diff --git a/src/game/entity.cpp b/src/game/entity.cpp
index 6a16b00..5755507 100644
--- a/src/game/entity.cpp
+++ b/src/game/entity.cpp
@@ -74,13 +74,13 @@ void game::Entity::Move(glm::vec3& velocity, float dt)
 		{
 			// Primary occurrence hit firstly
 			hit_fraction = occu_hit_fraction;
-			hit_normal = occu_->inv_basis_ * occu_hit_normal;
+			hit_normal = occu_->inv_normal_basis_ * occu_hit_normal;
 		}
 		else if (other_hit)
 		{
 			// Other occurrence hit firstly
 			hit_fraction = other_hit_fraction;
-			hit_normal = other_occu_->inv_basis_ * other_hit_normal;
+			hit_normal = other_occu_->inv_normal_basis_ * other_hit_normal;
 		}
 
 		// Update the position based on the hit fraction
@@ -153,6 +153,14 @@ game::EntityOccurrence::EntityOccurrence(Entity* entity, const CreateOccurrenceP
 	bt_capsule_(entity->GetCapsuleShape().radius * params.scale, entity->GetCapsuleShape().height * params.scale)
 {
 
+	// compute normalized basis
+	for (size_t i = 0; i < 3; ++i)
+	{
+		normal_basis_[i] = glm::normalize(basis_[i]);
+	}
+
+	// compute inverse normalized basis
+	inv_normal_basis_ = glm::inverse(normal_basis_);
 }
 
 bool game::EntityOccurrence::Sweep(const glm::vec3& target_position, float& hit_fraction, glm::vec3& hit_normal, const Portal** hit_portal)
@@ -169,7 +177,7 @@ bool game::EntityOccurrence::Sweep(const glm::vec3& target_position, float& hit_
 
 	return sector_->SweepCapsule(
 		bt_capsule_,
-		basis_,
+		normal_basis_,
 		position_,
 		target_position,
 		hit_fraction,
diff --git a/src/game/entity.hpp b/src/game/entity.hpp
index 04e07aa..0a4b345 100644
--- a/src/game/entity.hpp
+++ b/src/game/entity.hpp
@@ -30,9 +30,12 @@ namespace game
 		glm::vec3 position_;
 
 		float scale_;
-		glm::mat3 basis_; // Orthonormal basis in sector space
+		glm::mat3 basis_; // Orthogonal basis in sector space
 		glm::mat3 inv_basis_;
 
+		glm::mat3 normal_basis_; // Normalized basis for collision detection
+		glm::mat3 inv_normal_basis_;
+
 		btCapsuleShapeZ bt_capsule_;
 
 		friend class Entity;
diff --git a/src/game/player.cpp b/src/game/player.cpp
index 67ff3f3..339d5e5 100644
--- a/src/game/player.cpp
+++ b/src/game/player.cpp
@@ -87,7 +87,7 @@ void game::Player::Update(float dt)
 	
 	glm::vec3 velocity = glm::vec3(
 		velocity_xy,
-		-1.0f // No vertical movement for now
+		velocity_.z - gravity_ * dt // No vertical movement for now
 	);
 
 	velocity_ = velocity;
diff --git a/src/game/player.hpp b/src/game/player.hpp
index 4dea2eb..88e366d 100644
--- a/src/game/player.hpp
+++ b/src/game/player.hpp
@@ -20,6 +20,7 @@ namespace game
 		float max_speed_ = 4.0f;
 		float acceleration_ = 50.0f;
 		float deceleration_ = 20.0f;
+		float gravity_ = 9.81f; // Gravity acceleration
 
 		float time_ = 0.0f;
 		float current_speed_ = 0.0f;