diff --git a/include/geode/geometry/frame_transform.hpp b/include/geode/geometry/frame_transform.hpp
new file mode 100644
index 000000000..2293767fc
--- /dev/null
+++ b/include/geode/geometry/frame_transform.hpp
@@ -0,0 +1,65 @@
+/*
+ * Copyright (c) 2019 - 2025 Geode-solutions
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ */
+#pragma once
+
+#include <geode/basic/pimpl.hpp>
+
+#include <geode/geometry/common.hpp>
+
+namespace geode
+{
+    FORWARD_DECLARATION_DIMENSION_CLASS( Frame );
+    FORWARD_DECLARATION_DIMENSION_CLASS( Point );
+    FORWARD_DECLARATION_DIMENSION_CLASS( Vector );
+} // namespace geode
+
+namespace geode
+{
+    template < index_t dimension >
+    class FrameTransform
+    {
+    public:
+        FrameTransform(
+            const Frame< dimension >& from, const Frame< dimension >& to );
+        virtual ~FrameTransform();
+
+        [[nodiscard]] virtual local_index_t direction(
+            local_index_t index ) const;
+
+        [[nodiscard]] virtual signed_index_t orientation(
+            local_index_t index ) const;
+
+        [[nodiscard]] virtual Frame< dimension > apply(
+            const Frame< dimension >& frame ) const;
+
+        [[nodiscard]] virtual Vector< dimension > apply(
+            const Vector< dimension >& vector ) const;
+
+        [[nodiscard]] virtual Point< dimension > apply(
+            const Point< dimension >& point ) const;
+
+    private:
+        IMPLEMENTATION_MEMBER( impl_ );
+    };
+    ALIAS_2D_AND_3D( FrameTransform );
+} // namespace geode
\ No newline at end of file
diff --git a/include/geode/geometry/normal_frame_transform.hpp b/include/geode/geometry/normal_frame_transform.hpp
new file mode 100644
index 000000000..21dbcfa84
--- /dev/null
+++ b/include/geode/geometry/normal_frame_transform.hpp
@@ -0,0 +1,60 @@
+/*
+ * Copyright (c) 2019 - 2025 Geode-solutions
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ */
+#pragma once
+
+#include <geode/basic/pimpl.hpp>
+
+#include <geode/geometry/common.hpp>
+#include <geode/geometry/frame_transform.hpp>
+
+namespace geode
+{
+    FORWARD_DECLARATION_DIMENSION_CLASS( Frame );
+    FORWARD_DECLARATION_DIMENSION_CLASS( Point );
+    FORWARD_DECLARATION_DIMENSION_CLASS( Vector );
+} // namespace geode
+
+namespace geode
+{
+    template < index_t dimension >
+    class NormalFrameTransform : public FrameTransform< dimension >
+    {
+    public:
+        NormalFrameTransform(
+            const Frame< dimension >& from, const Frame< dimension >& to );
+        ~NormalFrameTransform();
+
+        [[nodiscard]] Frame< dimension > apply(
+            const Frame< dimension >& frame ) const final;
+
+        [[nodiscard]] Vector< dimension > apply(
+            const Vector< dimension >& vector ) const final;
+
+        [[nodiscard]] Point< dimension > apply(
+            const Point< dimension >& point ) const final;
+
+    private:
+        IMPLEMENTATION_MEMBER( impl_ );
+    };
+    ALIAS_2D_AND_3D( NormalFrameTransform );
+} // namespace geode
\ No newline at end of file
diff --git a/src/geode/geometry/CMakeLists.txt b/src/geode/geometry/CMakeLists.txt
index 954bdb19e..d37660496 100644
--- a/src/geode/geometry/CMakeLists.txt
+++ b/src/geode/geometry/CMakeLists.txt
@@ -42,11 +42,13 @@ add_geode_library(
         "distance.cpp"
         "dynamic_nn_search.cpp"
         "frame.cpp"
+        "frame_transform.cpp"
         "information.cpp"
         "intersection.cpp"
         "intersection_detection.cpp"
         "mensuration.cpp"
         "nn_search.cpp"
+        "normal_frame_transform.cpp"
         "perpendicular.cpp"
         "points_sort.cpp"
         "position.cpp"
@@ -77,11 +79,13 @@ add_geode_library(
         "distance.hpp"
         "dynamic_nn_search.hpp"
         "frame.hpp"
+        "frame_transform.hpp"
         "information.hpp"
         "intersection.hpp"
         "intersection_detection.hpp"
         "mensuration.hpp"
         "nn_search.hpp"
+        "normal_frame_transform.hpp"
         "perpendicular.hpp"
         "point.hpp"
         "points_sort.hpp"
diff --git a/src/geode/geometry/frame_transform.cpp b/src/geode/geometry/frame_transform.cpp
new file mode 100644
index 000000000..835ddd29f
--- /dev/null
+++ b/src/geode/geometry/frame_transform.cpp
@@ -0,0 +1,153 @@
+/*
+ * Copyright (c) 2019 - 2025 Geode-solutions
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ */
+
+#include <geode/geometry/frame_transform.hpp>
+
+#include <geode/basic/logger.hpp>
+#include <geode/basic/pimpl_impl.hpp>
+
+#include <geode/geometry/frame.hpp>
+#include <geode/geometry/vector.hpp>
+
+namespace geode
+{
+    template < index_t dimension >
+    class FrameTransform< dimension >::Impl
+    {
+    public:
+        Impl( const Frame< dimension >& from, const Frame< dimension >& to )
+        {
+            for( const auto d_from : LRange{ dimension } )
