Gjk, FPS view.

src/Simplex.cpp

@@ -0,0 +1,141 @@
+
+#include <Simplex.h>
+
+
+Vector3 polyhedron_support(Vector3AV polyhedron, const Vector3& direction) {
+    assert(polyhedron.size() > 0);
+
+    Index best = 0;
+    Real best_dot = polyhedron[0].dot(direction);
+
+    for (Index index = 1; index < polyhedron.size(); index += 1) {
+        Real dot = polyhedron[index].dot(direction);
+        if (dot > best_dot) {
+            best = index;
+            best_dot = dot;
+        }
+    }
+
+    return polyhedron[best];
+}
+
+
+Simplex::Simplex() = default;
+Simplex::Simplex(const Vector3& point)
+    : m_points{ point, Vector3{}, Vector3{}, Vector3{} }
+    , m_point_count(1)
+{}
+
+
+Gjk::Gjk(Vector3AV polyhedron0, Vector3AV polyhedron1, const Vector3& direction)
+    : m_polyhedron0(polyhedron0)
+    , m_polyhedron1(polyhedron1)
+    , m_direction(direction)
+{}
+
+Gjk::~Gjk() = default;
+
+const Vector3& Gjk::direction() const {
+    return m_direction;
+}
+
+bool Gjk::operator()() {
+    while (true) {
+        m_simplex.push(support(m_direction));
+
+        if (m_simplex.last().dot(m_direction) < Real(0))
+            return false;
+
+        if (nextSimplex())
+            return true;
+    }
+}
+
+bool Gjk::nextSimplex() {
+    switch(m_simplex.point_count()) {
+        case 1: return nextFromPoint();
+        case 2: return nextFromLine();
+        case 3: return nextFromTriangle();
+        case 4: return nextFromTetrahedron();
+    }
+    return false;
+}
+
+bool Gjk::nextFromPoint() {
+    m_direction = -m_simplex.last();
+
+    return false;
+}
+
+bool Gjk::nextFromLine() {
+    Vector3 v01 = m_simplex.point(1) - m_simplex.point(0);
+    Vector3 v1o = -m_simplex.point(1);
+
+    m_direction = v01.cross(v1o).cross(v01);
+
+    return false;
+}
+
+bool Gjk::nextFromTriangle() {
+    Vector3 v20 = m_simplex.point(0) - m_simplex.point(2);
+    Vector3 v21 = m_simplex.point(1) - m_simplex.point(2);
+    Vector3 v2o = -m_simplex.point(2);
+
+    Vector3 n = v20.cross(v21);
+    Vector3 n0 = n.cross(v21);
+    Vector3 n1 = v20.cross(n);
+
+    if(n0.dot(v2o) > Real(0)) {
+        m_simplex.pop(0);
+        m_direction = n0;
+    }
+    else if(n1.dot(v2o) > Real(0)) {
+        m_simplex.pop(1);
+        m_direction = n1;
+    }
+    else if(n.dot(v2o) > Real(0)) {
+        m_direction = n;
+    }
+    else {
+        m_simplex.swap(0, 1);
+        m_direction = -n;
+    }
+
+    return false;
+}
+
+bool Gjk::nextFromTetrahedron() {
+    Vector3 v30 = m_simplex.point(0) - m_simplex.point(3);
+    Vector3 v31 = m_simplex.point(1) - m_simplex.point(3);
+    Vector3 v32 = m_simplex.point(2) - m_simplex.point(3);
+    Vector3 v3o = -m_simplex.point(3);
+
+    Vector3 n[3] = {
+        v31.cross(v32),
+        v32.cross(v30),
+        v30.cross(v31),
+    };
+
+    Real d[3] = {
+        n[0].dot(v3o),
+        n[1].dot(v3o),
+        n[2].dot(v3o),
+    };
+
+    Index best = (d[0] > d[1])? ((d[0] > d[2])? 0: 2):
+                                ((d[1] > d[2])? 1: 2);
+
+    if(d[best] <= Real(0))
+        return true;
+
+    m_simplex.pop(best);
+    m_direction = n[best];
+
+    return false;
+}
+
+Vector3 Gjk::support(const Vector3& direction) const
+{
+    return polyhedron_support(m_polyhedron0, direction)
+        - polyhedron_support(m_polyhedron1, -direction);
+}

