Added inv() that invert point transformation functions.

dlib/geometry/point_transforms.h

@@ -126,6 +126,16 @@ namespace dlib
         dlib::vector<double,2> b;
     };
 
+// ----------------------------------------------------------------------------------------
+
+    inline point_transform_affine inv (
+        const point_transform_affine& trans
+    )
+    {
+        matrix<double,2,2> im = inv(trans.get_m());
+        return point_transform_affine(im, -im*trans.get_b());
+    }
+
 // ----------------------------------------------------------------------------------------
 
     template <typename T>
@@ -203,6 +213,15 @@ namespace dlib
         matrix<double,3,3> m;
     };
 
+// ----------------------------------------------------------------------------------------
+
+    inline point_transform_projective inv (
+        const point_transform_projective& trans
+    )
+    {
+        return point_transform_projective(inv(trans.get_m()));
+    }
+
 // ----------------------------------------------------------------------------------------
 
     namespace impl_proj

dlib/geometry/point_transforms_abstract.h

@@ -57,6 +57,17 @@ namespace dlib
 
     };
 
+// ----------------------------------------------------------------------------------------
+
+    point_transform_affine inv (
+        const point_transform_affine& trans
+    );
+    /*!
+        ensures
+            - If trans is an invertible transformation then this function returns a new
+              transformation that is the inverse of trans. 
+    !*/
+
 // ----------------------------------------------------------------------------------------
 
     template <typename T>
@@ -134,6 +145,17 @@ namespace dlib
 
     };
 
+// ----------------------------------------------------------------------------------------
+
+    point_transform_projective inv (
+        const point_transform_projective& trans
+    );
+    /*!
+        ensures
+            - If trans is an invertible transformation then this function returns a new
+              transformation that is the inverse of trans. 
+    !*/
+
 // ----------------------------------------------------------------------------------------
 
     point_transform_projective find_projective_transform (