.cpp
deleted file mode 100644
index e41e0eb703..0000000000
--- a/wpimath/src/main/native/cpp/jni/Pose3dJNI.cpp
+++ /dev/null
@@ -1,70 +0,0 @@
-// Copyright (c) FIRST and other WPILib contributors.
-// Open Source Software; you can modify and/or share it under the terms of
-// the WPILib BSD license file in the root directory of this project.
-
-#include <jni.h>
-
-#include <wpi/jni_util.h>
-
-#include "edu_wpi_first_math_jni_Pose3dJNI.h"
-#include "frc/geometry/Pose3d.h"
-
-using namespace wpi::java;
-
-extern "C" {
-
-/*
- * Class:     edu_wpi_first_math_jni_Pose3dJNI
- * Method:    exp
- * Signature: (DDDDDDDDDDDDD)[D
- */
-JNIEXPORT jdoubleArray JNICALL
-Java_edu_wpi_first_math_jni_Pose3dJNI_exp
-  (JNIEnv* env, jclass, jdouble poseX, jdouble poseY, jdouble poseZ,
-   jdouble poseQw, jdouble poseQx, jdouble poseQy, jdouble poseQz,
-   jdouble twistDx, jdouble twistDy, jdouble twistDz, jdouble twistRx,
-   jdouble twistRy, jdouble twistRz)
-{
-  frc::Pose3d pose{
-      units::meter_t{poseX}, units::meter_t{poseY}, units::meter_t{poseZ},
-      frc::Rotation3d{frc::Quaternion{poseQw, poseQx, poseQy, poseQz}}};
-  frc::Twist3d twist{units::meter_t{twistDx},  units::meter_t{twistDy},
-                     units::meter_t{twistDz},  units::radian_t{twistRx},
-                     units::radian_t{twistRy}, units::radian_t{twistRz}};
-
-  frc::Pose3d result = pose.Exp(twist);
-
-  const auto& resultQuaternion = result.Rotation().GetQuaternion();
-  return MakeJDoubleArray(
-      env, {{result.X().value(), result.Y().value(), result.Z().value(),
-             resultQuaternion.W(), resultQuaternion.X(), resultQuaternion.Y(),
-             resultQuaternion.Z()}});
-}
-
-/*
- * Class:     edu_wpi_first_math_jni_Pose3dJNI
- * Method:    log
- * Signature: (DDDDDDDDDDDDDD)[D
- */
-JNIEXPORT jdoubleArray JNICALL
-Java_edu_wpi_first_math_jni_Pose3dJNI_log
-  (JNIEnv* env, jclass, jdouble startX, jdouble startY, jdouble startZ,
-   jdouble startQw, jdouble startQx, jdouble startQy, jdouble startQz,
-   jdouble endX, jdouble endY, jdouble endZ, jdouble endQw, jdouble endQx,
-   jdouble endQy, jdouble endQz)
-{
-  frc::Pose3d startPose{
-      units::meter_t{startX}, units::meter_t{startY}, units::meter_t{startZ},
-      frc::Rotation3d{frc::Quaternion{startQw, startQx, startQy, startQz}}};
-  frc::Pose3d endPose{
-      units::meter_t{endX}, units::meter_t{endY}, units::meter_t{endZ},
-      frc::Rotation3d{frc::Quaternion{endQw, endQx, endQy, endQz}}};
-
-  frc::Twist3d result = startPose.Log(endPose);
-
-  return MakeJDoubleArray(
-      env, {{result.dx.value(), result.dy.value(), result.dz.value(),
-             result.rx.value(), result.ry.value(), result.rz.value()}});
-}
-
-}  // extern "C"
diff --git a/wpimath/src/main/native/cpp/jni/Transform3dJNI.cpp b/wpimath/src/main/native/cpp/jni/Transform3dJNI.cpp
new file mode 100644
index 0000000000..893da08b00
--- /dev/null
+++ b/wpimath/src/main/native/cpp/jni/Transform3dJNI.cpp
@@ -0,0 +1,42 @@
+// Copyright (c) FIRST and other WPILib contributors.
+// Open Source Software; you can modify and/or share it under the terms of
+// the WPILib BSD license file in the root directory of this project.
+
+#include <jni.h>
+
+#include <wpi/jni_util.h>
+
+#include "edu_wpi_first_math_jni_Transform3dJNI.h"
+#include "frc/geometry/Quaternion.h"
+#include "frc/geometry/Rotation3d.h"
+#include "frc/geometry/Transform3d.h"
+#include "frc/geometry/Twist3d.h"
+#include "units/angle.h"
+#include "units/length.h"
+
+using namespace wpi::java;
+
+extern "C" {
+
+/*
+ * Class:     edu_wpi_first_math_jni_Transform3dJNI
+ * Method:    log
+ * Signature: (DDDDDDD)[D
+ */
+JNIEXPORT jdoubleArray JNICALL
+Java_edu_wpi_first_math_jni_Transform3dJNI_log
+  (JNIEnv* env, jclass, jdouble relX, jdouble relY, jdouble relZ, jdouble relQw,
+   jdouble relQx, jdouble relQy, jdouble relQz)
+{
+  frc::Transform3d transform3d{
+      units::meter_t{relX}, units::meter_t{relY}, units::meter_t{relZ},
+      frc::Rotation3d{frc::Quaternion{relQw, relQx, relQy, relQz}}};
+
+  frc::Twist3d result = transform3d.Log();
+
+  return MakeJDoubleArray(
+      env, {{result.dx.value(), result.dy.value(), result.dz.value(),
+             result.rx.value(), result.ry.value(), result.rz.value()}});
+}
+
+}  // extern "C"
diff --git a/wpimath/src/main/native/cpp/jni/Twist3dJNI.cpp b/wpimath/src/main/native/cpp/jni/Twist3dJNI.cpp
new file mode 100644
index 0000000000..4cf5afa367
--- /dev/null
+++ b/wpimath/src/main/native/cpp/jni/Twist3dJNI.cpp
@@ -0,0 +1,42 @@
+// Copyright (c) FIRST and other WPILib contributors.
+// Open Source Software; you can modify and/or share it under the terms of
+// the WPILib BSD license file in the root directory of this project.
+
+#include <jni.h>
+
+#include <wpi/jni_util.h>
+
+#include "edu_wpi_first_math_jni_Twist3dJNI.h"
+#include "frc/geometry/Transform3d.h"
+#include "frc/geometry/Twist3d.h"
+#include "units/angle.h"
+#include "units/length.h"
+
+using namespace wpi::java;
+
+extern "C" {
+
+/*
+ * Class:     edu_wpi_first_math_jni_Twist3dJNI
+ * Method:    exp
+ * Signature: (DDDDDD)[D
+ */
+JNIEXPORT jdoubleArray JNICALL
+Java_edu_wpi_first_math_jni_Twist3dJNI_exp
+  (JNIEnv* env, jclass, jdouble twistDx, jdouble twistDy, jdouble twistDz,
+   jdouble twistRx, jdouble twistRy, jdouble twistRz)
+{
+  frc::Twist3d twist{units::meter_t{twistDx},  units::meter_t{twistDy},
+                     units::meter_t{twistDz},  units::radian_t{twistRx},
+                     units::radian_t{twistRy}, units::radian_t{twistRz}};
+
+  frc::Transform3d result = twist.Exp();
+
+  const auto& resultQuaternion = result.Rotation().GetQuaternion();
+  return MakeJDoubleArray(
+      env, {{result.X().value(), result.Y().value(), result.Z().value(),
+             resultQuaternion.W(), resultQuaternion.X(), resultQuaternion.Y(),
+             resultQuaternion.Z()}});
+}
+
+}  // extern "C"
diff --git a/wpimath/src/main/native/include/frc/estimator/PoseEstimator.h b/wpimath/src/main/native/include/frc/estimator/PoseEstimator.h
index 9c3bc4d6de..46d124f7de 100644
--- a/wpimath/src/main/native/include/frc/estimator/PoseEstimator.h
+++ b/wpimath/src/main/native/include/frc/estimator/PoseEstimator.h
@@ -263,7 +263,7 @@ class WPILIB_DLLEXPORT PoseEstimator {
 
     // Step 4: Measure the twist between the old pose estimate and the vision
     // pose.
-    auto twist = visionSample.value().Log(visionRobotPose);
+    auto twist = (visionRobotPose - visionSample.value()).Log();
 
     // Step 5: We should not trust the twist entirely, so instead we scale this
     // twist by a Kalman gain matrix representing how much we trust vision
@@ -278,7 +278,8 @@ class WPILIB_DLLEXPORT PoseEstimator {
                         units::radian_t{k_times_twist(2)}};
 
     // Step 7: Calculate and record the vision update.
-    VisionUpdate visionUpdate{visionSample->Exp(scaledTwist), *odometrySample};
+    VisionUpdate visionUpdate{visionSample.value() + scaledTwist.Exp(),
+                              *odometrySample};
     m_visionUpdates[timestamp] = visionUpdate;
 
     // Step 8: Remove later vision measurements. (Matches previous behavior)
diff --git a/wpimath/src/main/native/include/frc/estimator/PoseEstimator3d.h b/wpimath/src/main/native/include/frc/estimator/PoseEstimator3d.h
index bc8bdb08a6..68e99dd4f2 100644
--- a/wpimath/src/main/native/include/frc/estimator/PoseEstimator3d.h
+++ b/wpimath/src/main/native/include/frc/estimator/PoseEstimator3d.h
@@ -272,7 +272,7 @@ class WPILIB_DLLEXPORT PoseEstimator3d {
 
     // Step 4: Measure the twist between the old pose estimate and the vision
     // pose.
-    auto twist = visionSample.value().Log(visionRobotPose);
+    auto twist = (visionRobotPose - visionSample.value()).Log();
 
