diff --git a/src/main/java/pythagoras/d/AbstractTransform.java b/src/main/java/pythagoras/d/AbstractTransform.java
index 7851473..8a70678 100644
--- a/src/main/java/pythagoras/d/AbstractTransform.java
+++ b/src/main/java/pythagoras/d/AbstractTransform.java
@@ -97,6 +97,23 @@ public abstract class AbstractTransform implements Transform
         throw new UnsupportedOperationException();
     }
 
+    @Override // from Transform
+    public Transform shear (double sx, double sy) {
+        shearX(sx);
+        shearY(sy);
+        return this;
+    }
+
+    @Override // from Transform
+    public Transform shearX (double sx) {
+        throw new UnsupportedOperationException();
+    }
+
+    @Override // from Transform
+    public Transform shearY (double sy) {
+        throw new UnsupportedOperationException();
+    }
+
     @Override // from Transform
     public Transform setTx (double tx) {
         throw new UnsupportedOperationException();
diff --git a/src/main/java/pythagoras/d/AffineTransform.java b/src/main/java/pythagoras/d/AffineTransform.java
index fa2c0db..e6154b2 100644
--- a/src/main/java/pythagoras/d/AffineTransform.java
+++ b/src/main/java/pythagoras/d/AffineTransform.java
@@ -231,6 +231,21 @@ public class AffineTransform extends AbstractTransform
         return Transforms.multiply(this, 1, 0, 0, 1, 0, ty, this);
     }
 
+    @Override // from Transform
+    public Transform shear (double sx, double sy) {
+        return Transforms.multiply(this, 1, sy, sx, 1, 0, 0, this);
+    }
+
+    @Override // from Transform
+    public Transform shearX (double sx) {
+        return Transforms.multiply(this, 1, 0, sx, 1, 0, 0, this);
+    }
+
+    @Override // from Transform
+    public Transform shearY (double sy) {
+        return Transforms.multiply(this, 1, sy, 0, 1, 0, 0, this);
+    }
+
     @Override // from Transform
     public Transform invert () {
         // compute the determinant, storing the subdeterminants for later use
diff --git a/src/main/java/pythagoras/d/MathUtil.java b/src/main/java/pythagoras/d/MathUtil.java
index e071828..9b255ef 100644
--- a/src/main/java/pythagoras/d/MathUtil.java
+++ b/src/main/java/pythagoras/d/MathUtil.java
@@ -103,7 +103,7 @@ public class MathUtil
     public static double lerpa (double a1, double a2, double t) {
         double ma1 = mirrorAngle(a1), ma2 = mirrorAngle(a2);
         double d = Math.abs(a2 - a1), md = Math.abs(ma1 - ma2);
-        return (d < md) ? lerp(a1, a2, t) : mirrorAngle(lerp(ma1, ma2, t));
+        return (d <= md) ? lerp(a1, a2, t) : mirrorAngle(lerp(ma1, ma2, t));
     }
 
     /**
@@ -166,12 +166,23 @@ public class MathUtil
     }
 
     /**
-     * Returns the mirror angle of the specified angle (assumed to be in [-pi, +pi]).
+     * Returns the mirror angle of the specified angle (assumed to be in [-pi, +pi]). The angle is
+     * mirrored around the PI/2 if it is positive, and -PI/2 if it is negative. One can visualize
+     * this as mirroring around the "y-axis".
      */
     public static double mirrorAngle (double a) {
         return (a > 0f ? Math.PI : -Math.PI) - a;
     }
 
+    /**
+     * Returns the mirror angle of the specified angle (assumed to be in [-pi, +pi]). The angle is
+     * mirrored around the origin (zero degrees). One can visualize this as mirroring around the
+     * "x-axis".
+     */
+    public static double mirrorAngleOrigin (double a) {
+        return a + (a > 0f ? -Math.PI : Math.PI);
+    }
+
     /**
      * Sets the number of decimal places to show when formatting values. By default, they are
      * formatted to three decimal places.
diff --git a/src/main/java/pythagoras/d/Transform.java b/src/main/java/pythagoras/d/Transform.java
index b679960..7dfe8e1 100644
--- a/src/main/java/pythagoras/d/Transform.java
+++ b/src/main/java/pythagoras/d/Transform.java
@@ -137,6 +137,21 @@ public interface Transform
      * @throws UnsupportedOperationException if the transform is not rigid body or greater. */
     Transform translateY (double ty);
 
+    /** Shears this transform.
+     * @return this instance, for chaining.
+     * @throws UnsupportedOperationException if the transform is not affine or greater. */
+    Transform shear (double tx, double ty);
+
+    /** Shears this transform in the x dimension.
+     * @return this instance, for chaining.
+     * @throws UnsupportedOperationException if the transform is not affine or greater. */
+    Transform shearX (double tx);
+
+    /** Shears this transform in the y dimension.
+     * @return this instance, for chaining.
+     * @throws UnsupportedOperationException if the transform is not affine or greater. */
+    Transform shearY (double ty);
+
     /** Returns a new transform that represents the inverse of this transform.
      * @throws NoninvertibleTransformException if the transform is not invertible. */
     Transform invert ();