src/Simplex.h

@@ -0,0 +1,75 @@
+#pragma once
+
+#include <core.h>
+
+
+class Simplex {
+public:
+    Simplex();
+    Simplex(const Vector3& point);
+
+    inline Index point_count() const {
+        return m_point_count;
+    }
+
+    inline const Vector3& point(Index index) const {
+        assert(index < m_point_count);
+        return m_points[index];
+    }
+
+    inline const Vector3& last() const {
+        assert(m_point_count > 0);
+        return point(m_point_count - 1);
+    }
+
+    inline void push(const Vector3& point) {
+        assert(m_point_count < MaxPointCount);
+        m_points[m_point_count] = point;
+        m_point_count += 1;
+    }
+
+    inline void pop(Index index) {
+        assert(index < m_point_count);
+        for(Index i = index; i + 1 < m_point_count; i += 1)
+            m_points[i] = m_points[i + 1];
+        m_point_count -= 1;
+    }
+
+    inline void swap(Index index0, Index index1) {
+        using std::swap;
+        swap(m_points[index0], m_points[index1]);
+    }
+
+private:
+    static constexpr Index MaxPointCount = 4;
+
+private:
+    Vector3 m_points[MaxPointCount];
+    Index m_point_count = 0;
+};
+
+
+class Gjk {
+public:
+    Gjk(Vector3AV polyhedron0, Vector3AV polyhedron1, const Vector3& direction=Vector3::UnitX());
+    ~Gjk();
+
+    const Vector3& direction() const;
+
+    bool operator()();
+
+private:
+    bool nextSimplex();
+    bool nextFromPoint();
+    bool nextFromLine();
+    bool nextFromTriangle();
+    bool nextFromTetrahedron();
+
+    Vector3 support(const Vector3& direction) const;
+
+private:
+    Vector3AV m_polyhedron0;
+    Vector3AV m_polyhedron1;
+    Simplex m_simplex;
+    Vector3 m_direction;
+};

src/VkExpe.cpp

@@ -5,6 +5,7 @@
 
 #include <stdexcept>
 #include <iostream>
+#include <chrono>
 
 
 void SdlWindowDeleter::operator()(SDL_Window* window) const {
@@ -25,7 +26,7 @@ void VkExpe::initialize() {
     auto const window = SDL_CreateWindow(
         "vk_expe",
         SDL_WINDOWPOS_CENTERED, SDL_WINDOWPOS_CENTERED,
-        800, 600,
+        1920, 1080,
         SDL_WINDOW_VULKAN
         | SDL_WINDOW_ALLOW_HIGHDPI
         | SDL_WINDOW_SHOWN
@@ -60,6 +61,8 @@ void VkExpe::run() {
         m_running = false;
     });
 
+    auto last_time = std::chrono::high_resolution_clock::now();
+
     SDL_Event event;
     while(m_running) {
         while(SDL_PollEvent(&event)) {
@@ -72,17 +75,88 @@ void VkExpe::run() {
                     m_running = false;
                 break;
             }
+            case SDL_MOUSEMOTION: {
+                m_mouse_offset += Vector2(
+                    event.motion.xrel,
+                    event.motion.yrel
+                );
+                break;
+            }
             case SDL_WINDOWEVENT: {
                 switch(event.window.event) {
                 case SDL_WINDOWEVENT_RESIZED: {
                     m_vulkan.invalidate_swapchain();
+                    break;
+                }
+                case SDL_WINDOWEVENT_FOCUS_GAINED: {
+                    SDL_SetRelativeMouseMode(SDL_TRUE);
+                    break;
+                }
+                case SDL_WINDOWEVENT_FOCUS_LOST: {
+                    SDL_SetRelativeMouseMode(SDL_FALSE);
+                    break;
                 }
                 }
+                break;
             }
             }
         }
 
