From 9d30446c55dc1a1d78ea1a8da227862b47004f71 Mon Sep 17 00:00:00 2001
From: Orange <orange-cpp@yandex.ru>
Date: Wed, 15 Apr 2026 03:08:00 +0300
Subject: [PATCH 1/4] added ability to get view angles from view matrix

---
 .idea/editor.xml                       |  6 +-
 include/omath/projection/camera.hpp    |  6 ++
 tests/general/unit_test_projection.cpp | 86 ++++++++++++++++++++++++++
 3 files changed, 95 insertions(+), 3 deletions(-)

diff --git a/.idea/editor.xml b/.idea/editor.xml
index 9b5acf8e..bce786e3 100644
--- a/.idea/editor.xml
+++ b/.idea/editor.xml
@@ -103,7 +103,7 @@
     <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppImplicitDefaultConstructorNotAvailable/@EntryIndexedValue" value="WARNING" type="string" />
     <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppIncompatiblePointerConversion/@EntryIndexedValue" value="WARNING" type="string" />
     <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppIncompleteSwitchStatement/@EntryIndexedValue" value="WARNING" type="string" />
-    <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppInconsistentNaming/@EntryIndexedValue" value="DO_NOT_SHOW" type="string" />
+    <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppInconsistentNaming/@EntryIndexedValue" value="HINT" type="string" />
     <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppIntegralToPointerConversion/@EntryIndexedValue" value="WARNING" type="string" />
     <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppInvalidLineContinuation/@EntryIndexedValue" value="WARNING" type="string" />
     <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppJoinDeclarationAndAssignment/@EntryIndexedValue" value="SUGGESTION" type="string" />
@@ -202,7 +202,7 @@
     <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppStaticDataMemberInUnnamedStruct/@EntryIndexedValue" value="WARNING" type="string" />
     <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppStaticSpecifierOnAnonymousNamespaceMember/@EntryIndexedValue" value="SUGGESTION" type="string" />
     <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppStringLiteralToCharPointerConversion/@EntryIndexedValue" value="WARNING" type="string" />
-    <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppTabsAreDisallowed/@EntryIndexedValue" value="DO_NOT_SHOW" type="string" />
+    <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppTabsAreDisallowed/@EntryIndexedValue" value="WARNING" type="string" />
     <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppTemplateArgumentsCanBeDeduced/@EntryIndexedValue" value="HINT" type="string" />
     <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppTemplateParameterNeverUsed/@EntryIndexedValue" value="HINT" type="string" />
     <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppTemplateParameterShadowing/@EntryIndexedValue" value="WARNING" type="string" />
@@ -216,7 +216,7 @@
     <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppUnmatchedPragmaEndRegionDirective/@EntryIndexedValue" value="WARNING" type="string" />
     <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppUnmatchedPragmaRegionDirective/@EntryIndexedValue" value="WARNING" type="string" />
     <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppUnnamedNamespaceInHeaderFile/@EntryIndexedValue" value="WARNING" type="string" />
-    <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppUnnecessaryWhitespace/@EntryIndexedValue" value="DO_NOT_SHOW" type="string" />
+    <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppUnnecessaryWhitespace/@EntryIndexedValue" value="WARNING" type="string" />
     <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppUnsignedZeroComparison/@EntryIndexedValue" value="WARNING" type="string" />
     <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppUnusedIncludeDirective/@EntryIndexedValue" value="WARNING" type="string" />
     <option name="/Default/CodeInspection/Highlighting/InspectionSeverities/=CppUseAlgorithmWithCount/@EntryIndexedValue" value="SUGGESTION" type="string" />
diff --git a/include/omath/projection/camera.hpp b/include/omath/projection/camera.hpp
index 801dd439..57a56fa4 100644
--- a/include/omath/projection/camera.hpp
+++ b/include/omath/projection/camera.hpp
@@ -83,6 +83,12 @@ namespace omath::projection
         {
         }
 
