Add spring system. Improve orbit cam and first person cam

CMakeLists.txt

@@ -1,5 +1,6 @@
 cmake_minimum_required(VERSION 3.7)
 
+
 option(VERSION_STRING "Project version string" "0.0.0")
 
 project(antkeeper VERSION ${VERSION_STRING} LANGUAGES CXX)

src/animation/spring.hpp

@@ -84,6 +84,15 @@ T hz_to_rads(T hz);
 template <typename T>
 T rads_to_hz(T rads);
 
+/**
+ * Converts a period from seconds to radians per second.
+ *
+ * @param t Period, in seconds.
+ * @return Angular frequency, in radians per second.
+ */
+template <typename T>
+T period_to_rads(T t);
+
 template <typename T, typename S>
 void spring(T& x0, T& v, const T& x1, S z, S w, S dt)
 {
@@ -116,4 +125,10 @@ inline T rads_to_hz(T rads)
 	return rads / math::two_pi<T>;
 }
 
+template <typename T>
+inline T period_to_rads(T t)
+{
+	return math::two_pi<T> / t;
+}
+
 #endif // ANTKEEPER_SPRING_HPP

src/game/component/spring.hpp

@@ -0,0 +1,81 @@
+/*
+ * Copyright (C) 2021  Christopher J. Howard
+ *
+ * This file is part of Antkeeper source code.
+ *
+ * Antkeeper source code is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * Antkeeper source code is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with Antkeeper source code.  If not, see <http://www.gnu.org/licenses/>.
+ */
+
+#ifndef ANTKEEPER_GAME_COMPONENT_SPRING_HPP
+#define ANTKEEPER_GAME_COMPONENT_SPRING_HPP
+
+#include "animation/spring.hpp"
+#include "utility/fundamental-types.hpp"
+#include <functional>
+
+namespace game {
+namespace component {
+
+/**
+ * Numeric spring with one component.
+ */
+struct spring1
+{
+	/// Numeric spring with one component.
+	numeric_spring<float, float> spring;
+	
+	/// Spring solved callback.
+	std::function<void(float)> callback;
+};
+
+/**
+ * Numeric spring with two components.
+ */
+struct spring2
+{
+	/// Numeric spring with two components.
+	numeric_spring<float2, float> spring;
+	
+	/// Spring solved callback.
+	std::function<void(const float2&)> callback;
+};
+
+/**
+ * Numeric spring with three components.
+ */
+struct spring3
+{
+	/// Numeric spring with three components.
+	numeric_spring<float3, float> spring;
+	
+	/// Spring solved callback.
+	std::function<void(const float3&)> callback;
+};
+
+/**
+ * Numeric spring with four components.
+ */
+struct spring4
+{
+	/// Numeric spring with four components.
+	numeric_spring<float4, float> spring;
+	
+	/// Spring solved callback.
+	std::function<void(const float4&)> callback;
+};
+
+} // namespace component
+} // namespace game
+
+#endif // ANTKEEPER_GAME_COMPONENT_SPRING_HPP

src/game/context.hpp

@@ -98,6 +98,7 @@ namespace game
 		class samara;
 		class proteome;
 		class steering;
+		class spring;
 	}
 }
 
@@ -286,6 +287,7 @@ struct context
 	game::system::subterrain* subterrain_system;
 	game::system::terrain* terrain_system;
 	game::system::vegetation* vegetation_system;
+	game::system::spring* spring_system;
 	game::system::spatial* spatial_system;
 	game::system::painting* painting_system;
 	game::system::blackbody* blackbody_system;

src/game/state/boot.cpp

@@ -75,6 +75,7 @@
 #include "game/system/orbit.hpp"
 #include "game/system/proteome.hpp"
 #include "game/system/steering.hpp"
+#include "game/system/spring.hpp"
 #include "entity/commands.hpp"
 #include "utility/paths.hpp"
 #include "event/event-dispatcher.hpp"
@@ -874,6 +875,9 @@ void boot::setup_systems()
 	// Setup steering system
 	ctx.steering_system = new game::system::steering(*ctx.entity_registry);
 	
+	// Setup spring system
+	ctx.spring_system = new game::system::spring(*ctx.entity_registry);
+	
 	// Setup spatial system
 	ctx.spatial_system = new game::system::spatial(*ctx.entity_registry);
 	
@@ -892,7 +896,7 @@ void boot::setup_systems()
 	ctx.blackbody_system->set_illuminant(color::illuminant::deg2::d55<double>);
 	
 	// RGB wavelengths for atmospheric scatteering
-	ctx.rgb_wavelengths = {645, 575, 440};
+	ctx.rgb_wavelengths = {640, 575, 440};
 	
 	// Setup atmosphere system
 	ctx.atmosphere_system = new game::system::atmosphere(*ctx.entity_registry);
@@ -1139,6 +1143,7 @@ void boot::setup_loop()
 			ctx.blackbody_system->update(t, dt);
 			ctx.atmosphere_system->update(t, dt);
 			ctx.astronomy_system->update(t, dt);
+			ctx.spring_system->update(t, dt);
 			ctx.spatial_system->update(t, dt);
 			ctx.constraint_system->update(t, dt);
 			ctx.painting_system->update(t, dt);

src/game/state/main-menu.cpp

@@ -246,7 +246,7 @@ main_menu::main_menu(game::context& ctx, bool fade_in):
 	{
 		game::world::cosmogenesis(ctx);
 		game::world::create_observer(ctx);
-		game::load::biome(ctx, "debug.bio");
+		game::load::biome(ctx, "desert-scrub.bio");
 	}
 	
 	// Set world time
@@ -257,9 +257,13 @@ main_menu::main_menu(game::context& ctx, bool fade_in):
 	
 	ctx.surface_camera->set_active(true);
 	const float ev100_sunny16 = physics::light::ev::from_settings(16.0f, 1.0f / 100.0f, 100.0f);
-	ctx.surface_camera->set_exposure(15.5f);
+	ctx.surface_camera->set_exposure(ev100_sunny16);
 	
-	ctx.surface_camera->look_at({0, 10, 0}, {0, 0, 0}, {0, 0, 1});
+	const auto& viewport_dimensions = ctx.app->get_viewport_dimensions();
+	const float aspect_ratio = static_cast<float>(viewport_dimensions[0]) / static_cast<float>(viewport_dimensions[1]);
+	
+	ctx.surface_camera->look_at({0, 3.0f, 0}, {0, 0, 0}, {0, 0, 1});
+	ctx.surface_camera->set_perspective(math::vertical_fov(math::radians(100.0f), aspect_ratio), ctx.surface_camera->get_aspect_ratio(), ctx.surface_camera->get_clip_near(), ctx.surface_camera->get_clip_far());
 	ctx.surface_camera->update_tweens();
 	
