Merge pull request #160 from orange-cpp/feaure/gjk-epa-improvement

Feaure/gjk epa improvement

benchmark/benchmark_collision.cpp

@@ -0,0 +1,161 @@
+//
+// Created by Vlad on 3/2/2026.
+//
+#include <benchmark/benchmark.h>
+#include <memory_resource>
+#include <omath/collision/epa_algorithm.hpp>
+#include <omath/collision/gjk_algorithm.hpp>
+#include <omath/engines/source_engine/collider.hpp>
+#include <omath/engines/source_engine/mesh.hpp>
+
+using Mesh = omath::source_engine::Mesh;
+using Collider = omath::source_engine::MeshCollider;
+using Gjk = omath::collision::GjkAlgorithm<Collider>;
+using Epa = omath::collision::Epa<Collider>;
+
+namespace
+{
+    // Unit cube with half-extent 1 — 8 vertices in [-1,1]^3.
+    const std::vector<omath::primitives::Vertex<>> k_cube_vbo = {
+        { { -1.f, -1.f, -1.f }, {}, {} },
+        { { -1.f, -1.f,  1.f }, {}, {} },
+        { { -1.f,  1.f, -1.f }, {}, {} },
+        { { -1.f,  1.f,  1.f }, {}, {} },
+        { {  1.f,  1.f,  1.f }, {}, {} },
+        { {  1.f,  1.f, -1.f }, {}, {} },
+        { {  1.f, -1.f,  1.f }, {}, {} },
+        { {  1.f, -1.f, -1.f }, {}, {} },
+    };
+    const std::vector<omath::Vector3<std::uint32_t>> k_empty_vao{};
+} // namespace
+
+// ---------------------------------------------------------------------------
+// GJK benchmarks
+// ---------------------------------------------------------------------------
+
+// Separated cubes — origin distance 2.1, no overlap.
+// Exercises the early-exit path and the centroid-based initial direction.
+static void BM_Gjk_Separated(benchmark::State& state)
+{
+    const Collider a{Mesh{k_cube_vbo, k_empty_vao}};
+
+    Mesh mesh_b{k_cube_vbo, k_empty_vao};
+    mesh_b.set_origin({0.f, 2.1f, 0.f});
+    const Collider b{mesh_b};
+
+    for ([[maybe_unused]] auto _ : state)
+        benchmark::DoNotOptimize(Gjk::is_collide(a, b));
+}
+
+// Overlapping cubes — B offset by 0.5 along X, ~1.5 units penetration depth.
+static void BM_Gjk_Overlapping(benchmark::State& state)
+{
+    const Collider a{Mesh{k_cube_vbo, k_empty_vao}};
+
+    Mesh mesh_b{k_cube_vbo, k_empty_vao};
+    mesh_b.set_origin({0.5f, 0.f, 0.f});
+    const Collider b{mesh_b};
+
+    for ([[maybe_unused]] auto _ : state)
+        benchmark::DoNotOptimize(Gjk::is_collide(a, b));
+}
+
+// Identical cubes at the same origin — deep overlap / worst case for GJK.
+static void BM_Gjk_SameOrigin(benchmark::State& state)
+{
+    const Collider a{Mesh{k_cube_vbo, k_empty_vao}};
+    const Collider b{Mesh{k_cube_vbo, k_empty_vao}};
+
+    for ([[maybe_unused]] auto _ : state)
+        benchmark::DoNotOptimize(Gjk::is_collide(a, b));
+}
+
+// ---------------------------------------------------------------------------
+// EPA benchmarks
+// ---------------------------------------------------------------------------
+
+// EPA with a pre-allocated monotonic buffer (reset each iteration).
+// Isolates algorithmic cost from allocator overhead.
+static void BM_Epa_MonotonicBuffer(benchmark::State& state)
+{
+    const Collider a{Mesh{k_cube_vbo, k_empty_vao}};
+
+    Mesh mesh_b{k_cube_vbo, k_empty_vao};
+    mesh_b.set_origin({0.5f, 0.f, 0.f});
+    const Collider b{mesh_b};
+
+    const auto [hit, simplex] = Gjk::is_collide_with_simplex_info(a, b);
+    if (!hit)
+        return; // shouldn't happen, but guard for safety
+
+    constexpr Epa::Params params{.max_iterations = 64, .tolerance = 1e-4f};
+
+    // Pre-allocate a 32 KiB stack buffer — enough for typical polytope growth.
+    constexpr std::size_t k_buf_size = 32768;
+    alignas(std::max_align_t) char buf[k_buf_size];
+    std::pmr::monotonic_buffer_resource mr{buf, k_buf_size, std::pmr::null_memory_resource()};
+
+    for ([[maybe_unused]] auto _ : state)
+    {
+        mr.release(); // reset the buffer without touching the upstream resource
+        benchmark::DoNotOptimize(Epa::solve(a, b, simplex, params, mr));
+    }
+}
+
+// EPA with the default (malloc-backed) memory resource.
+// Shows total cost including allocator pressure.
+static void BM_Epa_DefaultResource(benchmark::State& state)
+{
+    const Collider a{Mesh{k_cube_vbo, k_empty_vao}};
+
+    Mesh mesh_b{k_cube_vbo, k_empty_vao};
+    mesh_b.set_origin({0.5f, 0.f, 0.f});
+    const Collider b{mesh_b};
+
+    const auto [hit, simplex] = Gjk::is_collide_with_simplex_info(a, b);
+    if (!hit)
+        return;
+
+    constexpr Epa::Params params{.max_iterations = 64, .tolerance = 1e-4f};
+
+    for ([[maybe_unused]] auto _ : state)
+        benchmark::DoNotOptimize(Epa::solve(a, b, simplex, params));
+}
+
+// ---------------------------------------------------------------------------
+// Combined GJK + EPA pipeline
+// ---------------------------------------------------------------------------
+
+// Full collision pipeline: GJK detects contact, EPA resolves penetration.
+// This is the hot path in a physics engine tick.
+static void BM_GjkEpa_Pipeline(benchmark::State& state)
+{
+    const Collider a{Mesh{k_cube_vbo, k_empty_vao}};
+
+    Mesh mesh_b{k_cube_vbo, k_empty_vao};
+    mesh_b.set_origin({0.5f, 0.f, 0.f});
+    const Collider b{mesh_b};
+
+    constexpr Epa::Params params{.max_iterations = 64, .tolerance = 1e-4f};
+
+    constexpr std::size_t k_buf_size = 32768;
+    alignas(std::max_align_t) char buf[k_buf_size];
+    std::pmr::monotonic_buffer_resource mr{buf, k_buf_size, std::pmr::null_memory_resource()};
+
+    for ([[maybe_unused]] auto _ : state)
+    {
+        mr.release();
+        const auto [hit, simplex] = Gjk::is_collide_with_simplex_info(a, b);
+        if (hit)
+            benchmark::DoNotOptimize(Epa::solve(a, b, simplex, params, mr));
+    }
+}
+
+BENCHMARK(BM_Gjk_Separated)->Iterations(100'000);
+BENCHMARK(BM_Gjk_Overlapping)->Iterations(100'000);
+BENCHMARK(BM_Gjk_SameOrigin)->Iterations(100'000);
+
+BENCHMARK(BM_Epa_MonotonicBuffer)->Iterations(100'000);
+BENCHMARK(BM_Epa_DefaultResource)->Iterations(100'000);
+
+BENCHMARK(BM_GjkEpa_Pipeline)->Iterations(100'000);

include/omath/collision/epa_algorithm.hpp

@@ -8,6 +8,7 @@
 #include <memory>
 #include <memory_resource>
 #include <queue>
+#include <unordered_map>
 #include <utility>
 #include <vector>
 