+        [[nodiscard]]
+        static ViewAnglesType calc_view_angles_from_view_matrix(const Mat4X4Type& view_matrix) noexcept
+        {
+            const Vector3<float> forward_vector = {view_matrix[2, 0], view_matrix[2, 1], view_matrix[2, 2]};
+            return TraitClass::calc_look_at_angle({}, forward_vector);
+        }
         void look_at(const Vector3<float>& target)
         {
             m_view_angles = TraitClass::calc_look_at_angle(m_origin, target);
diff --git a/tests/general/unit_test_projection.cpp b/tests/general/unit_test_projection.cpp
index 8e54a295..a9ffe838 100644
--- a/tests/general/unit_test_projection.cpp
+++ b/tests/general/unit_test_projection.cpp
@@ -510,4 +510,90 @@ TEST(UnitTestProjection, AabbUnityEngineStraddlesNearNotCulled)
     // Box straddles near plane (Unity: +Z forward)
     const omath::primitives::Aabb<float> aabb{{-1.f, -1.f, -5.f}, {1.f, 1.f, 5.f}};
     EXPECT_FALSE(cam.is_aabb_culled_by_frustum(aabb));
+}
+
+TEST(UnitTestProjection, CalcViewAnglesFromViewMatrix_LookingForward)
+{
+    constexpr float k_eps = 1e-4f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const omath::source_engine::ViewAngles angles{
+        omath::source_engine::PitchAngle::from_degrees(0.f),
+        omath::source_engine::YawAngle::from_degrees(0.f),
+        omath::source_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::source_engine::Camera({0, 0, 0}, angles, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto result = omath::source_engine::Camera::calc_view_angles_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(result.pitch.as_degrees(), 0.f, k_eps);
+    EXPECT_NEAR(result.yaw.as_degrees(), 0.f, k_eps);
+}
+
+TEST(UnitTestProjection, CalcViewAnglesFromViewMatrix_PositivePitchAndYaw)
+{
+    constexpr float k_eps = 1e-4f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const omath::source_engine::ViewAngles angles{
+        omath::source_engine::PitchAngle::from_degrees(30.f),
+        omath::source_engine::YawAngle::from_degrees(45.f),
+        omath::source_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::source_engine::Camera({0, 0, 0}, angles, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto result = omath::source_engine::Camera::calc_view_angles_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(result.pitch.as_degrees(), 30.f, k_eps);
+    EXPECT_NEAR(result.yaw.as_degrees(), 45.f, k_eps);
+}
+
+TEST(UnitTestProjection, CalcViewAnglesFromViewMatrix_NegativePitchAndYaw)
+{
+    constexpr float k_eps = 1e-4f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const omath::source_engine::ViewAngles angles{
+        omath::source_engine::PitchAngle::from_degrees(-45.f),
+        omath::source_engine::YawAngle::from_degrees(-90.f),
+        omath::source_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::source_engine::Camera({0, 0, 0}, angles, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto result = omath::source_engine::Camera::calc_view_angles_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(result.pitch.as_degrees(), -45.f, k_eps);
+    EXPECT_NEAR(result.yaw.as_degrees(), -90.f, k_eps);
+}
+
+TEST(UnitTestProjection, CalcViewAnglesFromViewMatrix_OffOriginCameraIgnored)
+{
+    // The forward vector from the view matrix does not depend on camera origin,
+    // so the same angles should be recovered regardless of position.
+    constexpr float k_eps = 1e-4f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const omath::source_engine::ViewAngles angles{
+        omath::source_engine::PitchAngle::from_degrees(20.f),
+        omath::source_engine::YawAngle::from_degrees(60.f),
+        omath::source_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::source_engine::Camera({100.f, 200.f, -50.f}, angles, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto result = omath::source_engine::Camera::calc_view_angles_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(result.pitch.as_degrees(), 20.f, k_eps);
+    EXPECT_NEAR(result.yaw.as_degrees(), 60.f, k_eps);
+}
+
+TEST(UnitTestProjection, CalcViewAnglesFromViewMatrix_RollAlwaysZero)
+{
+    // Roll cannot be encoded in the forward vector, so it is always 0 in the result.
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const omath::source_engine::ViewAngles angles{
+        omath::source_engine::PitchAngle::from_degrees(10.f),
+        omath::source_engine::YawAngle::from_degrees(30.f),
+        omath::source_engine::RollAngle::from_degrees(15.f)
+    };
+    const auto cam = omath::source_engine::Camera({0, 0, 0}, angles, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto result = omath::source_engine::Camera::calc_view_angles_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_FLOAT_EQ(result.roll.as_degrees(), 0.f);
 }
\ No newline at end of file

From dbe29926dc11e41d3c5f4bda688f843f9291af75 Mon Sep 17 00:00:00 2001
From: Orange <orange-cpp@yandex.ru>
Date: Wed, 15 Apr 2026 03:25:53 +0300
Subject: [PATCH 2/4] fixed unity bug

---
 include/omath/engines/unity_engine/camera.hpp |   2 +-
 include/omath/projection/camera.hpp           |  17 +-
 tests/general/unit_test_projection.cpp        | 185 ++++++++++++++++++
 3 files changed, 202 insertions(+), 2 deletions(-)

diff --git a/include/omath/engines/unity_engine/camera.hpp b/include/omath/engines/unity_engine/camera.hpp
index 55c82a80..7f818b4b 100644
--- a/include/omath/engines/unity_engine/camera.hpp
+++ b/include/omath/engines/unity_engine/camera.hpp
@@ -9,5 +9,5 @@
 