     // Step 5: We should not trust the twist entirely, so instead we scale this
     // twist by a Kalman gain matrix representing how much we trust vision
@@ -289,7 +289,8 @@ class WPILIB_DLLEXPORT PoseEstimator3d {
         units::radian_t{k_times_twist(4)}, units::radian_t{k_times_twist(5)}};
 
     // Step 7: Calculate and record the vision update.
-    VisionUpdate visionUpdate{visionSample->Exp(scaledTwist), *odometrySample};
+    VisionUpdate visionUpdate{visionSample.value() + scaledTwist.Exp(),
+                              *odometrySample};
     m_visionUpdates[timestamp] = visionUpdate;
 
     // Step 8: Remove later vision measurements. (Matches previous behavior)
diff --git a/wpimath/src/main/native/include/frc/geometry/Pose2d.h b/wpimath/src/main/native/include/frc/geometry/Pose2d.h
index d488e312a7..17328e8554 100644
--- a/wpimath/src/main/native/include/frc/geometry/Pose2d.h
+++ b/wpimath/src/main/native/include/frc/geometry/Pose2d.h
@@ -15,7 +15,6 @@
 
 #include "frc/geometry/Rotation2d.h"
 #include "frc/geometry/Translation2d.h"
-#include "frc/geometry/Twist2d.h"
 #include "units/length.h"
 
 namespace frc {
@@ -197,39 +196,6 @@ class WPILIB_DLLEXPORT Pose2d {
     return {m_translation.RotateAround(point, rot), m_rotation.RotateBy(rot)};
   }
 
-  /**
-   * Obtain a new Pose2d from a (constant curvature) velocity.
-   *
-   * See https://file.tavsys.net/control/controls-engineering-in-frc.pdf section
-   * 10.2 "Pose exponential" for a derivation.
-   *
-   * The twist is a change in pose in the robot's coordinate frame since the
-   * previous pose update. When the user runs exp() on the previous known
-   * field-relative pose with the argument being the twist, the user will
-   * receive the new field-relative pose.
-   *
-   * "Exp" represents the pose exponential, which is solving a differential
-   * equation moving the pose forward in time.
-   *
-   * @param twist The change in pose in the robot's coordinate frame since the
-   * previous pose update. For example, if a non-holonomic robot moves forward
-   * 0.01 meters and changes angle by 0.5 degrees since the previous pose
-   * update, the twist would be Twist2d{0.01_m, 0_m, 0.5_deg}.
-   *
-   * @return The new pose of the robot.
-   */
-  constexpr Pose2d Exp(const Twist2d& twist) const;
-
-  /**
-   * Returns a Twist2d that maps this pose to the end pose. If c is the output
-   * of a.Log(b), then a.Exp(c) would yield b.
-   *
-   * @param end The end pose for the transformation.
-   *
-   * @return The twist that maps this to end.
-   */
-  constexpr Twist2d Log(const Pose2d& end) const;
-
   /**
    * Returns an affine transformation matrix representation of this pose.
    */
@@ -328,51 +294,4 @@ constexpr Pose2d Pose2d::RelativeTo(const Pose2d& other) const {
   return {transform.Translation(), transform.Rotation()};
 }
 
-constexpr Pose2d Pose2d::Exp(const Twist2d& twist) const {
-  const auto dx = twist.dx;
-  const auto dy = twist.dy;
-  const auto dtheta = twist.dtheta.value();
-
-  const auto sinTheta = gcem::sin(dtheta);
-  const auto cosTheta = gcem::cos(dtheta);
-
-  double s, c;
-  if (gcem::abs(dtheta) < 1E-9) {
-    s = 1.0 - 1.0 / 6.0 * dtheta * dtheta;
-    c = 0.5 * dtheta;
-  } else {
-    s = sinTheta / dtheta;
-    c = (1 - cosTheta) / dtheta;
-  }
-
-  const Transform2d transform{Translation2d{dx * s - dy * c, dx * c + dy * s},
-                              Rotation2d{cosTheta, sinTheta}};
-
-  return *this + transform;
-}
-
-constexpr Twist2d Pose2d::Log(const Pose2d& end) const {
-  const auto transform = end.RelativeTo(*this);
-  const auto dtheta = transform.Rotation().Radians().value();
-  const auto halfDtheta = dtheta / 2.0;
-
-  const auto cosMinusOne = transform.Rotation().Cos() - 1;
-
-  double halfThetaByTanOfHalfDtheta;
-
-  if (gcem::abs(cosMinusOne) < 1E-9) {
-    halfThetaByTanOfHalfDtheta = 1.0 - 1.0 / 12.0 * dtheta * dtheta;
-  } else {
-    halfThetaByTanOfHalfDtheta =
-        -(halfDtheta * transform.Rotation().Sin()) / cosMinusOne;
-  }
-
-  const Translation2d translationPart =
-      transform.Translation().RotateBy(
-          {halfThetaByTanOfHalfDtheta, -halfDtheta}) *
-      gcem::hypot(halfThetaByTanOfHalfDtheta, halfDtheta);
-
-  return {translationPart.X(), translationPart.Y(), units::radian_t{dtheta}};
-}
-
 }  // namespace frc
diff --git a/wpimath/src/main/native/include/frc/geometry/Pose3d.h b/wpimath/src/main/native/include/frc/geometry/Pose3d.h
index e2ec7c4609..ebf4de6827 100644
--- a/wpimath/src/main/native/include/frc/geometry/Pose3d.h
+++ b/wpimath/src/main/native/include/frc/geometry/Pose3d.h
@@ -19,7 +19,6 @@
 #include "frc/geometry/Pose2d.h"
 #include "frc/geometry/Rotation3d.h"
 #include "frc/geometry/Translation3d.h"
-#include "frc/geometry/Twist3d.h"
 
 namespace frc {
 
@@ -223,37 +222,6 @@ class WPILIB_DLLEXPORT Pose3d {
     return {m_translation.RotateAround(point, rot), m_rotation.RotateBy(rot)};
   }
 
-  /**
-   * Obtain a new Pose3d from a (constant curvature) velocity.
-   *
-   * The twist is a change in pose in the robot's coordinate frame since the
-   * previous pose update. When the user runs exp() on the previous known
-   * field-relative pose with the argument being the twist, the user will
-   * receive the new field-relative pose.
-   *
-   * "Exp" represents the pose exponential, which is solving a differential
-   * equation moving the pose forward in time.
-   *
-   * @param twist The change in pose in the robot's coordinate frame since the
-   * previous pose update. For example, if a non-holonomic robot moves forward
-   * 0.01 meters and changes angle by 0.5 degrees since the previous pose
-   * update, the twist would be Twist3d{0.01_m, 0_m, 0_m, Rotation3d{0.0, 0.0,
-   * 0.5_deg}}.
-   *
-   * @return The new pose of the robot.
-   */
-  constexpr Pose3d Exp(const Twist3d& twist) const;
-
-  /**
-   * Returns a Twist3d that maps this pose to the end pose. If c is the output
-   * of a.Log(b), then a.Exp(c) would yield b.
-   *
-   * @param end The end pose for the transformation.
-   *
-   * @return The twist that maps this to end.
-   */
-  constexpr Twist3d Log(const Pose3d& end) const;
-
   /**
    * Returns an affine transformation matrix representation of this pose.
    */
@@ -336,56 +304,10 @@ void from_json(const wpi::json& json, Pose3d& pose);
 
 }  // namespace frc
 
-#include "frc/geometry/proto/Pose3dProto.h"
-#include "frc/geometry/struct/Pose3dStruct.h"
-
 #include "frc/geometry/Transform3d.h"
 
 namespace frc {
 
-namespace detail {
-
-/**
- * Applies the hat operator to a rotation vector.
- *
- * It takes a rotation vector and returns the corresponding matrix
- * representation of the Lie algebra element (a 3x3 rotation matrix).
- *
- * @param rotation The rotation vector.
- * @return The rotation vector as a 3x3 rotation matrix.
- */
-constexpr ct_matrix3d RotationVectorToMatrix(const ct_vector3d& rotation) {
-  // Given a rotation vector <a, b, c>,
-  //         [ 0 -c  b]
-  // Omega = [ c  0 -a]
-  //         [-b  a  0]
-  return ct_matrix3d{{0.0, -rotation(2), rotation(1)},
-                     {rotation(2), 0.0, -rotation(0)},
-                     {-rotation(1), rotation(0), 0.0}};
-}
-
-/**
- * Applies the hat operator to a rotation vector.
- *
- * It takes a rotation vector and returns the corresponding matrix
- * representation of the Lie algebra element (a 3x3 rotation matrix).
- *
- * @param rotation The rotation vector.
- * @return The rotation vector as a 3x3 rotation matrix.
- */
-constexpr Eigen::Matrix3d RotationVectorToMatrix(
-    const Eigen::Vector3d& rotation) {
-  // Given a rotation vector <a, b, c>,
-  //         [ 0 -c  b]
-  // Omega = [ c  0 -a]
-  //         [-b  a  0]
-  return Eigen::Matrix3d{{0.0, -rotation(2), rotation(1)},
-                         {rotation(2), 0.0, -rotation(0)},
-                         {-rotation(1), rotation(0), 0.0}};
-}
-
-}  // namespace detail
-
 constexpr Transform3d Pose3d::operator-(const Pose3d& other) const {
   const auto pose = this->RelativeTo(other);
   return Transform3d{pose.Translation(), pose.Rotation()};
@@ -401,121 +323,7 @@ constexpr Pose3d Pose3d::RelativeTo(const Pose3d& other) const {
   return {transform.Translation(), transform.Rotation()};
 }
 