+        const auto new_time = std::chrono::high_resolution_clock::now();
+        const auto elapsed = new_time - last_time;
+        last_time = new_time;
+
+        update(std::chrono::duration<double>(elapsed).count());
+
+        m_vulkan.set_camera(m_camera_position, m_camera_z, m_camera_y);
         m_vulkan.draw_frame();
-        // m_running = false;
+
+        m_mouse_offset = Vector2::Zero();
+    }
+}
+
+void VkExpe::update(double elapsed) {
+    int key_count = 0;
+    const auto keys = SDL_GetKeyboardState(&key_count);
+
+    const auto test_key = [key_count, keys](int scan_code) {
+        return scan_code < key_count && keys[scan_code];
+    };
+
+    if (!m_mouse_offset.isZero()) {
+        const Real x_sensi = 0.001;
+        const Real y_sensi = -0.001;
+
+        const Vector3 camera_x = m_camera_y.cross(m_camera_z);
+        Vector3 axis =
+            x_sensi * m_mouse_offset[0] * m_camera_y +
+            y_sensi * m_mouse_offset[1] * camera_x;
+        Real rot_norm = axis.norm();
+        AngleAxis rot(rot_norm, axis / rot_norm);
+        m_camera_y = rot * m_camera_y;
+        m_camera_z = rot * m_camera_z;
+    }
+
+    Vector3 walk_direction = Vector3::Zero();
+    if(test_key(SDL_SCANCODE_W))
+        walk_direction += Vector3::UnitZ();
+    if(test_key(SDL_SCANCODE_S))
+        walk_direction -= Vector3::UnitZ();
+    if(test_key(SDL_SCANCODE_A))
+        walk_direction -= Vector3::UnitX();
+    if(test_key(SDL_SCANCODE_D))
+        walk_direction += Vector3::UnitX();
+    if(test_key(SDL_SCANCODE_SPACE))
+        walk_direction -= Vector3::UnitY();
+    if(test_key(SDL_SCANCODE_LCTRL))
+        walk_direction += Vector3::UnitY();
+
+    if(!walk_direction.isZero()) {
+        walk_direction.normalize();
+        const Real base_velocity = 1;
+
+        Matrix3 camera_basis;
+        camera_basis << m_camera_y.cross(m_camera_z), m_camera_y, m_camera_z;
+        m_camera_position += elapsed * base_velocity * (camera_basis * walk_direction);
     }
 }

src/VkExpe.h

@@ -1,5 +1,6 @@
 #pragma once
 
+#include <core.h>
 #include <VulkanTutorial.h>
 
 #include <SDL2/SDL.h>
@@ -26,8 +27,17 @@ public:
 
     void run();
 
+    void update(double elapsed);
+
 private:
     VulkanTutorial m_vulkan;
+
+    Vector3 m_camera_position = Vector3(0.0f, 0.0f, -3.0f);
+    Vector3 m_camera_z = Vector3(0.0f, 0.0f, 1.0f);
+    Vector3 m_camera_y = Vector3(0.0f, 1.0f, 0.0f);
+
     WindowUP m_window;
     bool m_running = false;
+
+    Vector2 m_mouse_offset = Vector2::Zero();
 };

src/VulkanTutorial.cpp

@@ -196,6 +196,12 @@ void VulkanTutorial::shutdown() {
     m_context.shutdown();
 }
 
+void VulkanTutorial::set_camera(const Vector3& camera_position, const Vector3& camera_z, const Vector3& camera_y) {
+    m_camera_position = camera_position;
+    m_camera_z = camera_z;
+    m_camera_y = camera_y;
+}
+
 void VulkanTutorial::draw_frame() {
     m_swapchain.begin_frame();
     auto const image_index = m_swapchain.current_image_index();
@@ -206,15 +212,14 @@ void VulkanTutorial::draw_frame() {
     }
     m_last_frame_time = now;
 