@@ -56,83 +57,76 @@ namespace omath::collision
                                            const Simplex<VectorType>& simplex, const Params params = {},
                                            std::pmr::memory_resource& mem_resource = *std::pmr::get_default_resource())
         {
-            // --- Build initial polytope from simplex (4 points) ---
             std::pmr::vector<VectorType> vertexes = build_initial_polytope_from_simplex(simplex, mem_resource);
-
-            // Initial tetra faces (windings corrected in make_face)
             std::pmr::vector<Face> faces = create_initial_tetra_faces(mem_resource, vertexes);
 
-            auto heap = rebuild_heap(faces, mem_resource);
+            // Build initial min-heap by distance.
+            Heap heap = rebuild_heap(faces, mem_resource);
 
             Result out{};
 
+            // Hoisted outside the loop to reuse bucket allocation across iterations.
+            // Initial bucket count 16 covers a typical horizon without rehashing.
+            BoundaryMap boundary{16, &mem_resource};
+
             for (int it = 0; it < params.max_iterations; ++it)
             {
-                // If heap might be stale after face edits, rebuild lazily.
+                // Lazily discard stale (deleted or index-mismatched) heap entries.
-                if (heap.empty())
+                discard_stale_heap_entries(faces, heap);
-                    break;
-                // Rebuild when the "closest" face changed (simple cheap guard)
-                // (We could keep face handles; this is fine for small Ns.)
-
-                if (const auto top = heap.top(); faces[top.idx].d != top.d)
-                    heap = rebuild_heap(faces, mem_resource);
 
                 if (heap.empty())
                     break;
 
-                // FIXME: STORE REF VALUE, DO NOT USE
-                //  AFTER IF STATEMENT BLOCK
                 const Face& face = faces[heap.top().idx];
 
-                // Get the furthest point in face normal direction
                 const VectorType p = support_point(a, b, face.n);
                 const auto p_dist = face.n.dot(p);
 
-                // Converged if we can’t push the face closer than tolerance
+                // Converged: new support can't push the face closer than tolerance.
                 if (p_dist - face.d <= params.tolerance)
                 {
                     out.normal = face.n;
-                    out.depth = face.d; // along unit normal
+                    out.depth = face.d;
                     out.iterations = it + 1;
                     out.num_vertices = static_cast<int>(vertexes.size());
                     out.num_faces = static_cast<int>(faces.size());
-
                     out.penetration_vector = out.normal * out.depth;
                     return out;
                 }
 
-                // Add new vertex
                 const int new_idx = static_cast<int>(vertexes.size());
                 vertexes.emplace_back(p);
 
-                const auto [to_delete, boundary] = mark_visible_and_collect_horizon(faces, p);
+                // Tombstone visible faces and collect the horizon boundary.
+                // This avoids copying the faces array (O(n)) each iteration.
+                tombstone_visible_faces(faces, boundary, p);
 
-                erase_marked(faces, to_delete);
+                // Stitch new faces around the horizon and push them directly onto the
-
+                // heap — no full O(n log n) rebuild needed.
-                // Stitch new faces around the horizon
+                for (const auto& [key, e] : boundary)
-                for (const auto& e : boundary)
+                {
+                    const int fi = static_cast<int>(faces.size());
                     faces.emplace_back(make_face(vertexes, e.a, e.b, new_idx));
-
+                    heap.emplace(faces.back().d, fi);
-                // Rebuild heap after topology change
+                }
-                heap = rebuild_heap(faces, mem_resource);
 
                 if (!std::isfinite(vertexes.back().dot(vertexes.back())))
                     break; // safety
+
                 out.iterations = it + 1;
             }
 
-            if (faces.empty())
+            // Find the best surviving (non-deleted) face.
+            const Face* best = find_best_surviving_face(faces);
+
+            if (!best)
                 return std::nullopt;
 
-            const auto best = *std::ranges::min_element(faces, [](const auto& first, const auto& second)
+            out.normal = best->n;
-                                                        { return first.d < second.d; });
+            out.depth = best->d;
-            out.normal = best.n;
-            out.depth = best.d;
             out.num_vertices = static_cast<int>(vertexes.size());
             out.num_faces = static_cast<int>(faces.size());
-
             out.penetration_vector = out.normal * out.depth;
-
             return out;
         }
 
@@ -141,7 +135,8 @@ namespace omath::collision
         {
             int i0, i1, i2;
             VectorType n; // unit outward normal
-            FloatingType d; // n · v0  (>=0 ideally because origin is inside)
+            FloatingType d; // n · v0  (>= 0 ideally because origin is inside)
+            bool deleted{false}; // tombstone flag — avoids O(n) compaction per iteration
         };
 
         struct Edge final
@@ -154,6 +149,7 @@ namespace omath::collision
             FloatingType d;
             int idx;
         };
+
         struct HeapCmp final
         {
             [[nodiscard]]
@@ -165,35 +161,44 @@ namespace omath::collision
 
         using Heap = std::priority_queue<HeapItem, std::pmr::vector<HeapItem>, HeapCmp>;
 
+        // Horizon boundary: maps packed(a,b) → Edge.
+        // Opposite edges cancel in O(1) via hash lookup instead of O(h) linear scan.
+        using BoundaryMap = std::pmr::unordered_map<std::int64_t, Edge>;
+
+        [[nodiscard]]
+        static constexpr std::int64_t pack_edge(const int a, const int b) noexcept
+        {
+            return (static_cast<std::int64_t>(a) << 32) | static_cast<std::uint32_t>(b);
+        }
+
         [[nodiscard]]
         static Heap rebuild_heap(const std::pmr::vector<Face>& faces, auto& memory_resource)
         {
             std::pmr::vector<HeapItem> storage{&memory_resource};
-            storage.reserve(faces.size()); // optional but recommended
+            storage.reserve(faces.size());
-
             Heap h{HeapCmp{}, std::move(storage)};
-
             for (int i = 0; i < static_cast<int>(faces.size()); ++i)
+                if (!faces[i].deleted)
                     h.emplace(faces[i].d, i);
-
+            return h;
-            return h; // allocator is preserved
         }
 
         [[nodiscard]]
         static bool visible_from(const Face& f, const VectorType& p)
         {
-            // positive if p is in front of the face
             return f.n.dot(p) - f.d > static_cast<FloatingType>(1e-7);
         }
 