-constexpr Pose3d Pose3d::Exp(const Twist3d& twist) const {
-  // Implementation from Section 3.2 of https://ethaneade.org/lie.pdf
-
-  auto impl = [this]<typename Matrix3d, typename Vector3d>(
-                  const Twist3d& twist) -> Pose3d {
-    Vector3d u{{twist.dx.value(), twist.dy.value(), twist.dz.value()}};
-    Vector3d rvec{{twist.rx.value(), twist.ry.value(), twist.rz.value()}};
-    Matrix3d omega = detail::RotationVectorToMatrix(rvec);
-    Matrix3d omegaSq = omega * omega;
-    double theta = rvec.norm();
-    double thetaSq = theta * theta;
-
-    double A;
-    double B;
-    double C;
-    if (gcem::abs(theta) < 1E-7) {
-      // Taylor Expansions around θ = 0
-      // A = 1/1! - θ²/3! + θ⁴/5!
-      // B = 1/2! - θ²/4! + θ⁴/6!
-      // C = 1/3! - θ²/5! + θ⁴/7!
-      // sources:
-      // A:
-      // https://www.wolframalpha.com/input?i2d=true&i=series+expansion+of+Divide%5Bsin%5C%2840%29x%5C%2841%29%2Cx%5D+at+x%3D0
-      // B:
-      // https://www.wolframalpha.com/input?i2d=true&i=series+expansion+of+Divide%5B1-cos%5C%2840%29x%5C%2841%29%2CPower%5Bx%2C2%5D%5D+at+x%3D0
-      // C:
-      // https://www.wolframalpha.com/input?i2d=true&i=series+expansion+of+Divide%5B1-Divide%5Bsin%5C%2840%29x%5C%2841%29%2Cx%5D%2CPower%5Bx%2C2%5D%5D+at+x%3D0
-      A = 1 - thetaSq / 6 + thetaSq * thetaSq / 120;
-      B = 1 / 2.0 - thetaSq / 24 + thetaSq * thetaSq / 720;
-      C = 1 / 6.0 - thetaSq / 120 + thetaSq * thetaSq / 5040;
-    } else {
-      // A = std::sin(θ)/θ
-      // B = (1 - std::cos(θ)) / θ²
-      // C = (1 - A) / θ²
-      A = gcem::sin(theta) / theta;
-      B = (1 - gcem::cos(theta)) / thetaSq;
-      C = (1 - A) / thetaSq;
-    }
-
-    Matrix3d R = Matrix3d::Identity() + A * omega + B * omegaSq;
-    Matrix3d V = Matrix3d::Identity() + B * omega + C * omegaSq;
-
-    Vector3d translation_component = V * u;
-
-    const Transform3d transform{
-        Translation3d{units::meter_t{translation_component(0)},
-                      units::meter_t{translation_component(1)},
-                      units::meter_t{translation_component(2)}},
-        Rotation3d{R}};
-
-    return *this + transform;
-  };
-
-  if (std::is_constant_evaluated()) {
-    return impl.template operator()<ct_matrix3d, ct_vector3d>(twist);
-  } else {
-    return impl.template operator()<Eigen::Matrix3d, Eigen::Vector3d>(twist);
-  }
-}
-
-constexpr Twist3d Pose3d::Log(const Pose3d& end) const {
-  // Implementation from Section 3.2 of https://ethaneade.org/lie.pdf
-
-  auto impl = [this]<typename Matrix3d, typename Vector3d>(
-                  const Pose3d& end) -> Twist3d {
-    const auto transform = end.RelativeTo(*this);
-
-    Vector3d u{
-        {transform.X().value(), transform.Y().value(), transform.Z().value()}};
-    Vector3d rvec = transform.Rotation().ToVector();
-    Matrix3d omega = detail::RotationVectorToMatrix(rvec);
-    Matrix3d omegaSq = omega * omega;
-    double theta = rvec.norm();
-    double thetaSq = theta * theta;
-
-    double C;
-    if (gcem::abs(theta) < 1E-7) {
-      // Taylor Expansions around θ = 0
-      // A = 1/1! - θ²/3! + θ⁴/5!
-      // B = 1/2! - θ²/4! + θ⁴/6!
-      // C = 1/6 * (1/2 + θ²/5! + θ⁴/7!)
-      // sources:
-      // A:
-      // https://www.wolframalpha.com/input?i2d=true&i=series+expansion+of+Divide%5Bsin%5C%2840%29x%5C%2841%29%2Cx%5D+at+x%3D0
-      // B:
-      // https://www.wolframalpha.com/input?i2d=true&i=series+expansion+of+Divide%5B1-cos%5C%2840%29x%5C%2841%29%2CPower%5Bx%2C2%5D%5D+at+x%3D0
-      // C:
-      // https://www.wolframalpha.com/input?i2d=true&i=series+expansion+of+Divide%5B1-Divide%5BDivide%5Bsin%5C%2840%29x%5C%2841%29%2Cx%5D%2C2Divide%5B1-cos%5C%2840%29x%5C%2841%29%2CPower%5Bx%2C2%5D%5D%5D%2CPower%5Bx%2C2%5D%5D+at+x%3D0
-      C = 1 / 12.0 + thetaSq / 720 + thetaSq * thetaSq / 30240;
-    } else {
-      // A = std::sin(θ)/θ
-      // B = (1 - std::cos(θ)) / θ²
-      // C = (1 - A/(2*B)) / θ²
-      double A = gcem::sin(theta) / theta;
-      double B = (1 - gcem::cos(theta)) / thetaSq;
-      C = (1 - A / (2 * B)) / thetaSq;
-    }
-
-    Matrix3d V_inv = Matrix3d::Identity() - 0.5 * omega + C * omegaSq;
-
-    Vector3d translation_component = V_inv * u;
-
-    return Twist3d{units::meter_t{translation_component(0)},
-                   units::meter_t{translation_component(1)},
-                   units::meter_t{translation_component(2)},
-                   units::radian_t{rvec(0)},
-                   units::radian_t{rvec(1)},
-                   units::radian_t{rvec(2)}};
-  };
-
-  if (std::is_constant_evaluated()) {
-    return impl.template operator()<ct_matrix3d, ct_vector3d>(end);
-  } else {
-    return impl.template operator()<Eigen::Matrix3d, Eigen::Vector3d>(end);
-  }
-}
-
 }  // namespace frc
+
+#include "frc/geometry/proto/Pose3dProto.h"
+#include "frc/geometry/struct/Pose3dStruct.h"
diff --git a/wpimath/src/main/native/include/frc/geometry/Transform2d.h b/wpimath/src/main/native/include/frc/geometry/Transform2d.h
index 88c00550d0..d85abb4ded 100644
--- a/wpimath/src/main/native/include/frc/geometry/Transform2d.h
+++ b/wpimath/src/main/native/include/frc/geometry/Transform2d.h
@@ -14,6 +14,7 @@
 namespace frc {
 
 class Pose2d;
+struct Twist2d;
 
 /**
  * Represents a transformation for a Pose2d in the pose's frame.
@@ -109,6 +110,14 @@ class WPILIB_DLLEXPORT Transform2d {
    */
   constexpr const Rotation2d& Rotation() const { return m_rotation; }
 
+  /**
+   * Returns a Twist2d of the current transform (pose delta). If b is the output
+   * of {@code a.Log()}, then {@code b.Exp()} would yield a.
+   *
+   * @return The twist that maps the current transform.
+   */
+  constexpr Twist2d Log() const;
+
   /**
    * Invert the transformation. This is useful for undoing a transformation.
    *
@@ -163,6 +172,7 @@ class WPILIB_DLLEXPORT Transform2d {
 }  // namespace frc
 
 #include "frc/geometry/Pose2d.h"
+#include "frc/geometry/Twist2d.h"
 
 namespace frc {
 
@@ -180,6 +190,27 @@ constexpr Transform2d Transform2d::operator+(const Transform2d& other) const {
   return Transform2d{Pose2d{}, Pose2d{}.TransformBy(*this).TransformBy(other)};
 }
 
+constexpr Twist2d Transform2d::Log() const {
+  const auto dtheta = m_rotation.Radians().value();
+  const auto halfDtheta = dtheta / 2.0;
+
+  const auto cosMinusOne = m_rotation.Cos() - 1;
+
+  double halfThetaByTanOfHalfDtheta;
+
+  if (gcem::abs(cosMinusOne) < 1E-9) {
+    halfThetaByTanOfHalfDtheta = 1.0 - 1.0 / 12.0 * dtheta * dtheta;
+  } else {
+    halfThetaByTanOfHalfDtheta = -(halfDtheta * m_rotation.Sin()) / cosMinusOne;
+  }
+
+  const Translation2d translationPart =
+      m_translation.RotateBy({halfThetaByTanOfHalfDtheta, -halfDtheta}) *
+      gcem::hypot(halfThetaByTanOfHalfDtheta, halfDtheta);
+
+  return {translationPart.X(), translationPart.Y(), units::radian_t{dtheta}};
+}
+
 }  // namespace frc
 
 #include "frc/geometry/proto/Transform2dProto.h"
diff --git a/wpimath/src/main/native/include/frc/geometry/Transform3d.h b/wpimath/src/main/native/include/frc/geometry/Transform3d.h
index bd6ca9c41e..b424ddf48c 100644
--- a/wpimath/src/main/native/include/frc/geometry/Transform3d.h
+++ b/wpimath/src/main/native/include/frc/geometry/Transform3d.h
@@ -14,6 +14,7 @@
 namespace frc {
 
 class Pose3d;
+struct Twist3d;
 
 /**
  * Represents a transformation for a Pose3d in the pose's frame.
@@ -134,6 +135,14 @@ class WPILIB_DLLEXPORT Transform3d {
    */
   constexpr const Rotation3d& Rotation() const { return m_rotation; }
 