 namespace omath::unity_engine
 {
-    using Camera = projection::Camera<Mat4X4, ViewAngles, CameraTrait, false, NDCDepthRange::ZERO_TO_ONE>;
+    using Camera = projection::Camera<Mat4X4, ViewAngles, CameraTrait, true, NDCDepthRange::ZERO_TO_ONE>;
 } // namespace omath::unity_engine
\ No newline at end of file
diff --git a/include/omath/projection/camera.hpp b/include/omath/projection/camera.hpp
index 57a56fa4..d73111ca 100644
--- a/include/omath/projection/camera.hpp
+++ b/include/omath/projection/camera.hpp
@@ -86,9 +86,24 @@ namespace omath::projection
         [[nodiscard]]
         static ViewAnglesType calc_view_angles_from_view_matrix(const Mat4X4Type& view_matrix) noexcept
         {
-            const Vector3<float> forward_vector = {view_matrix[2, 0], view_matrix[2, 1], view_matrix[2, 2]};
+            Vector3<float> forward_vector = {view_matrix[2, 0], view_matrix[2, 1], view_matrix[2, 2]};
+            if constexpr (inverted_z)
+                forward_vector = -forward_vector;
             return TraitClass::calc_look_at_angle({}, forward_vector);
         }
+
+        [[nodiscard]]
+        static Vector3<float> calc_origin_from_view_matrix(const Mat4X4Type& view_matrix) noexcept
+        {
+            // The view matrix is R * T(-origin), so the last column stores t = -R * origin.
+            // Recovering origin: origin = -R^T * t
+            return {
+                -(view_matrix[0, 0] * view_matrix[0, 3] + view_matrix[1, 0] * view_matrix[1, 3] + view_matrix[2, 0] * view_matrix[2, 3]),
+                -(view_matrix[0, 1] * view_matrix[0, 3] + view_matrix[1, 1] * view_matrix[1, 3] + view_matrix[2, 1] * view_matrix[2, 3]),
+                -(view_matrix[0, 2] * view_matrix[0, 3] + view_matrix[1, 2] * view_matrix[1, 3] + view_matrix[2, 2] * view_matrix[2, 3]),
+            };
+        }
+
         void look_at(const Vector3<float>& target)
         {
             m_view_angles = TraitClass::calc_look_at_angle(m_origin, target);
diff --git a/tests/general/unit_test_projection.cpp b/tests/general/unit_test_projection.cpp
index a9ffe838..2b0bf31f 100644
--- a/tests/general/unit_test_projection.cpp
+++ b/tests/general/unit_test_projection.cpp
@@ -596,4 +596,189 @@ TEST(UnitTestProjection, CalcViewAnglesFromViewMatrix_RollAlwaysZero)
     const auto result = omath::source_engine::Camera::calc_view_angles_from_view_matrix(cam.get_view_matrix());
 