 	// Setup and enable sky and ground passes
@@ -271,7 +275,6 @@ main_menu::main_menu(game::context& ctx, bool fade_in):
 	
 	//if (!ctx.menu_bg_billboard->is_active())
 	//	game::menu::fade_in_bg(ctx);
-		
 	
 	ctx.logger->pop_task(EXIT_SUCCESS);
 }

src/game/state/nest-selection.hpp

@@ -21,6 +21,8 @@
 #define ANTKEEPER_GAME_STATE_NEST_SELECTION_HPP
 
 #include "game/state/base.hpp"
+#include "entity/id.hpp"
+#include "utility/fundamental-types.hpp"
 
 namespace game {
 namespace state {
@@ -32,15 +34,33 @@ public:
 	virtual ~nest_selection();
 	
 private:
-	void setup_camera();
+	void create_first_person_camera_rig();
+	void destroy_first_person_camera_rig();
+	
+	void set_first_person_camera_rig_pedestal(float pedestal);
+	void move_first_person_camera_rig(const float2& direction, float factor);
+	void satisfy_first_person_camera_rig_constraints();
 	
-	bool is_keeper;
-	void enable_keeper_controls();
-	void disable_keeper_controls();
-	void enable_ant_controls();
-	void disable_ant_controls();
 	void enable_controls();
 	void disable_controls();
+	
+	entity::id first_person_camera_rig_eid;
+	entity::id first_person_camera_rig_spring_translation_eid;
+	entity::id first_person_camera_rig_spring_rotation_eid;
+	entity::id first_person_camera_rig_fov_spring_eid;
+	float first_person_camera_rig_translation_spring_angular_frequency;
+	float first_person_camera_rig_rotation_spring_angular_frequency;
+	float first_person_camera_rig_fov_spring_angular_frequency;
+	float first_person_camera_rig_min_elevation;
+	float first_person_camera_rig_max_elevation;
+	float first_person_camera_near_fov;
+	float first_person_camera_far_fov;
+	float first_person_camera_near_speed;
+	float first_person_camera_far_speed;
+	float first_person_camera_rig_pedestal_speed;
+	float first_person_camera_rig_pedestal;
+	
+	bool mouse_look;
 };
 
 } // namespace state

src/game/state/nuptial-flight.cpp

@@ -19,6 +19,7 @@
 
 #include "game/state/nuptial-flight.hpp"
 #include "game/state/pause-menu.hpp"
+#include "game/state/nest-selection.hpp"
 #include "game/ant/swarm.hpp"
 #include "entity/archetype.hpp"
 #include "game/system/camera.hpp"
@@ -34,6 +35,8 @@
 #include "game/component/constraint-stack.hpp"
 #include "game/component/steering.hpp"
 #include "game/component/picking.hpp"
+#include "game/component/spring.hpp"
+#include "math/projection.hpp"
 #include "game/controls.hpp"
 #include "entity/commands.hpp"
 #include "animation/screen-transition.hpp"
@@ -83,7 +86,7 @@ nuptial_flight::nuptial_flight(game::context& ctx):
 	}
 	
 	// Load biome
-	game::load::biome(ctx, "desert-scrub.bio");
+	//game::load::biome(ctx, "desert-scrub.bio");
 	
 	// Set world time
 	game::world::set_time(ctx, 2022, 6, 21, 12, 0, 0.0);
@@ -106,6 +109,26 @@ nuptial_flight::nuptial_flight(game::context& ctx):
 	const float ev100_sunny16 = physics::light::ev::from_settings(16.0f, 1.0f / 100.0f, 100.0f);
 	ctx.surface_camera->set_exposure(ev100_sunny16);
 	
+	const auto& viewport_dimensions = ctx.app->get_viewport_dimensions();
+	const float aspect_ratio = static_cast<float>(viewport_dimensions[0]) / static_cast<float>(viewport_dimensions[1]);
+	
+	// Init camera rig params
+	camera_rig_near_distance = 1.0f;
+	camera_rig_far_distance = 150.0f;
+	camera_rig_near_fov = math::vertical_fov(math::radians(100.0f), aspect_ratio);
+	camera_rig_far_fov = math::vertical_fov(math::radians(60.0f), aspect_ratio);
+	camera_rig_zoom_speed = 4.0f;
+	camera_rig_translation_spring_angular_frequency = period_to_rads(0.125f);
+	camera_rig_rotation_spring_angular_frequency = period_to_rads(0.125f);
+	camera_rig_fov_spring_angular_frequency = period_to_rads(0.125f);
+	camera_rig_focus_ease_to_duration = 1.0f;
+	
+	// Read camera rig settingss
+	if (ctx.config->contains("near_fov"))
+		camera_rig_near_fov = math::vertical_fov(math::radians((*ctx.config)["near_fov"].get<float>()), aspect_ratio);
+	if (ctx.config->contains("far_fov"))
+		camera_rig_far_fov = math::vertical_fov(math::radians((*ctx.config)["far_fov"].get<float>()), aspect_ratio);
+	
 	// Create camera rig
 	create_camera_rig();
 	
@@ -150,7 +173,7 @@ void nuptial_flight::create_camera_rig()
 	component::constraint::ease_to camera_rig_focus_ease_to;
 	camera_rig_focus_ease_to.target = selected_eid;
 	camera_rig_focus_ease_to.start = {0, 0, 0};
-	camera_rig_focus_ease_to.duration = 1.0f;
+	camera_rig_focus_ease_to.duration = camera_rig_focus_ease_to_duration;
 	camera_rig_focus_ease_to.t = camera_rig_focus_ease_to.duration;
 	camera_rig_focus_ease_to.function = &ease<float3, float>::out_expo;
 	component::constraint_stack_node camera_rig_focus_ease_to_node;
@@ -215,7 +238,7 @@ void nuptial_flight::create_camera_rig()
 		{0.0f, 0.0f, 0.0f},
 		{0.0f, 0.0f, 0.0f},
 		1.0f,
-		hz_to_rads(8.0f)
+		camera_rig_rotation_spring_angular_frequency
 	};
 	component::constraint_stack_node camera_rig_spring_rotation_node;
 	camera_rig_spring_rotation_node.active = true;
@@ -233,7 +256,7 @@ void nuptial_flight::create_camera_rig()
 		{0.0f, 0.0f, 0.0f},
 		{0.0f, 0.0f, 0.0f},
 		1.0f,
-		hz_to_rads(8.0f)
+		camera_rig_translation_spring_angular_frequency
 	};
 	component::constraint_stack_node camera_rig_spring_translation_node;
 	camera_rig_spring_translation_node.active = true;
@@ -264,6 +287,25 @@ void nuptial_flight::create_camera_rig()
 	ctx.entity_registry->emplace<component::transform>(camera_rig_eid, camera_rig_transform);
 	ctx.entity_registry->emplace<component::constraint_stack>(camera_rig_eid, camera_rig_constraint_stack);
 	