+  /**
+   * Returns a Twist3d of the current transform (pose delta). If b is the output
+   * of {@code a.Log()}, then {@code b.Exp()} would yield a.
+   *
+   * @return The twist that maps the current transform.
+   */
+  constexpr Twist3d Log() const;
+
   /**
    * Invert the transformation. This is useful for undoing a transformation.
    *
@@ -188,6 +197,8 @@ class WPILIB_DLLEXPORT Transform3d {
 }  // namespace frc
 
 #include "frc/geometry/Pose3d.h"
+#include "frc/geometry/Twist3d.h"
+#include "frc/geometry/detail/RotationVectorToMatrix.h"
 
 namespace frc {
 
@@ -205,6 +216,59 @@ constexpr Transform3d Transform3d::operator+(const Transform3d& other) const {
   return Transform3d{Pose3d{}, Pose3d{}.TransformBy(*this).TransformBy(other)};
 }
 
+constexpr Twist3d Transform3d::Log() const {
+  // Implementation from Section 3.2 of https://ethaneade.org/lie.pdf
+
+  auto impl = [this]<typename Matrix3d, typename Vector3d>() -> Twist3d {
+    Vector3d u{{m_translation.X().value(), m_translation.Y().value(),
+                m_translation.Z().value()}};
+    Vector3d rvec = m_rotation.ToVector();
+    Matrix3d omega = detail::RotationVectorToMatrix(rvec);
+    Matrix3d omegaSq = omega * omega;
+    double theta = rvec.norm();
+    double thetaSq = theta * theta;
+
+    double C;
+    if (gcem::abs(theta) < 1E-7) {
+      // Taylor Expansions around θ = 0
+      // A = 1/1! - θ²/3! + θ⁴/5!
+      // B = 1/2! - θ²/4! + θ⁴/6!
+      // C = 1/6 * (1/2 + θ²/5! + θ⁴/7!)
+      // sources:
+      // A:
+      // https://www.wolframalpha.com/input?i2d=true&i=series+expansion+of+Divide%5Bsin%5C%2840%29x%5C%2841%29%2Cx%5D+at+x%3D0
+      // B:
+      // https://www.wolframalpha.com/input?i2d=true&i=series+expansion+of+Divide%5B1-cos%5C%2840%29x%5C%2841%29%2CPower%5Bx%2C2%5D%5D+at+x%3D0
+      // C:
+      // https://www.wolframalpha.com/input?i2d=true&i=series+expansion+of+Divide%5B1-Divide%5BDivide%5Bsin%5C%2840%29x%5C%2841%29%2Cx%5D%2C2Divide%5B1-cos%5C%2840%29x%5C%2841%29%2CPower%5Bx%2C2%5D%5D%5D%2CPower%5Bx%2C2%5D%5D+at+x%3D0
+      C = 1 / 12.0 + thetaSq / 720 + thetaSq * thetaSq / 30240;
+    } else {
+      // A = std::sin(θ)/θ
+      // B = (1 - std::cos(θ)) / θ²
+      // C = (1 - A/(2*B)) / θ²
+      double A = gcem::sin(theta) / theta;
+      double B = (1 - gcem::cos(theta)) / thetaSq;
+      C = (1 - A / (2 * B)) / thetaSq;
+    }
+
+    Matrix3d V_inv = Matrix3d::Identity() - 0.5 * omega + C * omegaSq;
+
+    Vector3d translation_component = V_inv * u;
+
+    return Twist3d{units::meter_t{translation_component(0)},
+                   units::meter_t{translation_component(1)},
+                   units::meter_t{translation_component(2)},
+                   units::radian_t{rvec(0)},
+                   units::radian_t{rvec(1)},
+                   units::radian_t{rvec(2)}};
+  };
+
+  if (std::is_constant_evaluated()) {
+    return impl.template operator()<ct_matrix3d, ct_vector3d>();
+  }
+  return impl.template operator()<Eigen::Matrix3d, Eigen::Vector3d>();
+}
+
 }  // namespace frc
 
 #include "frc/geometry/proto/Transform3dProto.h"
diff --git a/wpimath/src/main/native/include/frc/geometry/Twist2d.h b/wpimath/src/main/native/include/frc/geometry/Twist2d.h
index 40bef42e4e..043f334c2e 100644
--- a/wpimath/src/main/native/include/frc/geometry/Twist2d.h
+++ b/wpimath/src/main/native/include/frc/geometry/Twist2d.h
@@ -12,6 +12,8 @@
 
 namespace frc {
 
+class Transform2d;
+
 /**
  * A change in distance along a 2D arc since the last pose update. We can use
  * ideas from differential calculus to create new Pose2ds from a Twist2d and
@@ -35,6 +37,24 @@ struct WPILIB_DLLEXPORT Twist2d {
    */
   units::radian_t dtheta = 0_rad;
 
+  /**
+   * Obtain a new Transform2d from a (constant curvature) velocity.
+   *
+   * See "https://file.tavsys.net/control/controls-engineering-in-frc.pdf"
+   * Controls Engineering in the FIRST Robotics Competition</a> section 10.2
+   * "Pose exponential" for a derivation.
+   *
+   * The twist is a change in pose in the robot's coordinate frame since the
+   * previous pose update. When the user runs Exp() on the twist, the user will
+   * receive the pose delta.
+   *
+   * "Exp" represents the pose exponential, which is solving a differential
+   * equation moving the pose forward in time.
+   *
+   * @return The pose delta of the robot.
+   */
+  constexpr Transform2d Exp() const;
+
   /**
    * Checks equality between this Twist2d and another object.
    *
@@ -60,5 +80,29 @@ struct WPILIB_DLLEXPORT Twist2d {
 
 }  // namespace frc
 
+#include "frc/geometry/Transform2d.h"
+
+namespace frc {
+
+constexpr Transform2d Twist2d::Exp() const {
+  const auto theta = dtheta.value();
+  const auto sinTheta = gcem::sin(theta);
+  const auto cosTheta = gcem::cos(theta);
+
+  double s, c;
+  if (gcem::abs(theta) < 1E-9) {
+    s = 1.0 - 1.0 / 6.0 * theta * theta;
+    c = 0.5 * theta;
+  } else {
+    s = sinTheta / theta;
+    c = (1 - cosTheta) / theta;
+  }
+
+  return Transform2d(Translation2d{dx * s - dy * c, dx * c + dy * s},
+                     Rotation2d{cosTheta, sinTheta});
+}
+
+}  // namespace frc
+
 #include "frc/geometry/proto/Twist2dProto.h"
 #include "frc/geometry/struct/Twist2dStruct.h"
diff --git a/wpimath/src/main/native/include/frc/geometry/Twist3d.h b/wpimath/src/main/native/include/frc/geometry/Twist3d.h
index 57e6caa5e2..f7a21d51f5 100644
--- a/wpimath/src/main/native/include/frc/geometry/Twist3d.h
+++ b/wpimath/src/main/native/include/frc/geometry/Twist3d.h
@@ -12,6 +12,8 @@
 
 namespace frc {
 
+class Transform3d;
+
 /**
  * A change in distance along a 3D arc since the last pose update. We can use
  * ideas from differential calculus to create new Pose3ds from a Twist3d and
@@ -50,6 +52,24 @@ struct WPILIB_DLLEXPORT Twist3d {
    */
   units::radian_t rz = 0_rad;
 
+  /**
+   * Obtain a new Transform3d from a (constant curvature) velocity.
+   *
+   * See "https://file.tavsys.net/control/controls-engineering-in-frc.pdf"
+   * Controls Engineering in the FIRST Robotics Competition section 10.2
+   * "Pose exponential" for a derivation.
+   *
+   * The twist is a change in pose in the robot's coordinate frame since the
+   * previous pose update. When the user runs Exp() on the twist, the user will
+   * receive the pose delta.
+   *
+   * "Exp" represents the pose exponential, which is solving a differential
+   * equation moving the pose forward in time.
+   *
+   * @return The pose delta of the robot.
+   */
+  constexpr Transform3d Exp() const;
+
   /**
    * Checks equality between this Twist3d and another object.
    *
@@ -79,5 +99,70 @@ struct WPILIB_DLLEXPORT Twist3d {
 