     EXPECT_FLOAT_EQ(result.roll.as_degrees(), 0.f);
+}
+
+TEST(UnitTestProjection, CalcOriginFromViewMatrix_AtOrigin)
+{
+    constexpr float k_eps = 1e-4f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const auto cam = omath::source_engine::Camera({0, 0, 0}, {}, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto origin = omath::source_engine::Camera::calc_origin_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(origin.x, 0.f, k_eps);
+    EXPECT_NEAR(origin.y, 0.f, k_eps);
+    EXPECT_NEAR(origin.z, 0.f, k_eps);
+}
+
+TEST(UnitTestProjection, CalcOriginFromViewMatrix_ArbitraryPosition)
+{
+    constexpr float k_eps = 1e-3f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const omath::source_engine::ViewAngles angles{
+        omath::source_engine::PitchAngle::from_degrees(0.f),
+        omath::source_engine::YawAngle::from_degrees(0.f),
+        omath::source_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::source_engine::Camera({100.f, 200.f, -50.f}, angles, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto origin = omath::source_engine::Camera::calc_origin_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(origin.x, 100.f, k_eps);
+    EXPECT_NEAR(origin.y, 200.f, k_eps);
+    EXPECT_NEAR(origin.z, -50.f, k_eps);
+}
+
+TEST(UnitTestProjection, CalcOriginFromViewMatrix_WithRotation)
+{
+    // Origin recovery must work even when the camera is rotated.
+    constexpr float k_eps = 1e-3f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    const omath::source_engine::ViewAngles angles{
+        omath::source_engine::PitchAngle::from_degrees(30.f),
+        omath::source_engine::YawAngle::from_degrees(45.f),
+        omath::source_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::source_engine::Camera({300.f, -100.f, 75.f}, angles, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto origin = omath::source_engine::Camera::calc_origin_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(origin.x, 300.f, k_eps);
+    EXPECT_NEAR(origin.y, -100.f, k_eps);
+    EXPECT_NEAR(origin.z, 75.f, k_eps);
+}
+
+TEST(UnitTestProjection, CalcOriginFromViewMatrix_IndependentOfAngles)
+{
+    // Same position, different orientations — should always recover the same origin.
+    constexpr float k_eps = 1e-3f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(90.f);
+    constexpr omath::Vector3<float> expected_origin{50.f, 50.f, 50.f};
+
+    const omath::source_engine::ViewAngles angles_a{
+        omath::source_engine::PitchAngle::from_degrees(0.f),
+        omath::source_engine::YawAngle::from_degrees(0.f),
+        omath::source_engine::RollAngle::from_degrees(0.f)
+    };
+    const omath::source_engine::ViewAngles angles_b{
+        omath::source_engine::PitchAngle::from_degrees(-60.f),
+        omath::source_engine::YawAngle::from_degrees(135.f),
+        omath::source_engine::RollAngle::from_degrees(0.f)
+    };
+
+    const auto cam_a = omath::source_engine::Camera(expected_origin, angles_a, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+    const auto cam_b = omath::source_engine::Camera(expected_origin, angles_b, {1920.f, 1080.f}, fov, 0.01f, 1000.f);
+
+    const auto origin_a = omath::source_engine::Camera::calc_origin_from_view_matrix(cam_a.get_view_matrix());
+    const auto origin_b = omath::source_engine::Camera::calc_origin_from_view_matrix(cam_b.get_view_matrix());
+
+    EXPECT_NEAR(origin_a.x, expected_origin.x, k_eps);
+    EXPECT_NEAR(origin_a.y, expected_origin.y, k_eps);
+    EXPECT_NEAR(origin_a.z, expected_origin.z, k_eps);
+
+    EXPECT_NEAR(origin_b.x, expected_origin.x, k_eps);
+    EXPECT_NEAR(origin_b.y, expected_origin.y, k_eps);
+    EXPECT_NEAR(origin_b.z, expected_origin.z, k_eps);
+}
+
+// ---- Unity engine camera tests ----
+
+TEST(UnitTestProjection, Unity_CalcViewAnglesFromViewMatrix_LookingForward)
+{
+    constexpr float k_eps = 1e-4f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(60.f);
+    const omath::unity_engine::ViewAngles angles{
+        omath::unity_engine::PitchAngle::from_degrees(0.f),
+        omath::unity_engine::YawAngle::from_degrees(0.f),
+        omath::unity_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::unity_engine::Camera({0, 0, 0}, angles, {1280.f, 720.f}, fov, 0.03f, 1000.f);
+
+    const auto result = omath::unity_engine::Camera::calc_view_angles_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(result.pitch.as_degrees(), 0.f, k_eps);
+    EXPECT_NEAR(result.yaw.as_degrees(), 0.f, k_eps);
+}
+
+TEST(UnitTestProjection, Unity_CalcViewAnglesFromViewMatrix_PositivePitchAndYaw)
+{
+    constexpr float k_eps = 1e-4f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(60.f);
+    const omath::unity_engine::ViewAngles angles{
+        omath::unity_engine::PitchAngle::from_degrees(30.f),
+        omath::unity_engine::YawAngle::from_degrees(45.f),
+        omath::unity_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::unity_engine::Camera({0, 0, 0}, angles, {1280.f, 720.f}, fov, 0.03f, 1000.f);
+
+    const auto result = omath::unity_engine::Camera::calc_view_angles_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(result.pitch.as_degrees(), 30.f, k_eps);
+    EXPECT_NEAR(result.yaw.as_degrees(), 45.f, k_eps);
+}
+
+TEST(UnitTestProjection, Unity_CalcViewAnglesFromViewMatrix_NegativePitchAndYaw)
+{
+    constexpr float k_eps = 1e-4f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(60.f);
+    const omath::unity_engine::ViewAngles angles{
+        omath::unity_engine::PitchAngle::from_degrees(-45.f),
+        omath::unity_engine::YawAngle::from_degrees(-90.f),
+        omath::unity_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::unity_engine::Camera({0, 0, 0}, angles, {1280.f, 720.f}, fov, 0.03f, 1000.f);
+
+    const auto result = omath::unity_engine::Camera::calc_view_angles_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(result.pitch.as_degrees(), -45.f, k_eps);
+    EXPECT_NEAR(result.yaw.as_degrees(), -90.f, k_eps);
+}
+
+TEST(UnitTestProjection, Unity_CalcOriginFromViewMatrix_AtOrigin)
+{
+    constexpr float k_eps = 1e-4f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(60.f);
+    const auto cam = omath::unity_engine::Camera({0, 0, 0}, {}, {1280.f, 720.f}, fov, 0.03f, 1000.f);
+
+    const auto origin = omath::unity_engine::Camera::calc_origin_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(origin.x, 0.f, k_eps);
+    EXPECT_NEAR(origin.y, 0.f, k_eps);
+    EXPECT_NEAR(origin.z, 0.f, k_eps);
+}
+
+TEST(UnitTestProjection, Unity_CalcOriginFromViewMatrix_ArbitraryPosition)
+{
+    constexpr float k_eps = 1e-3f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(60.f);
+    const omath::unity_engine::ViewAngles angles{
+        omath::unity_engine::PitchAngle::from_degrees(0.f),
+        omath::unity_engine::YawAngle::from_degrees(0.f),
+        omath::unity_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::unity_engine::Camera({100.f, 200.f, -50.f}, angles, {1280.f, 720.f}, fov, 0.03f, 1000.f);
+
+    const auto origin = omath::unity_engine::Camera::calc_origin_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(origin.x, 100.f, k_eps);
+    EXPECT_NEAR(origin.y, 200.f, k_eps);
+    EXPECT_NEAR(origin.z, -50.f, k_eps);
+}
+
+TEST(UnitTestProjection, Unity_CalcOriginFromViewMatrix_WithRotation)
+{
+    constexpr float k_eps = 1e-3f;
+    constexpr auto fov = omath::projection::FieldOfView::from_degrees(60.f);
+    const omath::unity_engine::ViewAngles angles{
+        omath::unity_engine::PitchAngle::from_degrees(30.f),
+        omath::unity_engine::YawAngle::from_degrees(45.f),
+        omath::unity_engine::RollAngle::from_degrees(0.f)
+    };
+    const auto cam = omath::unity_engine::Camera({300.f, -100.f, 75.f}, angles, {1280.f, 720.f}, fov, 0.03f, 1000.f);
+
+    const auto origin = omath::unity_engine::Camera::calc_origin_from_view_matrix(cam.get_view_matrix());
+
+    EXPECT_NEAR(origin.x, 300.f, k_eps);
+    EXPECT_NEAR(origin.y, -100.f, k_eps);
+    EXPECT_NEAR(origin.z, 75.f, k_eps);
 }
\ No newline at end of file

From 79f64d9679d836cfc3911c99cee4f820abf7ff56 Mon Sep 17 00:00:00 2001
From: Orange <orange-cpp@yandex.ru>
Date: Wed, 15 Apr 2026 03:38:02 +0300
Subject: [PATCH 3/4] fixed unreal bug, improved interface