+            {
+                const auto from_vector = from.direction( d_from ).normalize();
+                double max_dot{ 0 };
+                for( const auto d_to : LRange{ dimension } )
+                {
+                    const auto to_vector = to.direction( d_to ).normalize();
+                    const auto dot = from_vector.dot( to_vector );
+                    const auto abs_dot = std::fabs( dot );
+                    if( abs_dot > max_dot )
+                    {
+                        directions_[d_from] = d_to;
+                        max_dot = abs_dot;
+                        orientations_[d_from] = dot > 0 ? 1 : -1;
+                    }
+                }
+            }
+        }
+
+        local_index_t direction( local_index_t index ) const
+        {
+            return directions_[index];
+        }
+
+        signed_index_t orientation( local_index_t index ) const
+        {
+            return orientations_[index];
+        }
+
+        Frame< dimension > apply( const Frame< dimension >& frame ) const
+        {
+            Frame< dimension > result;
+            for( const auto d : LRange{ dimension } )
+            {
+                result.set_direction(
+                    direction( d ), frame.direction( d ) * orientation( d ) );
+            }
+            return result;
+        }
+
+        Point< dimension > apply( const Point< dimension >& point ) const
+        {
+            Point< dimension > result;
+            for( const auto d : LRange{ dimension } )
+            {
+                result.set_value(
+                    d, orientations_[d] * point.value( directions_[d] ) );
+            }
+            return result;
+        }
+
+        Vector< dimension > apply( const Vector< dimension >& vector ) const
+        {
+            Vector< dimension > result;
+            for( const auto d : LRange{ dimension } )
+            {
+                result.set_value(
+                    d, orientations_[d] * vector.value( directions_[d] ) );
+            }
+            return result;
+        }
+
+    private:
+        std::array< local_index_t, dimension > directions_;
+        std::array< signed_index_t, dimension > orientations_;
+    };
+
+    template < index_t dimension >
+    FrameTransform< dimension >::FrameTransform(
+        const Frame< dimension >& from, const Frame< dimension >& to )
+        : impl_{ from, to }
+    {
+    }
+
+    template < index_t dimension >
+    FrameTransform< dimension >::~FrameTransform() = default;
+
+    template < index_t dimension >
+    local_index_t FrameTransform< dimension >::direction(
+        local_index_t index ) const
+    {
+        return impl_->direction( index );
+    }
+
+    template < index_t dimension >
+    signed_index_t FrameTransform< dimension >::orientation(
+        local_index_t index ) const
+    {
+        return impl_->orientation( index );
+    }
+
+    template < index_t dimension >
+    Frame< dimension > FrameTransform< dimension >::apply(
+        const Frame< dimension >& frame ) const
+    {
+        return impl_->apply( frame );
+    }
+
+    template < index_t dimension >
+    Vector< dimension > FrameTransform< dimension >::apply(
+        const Vector< dimension >& vector ) const
+    {
+        return impl_->apply( vector );
+    }
+
+    template < index_t dimension >
+    Point< dimension > FrameTransform< dimension >::apply(
+        const Point< dimension >& point ) const
+    {
+        return impl_->apply( point );
+    }
+    template opengeode_geometry_api class FrameTransform< 2 >;
+    template opengeode_geometry_api class FrameTransform< 3 >;
+} // namespace geode
diff --git a/src/geode/geometry/normal_frame_transform.cpp b/src/geode/geometry/normal_frame_transform.cpp
new file mode 100644
index 000000000..c3dec0cfd
--- /dev/null
+++ b/src/geode/geometry/normal_frame_transform.cpp
@@ -0,0 +1,127 @@
+/*
+ * Copyright (c) 2019 - 2025 Geode-solutions
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ */
+
+#include <geode/basic/logger.hpp>
+#include <geode/basic/pimpl_impl.hpp>
+
+#include <geode/geometry/frame.hpp>
+#include <geode/geometry/normal_frame_transform.hpp>
+#include <geode/geometry/vector.hpp>
+
+namespace geode
+{
+    template < index_t dimension >
+    class NormalFrameTransform< dimension >::Impl
+    {
+    public:
+        Impl( const NormalFrameTransform< dimension >& normal_frame_transform,
+            const Frame< dimension >& from,
+            const Frame< dimension >& to )
+        {
+            for( const auto d_from : LRange{ dimension } )
+            {
+                directions_[d_from] =
+                    normal_frame_transform.direction( d_from );
+                orientations_[d_from] =
+                    normal_frame_transform.orientation( d_from );