 }  // namespace frc
 
+#include "frc/geometry/Transform3d.h"
+#include "frc/geometry/detail/RotationVectorToMatrix.h"
+
+namespace frc {
+
+constexpr Transform3d Twist3d::Exp() const {
+  // Implementation from Section 3.2 of https://ethaneade.org/lie.pdf
+
+  auto impl = [this]<typename Matrix3d, typename Vector3d>() -> Transform3d {
+    Vector3d u{{dx.value(), dy.value(), dz.value()}};
+    Vector3d rvec{{rx.value(), ry.value(), rz.value()}};
+    Matrix3d omega = detail::RotationVectorToMatrix(rvec);
+    Matrix3d omegaSq = omega * omega;
+    double theta = rvec.norm();
+    double thetaSq = theta * theta;
+
+    double A;
+    double B;
+    double C;
+    if (gcem::abs(theta) < 1E-7) {
+      // Taylor Expansions around θ = 0
+      // A = 1/1! - θ²/3! + θ⁴/5!
+      // B = 1/2! - θ²/4! + θ⁴/6!
+      // C = 1/3! - θ²/5! + θ⁴/7!
+      // sources:
+      // A:
+      // https://www.wolframalpha.com/input?i2d=true&i=series+expansion+of+Divide%5Bsin%5C%2840%29x%5C%2841%29%2Cx%5D+at+x%3D0
+      // B:
+      // https://www.wolframalpha.com/input?i2d=true&i=series+expansion+of+Divide%5B1-cos%5C%2840%29x%5C%2841%29%2CPower%5Bx%2C2%5D%5D+at+x%3D0
+      // C:
+      // https://www.wolframalpha.com/input?i2d=true&i=series+expansion+of+Divide%5B1-Divide%5Bsin%5C%2840%29x%5C%2841%29%2Cx%5D%2CPower%5Bx%2C2%5D%5D+at+x%3D0
+      A = 1 - thetaSq / 6 + thetaSq * thetaSq / 120;
+      B = 1 / 2.0 - thetaSq / 24 + thetaSq * thetaSq / 720;
+      C = 1 / 6.0 - thetaSq / 120 + thetaSq * thetaSq / 5040;
+    } else {
+      // A = std::sin(θ)/θ
+      // B = (1 - std::cos(θ)) / θ²
+      // C = (1 - A) / θ²
+      A = gcem::sin(theta) / theta;
+      B = (1 - gcem::cos(theta)) / thetaSq;
+      C = (1 - A) / thetaSq;
+    }
+
+    Matrix3d R = Matrix3d::Identity() + A * omega + B * omegaSq;
+    Matrix3d V = Matrix3d::Identity() + B * omega + C * omegaSq;
+
+    Vector3d translation_component = V * u;
+
+    const Transform3d transform{
+        Translation3d{units::meter_t{translation_component(0)},
+                      units::meter_t{translation_component(1)},
+                      units::meter_t{translation_component(2)}},
+        Rotation3d{R}};
+
+    return transform;
+  };
+
+  if (std::is_constant_evaluated()) {
+    return impl.template operator()<ct_matrix3d, ct_vector3d>();
+  }
+  return impl.template operator()<Eigen::Matrix3d, Eigen::Vector3d>();
+}
+
+}  // namespace frc
+
 #include "frc/geometry/proto/Twist3dProto.h"
 #include "frc/geometry/struct/Twist3dStruct.h"
diff --git a/wpimath/src/main/native/include/frc/geometry/detail/RotationVectorToMatrix.h b/wpimath/src/main/native/include/frc/geometry/detail/RotationVectorToMatrix.h
new file mode 100644
index 0000000000..7d81e0f7ce
--- /dev/null
+++ b/wpimath/src/main/native/include/frc/geometry/detail/RotationVectorToMatrix.h
@@ -0,0 +1,26 @@
+// Copyright (c) FIRST and other WPILib contributors.
+// Open Source Software; you can modify and/or share it under the terms of
+// the WPILib BSD license file in the root directory of this project.
+
+#pragma once
+
+#include <Eigen/Core>
+
+#include "frc/ct_matrix.h"
+
+namespace frc::detail {
+
+constexpr ct_matrix3d RotationVectorToMatrix(const ct_vector3d& rotation) {
+  return ct_matrix3d{{0.0, -rotation(2), rotation(1)},
+                     {rotation(2), 0.0, -rotation(0)},
+                     {-rotation(1), rotation(0), 0.0}};
+}
+
+constexpr Eigen::Matrix3d RotationVectorToMatrix(
+    const Eigen::Vector3d& rotation) {
+  return Eigen::Matrix3d{{0.0, -rotation(2), rotation(1)},
+                         {rotation(2), 0.0, -rotation(0)},
+                         {-rotation(1), rotation(0), 0.0}};
+}
+
+}  // namespace frc::detail
diff --git a/wpimath/src/main/native/include/frc/interpolation/TimeInterpolatableBuffer.h b/wpimath/src/main/native/include/frc/interpolation/TimeInterpolatableBuffer.h
index 47bcc46b14..74824c2620 100644
--- a/wpimath/src/main/native/include/frc/interpolation/TimeInterpolatableBuffer.h
+++ b/wpimath/src/main/native/include/frc/interpolation/TimeInterpolatableBuffer.h
@@ -166,9 +166,9 @@ inline TimeInterpolatableBuffer<Pose2d>::TimeInterpolatableBuffer(
         } else if (t >= 1) {
           return end;
         } else {
-          Twist2d twist = start.Log(end);
+          Twist2d twist = (end - start).Log();
           Twist2d scaledTwist = twist * t;
-          return start.Exp(scaledTwist);
+          return start + scaledTwist.Exp();
         }
       }) {}
 
diff --git a/wpimath/src/main/native/include/frc/kinematics/ChassisSpeeds.h b/wpimath/src/main/native/include/frc/kinematics/ChassisSpeeds.h
index 9b520dff6e..b35e70a545 100644
--- a/wpimath/src/main/native/include/frc/kinematics/ChassisSpeeds.h
+++ b/wpimath/src/main/native/include/frc/kinematics/ChassisSpeeds.h
@@ -71,11 +71,11 @@ struct WPILIB_DLLEXPORT ChassisSpeeds {
   constexpr ChassisSpeeds Discretize(units::second_t dt) const {
     // Construct the desired pose after a timestep, relative to the current
     // pose. The desired pose has decoupled translation and rotation.
-    Pose2d desiredDeltaPose{vx * dt, vy * dt, omega * dt};
+    Transform2d desiredTransform{vx * dt, vy * dt, omega * dt};
 
     // Find the chassis translation/rotation deltas in the robot frame that move
     // the robot from its current pose to the desired pose
-    auto twist = Pose2d{}.Log(desiredDeltaPose);
+    auto twist = desiredTransform.Log();
 
     // Turn the chassis translation/rotation deltas into average velocities
     return {twist.dx / dt, twist.dy / dt, twist.dtheta / dt};
diff --git a/wpimath/src/main/native/include/frc/kinematics/Odometry.h b/wpimath/src/main/native/include/frc/kinematics/Odometry.h
index c73eed2248..6ac4f1c958 100644
--- a/wpimath/src/main/native/include/frc/kinematics/Odometry.h
+++ b/wpimath/src/main/native/include/frc/kinematics/Odometry.h
@@ -122,7 +122,7 @@ class WPILIB_DLLEXPORT Odometry {
         m_kinematics.ToTwist2d(m_previousWheelPositions, wheelPositions);
     twist.dtheta = (angle - m_previousAngle).Radians();
 
-    auto newPose = m_pose.Exp(twist);
+    auto newPose = m_pose + twist.Exp();
 
     m_previousAngle = angle;
     m_previousWheelPositions = wheelPositions;
diff --git a/wpimath/src/main/native/include/frc/kinematics/Odometry3d.h b/wpimath/src/main/native/include/frc/kinematics/Odometry3d.h
index f24d6f86f6..0c4b819bc0 100644
--- a/wpimath/src/main/native/include/frc/kinematics/Odometry3d.h
+++ b/wpimath/src/main/native/include/frc/kinematics/Odometry3d.h
@@ -131,7 +131,7 @@ class WPILIB_DLLEXPORT Odometry3d {
                   units::radian_t{angle_difference(1)},
                   units::radian_t{angle_difference(2)}};
 
-    auto newPose = m_pose.Exp(twist);
+    auto newPose = m_pose + twist.Exp();
 
     m_previousWheelPositions = wheelPositions;
     m_previousAngle = angle;
diff --git a/wpimath/src/main/native/include/frc/spline/SplineParameterizer.h b/wpimath/src/main/native/include/frc/spline/SplineParameterizer.h
index 46bfc7148f..cbcd9de13f 100644
--- a/wpimath/src/main/native/include/frc/spline/SplineParameterizer.h
+++ b/wpimath/src/main/native/include/frc/spline/SplineParameterizer.h
@@ -106,7 +106,7 @@ class WPILIB_DLLEXPORT SplineParameterizer {
         throw MalformedSplineException(kMalformedSplineExceptionMsg);
       }
 
-      const auto twist = start.value().first.Log(end.value().first);
+      const auto twist = (end.value().first - start.value().first).Log();
 
       if (units::math::abs(twist.dy) > kMaxDy ||
           units::math::abs(twist.dx) > kMaxDx ||
diff --git a/wpimath/src/test/java/edu/wpi/first/math/controller/LTVUnicycleControllerTest.java b/wpimath/src/test/java/edu/wpi/first/math/controller/LTVUnicycleControllerTest.java
index b75dcbd514..a52dc96e75 100644
--- a/wpimath/src/test/java/edu/wpi/first/math/controller/LTVUnicycleControllerTest.java
+++ b/wpimath/src/test/java/edu/wpi/first/math/controller/LTVUnicycleControllerTest.java
@@ -41,7 +41,7 @@ class LTVUnicycleControllerTest {
       var state = trajectory.sample(kDt * i);
 
       var output = controller.calculate(robotPose, state);
-      robotPose = robotPose.exp(new Twist2d(output.vx * kDt, 0, output.omega * kDt));
+      robotPose = robotPose.plus(new Twist2d(output.vx * kDt, 0, output.omega * kDt).exp());
     }
 
     final var states = trajectory.getStates();
diff --git a/wpimath/src/test/java/edu/wpi/first/math/geometry/Pose3dTest.java b/wpimath/src/test/java/edu/wpi/first/math/geometry/Pose3dTest.java
index 583e125fc0..71e61ca6c5 100644
--- a/wpimath/src/test/java/edu/wpi/first/math/geometry/Pose3dTest.java
+++ b/wpimath/src/test/java/edu/wpi/first/math/geometry/Pose3dTest.java
@@ -257,8 +257,8 @@ class Pose3dTest {
       var start = initial_poses.get(i);
       var end = final_poses.get(i);
 
-      var twist = start.log(end);
-      var start_exp = start.exp(twist);
+      var twist = end.minus(start).log();
+      var start_exp = start.plus(twist.exp());
 
       assertAll(
           () -> assertEquals(start_exp.getX(), end.getX(), eps),
@@ -314,7 +314,7 @@ class Pose3dTest {
       var start = initial_poses.get(i);
       var end = final_poses.get(i);
 