-        static void add_edge_boundary(std::pmr::vector<Edge>& boundary, int a, int b)
+        static void add_edge_boundary(BoundaryMap& boundary, int a, int b)
         {
-            // Keep edges that appear only once; erase if opposite already present
+            // O(1) cancel: if the opposite edge (b→a) is already in the map it is an
-            auto itb = std::ranges::find_if(boundary, [&](const Edge& e) { return e.a == b && e.b == a; });
+            // internal edge shared by two visible faces and must be removed.
-            if (itb != boundary.end())
+            // Otherwise this is a horizon edge and we insert it.
-                boundary.erase(itb); // internal edge cancels out
+            const std::int64_t rev = pack_edge(b, a);
+            if (const auto it = boundary.find(rev); it != boundary.end())
+                boundary.erase(it);
             else
-                boundary.emplace_back(a, b); // horizon edge (directed)
+                boundary.emplace(pack_edge(a, b), Edge{a, b});
         }
 
         [[nodiscard]]
@@ -204,9 +209,7 @@ namespace omath::collision
             const VectorType& a2 = vertexes[i2];
             VectorType n = (a1 - a0).cross(a2 - a0);
             if (n.dot(n) <= static_cast<FloatingType>(1e-30))
-            {
                 n = any_perp_vec(a1 - a0); // degenerate guard
-            }
             // Ensure normal points outward (away from origin): require n·a0 >= 0
             if (n.dot(a0) < static_cast<FloatingType>(0.0))
             {
@@ -243,6 +246,7 @@ namespace omath::collision
                     return d;
             return V{1, 0, 0};
         }
+
         [[nodiscard]]
         static std::pmr::vector<Face> create_initial_tetra_faces(std::pmr::memory_resource& mem_resource,
                                                                  const std::pmr::vector<VectorType>& vertexes)
@@ -262,48 +266,45 @@ namespace omath::collision
         {
             std::pmr::vector<VectorType> vertexes{&mem_resource};
             vertexes.reserve(simplex.size());
-
             for (std::size_t i = 0; i < simplex.size(); ++i)
                 vertexes.emplace_back(simplex[i]);
-
             return vertexes;
         }
-        static void erase_marked(std::pmr::vector<Face>& faces, const std::pmr::vector<bool>& to_delete)
+
+        static const Face* find_best_surviving_face(const std::pmr::vector<Face>& faces)
         {
-            auto* mr = faces.get_allocator().resource(); // keep same resource
+            const Face* best = nullptr;
-            std::pmr::vector<Face> kept{mr};
+            for (const auto& f : faces)
-            kept.reserve(faces.size());
+                if (!f.deleted && (best == nullptr || f.d < best->d))
-
+                    best = &f;
-            for (std::size_t i = 0; i < faces.size(); ++i)
+            return best;
-                if (!to_delete[i])
-                    kept.emplace_back(faces[i]);
-
-            faces.swap(kept);
         }
-        struct Horizon
+        static void tombstone_visible_faces(std::pmr::vector<Face>& faces, BoundaryMap& boundary,
+                                            const VectorType& p)
         {
-            std::pmr::vector<bool> to_delete;
+            boundary.clear();
-            std::pmr::vector<Edge> boundary;
+            for (auto& f : faces)
-        };
-
-        static Horizon mark_visible_and_collect_horizon(const std::pmr::vector<Face>& faces, const VectorType& p)
             {
-            auto* mr = faces.get_allocator().resource();
+                if (!f.deleted && visible_from(f, p))
-
-            Horizon horizon{std::pmr::vector<bool>(faces.size(), false, mr), std::pmr::vector<Edge>(mr)};
-            horizon.boundary.reserve(faces.size());
-
-            for (std::size_t i = 0; i < faces.size(); ++i)
-                if (visible_from(faces[i], p))
                 {
-                    const auto& rf = faces[i];
+                    f.deleted = true;
-                    horizon.to_delete[i] = true;
+                    add_edge_boundary(boundary, f.i0, f.i1);
-                    add_edge_boundary(horizon.boundary, rf.i0, rf.i1);
+                    add_edge_boundary(boundary, f.i1, f.i2);
-                    add_edge_boundary(horizon.boundary, rf.i1, rf.i2);
+                    add_edge_boundary(boundary, f.i2, f.i0);
-                    add_edge_boundary(horizon.boundary, rf.i2, rf.i0);
+                }
+            }
         }
 
-            return horizon;
+        static void discard_stale_heap_entries(const std::pmr::vector<Face>& faces,
+                                               std::priority_queue<HeapItem, std::pmr::vector<HeapItem>, HeapCmp>& heap)
+        {
+            while (!heap.empty())
+            {
+                const auto& top = heap.top();
+                if (!faces[top.idx].deleted && faces[top.idx].d == top.d)
+                    break;
+                heap.pop();
+            }
         }
     };
 } // namespace omath::collision

include/omath/collision/gjk_algorithm.hpp

@@ -43,7 +43,20 @@ namespace omath::collision
                                                                    const ColliderInterfaceType& collider_b,
                                                                    const GjkSettings& settings = {})
         {
-            auto support = find_support_vertex(collider_a, collider_b, VectorType{1, 0, 0});
+            // Use centroid difference as initial direction — greatly reduces iterations for separated shapes.
+            VectorType initial_dir;
+            if constexpr (requires { collider_b.get_origin() - collider_a.get_origin(); })
+            {
+                initial_dir = collider_b.get_origin() - collider_a.get_origin();
+                if (initial_dir.dot(initial_dir) < settings.epsilon * settings.epsilon)
+                    initial_dir = VectorType{1, 0, 0};
+            }
+            else
+            {
+                initial_dir = VectorType{1, 0, 0};
+            }
+
+            auto support = find_support_vertex(collider_a, collider_b, initial_dir);
 
             Simplex<VectorType> simplex;
             simplex.push_front(support);

include/omath/collision/mesh_collider.hpp

@@ -42,6 +42,16 @@ namespace omath::collision
             m_mesh.set_origin(new_origin);
         }
 
+        [[nodiscard]]
+        const MeshType& get_mesh() const
+        {
+            return m_mesh;
+        }
+        [[nodiscard]]
+        MeshType& get_mesh()
+        {
+            return m_mesh;
+        }
     private:
         [[nodiscard]]
         const VertexType& find_furthest_vertex(const VectorType& direction) const