+	// Construct camera rig fov spring
+	component::spring1 camera_rig_fov_spring;
+	camera_rig_fov_spring.spring =
+	{
+		0.0f,
+		0.0f,
+		0.0f,
+		1.0f,
+		camera_rig_fov_spring_angular_frequency
+	};
+	camera_rig_fov_spring.callback = [&](float fov)
+	{
+		ctx.surface_camera->set_perspective(fov, ctx.surface_camera->get_aspect_ratio(), ctx.surface_camera->get_clip_near(), ctx.surface_camera->get_clip_far());
+	};
+	
+	// Construct camera rig fov spring entity
+	camera_rig_fov_spring_eid = ctx.entity_registry->create();
+	ctx.entity_registry->emplace<component::spring1>(camera_rig_fov_spring_eid, camera_rig_fov_spring);
+	
 	set_camera_rig_zoom(0.25f);
 }
 
@@ -277,16 +319,15 @@ void nuptial_flight::destroy_camera_rig()
 	
 	ctx.entity_registry->destroy(camera_rig_focus_eid);
 	ctx.entity_registry->destroy(camera_rig_focus_ease_to_eid);
+	
+	ctx.entity_registry->destroy(camera_rig_fov_spring_eid);
 }
 
 void nuptial_flight::set_camera_rig_zoom(float zoom)
 {
-	const float near_distance = 1.0f;
-	const float far_distance = 50.0f;
-	
 	camera_rig_zoom = zoom;
-	const float distance = math::log_lerp(far_distance, near_distance, camera_rig_zoom);
 	
+	const float distance = math::log_lerp(camera_rig_far_distance, camera_rig_near_distance, camera_rig_zoom);
 	ctx.entity_registry->patch<component::constraint::spring_translation>
 	(
 		camera_rig_spring_translation_eid,
@@ -295,11 +336,21 @@ void nuptial_flight::set_camera_rig_zoom(float zoom)
 			component.spring.x1[2] = distance;
 		}
 	);
+	
+	const float fov = math::log_lerp(camera_rig_far_fov, camera_rig_near_fov, camera_rig_zoom);	
+	ctx.entity_registry->patch<component::spring1>
+	(
+		camera_rig_fov_spring_eid,
+		[&](auto& component)
+		{
+			component.spring.x1 = fov;
+		}
+	);
 }
 
 void nuptial_flight::satisfy_camera_rig_constraints()
 {
-	// Warp camera rig focus ease to
+	// Satisfy camera rig focus ease to constraint
 	ctx.entity_registry->patch<component::constraint::ease_to>
 	(
 		camera_rig_focus_ease_to_eid,
@@ -309,7 +360,7 @@ void nuptial_flight::satisfy_camera_rig_constraints()
 		}
 	);
 	
-	// Warp camera rig spring translation
+	// Satisfy camera rig spring translation constraint
 	ctx.entity_registry->patch<component::constraint::spring_translation>
 	(
 		camera_rig_spring_translation_eid,
@@ -320,7 +371,7 @@ void nuptial_flight::satisfy_camera_rig_constraints()
 		}
 	);
 	
-	// Warp camera rig spring rotation
+	// Satisfy camera rig spring rotation constraint
 	ctx.entity_registry->patch<component::constraint::spring_rotation>
 	(
 		camera_rig_spring_rotation_eid,
@@ -330,6 +381,17 @@ void nuptial_flight::satisfy_camera_rig_constraints()
 			component.spring.v *= 0.0f;
 		}
 	);
+	
+	// Satisfycamera rig fov spring
+	ctx.entity_registry->patch<component::spring1>
+	(
+		camera_rig_fov_spring_eid,
+		[&](auto& component)
+		{
+			component.spring.x0 = component.spring.x1;
+			component.spring.v *= 0.0f;
+		}
+	);
 }
 
 void nuptial_flight::enable_controls()
@@ -339,7 +401,6 @@ void nuptial_flight::enable_controls()
 	
 	double time_scale = 0.0;
 	double ff_time_scale = 60.0 * 200.0;
-	const float dolly_zoom_speed = 4.0f;
 	