-      var twist = start.log(end);
+      var twist = end.minus(start).log();
       assertAll(
           () -> assertFalse(((Double) twist.dx).isNaN()),
           () -> assertFalse(((Double) twist.dy).isNaN()),
diff --git a/wpimath/src/test/java/edu/wpi/first/math/geometry/Twist2dTest.java b/wpimath/src/test/java/edu/wpi/first/math/geometry/Twist2dTest.java
index 22d8f33e8f..4c8a7c3a11 100644
--- a/wpimath/src/test/java/edu/wpi/first/math/geometry/Twist2dTest.java
+++ b/wpimath/src/test/java/edu/wpi/first/math/geometry/Twist2dTest.java
@@ -13,27 +13,27 @@ class Twist2dTest {
   @Test
   void testStraight() {
     var straight = new Twist2d(5.0, 0.0, 0.0);
-    var straightPose = Pose2d.kZero.exp(straight);
+    var straightPose = straight.exp();
 
-    var expected = new Pose2d(5.0, 0.0, Rotation2d.kZero);
+    var expected = new Transform2d(5.0, 0.0, Rotation2d.kZero);
     assertEquals(expected, straightPose);
   }
 
   @Test
   void testQuarterCircle() {
     var quarterCircle = new Twist2d(5.0 / 2.0 * Math.PI, 0, Math.PI / 2.0);
-    var quarterCirclePose = Pose2d.kZero.exp(quarterCircle);
+    var quarterCirclePose = quarterCircle.exp();
 
-    var expected = new Pose2d(5.0, 5.0, Rotation2d.kCCW_Pi_2);
+    var expected = new Transform2d(5.0, 5.0, Rotation2d.kCCW_Pi_2);
     assertEquals(expected, quarterCirclePose);
   }
 
   @Test
   void testDiagonalNoDtheta() {
     var diagonal = new Twist2d(2.0, 2.0, 0.0);
-    var diagonalPose = Pose2d.kZero.exp(diagonal);
+    var diagonalPose = diagonal.exp();
 
-    var expected = new Pose2d(2.0, 2.0, Rotation2d.kZero);
+    var expected = new Transform2d(2.0, 2.0, Rotation2d.kZero);
     assertEquals(expected, diagonalPose);
   }
 
@@ -56,13 +56,13 @@ class Twist2dTest {
     final var start = Pose2d.kZero;
     final var end = new Pose2d(5.0, 5.0, Rotation2d.kCCW_Pi_2);
 
-    final var twist = start.log(end);
+    final var twist = end.minus(start).log();
 
     var expected = new Twist2d(5.0 / 2.0 * Math.PI, 0.0, Math.PI / 2.0);
     assertEquals(expected, twist);
 
     // Make sure computed twist gives back original end pose
-    final var reapplied = start.exp(twist);
+    final var reapplied = start.plus(twist.exp());
     assertEquals(end, reapplied);
   }
 }
diff --git a/wpimath/src/test/java/edu/wpi/first/math/geometry/Twist3dTest.java b/wpimath/src/test/java/edu/wpi/first/math/geometry/Twist3dTest.java
index 03ac6100dc..016205873f 100644
--- a/wpimath/src/test/java/edu/wpi/first/math/geometry/Twist3dTest.java
+++ b/wpimath/src/test/java/edu/wpi/first/math/geometry/Twist3dTest.java
@@ -15,27 +15,27 @@ class Twist3dTest {
   @Test
   void testStraightX() {
     var straight = new Twist3d(5.0, 0.0, 0.0, 0.0, 0.0, 0.0);
-    var straightPose = Pose3d.kZero.exp(straight);
+    var straightPose = straight.exp();
 
-    var expected = new Pose3d(5.0, 0.0, 0.0, Rotation3d.kZero);
+    var expected = new Transform3d(5.0, 0.0, 0.0, Rotation3d.kZero);
     assertEquals(expected, straightPose);
   }
 
   @Test
   void testStraightY() {
     var straight = new Twist3d(0.0, 5.0, 0.0, 0.0, 0.0, 0.0);
-    var straightPose = Pose3d.kZero.exp(straight);
+    var straightPose = straight.exp();
 
-    var expected = new Pose3d(0.0, 5.0, 0.0, Rotation3d.kZero);
+    var expected = new Transform3d(0.0, 5.0, 0.0, Rotation3d.kZero);
     assertEquals(expected, straightPose);
   }
 
   @Test
   void testStraightZ() {
     var straight = new Twist3d(0.0, 0.0, 5.0, 0.0, 0.0, 0.0);
-    var straightPose = Pose3d.kZero.exp(straight);
+    var straightPose = straight.exp();
 
-    var expected = new Pose3d(0.0, 0.0, 5.0, Rotation3d.kZero);
+    var expected = new Transform3d(0.0, 0.0, 5.0, Rotation3d.kZero);
     assertEquals(expected, straightPose);
   }
 
@@ -44,18 +44,19 @@ class Twist3dTest {
     var zAxis = VecBuilder.fill(0.0, 0.0, 1.0);
 
     var quarterCircle = new Twist3d(5.0 / 2.0 * Math.PI, 0.0, 0.0, 0.0, 0.0, Math.PI / 2.0);
-    var quarterCirclePose = Pose3d.kZero.exp(quarterCircle);
+    var quarterCirclePose = quarterCircle.exp();
 
-    var expected = new Pose3d(5.0, 5.0, 0.0, new Rotation3d(zAxis, Units.degreesToRadians(90.0)));
+    var expected =
+        new Transform3d(5.0, 5.0, 0.0, new Rotation3d(zAxis, Units.degreesToRadians(90.0)));
     assertEquals(expected, quarterCirclePose);
   }
 
   @Test
   void testDiagonalNoDtheta() {
     var diagonal = new Twist3d(2.0, 2.0, 0.0, 0.0, 0.0, 0.0);
-    var diagonalPose = Pose3d.kZero.exp(diagonal);
+    var diagonalPose = diagonal.exp();
 
-    var expected = new Pose3d(2.0, 2.0, 0.0, Rotation3d.kZero);
+    var expected = new Transform3d(2.0, 2.0, 0.0, Rotation3d.kZero);
     assertEquals(expected, diagonalPose);
   }
 
@@ -79,14 +80,14 @@ class Twist3dTest {
     final var end =
         new Pose3d(0.0, 5.0, 5.0, new Rotation3d(Units.degreesToRadians(90.0), 0.0, 0.0));
 
-    final var twist = start.log(end);
+    final var twist = end.minus(start).log();
 
     var expected =
         new Twist3d(0.0, 5.0 / 2.0 * Math.PI, 0.0, Units.degreesToRadians(90.0), 0.0, 0.0);
     assertEquals(expected, twist);
 
     // Make sure computed twist gives back original end pose
-    final var reapplied = start.exp(twist);
+    final var reapplied = start.plus(twist.exp());
     assertEquals(end, reapplied);
   }
 
@@ -96,13 +97,13 @@ class Twist3dTest {
     final var end =
         new Pose3d(5.0, 0.0, 5.0, new Rotation3d(0.0, Units.degreesToRadians(90.0), 0.0));
 
-    final var twist = start.log(end);
+    final var twist = end.minus(start).log();
 
     var expected = new Twist3d(0.0, 0.0, 5.0 / 2.0 * Math.PI, 0.0, Math.PI / 2.0, 0.0);
     assertEquals(expected, twist);
 
     // Make sure computed twist gives back original end pose
-    final var reapplied = start.exp(twist);
+    final var reapplied = start.plus(twist.exp());
     assertEquals(end, reapplied);
   }
 
@@ -112,13 +113,13 @@ class Twist3dTest {
     final var end =
         new Pose3d(5.0, 5.0, 0.0, new Rotation3d(0.0, 0.0, Units.degreesToRadians(90.0)));
 
-    final var twist = start.log(end);
+    final var twist = end.minus(start).log();
 
     var expected = new Twist3d(5.0 / 2.0 * Math.PI, 0.0, 0.0, 0.0, 0.0, Math.PI / 2.0);
     assertEquals(expected, twist);
 
     // Make sure computed twist gives back original end pose
-    final var reapplied = start.exp(twist);
+    final var reapplied = start.plus(twist.exp());
     assertEquals(end, reapplied);
   }
 }
diff --git a/wpimath/src/test/java/edu/wpi/first/math/jni/Transform3dJNITest.java b/wpimath/src/test/java/edu/wpi/first/math/jni/Transform3dJNITest.java
new file mode 100644
index 0000000000..0c4cad7e4a
--- /dev/null
+++ b/wpimath/src/test/java/edu/wpi/first/math/jni/Transform3dJNITest.java
@@ -0,0 +1,16 @@
+// Copyright (c) FIRST and other WPILib contributors.
+// Open Source Software; you can modify and/or share it under the terms of
+// the WPILib BSD license file in the root directory of this project.
+
+package edu.wpi.first.math.jni;
+
+import static org.junit.jupiter.api.Assertions.assertDoesNotThrow;
+
+import org.junit.jupiter.api.Test;
+
+public class Transform3dJNITest {
+  @Test
+  public void testLink() {
+    assertDoesNotThrow(Transform3dJNI::forceLoad);
+  }
+}
diff --git a/wpimath/src/test/java/edu/wpi/first/math/jni/Pose3dJNITest.java b/wpimath/src/test/java/edu/wpi/first/math/jni/Twist3dJNITest.java
similarity index 83%
rename from wpimath/src/test/java/edu/wpi/first/math/jni/Pose3dJNITest.java
rename to wpimath/src/test/java/edu/wpi/first/math/jni/Twist3dJNITest.java
index d7f90a98e2..391f11f2b4 100644
--- a/wpimath/src/test/java/edu/wpi/first/math/jni/Pose3dJNITest.java
+++ b/wpimath/src/test/java/edu/wpi/first/math/jni/Twist3dJNITest.java
@@ -8,9 +8,9 @@ import static org.junit.jupiter.api.Assertions.assertDoesNotThrow;
 
 import org.junit.jupiter.api.Test;
 