tests/general/unit_test_epa_comprehensive.cpp

@@ -0,0 +1,471 @@
+//
+// Comprehensive EPA tests.
+// Covers: all 3 axis directions, multiple depth levels, penetration-vector
+// round-trips, depth monotonicity, symmetry, asymmetric sizes, memory
+// resource variants, tolerance sensitivity, and iteration bookkeeping.
+//
+#include <cmath>
+#include <gtest/gtest.h>
+#include <memory_resource>
+#include <omath/collision/epa_algorithm.hpp>
+#include <omath/collision/gjk_algorithm.hpp>
+#include <omath/engines/source_engine/collider.hpp>
+#include <omath/engines/source_engine/mesh.hpp>
+
+using Mesh     = omath::source_engine::Mesh;
+using Collider = omath::source_engine::MeshCollider;
+using Gjk      = omath::collision::GjkAlgorithm<Collider>;
+using Epa      = omath::collision::Epa<Collider>;
+using Vec3     = omath::Vector3<float>;
+
+namespace
+{
+    const std::vector<omath::primitives::Vertex<>> k_cube_vbo = {
+        { { -1.f, -1.f, -1.f }, {}, {} },
+        { { -1.f, -1.f,  1.f }, {}, {} },
+        { { -1.f,  1.f, -1.f }, {}, {} },
+        { { -1.f,  1.f,  1.f }, {}, {} },
+        { {  1.f,  1.f,  1.f }, {}, {} },
+        { {  1.f,  1.f, -1.f }, {}, {} },
+        { {  1.f, -1.f,  1.f }, {}, {} },
+        { {  1.f, -1.f, -1.f }, {}, {} },
+    };
+    const std::vector<omath::Vector3<std::uint32_t>> k_empty_ebo{};
+
+    constexpr Epa::Params k_default_params{ .max_iterations = 64, .tolerance = 1e-4f };
+
+    Collider make_cube(const Vec3& origin = {}, const Vec3& scale = { 1, 1, 1 })
+    {
+        Mesh m{ k_cube_vbo, k_empty_ebo, scale };
+        m.set_origin(origin);
+        return Collider{ m };
+    }
+
+    // Run GJK then EPA; asserts GJK hit and EPA converged.
+    Epa::Result solve(const Collider& a, const Collider& b,
+                      const Epa::Params& params = k_default_params)
+    {
+        const auto [hit, simplex] = Gjk::is_collide_with_simplex_info(a, b);
+        EXPECT_TRUE(hit) << "GJK must detect collision before EPA can run";
+        auto result = Epa::solve(a, b, simplex, params);
+        EXPECT_TRUE(result.has_value()) << "EPA must converge";
+        return *result;
+    }
+} // namespace
+
+// ---------------------------------------------------------------------------
+// Normal direction per axis
+// ---------------------------------------------------------------------------
+
+// For two unit cubes (half-extent 1) with B offset by d along an axis:
+//   depth = 2 - d   (distance from origin to nearest face of Minkowski diff)
+//   normal component along that axis ≈ ±1
+
+TEST(EpaComprehensive, NormalAlongX_Positive)
+{
+    const auto r = solve(make_cube({ 0, 0, 0 }), make_cube({ 0.5f, 0, 0 }));
+    EXPECT_NEAR(std::abs(r.normal.x), 1.f, 1e-3f);
+    EXPECT_NEAR(r.normal.y, 0.f, 1e-3f);
+    EXPECT_NEAR(r.normal.z, 0.f, 1e-3f);
+}
+
+TEST(EpaComprehensive, NormalAlongX_Negative)
+{
+    const auto r = solve(make_cube({ 0, 0, 0 }), make_cube({ -0.5f, 0, 0 }));
+    EXPECT_NEAR(std::abs(r.normal.x), 1.f, 1e-3f);
+    EXPECT_NEAR(r.normal.y, 0.f, 1e-3f);
+    EXPECT_NEAR(r.normal.z, 0.f, 1e-3f);
+}
+
+TEST(EpaComprehensive, NormalAlongY_Positive)
+{
+    const auto r = solve(make_cube({ 0, 0, 0 }), make_cube({ 0, 0.5f, 0 }));
+    EXPECT_NEAR(r.normal.x, 0.f, 1e-3f);
+    EXPECT_NEAR(std::abs(r.normal.y), 1.f, 1e-3f);
+    EXPECT_NEAR(r.normal.z, 0.f, 1e-3f);
+}
+
+TEST(EpaComprehensive, NormalAlongY_Negative)
+{
+    const auto r = solve(make_cube({ 0, 0, 0 }), make_cube({ 0, -0.5f, 0 }));
+    EXPECT_NEAR(r.normal.x, 0.f, 1e-3f);
+    EXPECT_NEAR(std::abs(r.normal.y), 1.f, 1e-3f);
+    EXPECT_NEAR(r.normal.z, 0.f, 1e-3f);
+}
+
+TEST(EpaComprehensive, NormalAlongZ_Positive)
+{
+    const auto r = solve(make_cube({ 0, 0, 0 }), make_cube({ 0, 0, 0.5f }));
+    EXPECT_NEAR(r.normal.x, 0.f, 1e-3f);
+    EXPECT_NEAR(r.normal.y, 0.f, 1e-3f);
+    EXPECT_NEAR(std::abs(r.normal.z), 1.f, 1e-3f);
+}
+
+TEST(EpaComprehensive, NormalAlongZ_Negative)
+{
+    const auto r = solve(make_cube({ 0, 0, 0 }), make_cube({ 0, 0, -0.5f }));
+    EXPECT_NEAR(r.normal.x, 0.f, 1e-3f);
+    EXPECT_NEAR(r.normal.y, 0.f, 1e-3f);
+    EXPECT_NEAR(std::abs(r.normal.z), 1.f, 1e-3f);
+}
+
+// ---------------------------------------------------------------------------
+// Depth correctness  (depth = 2 - offset for unit cubes)
+// ---------------------------------------------------------------------------
+
+TEST(EpaComprehensive, Depth_ShallowOverlap)
+{
+    // offset 1.9 → depth 0.1
+    const auto r = solve(make_cube({ 0, 0, 0 }), make_cube({ 1.9f, 0, 0 }));
+    EXPECT_NEAR(r.depth, 0.1f, 1e-2f);
+}
+
+TEST(EpaComprehensive, Depth_QuarterOverlap)
+{
+    // offset 1.5 → depth 0.5
+    const auto r = solve(make_cube({ 0, 0, 0 }), make_cube({ 1.5f, 0, 0 }));
+    EXPECT_NEAR(r.depth, 0.5f, 1e-2f);
+}
+
+TEST(EpaComprehensive, Depth_HalfOverlap)
+{
+    // offset 1.0 → depth 1.0
+    const auto r = solve(make_cube({ 0, 0, 0 }), make_cube({ 1.0f, 0, 0 }));
+    EXPECT_NEAR(r.depth, 1.0f, 1e-2f);
+}
+
+TEST(EpaComprehensive, Depth_ThreeQuarterOverlap)
+{
+    // offset 0.5 → depth 1.5
+    const auto r = solve(make_cube({ 0, 0, 0 }), make_cube({ 0.5f, 0, 0 }));
+    EXPECT_NEAR(r.depth, 1.5f, 1e-2f);
+}
+
+TEST(EpaComprehensive, Depth_AlongY_HalfOverlap)
+{
+    const auto r = solve(make_cube({ 0, 0, 0 }), make_cube({ 0, 1.0f, 0 }));
+    EXPECT_NEAR(r.depth, 1.0f, 1e-2f);
+}
+
+TEST(EpaComprehensive, Depth_AlongZ_HalfOverlap)
+{
+    const auto r = solve(make_cube({ 0, 0, 0 }), make_cube({ 0, 0, 1.0f }));
+    EXPECT_NEAR(r.depth, 1.0f, 1e-2f);
+}
+
+// ---------------------------------------------------------------------------
+// Depth monotonicity — deeper overlap → larger depth
+// ---------------------------------------------------------------------------
+