 	// Init control settings
 	float mouse_tilt_sensitivity = 1.0f;
@@ -414,7 +475,7 @@ void nuptial_flight::enable_controls()
 			ctx.entity_registry->patch<component::constraint::spring_rotation>
 			(
 				camera_rig_spring_rotation_eid,
-				[&](auto& component)
+				[&, mouse_pan_factor](auto& component)
 				{
 					component.spring.x1[0] -= mouse_pan_factor * value;
 				}
@@ -428,7 +489,7 @@ void nuptial_flight::enable_controls()
 			ctx.entity_registry->patch<component::constraint::spring_rotation>
 			(
 				camera_rig_spring_rotation_eid,
-				[&](auto& component)
+				[&, gamepad_pan_factor](auto& component)
 				{
 					component.spring.x1[0] -= gamepad_pan_factor * value * static_cast<float>(ctx.loop.get_update_period());
 				}
@@ -447,7 +508,7 @@ void nuptial_flight::enable_controls()
 			ctx.entity_registry->patch<component::constraint::spring_rotation>
 			(
 				camera_rig_spring_rotation_eid,
-				[&](auto& component)
+				[&, mouse_pan_factor](auto& component)
 				{
 					component.spring.x1[0] += mouse_pan_factor * value;
 				}
@@ -461,7 +522,7 @@ void nuptial_flight::enable_controls()
 			ctx.entity_registry->patch<component::constraint::spring_rotation>
 			(
 				camera_rig_spring_rotation_eid,
-				[&](auto& component)
+				[&, gamepad_pan_factor](auto& component)
 				{
 					component.spring.x1[0] += gamepad_pan_factor * value * static_cast<float>(ctx.loop.get_update_period());
 				}
@@ -480,7 +541,7 @@ void nuptial_flight::enable_controls()
 			ctx.entity_registry->patch<component::constraint::spring_rotation>
 			(
 				camera_rig_spring_rotation_eid,
-				[&](auto& component)
+				[&, mouse_tilt_factor](auto& component)
 				{
 					component.spring.x1[1] -= mouse_tilt_factor * value;
 					component.spring.x1[1] = std::max(-math::half_pi<float>, component.spring.x1[1]);
@@ -495,7 +556,7 @@ void nuptial_flight::enable_controls()
 			ctx.entity_registry->patch<component::constraint::spring_rotation>
 			(
 				camera_rig_spring_rotation_eid,
-				[&](auto& component)
+				[&, gamepad_tilt_factor](auto& component)
 				{
 					component.spring.x1[1] -= gamepad_tilt_factor * value * static_cast<float>(ctx.loop.get_update_period());
 					component.spring.x1[1] = std::max(-math::half_pi<float>, component.spring.x1[1]);
@@ -515,7 +576,7 @@ void nuptial_flight::enable_controls()
 			ctx.entity_registry->patch<component::constraint::spring_rotation>
 			(
 				camera_rig_spring_rotation_eid,
-				[&](auto& component)
+				[&, mouse_tilt_factor](auto& component)
 				{
 					component.spring.x1[1] += mouse_tilt_factor * value;
 					component.spring.x1[1] = std::min(math::half_pi<float>, component.spring.x1[1]);
@@ -530,7 +591,7 @@ void nuptial_flight::enable_controls()
 			ctx.entity_registry->patch<component::constraint::spring_rotation>
 			(
 				camera_rig_spring_rotation_eid,
-				[&](auto& component)
+				[&, gamepad_tilt_factor](auto& component)
 				{
 					component.spring.x1[1] += gamepad_tilt_factor * value * static_cast<float>(ctx.loop.get_update_period());
 					component.spring.x1[1] = std::min(math::half_pi<float>, component.spring.x1[1]);
@@ -542,18 +603,18 @@ void nuptial_flight::enable_controls()
 	// Dolly in control
 	ctx.controls["move_up"]->set_active_callback
 	(
-		[&, dolly_zoom_speed](float value)
+		[&](float value)
 		{
-			set_camera_rig_zoom(std::min(1.0f, camera_rig_zoom + dolly_zoom_speed * static_cast<float>(ctx.loop.get_update_period())));
+			set_camera_rig_zoom(std::min(1.0f, camera_rig_zoom + camera_rig_zoom_speed * static_cast<float>(ctx.loop.get_update_period())));
 		}
 	);
 	
 	// Dolly out control
 	ctx.controls["move_down"]->set_active_callback
 	(
-		[&, dolly_zoom_speed](float value)
+		[&](float value)
 		{
-			set_camera_rig_zoom(std::max(0.0f, camera_rig_zoom - dolly_zoom_speed * static_cast<float>(ctx.loop.get_update_period())));
+			set_camera_rig_zoom(std::max(0.0f, camera_rig_zoom - camera_rig_zoom_speed * static_cast<float>(ctx.loop.get_update_period())));
 		}
 	);
 	
@@ -628,7 +689,12 @@ void nuptial_flight::enable_controls()
 	(
 		[&]()
 		{
+			// Disable controls
+			disable_controls();
 			
+			// Change to nest selection state
+			ctx.state_machine.pop();
+			ctx.state_machine.emplace(new game::state::nest_selection(ctx));
 		}
 	);
 	
@@ -781,30 +847,37 @@ void nuptial_flight::disable_controls()
 		ctx.app->set_relative_mouse_mode(false);
 	}
 	
-	ctx.controls["move_forward"]->set_activated_callback(nullptr);
-	ctx.controls["move_back"]->set_activated_callback(nullptr);
-	ctx.controls["move_right"]->set_activated_callback(nullptr);
-	ctx.controls["move_left"]->set_activated_callback(nullptr);
-	ctx.controls["move_up"]->set_active_callback(nullptr);
-	ctx.controls["move_down"]->set_active_callback(nullptr);
 	ctx.controls["mouse_look"]->set_activated_callback(nullptr);
 	ctx.controls["mouse_look"]->set_deactivated_callback(nullptr);
-	ctx.controls["look_left_gamepad"]->set_active_callback(nullptr);
-	ctx.controls["look_left_mouse"]->set_active_callback(nullptr);
-	ctx.controls["look_right_gamepad"]->set_active_callback(nullptr);
 	ctx.controls["look_right_mouse"]->set_active_callback(nullptr);
-	ctx.controls["look_up_gamepad"]->set_active_callback(nullptr);
+	ctx.controls["look_right_gamepad"]->set_active_callback(nullptr);
+	ctx.controls["look_left_mouse"]->set_active_callback(nullptr);
+	ctx.controls["look_left_gamepad"]->set_active_callback(nullptr);
 	ctx.controls["look_up_mouse"]->set_active_callback(nullptr);
-	ctx.controls["look_down_gamepad"]->set_active_callback(nullptr);
+	ctx.controls["look_up_gamepad"]->set_active_callback(nullptr);
 	ctx.controls["look_down_mouse"]->set_active_callback(nullptr);
+	ctx.controls["look_down_gamepad"]->set_active_callback(nullptr);
+	ctx.controls["move_up"]->set_active_callback(nullptr);
+	ctx.controls["move_down"]->set_active_callback(nullptr);
 	ctx.controls["select_mouse"]->set_activated_callback(nullptr);
+	ctx.controls["move_forward"]->set_activated_callback(nullptr);
+	ctx.controls["move_back"]->set_activated_callback(nullptr);
+	ctx.controls["move_right"]->set_activated_callback(nullptr);
+	ctx.controls["move_left"]->set_activated_callback(nullptr);
 	ctx.controls["action"]->set_activated_callback(nullptr);
-	ctx.controls["switch_pov"]->set_activated_callback(nullptr);
 	ctx.controls["fast_forward"]->set_activated_callback(nullptr);
+	ctx.controls["fast_forward"]->set_deactivated_callback(nullptr);
 	ctx.controls["rewind"]->set_activated_callback(nullptr);
+	ctx.controls["rewind"]->set_deactivated_callback(nullptr);
 	ctx.controls["pause"]->set_activated_callback(nullptr);
-	ctx.controls["increase_exposure"]->set_activated_callback(nullptr);
-	ctx.controls["decrease_exposure"]->set_activated_callback(nullptr);
+	ctx.controls["increase_exposure"]->set_active_callback(nullptr);
+	ctx.controls["decrease_exposure"]->set_active_callback(nullptr);
+	ctx.controls["dec_red"]->set_active_callback(nullptr);
+	ctx.controls["inc_red"]->set_active_callback(nullptr);
+	ctx.controls["dec_green"]->set_active_callback(nullptr);
+	ctx.controls["inc_green"]->set_active_callback(nullptr);
+	ctx.controls["dec_blue"]->set_active_callback(nullptr);
+	ctx.controls["inc_blue"]->set_active_callback(nullptr);
 }
 
 void nuptial_flight::select_entity(entity::id entity_id)

src/game/state/nuptial-flight.hpp

@@ -54,9 +54,21 @@ private:
 	entity::id camera_rig_spring_rotation_eid;
 	entity::id camera_rig_copy_translation_eid;
 	entity::id camera_rig_pivot_eid;
-	
+	float camera_rig_near_distance;
+	float camera_rig_far_distance;
+	float camera_rig_near_fov;
+	float camera_rig_far_fov;
+	float camera_rig_zoom_speed;
 	float camera_rig_zoom;
 	