-public class Pose3dJNITest {
+public class Twist3dJNITest {
   @Test
   public void testLink() {
-    assertDoesNotThrow(Pose3dJNI::forceLoad);
+    assertDoesNotThrow(Twist3dJNI::forceLoad);
   }
 }
diff --git a/wpimath/src/test/java/edu/wpi/first/math/kinematics/ChassisSpeedsTest.java b/wpimath/src/test/java/edu/wpi/first/math/kinematics/ChassisSpeedsTest.java
index 38ac1ce249..1101da623d 100644
--- a/wpimath/src/test/java/edu/wpi/first/math/kinematics/ChassisSpeedsTest.java
+++ b/wpimath/src/test/java/edu/wpi/first/math/kinematics/ChassisSpeedsTest.java
@@ -28,7 +28,7 @@ class ChassisSpeedsTest {
 
     var pose = Pose2d.kZero;
     for (double time = 0; time < duration; time += dt) {
-      pose = pose.exp(twist);
+      pose = pose.plus(twist.exp());
     }
 
     final var result = pose; // For lambda capture
diff --git a/wpimath/src/test/java/edu/wpi/first/math/spline/CubicHermiteSplineTest.java b/wpimath/src/test/java/edu/wpi/first/math/spline/CubicHermiteSplineTest.java
index f613abcc6c..e0d7ca3b60 100644
--- a/wpimath/src/test/java/edu/wpi/first/math/spline/CubicHermiteSplineTest.java
+++ b/wpimath/src/test/java/edu/wpi/first/math/spline/CubicHermiteSplineTest.java
@@ -53,7 +53,7 @@ class CubicHermiteSplineTest {
       var p1 = poses.get(i + 1);
 
       // Make sure the twist is under the tolerance defined by the Spline class.
-      var twist = p0.pose.log(p1.pose);
+      var twist = p1.pose.minus(p0.pose).log();
       assertAll(
           () -> assertTrue(Math.abs(twist.dx) < kMaxDx),
           () -> assertTrue(Math.abs(twist.dy) < kMaxDy),
@@ -62,11 +62,13 @@ class CubicHermiteSplineTest {
 
     // Check first point
     assertAll(
-        () -> assertEquals(a.getX(), poses.get(0).pose.getX(), 1E-9),
-        () -> assertEquals(a.getY(), poses.get(0).pose.getY(), 1E-9),
+        () -> assertEquals(a.getX(), poses.getFirst().pose.getX(), 1E-9),
+        () -> assertEquals(a.getY(), poses.getFirst().pose.getY(), 1E-9),
         () ->
             assertEquals(
-                a.getRotation().getRadians(), poses.get(0).pose.getRotation().getRadians(), 1E-9));
+                a.getRotation().getRadians(),
+                poses.getFirst().pose.getRotation().getRadians(),
+                1E-9));
 
     // Check interior waypoints
     boolean interiorsGood = true;
@@ -84,12 +86,12 @@ class CubicHermiteSplineTest {
 
     // Check last point
     assertAll(
-        () -> assertEquals(b.getX(), poses.get(poses.size() - 1).pose.getX(), 1E-9),
-        () -> assertEquals(b.getY(), poses.get(poses.size() - 1).pose.getY(), 1E-9),
+        () -> assertEquals(b.getX(), poses.getLast().pose.getX(), 1E-9),
+        () -> assertEquals(b.getY(), poses.getLast().pose.getY(), 1E-9),
         () ->
             assertEquals(
                 b.getRotation().getRadians(),
-                poses.get(poses.size() - 1).pose.getRotation().getRadians(),
+                poses.getLast().pose.getRotation().getRadians(),
                 1E-9));
   }
 
diff --git a/wpimath/src/test/java/edu/wpi/first/math/spline/QuinticHermiteSplineTest.java b/wpimath/src/test/java/edu/wpi/first/math/spline/QuinticHermiteSplineTest.java
index de8835f20e..d5c0559224 100644
--- a/wpimath/src/test/java/edu/wpi/first/math/spline/QuinticHermiteSplineTest.java
+++ b/wpimath/src/test/java/edu/wpi/first/math/spline/QuinticHermiteSplineTest.java
@@ -39,7 +39,7 @@ class QuinticHermiteSplineTest {
       var p1 = poses.get(i + 1);
 
       // Make sure the twist is under the tolerance defined by the Spline class.
-      var twist = p0.pose.log(p1.pose);
+      var twist = p1.pose.minus(p0.pose).log();
       assertAll(
           () -> assertTrue(Math.abs(twist.dx) < kMaxDx),
           () -> assertTrue(Math.abs(twist.dy) < kMaxDy),
@@ -48,20 +48,22 @@ class QuinticHermiteSplineTest {
 
     // Check first point
     assertAll(
-        () -> assertEquals(a.getX(), poses.get(0).pose.getX(), 1E-9),
-        () -> assertEquals(a.getY(), poses.get(0).pose.getY(), 1E-9),
+        () -> assertEquals(a.getX(), poses.getFirst().pose.getX(), 1E-9),
+        () -> assertEquals(a.getY(), poses.getFirst().pose.getY(), 1E-9),
         () ->
             assertEquals(
-                a.getRotation().getRadians(), poses.get(0).pose.getRotation().getRadians(), 1E-9));
+                a.getRotation().getRadians(),
+                poses.getFirst().pose.getRotation().getRadians(),
+                1E-9));
 
     // Check last point
     assertAll(
-        () -> assertEquals(b.getX(), poses.get(poses.size() - 1).pose.getX(), 1E-9),
-        () -> assertEquals(b.getY(), poses.get(poses.size() - 1).pose.getY(), 1E-9),
+        () -> assertEquals(b.getX(), poses.getLast().pose.getX(), 1E-9),
+        () -> assertEquals(b.getY(), poses.getLast().pose.getY(), 1E-9),
         () ->
             assertEquals(
                 b.getRotation().getRadians(),
-                poses.get(poses.size() - 1).pose.getRotation().getRadians(),
+                poses.getLast().pose.getRotation().getRadians(),
                 1E-9));
   }
 
diff --git a/wpimath/src/test/native/cpp/controller/LTVUnicycleControllerTest.cpp b/wpimath/src/test/native/cpp/controller/LTVUnicycleControllerTest.cpp
index 93b4e74c42..bb7914dc51 100644
--- a/wpimath/src/test/native/cpp/controller/LTVUnicycleControllerTest.cpp
+++ b/wpimath/src/test/native/cpp/controller/LTVUnicycleControllerTest.cpp
@@ -33,7 +33,7 @@ TEST(LTVUnicycleControllerTest, ReachesReference) {
     auto [vx, vy, omega] = controller.Calculate(robotPose, state);
     static_cast<void>(vy);
 
-    robotPose = robotPose.Exp(frc::Twist2d{vx * kDt, 0_m, omega * kDt});
+    robotPose = robotPose + frc::Twist2d{vx * kDt, 0_m, omega * kDt}.Exp();
   }
 
   auto& endPose = trajectory.States().back().pose;
diff --git a/wpimath/src/test/native/cpp/geometry/Pose3dTest.cpp b/wpimath/src/test/native/cpp/geometry/Pose3dTest.cpp
index 7a84718ea1..045870c792 100644
--- a/wpimath/src/test/native/cpp/geometry/Pose3dTest.cpp
+++ b/wpimath/src/test/native/cpp/geometry/Pose3dTest.cpp
@@ -170,8 +170,8 @@ TEST(Pose3dTest, ComplexTwists) {
     auto start = initial_poses[i];
     auto end = final_poses[i];
 
-    auto twist = start.Log(end);
-    auto start_exp = start.Exp(twist);
+    auto twist = (end - start).Log();
+    auto start_exp = start + twist.Exp();
 
     auto eps = 1E-5;
 
@@ -211,7 +211,7 @@ TEST(Pose3dTest, TwistNaN) {
   for (size_t i = 0; i < initial_poses.size(); i++) {
     auto start = initial_poses[i];
     auto end = final_poses[i];
-    auto twist = start.Log(end);
+    auto twist = (end - start).Log();
 
     EXPECT_FALSE(std::isnan(twist.dx.value()));
     EXPECT_FALSE(std::isnan(twist.dy.value()));
diff --git a/wpimath/src/test/native/cpp/geometry/Twist2dTest.cpp b/wpimath/src/test/native/cpp/geometry/Twist2dTest.cpp
index 7f121c0b1e..d4a03b7a8e 100644
--- a/wpimath/src/test/native/cpp/geometry/Twist2dTest.cpp
+++ b/wpimath/src/test/native/cpp/geometry/Twist2dTest.cpp
@@ -13,7 +13,7 @@ using namespace frc;
 
 TEST(Twist2dTest, Straight) {
   const Twist2d straight{5_m, 0_m, 0_rad};
-  const auto straightPose = Pose2d{}.Exp(straight);
+  const auto straightPose = straight.Exp();
 
   EXPECT_DOUBLE_EQ(5.0, straightPose.X().value());
   EXPECT_DOUBLE_EQ(0.0, straightPose.Y().value());
@@ -23,7 +23,7 @@ TEST(Twist2dTest, Straight) {
 TEST(Twist2dTest, QuarterCircle) {
   const Twist2d quarterCircle{5_m / 2.0 * std::numbers::pi, 0_m,
                               units::radian_t{std::numbers::pi / 2.0}};
-  const auto quarterCirclePose = Pose2d{}.Exp(quarterCircle);
+  const auto quarterCirclePose = quarterCircle.Exp();
 