---
 include/omath/engines/cry_engine/camera.hpp   |   2 +-
 .../omath/engines/frostbite_engine/camera.hpp |   2 +-
 include/omath/engines/iw_engine/camera.hpp    |   2 +-
 .../omath/engines/opengl_engine/camera.hpp    |   2 +-
 .../omath/engines/source_engine/camera.hpp    |   2 +-
 include/omath/engines/unity_engine/camera.hpp |   2 +-
 .../omath/engines/unreal_engine/camera.hpp    |   2 +-
 include/omath/projection/camera.hpp           |  17 +-
 tests/general/unit_test_projection.cpp        | 161 +++++++++++++++++-
 9 files changed, 180 insertions(+), 12 deletions(-)

diff --git a/include/omath/engines/cry_engine/camera.hpp b/include/omath/engines/cry_engine/camera.hpp
index d02ec6ac..df5c03af 100644
--- a/include/omath/engines/cry_engine/camera.hpp
+++ b/include/omath/engines/cry_engine/camera.hpp
@@ -9,5 +9,5 @@
 
 namespace omath::cry_engine
 {
-    using Camera = projection::Camera<Mat4X4, ViewAngles, CameraTrait, false, NDCDepthRange::ZERO_TO_ONE>;
+    using Camera = projection::Camera<Mat4X4, ViewAngles, CameraTrait, NDCDepthRange::ZERO_TO_ONE>;
 } // namespace omath::cry_engine
\ No newline at end of file
diff --git a/include/omath/engines/frostbite_engine/camera.hpp b/include/omath/engines/frostbite_engine/camera.hpp
index 977dc42e..8c02cf1d 100644
--- a/include/omath/engines/frostbite_engine/camera.hpp
+++ b/include/omath/engines/frostbite_engine/camera.hpp
@@ -9,5 +9,5 @@
 
 namespace omath::frostbite_engine
 {
-    using Camera =  projection::Camera<Mat4X4, ViewAngles, CameraTrait, false, NDCDepthRange::ZERO_TO_ONE>;
+    using Camera =  projection::Camera<Mat4X4, ViewAngles, CameraTrait, NDCDepthRange::ZERO_TO_ONE>;
 } // namespace omath::unity_engine
\ No newline at end of file
diff --git a/include/omath/engines/iw_engine/camera.hpp b/include/omath/engines/iw_engine/camera.hpp
index b7213ad2..52247d9d 100644
--- a/include/omath/engines/iw_engine/camera.hpp
+++ b/include/omath/engines/iw_engine/camera.hpp
@@ -9,5 +9,5 @@
 
 namespace omath::iw_engine
 {
-    using Camera =  projection::Camera<Mat4X4, ViewAngles, CameraTrait, false, NDCDepthRange::ZERO_TO_ONE>;
+    using Camera =  projection::Camera<Mat4X4, ViewAngles, CameraTrait, NDCDepthRange::ZERO_TO_ONE>;
 } // namespace omath::iw_engine
\ No newline at end of file
diff --git a/include/omath/engines/opengl_engine/camera.hpp b/include/omath/engines/opengl_engine/camera.hpp
index de01bd56..a1ef66ed 100644
--- a/include/omath/engines/opengl_engine/camera.hpp
+++ b/include/omath/engines/opengl_engine/camera.hpp
@@ -8,5 +8,5 @@
 
 namespace omath::opengl_engine
 {
-    using Camera =  projection::Camera<Mat4X4, ViewAngles, CameraTrait, true, NDCDepthRange::NEGATIVE_ONE_TO_ONE>;
+    using Camera = projection::Camera<Mat4X4, ViewAngles, CameraTrait, NDCDepthRange::NEGATIVE_ONE_TO_ONE, {.inverted_forward = true}>;
 } // namespace omath::opengl_engine
\ No newline at end of file
diff --git a/include/omath/engines/source_engine/camera.hpp b/include/omath/engines/source_engine/camera.hpp
index 68871a91..2936f5cd 100644
--- a/include/omath/engines/source_engine/camera.hpp
+++ b/include/omath/engines/source_engine/camera.hpp
@@ -7,5 +7,5 @@
 #include "traits/camera_trait.hpp"
 namespace omath::source_engine
 {
-    using Camera =  projection::Camera<Mat4X4, ViewAngles, CameraTrait, false, NDCDepthRange::ZERO_TO_ONE>;
+    using Camera =  projection::Camera<Mat4X4, ViewAngles, CameraTrait, NDCDepthRange::ZERO_TO_ONE>;
 } // namespace omath::source_engine
\ No newline at end of file
diff --git a/include/omath/engines/unity_engine/camera.hpp b/include/omath/engines/unity_engine/camera.hpp
index 7f818b4b..5bccf0da 100644
--- a/include/omath/engines/unity_engine/camera.hpp
+++ b/include/omath/engines/unity_engine/camera.hpp
@@ -9,5 +9,5 @@
 
 namespace omath::unity_engine
 {
-    using Camera = projection::Camera<Mat4X4, ViewAngles, CameraTrait, true, NDCDepthRange::ZERO_TO_ONE>;
+    using Camera = projection::Camera<Mat4X4, ViewAngles, CameraTrait, NDCDepthRange::ZERO_TO_ONE, {.inverted_forward = true}>;
 } // namespace omath::unity_engine
\ No newline at end of file
diff --git a/include/omath/engines/unreal_engine/camera.hpp b/include/omath/engines/unreal_engine/camera.hpp
index 6565e137..4b5283ef 100644
--- a/include/omath/engines/unreal_engine/camera.hpp
+++ b/include/omath/engines/unreal_engine/camera.hpp
@@ -9,5 +9,5 @@
 