+	entity::id camera_rig_fov_spring_eid;
+	
+	float camera_rig_translation_spring_angular_frequency;
+	float camera_rig_rotation_spring_angular_frequency;
+	float camera_rig_fov_spring_angular_frequency;
+	float camera_rig_focus_ease_to_duration;
+
+	
 	entity::id swarm_eid;
 	
 	std::uint32_t selected_picking_flag;

src/game/state/splash.cpp

@@ -19,7 +19,6 @@
 
 #include "game/state/splash.hpp"
 #include "game/state/main-menu.hpp"
-#include "game/state/nuptial-flight.hpp"
 #include "animation/screen-transition.hpp"
 #include "animation/animation.hpp"
 #include "animation/animator.hpp"
@@ -118,7 +117,6 @@ splash::splash(game::context& ctx):
 				{
 					ctx.state_machine.pop();
 					ctx.state_machine.emplace(new game::state::main_menu(ctx, true));
-					//ctx.state_machine.emplace(new game::state::nuptial_flight(ctx));
 				}
 			);
 		}
@@ -147,7 +145,6 @@ splash::splash(game::context& ctx):
 				// Change to main menu state
 				ctx.state_machine.pop();
 				ctx.state_machine.emplace(new game::state::main_menu(ctx, true));
-				//ctx.state_machine.emplace(new game::state::nuptial_flight(ctx));
 			}
 		}
 	);

src/game/system/constraint.cpp

@@ -17,7 +17,7 @@
  * along with Antkeeper source code.  If not, see <http://www.gnu.org/licenses/>.
  */
 
-#include "constraint.hpp"
+#include "game/system/constraint.hpp"
 #include "game/component/constraint-stack.hpp"
 
 namespace game {

src/game/system/spring.cpp

@@ -0,0 +1,80 @@
+/*
+ * Copyright (C) 2021  Christopher J. Howard
+ *
+ * This file is part of Antkeeper source code.
+ *
+ * Antkeeper source code is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * Antkeeper source code is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with Antkeeper source code.  If not, see <http://www.gnu.org/licenses/>.
+ */
+
+#include "game/system/spring.hpp"
+#include "game/component/spring.hpp"
+#include "entity/id.hpp"
+
+namespace game {
+namespace system {
+
+spring::spring(entity::registry& registry):
+	updatable(registry)
+{}
+
+spring::~spring()
+{}
+
+void spring::update(double t, double dt)
+{
+	const float dtf = static_cast<float>(dt);
+	
+	registry.view<component::spring1>().each
+	(
+		[&](entity::id spring_eid, auto& component)
+		{
+			solve_numeric_spring<float, float>(component.spring, dtf);
+			if (component.callback)
+				component.callback(component.spring.x0);
+		}
+	);
+	
+	registry.view<component::spring2>().each
+	(
+		[&](entity::id spring_eid, auto& component)
+		{
+			solve_numeric_spring<float2, float>(component.spring, dtf);
+			if (component.callback)
+				component.callback(component.spring.x0);
+		}
+	);
+	
+	registry.view<component::spring3>().each
+	(
+		[&](entity::id spring_eid, auto& component)
+		{
+			solve_numeric_spring<float3, float>(component.spring, dtf);
+			if (component.callback)
+				component.callback(component.spring.x0);
+		}
+	);
+	
+	registry.view<component::spring4>().each
+	(
+		[&](entity::id spring_eid, auto& component)
+		{
+			solve_numeric_spring<float4, float>(component.spring, dtf);
+			if (component.callback)
+				component.callback(component.spring.x0);
+		}
+	);
+}
+
+} // namespace system
+} // namespace game

src/game/system/spring.hpp

@@ -0,0 +1,44 @@
+/*
+ * Copyright (C) 2021  Christopher J. Howard
+ *
+ * This file is part of Antkeeper source code.
+ *
+ * Antkeeper source code is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * Antkeeper source code is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with Antkeeper source code.  If not, see <http://www.gnu.org/licenses/>.
+ */
+
+#ifndef ANTKEEPER_GAME_SYSTEM_SPRING_HPP
+#define ANTKEEPER_GAME_SYSTEM_SPRING_HPP
+
+#include "game/system/updatable.hpp"
+
+namespace game {
+namespace system {
+
+/**
+ * Solves numeric springs.
+ */
+class spring:
+	public updatable
+{
+public:
+	spring(entity::registry& registry);
+	~spring();
+	
+	virtual void update(double t, double dt);
+};
+
+} // namespace system
+} // namespace game
+
+#endif // ANTKEEPER_GAME_SYSTEM_SPRING_HPP