   EXPECT_DOUBLE_EQ(5.0, quarterCirclePose.X().value());
   EXPECT_DOUBLE_EQ(5.0, quarterCirclePose.Y().value());
@@ -32,7 +32,7 @@ TEST(Twist2dTest, QuarterCircle) {
 
 TEST(Twist2dTest, DiagonalNoDtheta) {
   const Twist2d diagonal{2_m, 2_m, 0_deg};
-  const auto diagonalPose = Pose2d{}.Exp(diagonal);
+  const auto diagonalPose = diagonal.Exp();
 
   EXPECT_DOUBLE_EQ(2.0, diagonalPose.X().value());
   EXPECT_DOUBLE_EQ(2.0, diagonalPose.Y().value());
@@ -55,14 +55,14 @@ TEST(Twist2dTest, Pose2dLog) {
   const Pose2d end{5_m, 5_m, 90_deg};
   const Pose2d start;
 
-  const auto twist = start.Log(end);
+  const auto twist = (end - start).Log();
 
   Twist2d expected{units::meter_t{5.0 / 2.0 * std::numbers::pi}, 0_m,
                    units::radian_t{std::numbers::pi / 2.0}};
   EXPECT_EQ(expected, twist);
 
   // Make sure computed twist gives back original end pose
-  const auto reapplied = start.Exp(twist);
+  const auto reapplied = start + twist.Exp();
   EXPECT_EQ(end, reapplied);
 }
 
diff --git a/wpimath/src/test/native/cpp/geometry/Twist3dTest.cpp b/wpimath/src/test/native/cpp/geometry/Twist3dTest.cpp
index 245ec17517..ddf429a8fe 100644
--- a/wpimath/src/test/native/cpp/geometry/Twist3dTest.cpp
+++ b/wpimath/src/test/native/cpp/geometry/Twist3dTest.cpp
@@ -13,25 +13,25 @@ using namespace frc;
 
 TEST(Twist3dTest, StraightX) {
   const Twist3d straight{5_m, 0_m, 0_m, 0_rad, 0_rad, 0_rad};
-  const auto straightPose = Pose3d{}.Exp(straight);
+  const auto straightPose = straight.Exp();
 
-  Pose3d expected{5_m, 0_m, 0_m, Rotation3d{}};
+  Transform3d expected{5_m, 0_m, 0_m, Rotation3d{}};
   EXPECT_EQ(expected, straightPose);
 }
 
 TEST(Twist3dTest, StraightY) {
   const Twist3d straight{0_m, 5_m, 0_m, 0_rad, 0_rad, 0_rad};
-  const auto straightPose = Pose3d{}.Exp(straight);
+  const auto straightPose = straight.Exp();
 
-  Pose3d expected{0_m, 5_m, 0_m, Rotation3d{}};
+  Transform3d expected{0_m, 5_m, 0_m, Rotation3d{}};
   EXPECT_EQ(expected, straightPose);
 }
 
 TEST(Twist3dTest, StraightZ) {
   const Twist3d straight{0_m, 0_m, 5_m, 0_rad, 0_rad, 0_rad};
-  const auto straightPose = Pose3d{}.Exp(straight);
+  const auto straightPose = straight.Exp();
 
-  Pose3d expected{0_m, 0_m, 5_m, Rotation3d{}};
+  Transform3d expected{0_m, 0_m, 5_m, Rotation3d{}};
   EXPECT_EQ(expected, straightPose);
 }
 
@@ -41,17 +41,17 @@ TEST(Twist3dTest, QuarterCircle) {
   const Twist3d quarterCircle{
       5_m / 2.0 * std::numbers::pi,           0_m, 0_m, 0_rad, 0_rad,
       units::radian_t{std::numbers::pi / 2.0}};
-  const auto quarterCirclePose = Pose3d{}.Exp(quarterCircle);
+  const auto quarterCirclePose = quarterCircle.Exp();
 
-  Pose3d expected{5_m, 5_m, 0_m, Rotation3d{zAxis, 90_deg}};
+  Transform3d expected{5_m, 5_m, 0_m, Rotation3d{zAxis, 90_deg}};
   EXPECT_EQ(expected, quarterCirclePose);
 }
 
 TEST(Twist3dTest, DiagonalNoDtheta) {
   const Twist3d diagonal{2_m, 2_m, 0_m, 0_rad, 0_rad, 0_rad};
-  const auto diagonalPose = Pose3d{}.Exp(diagonal);
+  const auto diagonalPose = diagonal.Exp();
 
-  Pose3d expected{2_m, 2_m, 0_m, Rotation3d{}};
+  Transform3d expected{2_m, 2_m, 0_m, Rotation3d{}};
   EXPECT_EQ(expected, diagonalPose);
 }
 
@@ -71,7 +71,7 @@ TEST(Twist3dTest, Pose3dLogX) {
   const Pose3d end{0_m, 5_m, 5_m, Rotation3d{90_deg, 0_deg, 0_deg}};
   const Pose3d start;
 
-  const auto twist = start.Log(end);
+  const auto twist = (end - start).Log();
 
   Twist3d expected{0_m,   units::meter_t{5.0 / 2.0 * std::numbers::pi},
                    0_m,   90_deg,
@@ -79,7 +79,7 @@ TEST(Twist3dTest, Pose3dLogX) {
   EXPECT_EQ(expected, twist);
 
   // Make sure computed twist gives back original end pose
-  const auto reapplied = start.Exp(twist);
+  const auto reapplied = start + twist.Exp();
   EXPECT_EQ(end, reapplied);
 }
 
@@ -87,14 +87,14 @@ TEST(Twist3dTest, Pose3dLogY) {
   const Pose3d end{5_m, 0_m, 5_m, Rotation3d{0_deg, 90_deg, 0_deg}};
   const Pose3d start;
 
-  const auto twist = start.Log(end);
+  const auto twist = (end - start).Log();
 
   Twist3d expected{0_m,   0_m,    units::meter_t{5.0 / 2.0 * std::numbers::pi},
                    0_deg, 90_deg, 0_deg};
   EXPECT_EQ(expected, twist);
 
   // Make sure computed twist gives back original end pose
-  const auto reapplied = start.Exp(twist);
+  const auto reapplied = start + twist.Exp();
   EXPECT_EQ(end, reapplied);
 }
 
@@ -102,7 +102,7 @@ TEST(Twist3dTest, Pose3dLogZ) {
   const Pose3d end{5_m, 5_m, 0_m, Rotation3d{0_deg, 0_deg, 90_deg}};
   const Pose3d start;
 
-  const auto twist = start.Log(end);
+  const auto twist = (end - start).Log();
 
   Twist3d expected{units::meter_t{5.0 / 2.0 * std::numbers::pi},
                    0_m,
@@ -113,7 +113,7 @@ TEST(Twist3dTest, Pose3dLogZ) {
   EXPECT_EQ(expected, twist);
 
   // Make sure computed twist gives back original end pose
-  const auto reapplied = start.Exp(twist);
+  const auto reapplied = start + twist.Exp();
   EXPECT_EQ(end, reapplied);
 }
 
diff --git a/wpimath/src/test/native/cpp/kinematics/ChassisSpeedsTest.cpp b/wpimath/src/test/native/cpp/kinematics/ChassisSpeedsTest.cpp
index 993ae40654..60c76aca54 100644
--- a/wpimath/src/test/native/cpp/kinematics/ChassisSpeedsTest.cpp
+++ b/wpimath/src/test/native/cpp/kinematics/ChassisSpeedsTest.cpp
@@ -20,7 +20,7 @@ TEST(ChassisSpeedsTest, Discretize) {
 
   frc::Pose2d pose;
   for (units::second_t time = 0_s; time < duration; time += dt) {
-    pose = pose.Exp(twist);
+    pose = pose + twist.Exp();
   }
 
   EXPECT_NEAR((target.vx * duration).value(), pose.X().value(), kEpsilon);
diff --git a/wpimath/src/test/native/cpp/spline/CubicHermiteSplineTest.cpp b/wpimath/src/test/native/cpp/spline/CubicHermiteSplineTest.cpp
index d16444cd67..744680bd03 100644
--- a/wpimath/src/test/native/cpp/spline/CubicHermiteSplineTest.cpp
+++ b/wpimath/src/test/native/cpp/spline/CubicHermiteSplineTest.cpp
@@ -42,7 +42,7 @@ class CubicHermiteSplineTest : public ::testing::Test {
       auto& p1 = poses[i + 1];
 
       // Make sure the twist is under the tolerance defined by the Spline class.
-      auto twist = p0.first.Log(p1.first);
+      auto twist = (p1.first - p0.first).Log();
       EXPECT_LT(std::abs(twist.dx.value()),
                 SplineParameterizer::kMaxDx.value());
       EXPECT_LT(std::abs(twist.dy.value()),
diff --git a/wpimath/src/test/native/cpp/spline/QuinticHermiteSplineTest.cpp b/wpimath/src/test/native/cpp/spline/QuinticHermiteSplineTest.cpp
index 5f80f3ad51..8a6d2653ef 100644
--- a/wpimath/src/test/native/cpp/spline/QuinticHermiteSplineTest.cpp
+++ b/wpimath/src/test/native/cpp/spline/QuinticHermiteSplineTest.cpp
@@ -29,7 +29,7 @@ class QuinticHermiteSplineTest : public ::testing::Test {
       auto& p1 = poses[i + 1];
 
       // Make sure the twist is under the tolerance defined by the Spline class.
-      auto twist = p0.first.Log(p1.first);
+      auto twist = (p1.first - p0.first).Log();
       EXPECT_LT(std::abs(twist.dx.value()),
                 SplineParameterizer::kMaxDx.value());
       EXPECT_LT(std::abs(twist.dy.value()),