+TEST(EpaComprehensive, DepthMonotonic_AlongX)
+{
+    const float d1 = solve(make_cube({ 0, 0, 0 }), make_cube({ 1.9f, 0, 0 })).depth; // ~0.1
+    const float d2 = solve(make_cube({ 0, 0, 0 }), make_cube({ 1.5f, 0, 0 })).depth; // ~0.5
+    const float d3 = solve(make_cube({ 0, 0, 0 }), make_cube({ 1.0f, 0, 0 })).depth; // ~1.0
+    const float d4 = solve(make_cube({ 0, 0, 0 }), make_cube({ 0.5f, 0, 0 })).depth; // ~1.5
+
+    EXPECT_LT(d1, d2);
+    EXPECT_LT(d2, d3);
+    EXPECT_LT(d3, d4);
+}
+
+// ---------------------------------------------------------------------------
+// Normal is a unit vector
+// ---------------------------------------------------------------------------
+
+TEST(EpaComprehensive, NormalIsUnit_AlongX)
+{
+    const auto r = solve(make_cube({ 0, 0, 0 }), make_cube({ 0.5f, 0, 0 }));
+    EXPECT_NEAR(r.normal.dot(r.normal), 1.f, 1e-5f);
+}
+
+TEST(EpaComprehensive, NormalIsUnit_AlongY)
+{
+    const auto r = solve(make_cube({ 0, 0, 0 }), make_cube({ 0, 1.2f, 0 }));
+    EXPECT_NEAR(r.normal.dot(r.normal), 1.f, 1e-5f);
+}
+
+TEST(EpaComprehensive, NormalIsUnit_AlongZ)
+{
+    const auto r = solve(make_cube({ 0, 0, 0 }), make_cube({ 0, 0, 0.8f }));
+    EXPECT_NEAR(r.normal.dot(r.normal), 1.f, 1e-5f);
+}
+
+// ---------------------------------------------------------------------------
+// Penetration vector = normal * depth
+// ---------------------------------------------------------------------------
+
+TEST(EpaComprehensive, PenetrationVectorLength_EqualsDepth)
+{
+    const auto r = solve(make_cube({ 0, 0, 0 }), make_cube({ 0.5f, 0, 0 }));
+    const float pen_len = std::sqrt(r.penetration_vector.dot(r.penetration_vector));
+    EXPECT_NEAR(pen_len, r.depth, 1e-5f);
+}
+
+TEST(EpaComprehensive, PenetrationVectorDirection_ParallelToNormal)
+{
+    const auto r = solve(make_cube({ 0, 0, 0 }), make_cube({ 0, 1.0f, 0 }));
+    // penetration_vector = normal * depth → cross product must be ~zero
+    const auto cross = r.penetration_vector.cross(r.normal);
+    EXPECT_NEAR(cross.dot(cross), 0.f, 1e-8f);
+}
+
+// ---------------------------------------------------------------------------
+// Round-trip: applying penetration_vector separates the shapes
+// ---------------------------------------------------------------------------
+
+TEST(EpaComprehensive, RoundTrip_AlongX)
+{
+    const auto a = make_cube({ 0, 0, 0 });
+    Mesh mesh_b{ k_cube_vbo, k_empty_ebo };
+    mesh_b.set_origin({ 0.5f, 0, 0 });
+    const auto b = Collider{ mesh_b };
+
+    const auto r = solve(a, b);
+    constexpr float margin = 1.f + 1e-3f;
+
+    // Move B along the penetration vector; it should separate from A
+    Mesh mesh_sep{ k_cube_vbo, k_empty_ebo };
+    mesh_sep.set_origin(mesh_b.get_origin() + r.penetration_vector * margin);
+    EXPECT_FALSE(Gjk::is_collide(a, Collider{ mesh_sep })) << "Applying pen vector must separate";
+
+    // Moving the wrong way must still collide
+    Mesh mesh_wrong{ k_cube_vbo, k_empty_ebo };
+    mesh_wrong.set_origin(mesh_b.get_origin() - r.penetration_vector * margin);
+    EXPECT_TRUE(Gjk::is_collide(a, Collider{ mesh_wrong })) << "Opposite direction must still collide";
+}
+
+TEST(EpaComprehensive, RoundTrip_AlongY)
+{
+    const auto a = make_cube({ 0, 0, 0 });
+    Mesh mesh_b{ k_cube_vbo, k_empty_ebo };
+    mesh_b.set_origin({ 0, 0.8f, 0 });
+    const auto b = Collider{ mesh_b };
+
+    const auto r = solve(a, b);
+    constexpr float margin = 1.f + 1e-3f;
+
+    Mesh mesh_sep{ k_cube_vbo, k_empty_ebo };
+    mesh_sep.set_origin(mesh_b.get_origin() + r.penetration_vector * margin);
+    EXPECT_FALSE(Gjk::is_collide(a, Collider{ mesh_sep }));
+
+    Mesh mesh_wrong{ k_cube_vbo, k_empty_ebo };
+    mesh_wrong.set_origin(mesh_b.get_origin() - r.penetration_vector * margin);
+    EXPECT_TRUE(Gjk::is_collide(a, Collider{ mesh_wrong }));
+}
+
+TEST(EpaComprehensive, RoundTrip_AlongZ)
+{
+    const auto a = make_cube({ 0, 0, 0 });
+    Mesh mesh_b{ k_cube_vbo, k_empty_ebo };
+    mesh_b.set_origin({ 0, 0, 1.2f });
+    const auto b = Collider{ mesh_b };
+
+    const auto r = solve(a, b);
+    constexpr float margin = 1.f + 1e-3f;
+
+    Mesh mesh_sep{ k_cube_vbo, k_empty_ebo };
+    mesh_sep.set_origin(mesh_b.get_origin() + r.penetration_vector * margin);
+    EXPECT_FALSE(Gjk::is_collide(a, Collider{ mesh_sep }));
+}
+
+// ---------------------------------------------------------------------------
+// Symmetry — swapping A and B preserves depth
+// ---------------------------------------------------------------------------
+
+TEST(EpaComprehensive, Symmetry_DepthIsIndependentOfOrder)
+{
+    const auto a = make_cube({ 0, 0, 0 });
+    const auto b = make_cube({ 0.5f, 0, 0 });
+
+    const float depth_ab = solve(a, b).depth;
+    const float depth_ba = solve(b, a).depth;
+
+    EXPECT_NEAR(depth_ab, depth_ba, 1e-2f);
+}
+
+TEST(EpaComprehensive, Symmetry_NormalsAreOpposite)
+{
+    const auto a = make_cube({ 0, 0, 0 });
+    const auto b = make_cube({ 0.5f, 0, 0 });
+
+    const Vec3 n_ab = solve(a, b).normal;
+    const Vec3 n_ba = solve(b, a).normal;
+
+    // The normals should be anti-parallel: n_ab · n_ba ≈ -1
+    EXPECT_NEAR(n_ab.dot(n_ba), -1.f, 1e-3f);
+}
+
+// ---------------------------------------------------------------------------
+// Asymmetric sizes
+// ---------------------------------------------------------------------------
+
+TEST(EpaComprehensive, LargeVsSmall_DepthCorrect)
+{
+    // Big (half-ext 2) at origin, small (half-ext 0.5) at (2.0, 0, 0)
+    // Minkowski diff closest face in X at distance 0.5
+    const auto r = solve(make_cube({ 0, 0, 0 }, { 2, 2, 2 }), make_cube({ 2.0f, 0, 0 }, { 0.5f, 0.5f, 0.5f }));
+    EXPECT_NEAR(r.depth, 0.5f, 1e-2f);
+    EXPECT_NEAR(std::abs(r.normal.x), 1.f, 1e-3f);
+}
+
+TEST(EpaComprehensive, LargeVsSmall_RoundTrip)