src/geom/marching-cubes.cpp

@@ -41,297 +41,297 @@ static constexpr std::uint_fast8_t vertex_table[12][2] =
 
 static constexpr std::uint_fast16_t edge_table[256] =
 {
-	0x000, 0x109, 0x203, 0x30a, 0x406, 0x50f, 0x605, 0x70c,
-	0x80c, 0x905, 0xa0f, 0xb06, 0xc0a, 0xd03, 0xe09, 0xf00,
-	0x190, 0x099, 0x393, 0x29a, 0x596, 0x49f, 0x795, 0x69c,
-	0x99c, 0x895, 0xb9f, 0xa96, 0xd9a, 0xc93, 0xf99, 0xe90,
-	0x230, 0x339, 0x033, 0x13a, 0x636, 0x73f, 0x435, 0x53c,
-	0xa3c, 0xb35, 0x83f, 0x936, 0xe3a, 0xf33, 0xc39, 0xd30,
-	0x3a0, 0x2a9, 0x1a3, 0x0aa, 0x7a6, 0x6af, 0x5a5, 0x4ac,
-	0xbac, 0xaa5, 0x9af, 0x8a6, 0xfaa, 0xea3, 0xda9, 0xca0,
-	0x460, 0x569, 0x663, 0x76a, 0x066, 0x16f, 0x265, 0x36c,
-	0xc6c, 0xd65, 0xe6f, 0xf66, 0x86a, 0x963, 0xa69, 0xb60,
-	0x5f0, 0x4f9, 0x7f3, 0x6fa, 0x1f6, 0x0ff, 0x3f5, 0x2fc,
-	0xdfc, 0xcf5, 0xfff, 0xef6, 0x9fa, 0x8f3, 0xbf9, 0xaf0,
-	0x650, 0x759, 0x453, 0x55a, 0x256, 0x35f, 0x055, 0x15c,
-	0xe5c, 0xf55, 0xc5f, 0xd56, 0xa5a, 0xb53, 0x859, 0x950,
-	0x7c0, 0x6c9, 0x5c3, 0x4ca, 0x3c6, 0x2cf, 0x1c5, 0x0cc,
-	0xfcc, 0xec5, 0xdcf, 0xcc6, 0xbca, 0xac3, 0x9c9, 0x8c0,
-	0x8c0, 0x9c9, 0xac3, 0xbca, 0xcc6, 0xdcf, 0xec5, 0xfcc,
-	0x0cc, 0x1c5, 0x2cf, 0x3c6, 0x4ca, 0x5c3, 0x6c9, 0x7c0,
-	0x950, 0x859, 0xb53, 0xa5a, 0xd56, 0xc5f, 0xf55, 0xe5c,
-	0x15c, 0x055, 0x35f, 0x256, 0x55a, 0x453, 0x759, 0x650,
-	0xaf0, 0xbf9, 0x8f3, 0x9fa, 0xef6, 0xfff, 0xcf5, 0xdfc,
-	0x2fc, 0x3f5, 0x0ff, 0x1f6, 0x6fa, 0x7f3, 0x4f9, 0x5f0,
-	0xb60, 0xa69, 0x963, 0x86a, 0xf66, 0xe6f, 0xd65, 0xc6c,
-	0x36c, 0x265, 0x16f, 0x066, 0x76a, 0x663, 0x569, 0x460,
-	0xca0, 0xda9, 0xea3, 0xfaa, 0x8a6, 0x9af, 0xaa5, 0xbac,
-	0x4ac, 0x5a5, 0x6af, 0x7a6, 0x0aa, 0x1a3, 0x2a9, 0x3a0,
-	0xd30, 0xc39, 0xf33, 0xe3a, 0x936, 0x83f, 0xb35, 0xa3c,
-	0x53c, 0x435, 0x73f, 0x636, 0x13a, 0x033, 0x339, 0x230,
-	0xe90, 0xf99, 0xc93, 0xd9a, 0xa96, 0xb9f, 0x895, 0x99c,
-	0x69c, 0x795, 0x49f, 0x596, 0x29a, 0x393, 0x099, 0x190,
-	0xf00, 0xe09, 0xd03, 0xc0a, 0xb06, 0xa0f, 0x905, 0x80c,
-	0x70c, 0x605, 0x50f, 0x406, 0x30a, 0x203, 0x109, 0x000
+	0x000, 0x109, 0x203, 0x30A, 0x406, 0x50F, 0x605, 0x70C,
+	0x80C, 0x905, 0xA0F, 0xB06, 0xC0A, 0xD03, 0xE09, 0xF00,
+	0x190, 0x099, 0x393, 0x29A, 0x596, 0x49F, 0x795, 0x69C,
+	0x99C, 0x895, 0xB9F, 0xA96, 0xD9A, 0xC93, 0xF99, 0xE90,
+	0x230, 0x339, 0x033, 0x13A, 0x636, 0x73F, 0x435, 0x53C,
+	0xA3C, 0xB35, 0x83F, 0x936, 0xE3A, 0xF33, 0xC39, 0xD30,
+	0x3A0, 0x2A9, 0x1A3, 0x0AA, 0x7A6, 0x6AF, 0x5A5, 0x4AC,
+	0xBAC, 0xAA5, 0x9AF, 0x8A6, 0xFAA, 0xEA3, 0xDA9, 0xCA0,
+	0x460, 0x569, 0x663, 0x76A, 0x066, 0x16F, 0x265, 0x36C,
+	0xC6C, 0xD65, 0xE6F, 0xF66, 0x86A, 0x963, 0xA69, 0xB60,
+	0x5F0, 0x4F9, 0x7F3, 0x6FA, 0x1F6, 0x0FF, 0x3F5, 0x2FC,
+	0xDFC, 0xCF5, 0xFFF, 0xEF6, 0x9FA, 0x8F3, 0xBF9, 0xAF0,
+	0x650, 0x759, 0x453, 0x55A, 0x256, 0x35F, 0x055, 0x15C,
+	0xE5C, 0xF55, 0xC5F, 0xD56, 0xA5A, 0xB53, 0x859, 0x950,
+	0x7C0, 0x6C9, 0x5C3, 0x4CA, 0x3C6, 0x2CF, 0x1C5, 0x0CC,
+	0xFCC, 0xEC5, 0xDCF, 0xCC6, 0xBCA, 0xAC3, 0x9C9, 0x8C0,
+	0x8C0, 0x9C9, 0xAC3, 0xBCA, 0xCC6, 0xDCF, 0xEC5, 0xFCC,
+	0x0CC, 0x1C5, 0x2CF, 0x3C6, 0x4CA, 0x5C3, 0x6C9, 0x7C0,
+	0x950, 0x859, 0xB53, 0xA5A, 0xD56, 0xC5F, 0xF55, 0xE5C,
+	0x15C, 0x055, 0x35F, 0x256, 0x55A, 0x453, 0x759, 0x650,
+	0xAF0, 0xBF9, 0x8F3, 0x9FA, 0xEF6, 0xFFF, 0xCF5, 0xDFC,
+	0x2FC, 0x3F5, 0x0FF, 0x1F6, 0x6FA, 0x7F3, 0x4F9, 0x5F0,
+	0xB60, 0xA69, 0x963, 0x86A, 0xF66, 0xE6F, 0xD65, 0xC6C,
+	0x36C, 0x265, 0x16F, 0x066, 0x76A, 0x663, 0x569, 0x460,
+	0xCA0, 0xDA9, 0xEA3, 0xFAA, 0x8A6, 0x9AF, 0xAA5, 0xBAC,
+	0x4AC, 0x5A5, 0x6AF, 0x7A6, 0x0AA, 0x1A3, 0x2A9, 0x3A0,
+	0xD30, 0xC39, 0xF33, 0xE3A, 0x936, 0x83F, 0xB35, 0xA3C,
+	0x53C, 0x435, 0x73F, 0x636, 0x13A, 0x033, 0x339, 0x230,
+	0xE90, 0xF99, 0xC93, 0xD9A, 0xA96, 0xB9F, 0x895, 0x99C,
+	0x69C, 0x795, 0x49F, 0x596, 0x29A, 0x393, 0x099, 0x190,
+	0xF00, 0xE09, 0xD03, 0xC0A, 0xB06, 0xA0F, 0x905, 0x80C,
+	0x70C, 0x605, 0x50F, 0x406, 0x30A, 0x203, 0x109, 0x000
 };
 