 namespace omath::unreal_engine
 {
-    using Camera = projection::Camera<Mat4X4, ViewAngles, CameraTrait, false, NDCDepthRange::ZERO_TO_ONE>;
+    using Camera = projection::Camera<Mat4X4, ViewAngles, CameraTrait, NDCDepthRange::ZERO_TO_ONE, {.inverted_right = true}>;
 } // namespace omath::unreal_engine
\ No newline at end of file
diff --git a/include/omath/projection/camera.hpp b/include/omath/projection/camera.hpp
index d73111ca..a3d285e4 100644
--- a/include/omath/projection/camera.hpp
+++ b/include/omath/projection/camera.hpp
@@ -42,6 +42,12 @@ namespace omath::projection
         AUTO,
         MANUAL,
     };
+    struct CameraAxes
+    {
+        bool inverted_forward = false;
+        bool inverted_right   = false;
+    };
+
     template<class T, class MatType, class ViewAnglesType>
     concept CameraEngineConcept =
             requires(const Vector3<float>& cam_origin, const Vector3<float>& look_at, const ViewAnglesType& angles,
@@ -58,8 +64,9 @@ namespace omath::projection
                 requires noexcept(T::calc_projection_matrix(fov, viewport, znear, zfar, ndc_depth_range));
             };
 
-    template<class Mat4X4Type, class ViewAnglesType, class TraitClass, bool inverted_z = false,
-             NDCDepthRange depth_range = NDCDepthRange::NEGATIVE_ONE_TO_ONE>
+    template<class Mat4X4Type, class ViewAnglesType, class TraitClass,
+             NDCDepthRange depth_range = NDCDepthRange::NEGATIVE_ONE_TO_ONE,
+             CameraAxes axes = {}>
     requires CameraEngineConcept<TraitClass, Mat4X4Type, ViewAnglesType>
     class Camera final
     {
@@ -87,7 +94,7 @@ namespace omath::projection
         static ViewAnglesType calc_view_angles_from_view_matrix(const Mat4X4Type& view_matrix) noexcept
         {
             Vector3<float> forward_vector = {view_matrix[2, 0], view_matrix[2, 1], view_matrix[2, 2]};
-            if constexpr (inverted_z)
+            if constexpr (axes.inverted_forward)
                 forward_vector = -forward_vector;
             return TraitClass::calc_look_at_angle({}, forward_vector);
         }
@@ -121,7 +128,7 @@ namespace omath::projection
         {
             const auto& view_matrix = get_view_matrix();
 
-            if constexpr (inverted_z)
+            if constexpr (axes.inverted_forward)
                 return -Vector3<float>{view_matrix[2, 0], view_matrix[2, 1], view_matrix[2, 2]};
             return {view_matrix[2, 0], view_matrix[2, 1], view_matrix[2, 2]};
         }
@@ -130,6 +137,8 @@ namespace omath::projection
         Vector3<float> get_right() const noexcept
         {
             const auto& view_matrix = get_view_matrix();
+            if constexpr (axes.inverted_right)
+                return -Vector3<float>{view_matrix[0, 0], view_matrix[0, 1], view_matrix[0, 2]};
             return {view_matrix[0, 0], view_matrix[0, 1], view_matrix[0, 2]};
         }
 