+{
+    const auto a = make_cube({ 0, 0, 0 }, { 2, 2, 2 });
+
+    Mesh mesh_b{ k_cube_vbo, k_empty_ebo, { 0.5f, 0.5f, 0.5f } };
+    mesh_b.set_origin({ 2.0f, 0, 0 });
+    const auto b = Collider{ mesh_b };
+
+    const auto r = solve(a, b);
+    constexpr float margin = 1.f + 1e-3f;
+
+    Mesh mesh_sep{ k_cube_vbo, k_empty_ebo, { 0.5f, 0.5f, 0.5f } };
+    mesh_sep.set_origin(mesh_b.get_origin() + r.penetration_vector * margin);
+    EXPECT_FALSE(Gjk::is_collide(a, Collider{ mesh_sep }));
+}
+
+// ---------------------------------------------------------------------------
+// Memory resource variants
+// ---------------------------------------------------------------------------
+
+TEST(EpaComprehensive, MonotonicBuffer_ConvergesCorrectly)
+{
+    const auto a = make_cube({ 0, 0, 0 });
+    const auto b = make_cube({ 0.5f, 0, 0 });
+    const auto [hit, simplex] = Gjk::is_collide_with_simplex_info(a, b);
+    ASSERT_TRUE(hit);
+
+    constexpr std::size_t k_buf = 32768;
+    alignas(std::max_align_t) char buf[k_buf];
+    std::pmr::monotonic_buffer_resource mr{ buf, k_buf, std::pmr::null_memory_resource() };
+
+    const auto r = Epa::solve(a, b, simplex, k_default_params, mr);
+    ASSERT_TRUE(r.has_value());
+    EXPECT_NEAR(r->depth, 1.5f, 1e-2f);
+}
+
+TEST(EpaComprehensive, MonotonicBuffer_MultipleReleaseCycles)
+{
+    // Verify mr.release() correctly resets the buffer across multiple calls
+    const auto a = make_cube({ 0, 0, 0 });
+    const auto b = make_cube({ 0.5f, 0, 0 });
+    const auto [hit, simplex] = Gjk::is_collide_with_simplex_info(a, b);
+    ASSERT_TRUE(hit);
+
+    constexpr std::size_t k_buf = 32768;
+    alignas(std::max_align_t) char buf[k_buf];
+    std::pmr::monotonic_buffer_resource mr{ buf, k_buf, std::pmr::null_memory_resource() };
+
+    float first_depth = 0.f;
+    for (int i = 0; i < 5; ++i)
+    {
+        mr.release();
+        const auto r = Epa::solve(a, b, simplex, k_default_params, mr);
+        ASSERT_TRUE(r.has_value()) << "solve must converge on iteration " << i;
+        if (i == 0)
+            first_depth = r->depth;
+        else
+            EXPECT_NEAR(r->depth, first_depth, 1e-6f) << "depth must be deterministic";
+    }
+}
+
+TEST(EpaComprehensive, DefaultResource_ConvergesCorrectly)
+{
+    const auto a = make_cube({ 0, 0, 0 });
+    const auto b = make_cube({ 1.0f, 0, 0 });
+    const auto [hit, simplex] = Gjk::is_collide_with_simplex_info(a, b);
+    ASSERT_TRUE(hit);
+
+    const auto r = Epa::solve(a, b, simplex);
+    ASSERT_TRUE(r.has_value());
+    EXPECT_NEAR(r->depth, 1.0f, 1e-2f);
+}
+
+// ---------------------------------------------------------------------------
+// Tolerance sensitivity
+// ---------------------------------------------------------------------------
+
+TEST(EpaComprehensive, TighterTolerance_MoreAccurateDepth)
+{
+    const auto a = make_cube({ 0, 0, 0 });
+    const auto b = make_cube({ 1.0f, 0, 0 });
+    const auto [hit, simplex] = Gjk::is_collide_with_simplex_info(a, b);
+    ASSERT_TRUE(hit);
+
+    const Epa::Params loose{ .max_iterations = 64, .tolerance = 1e-2f };
+    const Epa::Params tight{ .max_iterations = 64, .tolerance = 1e-5f };
+
+    const auto r_loose = Epa::solve(a, b, simplex, loose);
+    const auto r_tight = Epa::solve(a, b, simplex, tight);
+    ASSERT_TRUE(r_loose.has_value());
+    ASSERT_TRUE(r_tight.has_value());
+
+    // Tighter tolerance must yield a result at least as accurate
+    EXPECT_LE(std::abs(r_tight->depth - 1.0f), std::abs(r_loose->depth - 1.0f) + 1e-4f);
+}
+
+// ---------------------------------------------------------------------------
+// Bookkeeping fields
+// ---------------------------------------------------------------------------
+
+TEST(EpaComprehensive, Bookkeeping_IterationsInBounds)
+{
+    const auto a = make_cube({ 0, 0, 0 });
+    const auto b = make_cube({ 0.5f, 0, 0 });
+    const auto r = solve(a, b);
+
+    EXPECT_GT(r.iterations, 0);
+    EXPECT_LE(r.iterations, k_default_params.max_iterations);
+}
+
+TEST(EpaComprehensive, Bookkeeping_FacesAndVerticesGrow)
+{
+    const auto a = make_cube({ 0, 0, 0 });
+    const auto b = make_cube({ 0.5f, 0, 0 });
+    const auto r = solve(a, b);
+
+    // Started with a tetrahedron (4 faces, 4 vertices); EPA must have expanded it
+    EXPECT_GE(r.num_faces, 4);
+    EXPECT_GE(r.num_vertices, 4);
+}
+
+TEST(EpaComprehensive, Bookkeeping_MaxIterationsRespected)
+{
+    const auto a = make_cube({ 0, 0, 0 });
+    const auto b = make_cube({ 0.5f, 0, 0 });
+    const auto [hit, simplex] = Gjk::is_collide_with_simplex_info(a, b);
+    ASSERT_TRUE(hit);
+
+    constexpr Epa::Params tight{ .max_iterations = 3, .tolerance = 1e-10f };
+    const auto r = Epa::solve(a, b, simplex, tight);
+
+    // Must return something (fallback best-face path) and respect the cap
+    if (r.has_value())
+        EXPECT_LE(r->iterations, tight.max_iterations);
+}
+
+// ---------------------------------------------------------------------------
+// Determinism
+// ---------------------------------------------------------------------------
+
+TEST(EpaComprehensive, Deterministic_SameResultOnRepeatedCalls)
+{
+    const auto a = make_cube({ 0, 0, 0 });
+    const auto b = make_cube({ 0.7f, 0, 0 });
+    const auto [hit, simplex] = Gjk::is_collide_with_simplex_info(a, b);
+    ASSERT_TRUE(hit);
+
+    const auto first = Epa::solve(a, b, simplex);
+    ASSERT_TRUE(first.has_value());
+
+    for (int i = 0; i < 5; ++i)
+    {
+        const auto r = Epa::solve(a, b, simplex);
+        ASSERT_TRUE(r.has_value());
+        EXPECT_NEAR(r->depth, first->depth, 1e-6f);
+        EXPECT_NEAR(r->normal.x, first->normal.x, 1e-6f);
+        EXPECT_NEAR(r->normal.y, first->normal.y, 1e-6f);
+        EXPECT_NEAR(r->normal.z, first->normal.z, 1e-6f);
+    }
+}