 static constexpr std::int_fast8_t triangle_table[256][16] =
-{
+{                            
 	{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{0, 1, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{1, 8, 3, 9, 8, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{0, 8, 3, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{9, 2, 10, 0, 2, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{2, 8, 3, 2, 10, 8, 10, 9, 8, -1, -1, -1, -1, -1, -1, -1},
-	{3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{0, 11, 2, 8, 11, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{1, 9, 0, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{1, 11, 2, 1, 9, 11, 9, 8, 11, -1, -1, -1, -1, -1, -1, -1},
-	{3, 10, 1, 11, 10, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{0, 10, 1, 0, 8, 10, 8, 11, 10, -1, -1, -1, -1, -1, -1, -1},
-	{3, 9, 0, 3, 11, 9, 11, 10, 9, -1, -1, -1, -1, -1, -1, -1},
-	{9, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{4, 3, 0, 7, 3, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{0, 1, 9, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{4, 1, 9, 4, 7, 1, 7, 3, 1, -1, -1, -1, -1, -1, -1, -1},
-	{1, 2, 10, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{3, 4, 7, 3, 0, 4, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1},
-	{9, 2, 10, 9, 0, 2, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1},
-	{2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4, -1, -1, -1, -1},
-	{8, 4, 7, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{11, 4, 7, 11, 2, 4, 2, 0, 4, -1, -1, -1, -1, -1, -1, -1},
-	{9, 0, 1, 8, 4, 7, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1},
-	{4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1, -1, -1, -1, -1},
-	{3, 10, 1, 3, 11, 10, 7, 8, 4, -1, -1, -1, -1, -1, -1, -1},
-	{1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4, -1, -1, -1, -1},
-	{4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3, -1, -1, -1, -1},
-	{4, 7, 11, 4, 11, 9, 9, 11, 10, -1, -1, -1, -1, -1, -1, -1},
-	{9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{9, 5, 4, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{0, 5, 4, 1, 5, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{8, 5, 4, 8, 3, 5, 3, 1, 5, -1, -1, -1, -1, -1, -1, -1},
-	{1, 2, 10, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{3, 0, 8, 1, 2, 10, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1},
-	{5, 2, 10, 5, 4, 2, 4, 0, 2, -1, -1, -1, -1, -1, -1, -1},
-	{2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8, -1, -1, -1, -1},
-	{9, 5, 4, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{0, 11, 2, 0, 8, 11, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1},
-	{0, 5, 4, 0, 1, 5, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1},
-	{2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5, -1, -1, -1, -1},
-	{10, 3, 11, 10, 1, 3, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1},
-	{4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10, -1, -1, -1, -1},
-	{5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3, -1, -1, -1, -1},
-	{5, 4, 8, 5, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1},
-	{9, 7, 8, 5, 7, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{9, 3, 0, 9, 5, 3, 5, 7, 3, -1, -1, -1, -1, -1, -1, -1},
-	{0, 7, 8, 0, 1, 7, 1, 5, 7, -1, -1, -1, -1, -1, -1, -1},
-	{1, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{9, 7, 8, 9, 5, 7, 10, 1, 2, -1, -1, -1, -1, -1, -1, -1},
-	{10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3, -1, -1, -1, -1},
-	{8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2, -1, -1, -1, -1},
-	{2, 10, 5, 2, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1},
-	{7, 9, 5, 7, 8, 9, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1},
-	{9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11, -1, -1, -1, -1},
-	{2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7, -1, -1, -1, -1},
-	{11, 2, 1, 11, 1, 7, 7, 1, 5, -1, -1, -1, -1, -1, -1, -1},
-	{9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11, -1, -1, -1, -1},
-	{5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0, -1},
-	{11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0, -1},
-	{11, 10, 5, 7, 11, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{0, 8, 3, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{9, 0, 1, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{1, 8, 3, 1, 9, 8, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1},
-	{1, 6, 5, 2, 6, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{1, 6, 5, 1, 2, 6, 3, 0, 8, -1, -1, -1, -1, -1, -1, -1},
-	{9, 6, 5, 9, 0, 6, 0, 2, 6, -1, -1, -1, -1, -1, -1, -1},
-	{5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8, -1, -1, -1, -1},
-	{2, 3, 11, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{11, 0, 8, 11, 2, 0, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1},
-	{0, 1, 9, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1},
-	{5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11, -1, -1, -1, -1},
-	{6, 3, 11, 6, 5, 3, 5, 1, 3, -1, -1, -1, -1, -1, -1, -1},
-	{0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6, -1, -1, -1, -1},
-	{3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9, -1, -1, -1, -1},
-	{6, 5, 9, 6, 9, 11, 11, 9, 8, -1, -1, -1, -1, -1, -1, -1},
-	{5, 10, 6, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{4, 3, 0, 4, 7, 3, 6, 5, 10, -1, -1, -1, -1, -1, -1, -1},
-	{1, 9, 0, 5, 10, 6, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1},
-	{10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4, -1, -1, -1, -1},
-	{6, 1, 2, 6, 5, 1, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1},
-	{1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7, -1, -1, -1, -1},
-	{8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6, -1, -1, -1, -1},
-	{7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9, -1},
-	{3, 11, 2, 7, 8, 4, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1},
-	{5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11, -1, -1, -1, -1},
-	{0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1},
-	{9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6, -1},
-	{8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6, -1, -1, -1, -1},
-	{5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11, -1},
-	{0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7, -1},
-	{6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9, -1, -1, -1, -1},
-	{10, 4, 9, 6, 4, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{4, 10, 6, 4, 9, 10, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1},
-	{10, 0, 1, 10, 6, 0, 6, 4, 0, -1, -1, -1, -1, -1, -1, -1},
-	{8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10, -1, -1, -1, -1},
-	{1, 4, 9, 1, 2, 4, 2, 6, 4, -1, -1, -1, -1, -1, -1, -1},
-	{3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4, -1, -1, -1, -1},
-	{0, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{8, 3, 2, 8, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1},
-	{10, 4, 9, 10, 6, 4, 11, 2, 3, -1, -1, -1, -1, -1, -1, -1},
-	{0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6, -1, -1, -1, -1},
-	{3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10, -1, -1, -1, -1},
-	{6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1, -1},
-	{9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3, -1, -1, -1, -1},
