Fixed shadow pass and physics system a little bit

src/Engine/Graphics/RenderPass/ShadowPass.cpp

@@ -72,9 +72,14 @@ void ShadowPass::beginFrame(const Component::Camera& camera, const Component::Tr
     updateViewParameters(camera, transform);
     Matrix4 invCam = viewParams.inverseViewProjectionMatrix;
     float lastSplitDist = 0.0;
+    constexpr float cascadeOverlap = 0.1f; // overlap factor to prevent gaps at cascade boundaries
     for (uint32 i = 0; i < NUM_CASCADES; ++i) {
         float splitDist = cascadeSplits[i];
 
+        // Extend each cascade's frustum slice slightly into adjacent cascades
+        float overlapNear = (i > 0) ? lastSplitDist - cascadeOverlap * (lastSplitDist - (i > 1 ? cascadeSplits[i - 2] : 0.0f)) : 0.0f;
+        float overlapFar = (i < NUM_CASCADES - 1) ? splitDist + cascadeOverlap * (cascadeSplits[i + 1] - splitDist) : splitDist;
+
         Array<Vector> frustumCorners = {
             Vector(-1.0f, 1.0f, 0.0f), Vector(1.0f, 1.0f, 0.0f), Vector(1.0f, -1.0f, 0.0f), Vector(-1.0f, -1.0f, 0.0f),
             Vector(-1.0f, 1.0f, 1.0f), Vector(1.0f, 1.0f, 1.0f), Vector(1.0f, -1.0f, 1.0f), Vector(-1.0f, -1.0f, 1.0f),
@@ -86,8 +91,8 @@ void ShadowPass::beginFrame(const Component::Camera& camera, const Component::Tr
         }
         for (uint32 j = 0; j < 4; j++) {
             Vector dist = frustumCorners[j + 4] - frustumCorners[j];
-            frustumCorners[j + 4] = frustumCorners[j] + (dist * splitDist);
-            frustumCorners[j] = frustumCorners[j] + (dist * lastSplitDist);
+            frustumCorners[j + 4] = frustumCorners[j] + (dist * overlapFar);
+            frustumCorners[j] = frustumCorners[j] + (dist * overlapNear);
         }
 
         Vector frustumCenter = Vector(0);
@@ -108,10 +113,10 @@ void ShadowPass::beginFrame(const Component::Camera& camera, const Component::Tr
 
         for (uint32 s = 0; s < scene->getLightEnvironment()->getNumDirectionalLights(); ++s) {
             Vector lightDir = glm::normalize(scene->getLightEnvironment()->getDirectionalLight(s).direction);
-            Vector cameraPos = frustumCenter - lightDir * -minExtents.z;
+            Vector cameraPos = frustumCenter - lightDir * (100.0f * -minExtents.z);
             Matrix4 viewMatrix = glm::lookAt(cameraPos, frustumCenter, Vector(0, 1, 0));
             Matrix4 projectionMatrix =
-                orthographicProjection(minExtents.x, maxExtents.x, minExtents.y, maxExtents.y, 0.0f, maxExtents.z - minExtents.z);
+                orthographicProjection(minExtents.x, maxExtents.x, minExtents.y, maxExtents.y, 0.0f, maxExtents.z - (100.0f * minExtents.z));
             Matrix4 viewProjectionMatrix = projectionMatrix * viewMatrix;
             viewParams = {
                 .viewMatrix = viewMatrix,
@@ -193,7 +198,7 @@ void ShadowPass::render() {
                         .pipelineLayout = collection->pipelineLayout,
                         .rasterizationState =
                             {
-                                .cullMode = Gfx::SE_CULL_MODE_NONE,
+                                .cullMode = Gfx::SE_CULL_MODE_FRONT_BIT,
                                 .depthBiasEnable = true,
                                 .depthBiasConstantFactor = depthBiasConstant,
                                 .depthBiasSlopeFactor = depthBiasSlope,

src/Engine/Physics/PhysicsSystem.cpp

@@ -1,6 +1,5 @@
 #include "PhysicsSystem.h"
 #include <iostream>
-#include <random>
 
 
 using namespace Seele;
@@ -466,27 +465,44 @@ void PhysicsSystem::computeBVector(const Array<Contact>& contacts, Array<float>&
     }
 }
 
-void PhysicsSystem::solveQP(const Array<Array<float>>& CI, const Array<float>& ci0, Array<float>& sol) const {
-    static std::mt19937_64 generator;
-    static std::uniform_real_distribution<float> dist(0.01f, 0.1f);
-    sol.resize(CI.size());
-    bool solved = false;
-    while (!solved) {
-        for (size_t i = 0; i < sol.size(); ++i) {
-            sol[i] = dist(generator);
-        }
-        solved = true;
-        for (size_t i = 0; i < sol.size(); ++i) {
-            float res = 0;
-            for (size_t j = 0; j < sol.size(); ++j) {
-                res += CI[i][j] * sol[j] + ci0[i];
+void PhysicsSystem::solveQP(const Array<Array<float>>& A, const Array<float>& b, Array<float>& f) const {
+    // Solves the LCP: find f >= 0 such that Af + b >= 0 and f^T(Af + b) = 0
+    // using Projected Gauss-Seidel (PGS) iteration
+    const size_t n = A.size();
+    f.resize(n);
+
+    for (size_t i = 0; i < n; ++i) {
+        f[i] = 0.0f;
+    }
+
+    constexpr size_t maxIterations = 200;
+    constexpr float tolerance = 1e-6f;
+
+    for (size_t iter = 0; iter < maxIterations; ++iter) {
+        float maxDelta = 0.0f;
+
+        for (size_t i = 0; i < n; ++i) {
+            float sigma = b[i];
+            for (size_t j = 0; j < n; ++j) {
+                if (j != i) {
+                    sigma += A[i][j] * f[j];
+                }
             }
-            if (res < 0) {
-                solved = false;
-                std::cout << "failed to solve QP" << std::endl;
-                continue;
+
+            float diagonal = A[i][i];
+            float newF;
+            if (std::abs(diagonal) > 1e-10f) {
+                newF = std::max(0.0f, -sigma / diagonal);
+            } else {
+                newF = 0.0f;
             }
+
+            maxDelta = std::max(maxDelta, std::abs(newF - f[i]));
+            f[i] = newF;
+        }
+
+        if (maxDelta < tolerance) {
+            return;
         }
-        return;
     }
 }