+                magnitudes_[d_from] =
+                    to.direction( normal_frame_transform.direction( d_from ) )
+                        .length()
+                    / from.direction( d_from ).length();
+            }
+        }
+
+        Frame< dimension > apply( const Frame< dimension >& frame ) const
+        {
+            Frame< dimension > result;
+            for( const auto d : LRange{ dimension } )
+            {
+                result.set_direction( directions_[d],
+                    frame.direction( d ) * orientations_[d] * magnitudes_[d] );
+            }
+            return result;
+        }
+
+        Point< dimension > apply( const Point< dimension >& point ) const
+        {
+            Point< dimension > result;
+            for( const auto d : LRange{ dimension } )
+            {
+                result.set_value( d, orientations_[d]
+                                         * point.value( directions_[d] )
+                                         * magnitudes_[d] );
+            }
+            return result;
+        }
+
+        Vector< dimension > apply( const Vector< dimension >& vector ) const
+        {
+            Vector< dimension > result;
+            for( const auto d : LRange{ dimension } )
+            {
+                result.set_value( d, orientations_[d]
+                                         * vector.value( directions_[d] )
+                                         * magnitudes_[d] );
+            }
+            return result;
+        }
+
+    private:
+        std::array< local_index_t, dimension > directions_;
+        std::array< signed_index_t, dimension > orientations_;
+        std::array< double, dimension > magnitudes_;
+    };
+
+    template < index_t dimension >
+    NormalFrameTransform< dimension >::NormalFrameTransform(
+        const Frame< dimension >& from, const Frame< dimension >& to )
+        : FrameTransform< dimension >( from, to ), impl_{ *this, from, to }
+    {
+    }
+
+    template < index_t dimension >
+    NormalFrameTransform< dimension >::~NormalFrameTransform() = default;
+
+    template < index_t dimension >
+    Frame< dimension > NormalFrameTransform< dimension >::apply(
+        const Frame< dimension >& frame ) const
+    {
+        return impl_->apply( frame );
+    }
+
+    template < index_t dimension >
+    Vector< dimension > NormalFrameTransform< dimension >::apply(
+        const Vector< dimension >& vector ) const
+    {
+        return impl_->apply( vector );
+    }
+
+    template < index_t dimension >
+    Point< dimension > NormalFrameTransform< dimension >::apply(
+        const Point< dimension >& point ) const
+    {
+        return impl_->apply( point );
+    }
+    template opengeode_geometry_api class NormalFrameTransform< 2 >;
+    template opengeode_geometry_api class NormalFrameTransform< 3 >;
+} // namespace geode
diff --git a/tests/geometry/CMakeLists.txt b/tests/geometry/CMakeLists.txt
index c62766c0e..ca4fd469b 100644
--- a/tests/geometry/CMakeLists.txt
+++ b/tests/geometry/CMakeLists.txt
@@ -92,6 +92,14 @@ add_geode_test(
         ${PROJECT_NAME}::basic
         ${PROJECT_NAME}::geometry
 )
+
+add_geode_test(
+    SOURCE "test-normal-frame-transform.cpp"
+    DEPENDENCIES
+        ${PROJECT_NAME}::basic
+        ${PROJECT_NAME}::geometry
+)
+
 add_geode_test(
     SOURCE "test-perpendicular.cpp"
     DEPENDENCIES
@@ -158,3 +166,4 @@ add_geode_test(
         ${PROJECT_NAME}::basic
         ${PROJECT_NAME}::geometry
 )
+
diff --git a/tests/geometry/test-normal-frame-transform.cpp b/tests/geometry/test-normal-frame-transform.cpp
new file mode 100644
index 000000000..8ae51fc84
--- /dev/null
+++ b/tests/geometry/test-normal-frame-transform.cpp
@@ -0,0 +1,53 @@
+/*
+ * Copyright (c) 2019 - 2025 Geode-solutions
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ */
+
+#include <geode/basic/assert.hpp>
+#include <geode/basic/logger.hpp>
+
+#include <geode/geometry/frame.hpp>
+#include <geode/geometry/normal_frame_transform.hpp>
+#include <geode/geometry/vector.hpp>
+
+#include <geode/tests/common.hpp>
+
+void test_normal_frame_transform()
+{
+    geode::Frame2D from{ { geode::Vector< 2 >{ { 1, 0 } },
+        geode::Vector2D{ { 0, 1 } } } };
+    geode::Frame2D to{ { geode::Vector2D{ { 1, 0 } },
+        geode::Vector2D{ { 0, 0.1 } } } };
+    geode::NormalFrameTransform2D frame_transform{ from, to };
+    geode::Vector2D test_vector{ { 1, 1 } };
+    const auto result = frame_transform.apply( test_vector );
+    const auto correct_result = geode::Vector2D{ { 1, 0.1 } };
+    OPENGEODE_EXCEPTION( result == correct_result,
+        "[Test] Wrong result for normal frame transform" );
+    geode::Logger::info( "TEST SUCCESS" );
+}
+
+void test()
+{
+    test_normal_frame_transform();
+}
+
+OPENGEODE_TEST( "normal-frame-transform" )
\ No newline at end of file