feat(physics): Implement SDF-based physics engine and BVH

Completed Task #49.
- Implemented CPU-side SDF library (sphere, box, torus, plane).
- Implemented Dynamic BVH construction (rebuilt every frame).
- Implemented PhysicsSystem with semi-implicit Euler integration and collision resolution.
- Added visual debugging for BVH nodes.
- Created test_3d_physics interactive test and test_physics unit tests.
- Updated project docs and triaged new tasks.

1 files changed, 151 insertions, 0 deletions

diff --git a/src/tests/test_physics.cc b/src/tests/test_physics.cc
new file mode 100644
index 0000000..a59502c
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+++ b/src/tests/test_physics.cc
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+// This file is part of the 64k demo project.
+// It tests the CPU-side SDF library and BVH for physics and collision.
+
+#include "3d/bvh.h"
+#include "3d/physics.h"
+#include "3d/sdf_cpu.h"
+#include <cassert>
+#include <cmath>
+#include <iostream>
+
+bool near(float a, float b, float e = 0.001f) {
+  return std::abs(a - b) < e;
+}
+
+void test_sdf_sphere() {
+  std::cout << "Testing sdSphere..." << std::endl;
+  float r = 1.0f;
+  assert(near(sdf::sdSphere({0, 0, 0}, r), -1.0f));
+  assert(near(sdf::sdSphere({1, 0, 0}, r), 0.0f));
+  assert(near(sdf::sdSphere({2, 0, 0}, r), 1.0f));
+}
+
+void test_sdf_box() {
+  std::cout << "Testing sdBox..." << std::endl;
+  vec3 b(1, 1, 1);
+  assert(near(sdf::sdBox({0, 0, 0}, b), -1.0f));
+  assert(near(sdf::sdBox({1, 1, 1}, b), 0.0f));
+  assert(near(sdf::sdBox({2, 0, 0}, b), 1.0f));
+}
+
+void test_sdf_torus() {
+  std::cout << "Testing sdTorus..." << std::endl;
+  vec2 t(1.0f, 0.2f);
+  // Point on the ring: length(p.xz) = 1.0, p.y = 0
+  assert(near(sdf::sdTorus({1, 0, 0}, t), -0.2f));
+  assert(near(sdf::sdTorus({1.2f, 0, 0}, t), 0.0f));
+}
+
+void test_sdf_plane() {
+  std::cout << "Testing sdPlane..." << std::endl;
+  vec3 n(0, 1, 0);
+  float h = 1.0f; // Plane is at y = -1 (dot(p,n) + 1 = 0 => y = -1)
+  assert(near(sdf::sdPlane({0, 0, 0}, n, h), 1.0f));
+  assert(near(sdf::sdPlane({0, -1, 0}, n, h), 0.0f));
+}
+
+void test_calc_normal() {
+  std::cout << "Testing calc_normal..." << std::endl;
+
+  // Sphere normal at (1,0,0) should be (1,0,0)
+  auto sphere_sdf = [](vec3 p) { return sdf::sdSphere(p, 1.0f); };
+  vec3 n = sdf::calc_normal({1, 0, 0}, sphere_sdf);
+  assert(near(n.x, 1.0f) && near(n.y, 0.0f) && near(n.z, 0.0f));
+
+  // Box normal at side
+  auto box_sdf = [](vec3 p) { return sdf::sdBox(p, {1, 1, 1}); };
+  n = sdf::calc_normal({1, 0, 0}, box_sdf);
+  assert(near(n.x, 1.0f) && near(n.y, 0.0f) && near(n.z, 0.0f));
+
+  // Plane normal should be n
+  vec3 plane_n(0, 1, 0);
+  auto plane_sdf = [plane_n](vec3 p) { return sdf::sdPlane(p, plane_n, 1.0f); };
+  n = sdf::calc_normal({0, 0, 0}, plane_sdf);
+  assert(near(n.x, plane_n.x) && near(n.y, plane_n.y) && near(n.z, plane_n.z));
+}
+
+void test_bvh() {
+  std::cout << "Testing BVH..." << std::endl;
+  std::vector<Object3D> objects;
+
+  // Object 0: Left side
+  Object3D obj0(ObjectType::BOX);
+  obj0.position = {-10, 0, 0};
+  objects.push_back(obj0);
+
+  // Object 1: Right side
+  Object3D obj1(ObjectType::BOX);
+  obj1.position = {10, 0, 0};
+  objects.push_back(obj1);
+
+  BVH bvh;
+  BVHBuilder::build(bvh, objects);
+
+  assert(bvh.nodes.size() == 3); // 1 root + 2 leaves
+
+  // Query left side
+  std::vector<int> results;
+  bvh.query({{-12, -2, -2}, {-8, 2, 2}}, results);
+  assert(results.size() == 1);
+  assert(results[0] == 0);
+
+  // Query right side
+  results.clear();
+  bvh.query({{8, -2, -2}, {12, 2, 2}}, results);
+  assert(results.size() == 1);
+  assert(results[0] == 1);
+
+  // Query center (should miss both)
+  results.clear();
+  bvh.query({{-2, -2, -2}, {2, 2, 2}}, results);
+  assert(results.size() == 0);
+
+  // Query both
+    results.clear();
+    bvh.query({{-12, -2, -2}, {12, 2, 2}}, results);
+    assert(results.size() == 2);
+  }
+  
+  void test_physics_falling() {
+    std::cout << "Testing Physics falling..." << std::endl;
+    Scene scene;
+  
+    // Plane at y = -1
+    Object3D plane(ObjectType::PLANE);
+    plane.position = {0, -1, 0};
+    plane.is_static = true;
+    scene.add_object(plane);
+  
+    // Sphere at y = 5
+    Object3D sphere(ObjectType::SPHERE);
+    sphere.position = {0, 5, 0};
+    sphere.velocity = {0, 0, 0};
+    sphere.restitution = 0.0f; // No bounce for simple test
+    scene.add_object(sphere);
+  
+    PhysicsSystem physics;
+    float dt = 0.016f;
+    for (int i = 0; i < 100; ++i) {
+      physics.update(scene, dt);
+    }
+  
+    // Sphere should be above or at plane (y >= 0 because sphere radius is 1,
+    // plane is at -1)
+    assert(scene.objects[1].position.y >= -0.01f);
+    // Also should have slowed down
+    assert(scene.objects[1].velocity.y > -1.0f);
+  }
+  
+  int main() {
+    test_sdf_sphere();
+    test_sdf_box();
+    test_sdf_torus();
+    test_sdf_plane();
+    test_calc_normal();
+    test_bvh();
+    test_physics_falling();
+  
+    std::cout << "--- ALL PHYSICS TESTS PASSED ---" << std::endl;
+    return 0;
+  }
+  
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