-    const float alpha = SecondsD(m_time).count() * (2.0 * M_PI) / 10.0;
-    const float dist = 2.0f;
-    const Eigen::Matrix4f view = look_at_matrix(
-        // Eigen::Vector3f(0.0f, 0.0f, -dist),
-        Eigen::Vector3f(0.0f, -dist, -dist),
-        // dist * Eigen::Vector3f(std::cos(alpha), std::sin(alpha), -1.0),
-        Eigen::Vector3f::Zero(),
-        -Eigen::Vector3f::UnitY()
-    );
+    Matrix3 linear_view;
+    linear_view <<
+        m_camera_y.cross(m_camera_z).transpose(),
+        m_camera_y.transpose(),
+        m_camera_z.transpose();
+    Matrix4 view;
+    view << linear_view, linear_view * -m_camera_position,
+        Vector4::UnitW().transpose();
 
     const float fov = M_PI / 3.0f;
     const float near = 0.1f;
@@ -227,12 +232,7 @@ void VulkanTutorial::draw_frame() {
         near, far
     );
 
-    using Transform = Eigen::Transform<float, 3, Eigen::Affine>;
     Transform model = Transform::Identity();
-    model.rotate(Eigen::AngleAxisf(
-        alpha,
-        Eigen::Vector3f::UnitY()
-    ));
 
     const Uniforms uniforms = {
         .scene_from_model = model.matrix(),
@@ -241,7 +241,7 @@ void VulkanTutorial::draw_frame() {
             0.5 * m_swapchain.extent().width,
             0.5 * m_swapchain.extent().height,
         },
-        .lod = std::cos(alpha) * 0.5f + 0.5f,
+        // .lod = std::cos(alpha) * 0.5f + 0.5f,
     };
 
     void* uniform_buffer;

src/VulkanTutorial.h

@@ -1,5 +1,7 @@
 #pragma once
 
+#include <core.h>
+
 #include <Vulkan/Context.h>
 #include <Vulkan/Swapchain.h>
 
@@ -35,6 +37,8 @@ public:
     void initialize(SDL_Window* window);
     void shutdown();
 
+    void set_camera(const Vector3& camera_position, const Vector3& camera_z, const Vector3& camera_y);
+
     void draw_frame();
     void invalidate_swapchain();
 
@@ -78,6 +82,10 @@ private:
     std::vector<VkCommandBuffer> m_command_buffers;
     std::vector<VkSemaphore> m_render_done;
 
+    Vector3 m_camera_position = Vector3(0.0f, 0.0f, -3.0f);
+    Vector3 m_camera_z = Vector3(0.0f, 0.0f, 1.0f);
+    Vector3 m_camera_y = Vector3(0.0f, 1.0f, 0.0f);
+
     TimePoint m_last_frame_time;
     Duration m_time = Duration(0);
 };

src/core.h

@@ -8,8 +8,21 @@
 
 using Byte = unsigned char;
 using Index = uint32_t;
+
 using Real = float;
+
+using Vector2 = Eigen::Matrix<Real, 2, 1>;
 using Vector3 = Eigen::Matrix<Real, 3, 1>;
+using Vector4 = Eigen::Matrix<Real, 4, 1>;
+
+using Matrix2 = Eigen::Matrix<Real, 2, 2>;
+using Matrix3 = Eigen::Matrix<Real, 3, 3>;
+using Matrix4 = Eigen::Matrix<Real, 4, 4>;
+
+using Transform = Eigen::Transform<Real, 3, Eigen::Affine>;
+using AngleAxis = Eigen::AngleAxis<Real>;
+using Quaternion = Eigen::Quaternion<Real>;
+
 using Triangle = Eigen::Array<Index, 3, 1>;