diff --git a/tests/general/unit_test_projection.cpp b/tests/general/unit_test_projection.cpp
index 2b0bf31f..1c46e59a 100644
--- a/tests/general/unit_test_projection.cpp
+++ b/tests/general/unit_test_projection.cpp
@@ -5,8 +5,12 @@
 #include <complex>
 #include <gtest/gtest.h>
 #include <omath/3d_primitives/aabb.hpp>
+#include <omath/engines/cry_engine/camera.hpp>
+#include <omath/engines/frostbite_engine/camera.hpp>
+#include <omath/engines/iw_engine/camera.hpp>
 #include <omath/engines/opengl_engine/camera.hpp>
 #include <omath/engines/source_engine/camera.hpp>
+#include <omath/engines/unreal_engine/camera.hpp>
 #include <omath/projection/camera.hpp>
 #include <print>
 #include <random>
@@ -781,4 +785,159 @@ TEST(UnitTestProjection, Unity_CalcOriginFromViewMatrix_WithRotation)
     EXPECT_NEAR(origin.x, 300.f, k_eps);
     EXPECT_NEAR(origin.y, -100.f, k_eps);
     EXPECT_NEAR(origin.z, 75.f, k_eps);
-}
\ No newline at end of file
+}
+// ---- Camera basis vectors at zero angles ----
+
+TEST(UnitTestProjection, SourceEngine_ZeroAngles_BasisVectors)
+{
+    constexpr float k_eps = 1e-5f;
+    const auto cam = omath::source_engine::Camera({}, {}, {1920.f, 1080.f},
+                                                  omath::projection::FieldOfView::from_degrees(90.f), 0.01f, 1000.f);
+    const auto fwd   = cam.get_forward();
+    const auto right = cam.get_right();
+    const auto up    = cam.get_up();
+
+    EXPECT_NEAR(fwd.x,   omath::source_engine::k_abs_forward.x, k_eps);
+    EXPECT_NEAR(fwd.y,   omath::source_engine::k_abs_forward.y, k_eps);
+    EXPECT_NEAR(fwd.z,   omath::source_engine::k_abs_forward.z, k_eps);
+
+    EXPECT_NEAR(right.x, omath::source_engine::k_abs_right.x, k_eps);
+    EXPECT_NEAR(right.y, omath::source_engine::k_abs_right.y, k_eps);
+    EXPECT_NEAR(right.z, omath::source_engine::k_abs_right.z, k_eps);
+
+    EXPECT_NEAR(up.x,    omath::source_engine::k_abs_up.x, k_eps);
+    EXPECT_NEAR(up.y,    omath::source_engine::k_abs_up.y, k_eps);
+    EXPECT_NEAR(up.z,    omath::source_engine::k_abs_up.z, k_eps);
+}
+
+TEST(UnitTestProjection, UnityEngine_ZeroAngles_BasisVectors)
+{
+    constexpr float k_eps = 1e-5f;
+    const auto cam = omath::unity_engine::Camera({}, {}, {1280.f, 720.f},
+                                                 omath::projection::FieldOfView::from_degrees(60.f), 0.03f, 1000.f);
+    const auto fwd   = cam.get_forward();
+    const auto right = cam.get_right();
+    const auto up    = cam.get_up();
+
+    EXPECT_NEAR(fwd.x,   omath::unity_engine::k_abs_forward.x, k_eps);
+    EXPECT_NEAR(fwd.y,   omath::unity_engine::k_abs_forward.y, k_eps);
+    EXPECT_NEAR(fwd.z,   omath::unity_engine::k_abs_forward.z, k_eps);
+
+    EXPECT_NEAR(right.x, omath::unity_engine::k_abs_right.x, k_eps);
+    EXPECT_NEAR(right.y, omath::unity_engine::k_abs_right.y, k_eps);
+    EXPECT_NEAR(right.z, omath::unity_engine::k_abs_right.z, k_eps);
+
+    EXPECT_NEAR(up.x,    omath::unity_engine::k_abs_up.x, k_eps);
+    EXPECT_NEAR(up.y,    omath::unity_engine::k_abs_up.y, k_eps);
+    EXPECT_NEAR(up.z,    omath::unity_engine::k_abs_up.z, k_eps);
+}
+
+TEST(UnitTestProjection, OpenGLEngine_ZeroAngles_BasisVectors)
+{
+    constexpr float k_eps = 1e-5f;
+    const auto cam = omath::opengl_engine::Camera({}, {}, {1920.f, 1080.f},
+                                                  omath::projection::FieldOfView::from_degrees(90.f), 0.01f, 1000.f);
+    const auto fwd   = cam.get_forward();
+    const auto right = cam.get_right();
+    const auto up    = cam.get_up();
+
+    EXPECT_NEAR(fwd.x,   omath::opengl_engine::k_abs_forward.x, k_eps);
+    EXPECT_NEAR(fwd.y,   omath::opengl_engine::k_abs_forward.y, k_eps);
+    EXPECT_NEAR(fwd.z,   omath::opengl_engine::k_abs_forward.z, k_eps);
+
+    EXPECT_NEAR(right.x, omath::opengl_engine::k_abs_right.x, k_eps);
+    EXPECT_NEAR(right.y, omath::opengl_engine::k_abs_right.y, k_eps);
+    EXPECT_NEAR(right.z, omath::opengl_engine::k_abs_right.z, k_eps);
+
+    EXPECT_NEAR(up.x,    omath::opengl_engine::k_abs_up.x, k_eps);
+    EXPECT_NEAR(up.y,    omath::opengl_engine::k_abs_up.y, k_eps);
+    EXPECT_NEAR(up.z,    omath::opengl_engine::k_abs_up.z, k_eps);
+}
+
+TEST(UnitTestProjection, UnrealEngine_ZeroAngles_BasisVectors)
+{
+    constexpr float k_eps = 1e-5f;
+    const auto cam = omath::unreal_engine::Camera({}, {}, {1920.f, 1080.f},
+                                                  omath::projection::FieldOfView::from_degrees(90.f), 0.01f, 1000.f);
+    const auto fwd   = cam.get_forward();
+    const auto right = cam.get_right();
+    const auto up    = cam.get_up();
+
+    EXPECT_NEAR(fwd.x,   omath::unreal_engine::k_abs_forward.x, k_eps);