tests/general/unit_test_gjk_comprehensive.cpp

@@ -0,0 +1,277 @@
+//
+// Comprehensive GJK tests.
+// Covers: all 6 axis directions, diagonal cases, boundary touching,
+// asymmetric sizes, nesting, symmetry, simplex info, far separation.
+//
+#include <gtest/gtest.h>
+#include <omath/collision/gjk_algorithm.hpp>
+#include <omath/engines/source_engine/collider.hpp>
+#include <omath/engines/source_engine/mesh.hpp>
+
+using Mesh     = omath::source_engine::Mesh;
+using Collider = omath::source_engine::MeshCollider;
+using Gjk      = omath::collision::GjkAlgorithm<Collider>;
+using Vec3     = omath::Vector3<float>;
+
+namespace
+{
+    // Unit cube [-1, 1]^3 in local space.
+    const std::vector<omath::primitives::Vertex<>> k_cube_vbo = {
+        { { -1.f, -1.f, -1.f }, {}, {} },
+        { { -1.f, -1.f,  1.f }, {}, {} },
+        { { -1.f,  1.f, -1.f }, {}, {} },
+        { { -1.f,  1.f,  1.f }, {}, {} },
+        { {  1.f,  1.f,  1.f }, {}, {} },
+        { {  1.f,  1.f, -1.f }, {}, {} },
+        { {  1.f, -1.f,  1.f }, {}, {} },
+        { {  1.f, -1.f, -1.f }, {}, {} },
+    };
+    const std::vector<omath::Vector3<std::uint32_t>> k_empty_ebo{};
+
+    Collider make_cube(const Vec3& origin = {}, const Vec3& scale = { 1, 1, 1 })
+    {
+        Mesh m{ k_cube_vbo, k_empty_ebo, scale };
+        m.set_origin(origin);
+        return Collider{ m };
+    }
+} // namespace
+
+// ---------------------------------------------------------------------------
+// Separation — expect false
+// ---------------------------------------------------------------------------
+
+TEST(GjkComprehensive, Separated_AlongPosX)
+{
+    // A extends to x=1, B starts at x=1.1 → clear gap
+    EXPECT_FALSE(Gjk::is_collide(make_cube({ 0, 0, 0 }), make_cube({ 2.1f, 0, 0 })));
+}
+
+TEST(GjkComprehensive, Separated_AlongNegX)
+{
+    // B to the left of A
+    EXPECT_FALSE(Gjk::is_collide(make_cube({ 0, 0, 0 }), make_cube({ -2.1f, 0, 0 })));
+}
+
+TEST(GjkComprehensive, Separated_AlongPosY)
+{
+    EXPECT_FALSE(Gjk::is_collide(make_cube({ 0, 0, 0 }), make_cube({ 0, 2.1f, 0 })));
+}
+
+TEST(GjkComprehensive, Separated_AlongNegY)
+{
+    EXPECT_FALSE(Gjk::is_collide(make_cube({ 0, 0, 0 }), make_cube({ 0, -2.1f, 0 })));
+}
+
+TEST(GjkComprehensive, Separated_AlongPosZ)
+{
+    EXPECT_FALSE(Gjk::is_collide(make_cube({ 0, 0, 0 }), make_cube({ 0, 0, 2.1f })));
+}
+
+TEST(GjkComprehensive, Separated_AlongNegZ)
+{
+    EXPECT_FALSE(Gjk::is_collide(make_cube({ 0, 0, 0 }), make_cube({ 0, 0, -2.1f })));
+}
+
+TEST(GjkComprehensive, Separated_AlongDiagonal)
+{
+    // All components exceed 2.0 — no overlap on any axis
+    EXPECT_FALSE(Gjk::is_collide(make_cube({ 0, 0, 0 }), make_cube({ 2.1f, 2.1f, 2.1f })));
+}
+
+TEST(GjkComprehensive, Separated_LargeDistance)
+{
+    EXPECT_FALSE(Gjk::is_collide(make_cube({ 0, 0, 0 }), make_cube({ 100.f, 0, 0 })));
+}
+
+TEST(GjkComprehensive, Separated_AsymmetricSizes)
+{
+    // Big (scale 2, half-ext 2), small (scale 0.5, half-ext 0.5) at 2.6 → gap of 0.1
+    EXPECT_FALSE(Gjk::is_collide(make_cube({ 0, 0, 0 }, { 2, 2, 2 }), make_cube({ 2.6f, 0, 0 }, { 0.5f, 0.5f, 0.5f })));
+}
+
+// ---------------------------------------------------------------------------
+// Overlap — expect true
+// ---------------------------------------------------------------------------
+
+TEST(GjkComprehensive, Overlapping_AlongPosX)
+{
+    // B offset 1.5 → overlap depth 0.5 in X
+    EXPECT_TRUE(Gjk::is_collide(make_cube({ 0, 0, 0 }), make_cube({ 1.5f, 0, 0 })));
+}
+
+TEST(GjkComprehensive, Overlapping_AlongNegX)
+{
+    EXPECT_TRUE(Gjk::is_collide(make_cube({ 0, 0, 0 }), make_cube({ -1.5f, 0, 0 })));
+}
+
+TEST(GjkComprehensive, Overlapping_AlongPosZ)
+{
+    EXPECT_TRUE(Gjk::is_collide(make_cube({ 0, 0, 0 }), make_cube({ 0, 0, 1.5f })));
+}
+
+TEST(GjkComprehensive, Overlapping_AlongNegZ)
+{
+    EXPECT_TRUE(Gjk::is_collide(make_cube({ 0, 0, 0 }), make_cube({ 0, 0, -1.5f })));
+}
+
+TEST(GjkComprehensive, Overlapping_AlongDiagonalXY)
+{
+    // Minkowski sum extends ±2 on each axis; offset (1,1,0) is inside
+    EXPECT_TRUE(Gjk::is_collide(make_cube({ 0, 0, 0 }), make_cube({ 1.f, 1.f, 0.f })));
+}
+
+TEST(GjkComprehensive, Overlapping_AlongDiagonalXYZ)
+{
+    // All three axes overlap: (1,1,1) is inside the Minkowski sum
+    EXPECT_TRUE(Gjk::is_collide(make_cube({ 0, 0, 0 }), make_cube({ 1.f, 1.f, 1.f })));
+}
+
+TEST(GjkComprehensive, FullyNested_SmallInsideBig)
+{
+    // Small cube (half-ext 0.5) fully inside big cube (half-ext 2)
+    EXPECT_TRUE(Gjk::is_collide(make_cube({ 0, 0, 0 }, { 2, 2, 2 }), make_cube({ 0, 0, 0 }, { 0.5f, 0.5f, 0.5f })));
+}
+
+TEST(GjkComprehensive, FullyNested_OffCenter)
+{
+    // Small at (0.5, 0, 0) still fully inside big (half-ext 2)
+    EXPECT_TRUE(Gjk::is_collide(make_cube({ 0, 0, 0 }, { 2, 2, 2 }), make_cube({ 0.5f, 0, 0 }, { 0.5f, 0.5f, 0.5f })));
+}
+
+TEST(GjkComprehensive, Overlapping_AsymmetricSizes)