+    EXPECT_NEAR(fwd.y,   omath::unreal_engine::k_abs_forward.y, k_eps);
+    EXPECT_NEAR(fwd.z,   omath::unreal_engine::k_abs_forward.z, k_eps);
+
+    EXPECT_NEAR(right.x, omath::unreal_engine::k_abs_right.x, k_eps);
+    EXPECT_NEAR(right.y, omath::unreal_engine::k_abs_right.y, k_eps);
+    EXPECT_NEAR(right.z, omath::unreal_engine::k_abs_right.z, k_eps);
+
+    EXPECT_NEAR(up.x,    omath::unreal_engine::k_abs_up.x, k_eps);
+    EXPECT_NEAR(up.y,    omath::unreal_engine::k_abs_up.y, k_eps);
+    EXPECT_NEAR(up.z,    omath::unreal_engine::k_abs_up.z, k_eps);
+}
+
+TEST(UnitTestProjection, FrostbiteEngine_ZeroAngles_BasisVectors)
+{
+    constexpr float k_eps = 1e-5f;
+    const auto cam = omath::frostbite_engine::Camera({}, {}, {1920.f, 1080.f},
+                                                     omath::projection::FieldOfView::from_degrees(90.f), 0.01f, 1000.f);
+    const auto fwd   = cam.get_forward();
+    const auto right = cam.get_right();
+    const auto up    = cam.get_up();
+
+    EXPECT_NEAR(fwd.x,   omath::frostbite_engine::k_abs_forward.x, k_eps);
+    EXPECT_NEAR(fwd.y,   omath::frostbite_engine::k_abs_forward.y, k_eps);
+    EXPECT_NEAR(fwd.z,   omath::frostbite_engine::k_abs_forward.z, k_eps);
+
+    EXPECT_NEAR(right.x, omath::frostbite_engine::k_abs_right.x, k_eps);
+    EXPECT_NEAR(right.y, omath::frostbite_engine::k_abs_right.y, k_eps);
+    EXPECT_NEAR(right.z, omath::frostbite_engine::k_abs_right.z, k_eps);
+
+    EXPECT_NEAR(up.x,    omath::frostbite_engine::k_abs_up.x, k_eps);
+    EXPECT_NEAR(up.y,    omath::frostbite_engine::k_abs_up.y, k_eps);
+    EXPECT_NEAR(up.z,    omath::frostbite_engine::k_abs_up.z, k_eps);
+}
+
+TEST(UnitTestProjection, CryEngine_ZeroAngles_BasisVectors)
+{
+    constexpr float k_eps = 1e-5f;
+    const auto cam = omath::cry_engine::Camera({}, {}, {1920.f, 1080.f},
+                                               omath::projection::FieldOfView::from_degrees(90.f), 0.01f, 1000.f);
+    const auto fwd   = cam.get_forward();
+    const auto right = cam.get_right();
+    const auto up    = cam.get_up();
+
+    EXPECT_NEAR(fwd.x,   omath::cry_engine::k_abs_forward.x, k_eps);
+    EXPECT_NEAR(fwd.y,   omath::cry_engine::k_abs_forward.y, k_eps);
+    EXPECT_NEAR(fwd.z,   omath::cry_engine::k_abs_forward.z, k_eps);
+
+    EXPECT_NEAR(right.x, omath::cry_engine::k_abs_right.x, k_eps);
+    EXPECT_NEAR(right.y, omath::cry_engine::k_abs_right.y, k_eps);
+    EXPECT_NEAR(right.z, omath::cry_engine::k_abs_right.z, k_eps);
+
+    EXPECT_NEAR(up.x,    omath::cry_engine::k_abs_up.x, k_eps);
+    EXPECT_NEAR(up.y,    omath::cry_engine::k_abs_up.y, k_eps);
+    EXPECT_NEAR(up.z,    omath::cry_engine::k_abs_up.z, k_eps);
+}
+
+TEST(UnitTestProjection, IWEngine_ZeroAngles_BasisVectors)
+{
+    constexpr float k_eps = 1e-5f;
+    const auto cam = omath::iw_engine::Camera({}, {}, {1920.f, 1080.f},
+                                              omath::projection::FieldOfView::from_degrees(90.f), 0.01f, 1000.f);
+    const auto fwd   = cam.get_forward();
+    const auto right = cam.get_right();
+    const auto up    = cam.get_up();
+
+    EXPECT_NEAR(fwd.x,   omath::iw_engine::k_abs_forward.x, k_eps);
+    EXPECT_NEAR(fwd.y,   omath::iw_engine::k_abs_forward.y, k_eps);
+    EXPECT_NEAR(fwd.z,   omath::iw_engine::k_abs_forward.z, k_eps);
+
+    EXPECT_NEAR(right.x, omath::iw_engine::k_abs_right.x, k_eps);
+    EXPECT_NEAR(right.y, omath::iw_engine::k_abs_right.y, k_eps);
+    EXPECT_NEAR(right.z, omath::iw_engine::k_abs_right.z, k_eps);
+
+    EXPECT_NEAR(up.x,    omath::iw_engine::k_abs_up.x, k_eps);
+    EXPECT_NEAR(up.y,    omath::iw_engine::k_abs_up.y, k_eps);
+    EXPECT_NEAR(up.z,    omath::iw_engine::k_abs_up.z, k_eps);
+}

From 0419043720c5edea4b3276c843fb4a29e7024330 Mon Sep 17 00:00:00 2001
From: Orange++ <orange-cpp@yandex.ru>
Date: Wed, 15 Apr 2026 03:48:03 +0300
Subject: [PATCH 4/4] Update include/omath/engines/frostbite_engine/camera.hpp

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>
---
 include/omath/engines/frostbite_engine/camera.hpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/include/omath/engines/frostbite_engine/camera.hpp b/include/omath/engines/frostbite_engine/camera.hpp
index 8c02cf1d..25b4d3fb 100644
--- a/include/omath/engines/frostbite_engine/camera.hpp
+++ b/include/omath/engines/frostbite_engine/camera.hpp
@@ -10,4 +10,4 @@
 namespace omath::frostbite_engine
 {
     using Camera =  projection::Camera<Mat4X4, ViewAngles, CameraTrait, NDCDepthRange::ZERO_TO_ONE>;
-} // namespace omath::unity_engine
\ No newline at end of file
+} // namespace omath::frostbite_engine
\ No newline at end of file