+{
+    // Big (scale 2, half-ext 2) and small (scale 0.5, half-ext 0.5) at 2.0 → overlap 0.5 in X
+    EXPECT_TRUE(Gjk::is_collide(make_cube({ 0, 0, 0 }, { 2, 2, 2 }), make_cube({ 2.0f, 0, 0 }, { 0.5f, 0.5f, 0.5f })));
+}
+
+// ---------------------------------------------------------------------------
+// Boundary cases
+// ---------------------------------------------------------------------------
+
+TEST(GjkComprehensive, BoundaryCase_JustColliding)
+{
+    // B at 1.999 — 0.001 overlap in X
+    EXPECT_TRUE(Gjk::is_collide(make_cube({ 0, 0, 0 }), make_cube({ 1.999f, 0, 0 })));
+}
+
+TEST(GjkComprehensive, BoundaryCase_JustSeparated)
+{
+    // B at 2.001 — 0.001 gap in X
+    EXPECT_FALSE(Gjk::is_collide(make_cube({ 0, 0, 0 }), make_cube({ 2.001f, 0, 0 })));
+}
+
+// ---------------------------------------------------------------------------
+// Symmetry
+// ---------------------------------------------------------------------------
+
+TEST(GjkComprehensive, Symmetry_WhenColliding)
+{
+    const auto a = make_cube({ 0, 0, 0 });
+    const auto b = make_cube({ 1.5f, 0, 0 });
+    EXPECT_EQ(Gjk::is_collide(a, b), Gjk::is_collide(b, a));
+}
+
+TEST(GjkComprehensive, Symmetry_WhenSeparated)
+{
+    const auto a = make_cube({ 0, 0, 0 });
+    const auto b = make_cube({ 2.1f, 0.5f, 0 });
+    EXPECT_EQ(Gjk::is_collide(a, b), Gjk::is_collide(b, a));
+}
+
+TEST(GjkComprehensive, Symmetry_DiagonalSeparation)
+{
+    const auto a = make_cube({ 0, 0, 0 });
+    const auto b = make_cube({ 1.5f, 1.5f, 1.5f });
+    EXPECT_EQ(Gjk::is_collide(a, b), Gjk::is_collide(b, a));
+}
+
+// ---------------------------------------------------------------------------
+// Simplex info
+// ---------------------------------------------------------------------------
+
+TEST(GjkComprehensive, SimplexInfo_HitProducesSimplex4)
+{
+    // On collision the simplex must be a full tetrahedron (4 points)
+    const auto [hit, simplex] = Gjk::is_collide_with_simplex_info(make_cube({ 0, 0, 0 }), make_cube({ 0.5f, 0, 0 }));
+    EXPECT_TRUE(hit);
+    EXPECT_EQ(simplex.size(), 4u);
+}
+
+TEST(GjkComprehensive, SimplexInfo_MissProducesLessThan4)
+{
+    // On non-collision the simplex can never be a full tetrahedron
+    const auto [hit, simplex] = Gjk::is_collide_with_simplex_info(make_cube({ 0, 0, 0 }), make_cube({ 2.1f, 0, 0 }));
+    EXPECT_FALSE(hit);
+    EXPECT_LT(simplex.size(), 4u);
+}
+
+TEST(GjkComprehensive, SimplexInfo_HitAlongY)
+{
+    const auto [hit, simplex] = Gjk::is_collide_with_simplex_info(make_cube({ 0, 0, 0 }), make_cube({ 0, 1.5f, 0 }));
+    EXPECT_TRUE(hit);
+    EXPECT_EQ(simplex.size(), 4u);
+}
+
+TEST(GjkComprehensive, SimplexInfo_HitAlongZ)
+{
+    const auto [hit, simplex] = Gjk::is_collide_with_simplex_info(make_cube({ 0, 0, 0 }), make_cube({ 0, 0, 1.5f }));
+    EXPECT_TRUE(hit);
+    EXPECT_EQ(simplex.size(), 4u);
+}
+
+TEST(GjkComprehensive, SimplexInfo_MissAlongDiagonal)
+{
+    const auto [hit, simplex] = Gjk::is_collide_with_simplex_info(make_cube({ 0, 0, 0 }), make_cube({ 2.1f, 2.1f, 2.1f }));
+    EXPECT_FALSE(hit);
+    EXPECT_LT(simplex.size(), 4u);
+}
+
+// ---------------------------------------------------------------------------
+// Non-trivial geometry — tetrahedron shaped colliders
+// ---------------------------------------------------------------------------
+
+TEST(GjkComprehensive, TetrahedronShapes_Overlapping)
+{
+    // A rough tetrahedron mesh; two of them close enough to overlap
+    const std::vector<omath::primitives::Vertex<>> tet_vbo = {
+        { {  0.f,  1.f,  0.f }, {}, {} },
+        { { -1.f, -1.f,  1.f }, {}, {} },
+        { {  1.f, -1.f,  1.f }, {}, {} },
+        { {  0.f, -1.f, -1.f }, {}, {} },
+    };
+
+    Mesh m_a{ tet_vbo, k_empty_ebo };
+    Mesh m_b{ tet_vbo, k_empty_ebo };
+    m_b.set_origin({ 0.5f, 0.f, 0.f });
+
+    EXPECT_TRUE(Gjk::is_collide(Collider{ m_a }, Collider{ m_b }));
+}
+
+TEST(GjkComprehensive, TetrahedronShapes_Separated)
+{
+    const std::vector<omath::primitives::Vertex<>> tet_vbo = {
+        { {  0.f,  1.f,  0.f }, {}, {} },
+        { { -1.f, -1.f,  1.f }, {}, {} },
+        { {  1.f, -1.f,  1.f }, {}, {} },
+        { {  0.f, -1.f, -1.f }, {}, {} },
+    };
+
+    Mesh m_a{ tet_vbo, k_empty_ebo };
+    Mesh m_b{ tet_vbo, k_empty_ebo };
+    m_b.set_origin({ 3.f, 0.f, 0.f });
+
+    EXPECT_FALSE(Gjk::is_collide(Collider{ m_a }, Collider{ m_b }));
+}
+
+// ---------------------------------------------------------------------------
+// Determinism
+// ---------------------------------------------------------------------------
+
+TEST(GjkComprehensive, Deterministic_SameResultOnRepeatedCalls)
+{
+    const auto a = make_cube({ 0, 0, 0 });
+    const auto b = make_cube({ 1.2f, 0.3f, 0.1f });
+    const bool first = Gjk::is_collide(a, b);
+    for (int i = 0; i < 10; ++i)
+        EXPECT_EQ(Gjk::is_collide(a, b), first);
+}