-	{8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1, -1},
-	{3, 11, 6, 3, 6, 0, 0, 6, 4, -1, -1, -1, -1, -1, -1, -1},
-	{6, 4, 8, 11, 6, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{7, 10, 6, 7, 8, 10, 8, 9, 10, -1, -1, -1, -1, -1, -1, -1},
-	{0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10, -1, -1, -1, -1},
-	{10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0, -1, -1, -1, -1},
-	{10, 6, 7, 10, 7, 1, 1, 7, 3, -1, -1, -1, -1, -1, -1, -1},
-	{1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7, -1, -1, -1, -1},
-	{2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9, -1},
-	{7, 8, 0, 7, 0, 6, 6, 0, 2, -1, -1, -1, -1, -1, -1, -1},
-	{7, 3, 2, 6, 7, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7, -1, -1, -1, -1},
-	{2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7, -1},
-	{1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11, -1},
-	{11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1, -1, -1, -1, -1},
-	{8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6, -1},
-	{0, 9, 1, 11, 6, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0, -1, -1, -1, -1},
-	{7, 11, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{3, 0, 8, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{0, 1, 9, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{8, 1, 9, 8, 3, 1, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1},
-	{10, 1, 2, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{1, 2, 10, 3, 0, 8, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1},
-	{2, 9, 0, 2, 10, 9, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1},
-	{6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8, -1, -1, -1, -1},
-	{7, 2, 3, 6, 2, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{7, 0, 8, 7, 6, 0, 6, 2, 0, -1, -1, -1, -1, -1, -1, -1},
-	{2, 7, 6, 2, 3, 7, 0, 1, 9, -1, -1, -1, -1, -1, -1, -1},
-	{1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6, -1, -1, -1, -1},
-	{10, 7, 6, 10, 1, 7, 1, 3, 7, -1, -1, -1, -1, -1, -1, -1},
-	{10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8, -1, -1, -1, -1},
-	{0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7, -1, -1, -1, -1},
-	{7, 6, 10, 7, 10, 8, 8, 10, 9, -1, -1, -1, -1, -1, -1, -1},
-	{6, 8, 4, 11, 8, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{3, 6, 11, 3, 0, 6, 0, 4, 6, -1, -1, -1, -1, -1, -1, -1},
-	{8, 6, 11, 8, 4, 6, 9, 0, 1, -1, -1, -1, -1, -1, -1, -1},
-	{9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6, -1, -1, -1, -1},
-	{6, 8, 4, 6, 11, 8, 2, 10, 1, -1, -1, -1, -1, -1, -1, -1},
-	{1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6, -1, -1, -1, -1},
-	{4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9, -1, -1, -1, -1},
-	{10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3, -1},
-	{8, 2, 3, 8, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1},
-	{0, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8, -1, -1, -1, -1},
-	{1, 9, 4, 1, 4, 2, 2, 4, 6, -1, -1, -1, -1, -1, -1, -1},
-	{8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1, -1, -1, -1, -1},
-	{10, 1, 0, 10, 0, 6, 6, 0, 4, -1, -1, -1, -1, -1, -1, -1},
-	{4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3, -1},
-	{10, 9, 4, 6, 10, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{4, 9, 5, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{0, 8, 3, 4, 9, 5, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1},
-	{5, 0, 1, 5, 4, 0, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1},
-	{11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5, -1, -1, -1, -1},
-	{9, 5, 4, 10, 1, 2, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1},
-	{6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5, -1, -1, -1, -1},
-	{7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2, -1, -1, -1, -1},
-	{3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6, -1},
-	{7, 2, 3, 7, 6, 2, 5, 4, 9, -1, -1, -1, -1, -1, -1, -1},
-	{9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7, -1, -1, -1, -1},
-	{3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0, -1, -1, -1, -1},
-	{6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8, -1},
-	{9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7, -1, -1, -1, -1},
-	{1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4, -1},
-	{4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10, -1},
-	{7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10, -1, -1, -1, -1},
-	{6, 9, 5, 6, 11, 9, 11, 8, 9, -1, -1, -1, -1, -1, -1, -1},
-	{3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5, -1, -1, -1, -1},
-	{0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11, -1, -1, -1, -1},
-	{6, 11, 3, 6, 3, 5, 5, 3, 1, -1, -1, -1, -1, -1, -1, -1},
-	{1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6, -1, -1, -1, -1},
-	{0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10, -1},
-	{11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5, -1},
-	{6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3, -1, -1, -1, -1},
-	{5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2, -1, -1, -1, -1},
-	{9, 5, 6, 9, 6, 0, 0, 6, 2, -1, -1, -1, -1, -1, -1, -1},
-	{1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8, -1},
-	{1, 5, 6, 2, 1, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6, -1},
-	{10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0, -1, -1, -1, -1},
-	{0, 3, 8, 5, 6, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{10, 5, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{11, 5, 10, 7, 5, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{11, 5, 10, 11, 7, 5, 8, 3, 0, -1, -1, -1, -1, -1, -1, -1},
-	{5, 11, 7, 5, 10, 11, 1, 9, 0, -1, -1, -1, -1, -1, -1, -1},
-	{10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1, -1, -1, -1, -1},
-	{11, 1, 2, 11, 7, 1, 7, 5, 1, -1, -1, -1, -1, -1, -1, -1},
-	{0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11, -1, -1, -1, -1},
-	{9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7, -1, -1, -1, -1},
-	{7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2, -1},
-	{2, 5, 10, 2, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1},
-	{8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5, -1, -1, -1, -1},
-	{9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2, -1, -1, -1, -1},
-	{9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2, -1},
-	{1, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{0, 8, 7, 0, 7, 1, 1, 7, 5, -1, -1, -1, -1, -1, -1, -1},
-	{9, 0, 3, 9, 3, 5, 5, 3, 7, -1, -1, -1, -1, -1, -1, -1},
-	{9, 8, 7, 5, 9, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{5, 8, 4, 5, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1},
-	{5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0, -1, -1, -1, -1},
-	{0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5, -1, -1, -1, -1},
-	{10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4, -1},
-	{2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8, -1, -1, -1, -1},
-	{0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11, -1},
-	{0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5, -1},
-	{9, 4, 5, 2, 11, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4, -1, -1, -1, -1},
-	{5, 10, 2, 5, 2, 4, 4, 2, 0, -1, -1, -1, -1, -1, -1, -1},
-	{3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9, -1},
-	{5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2, -1, -1, -1, -1},
-	{8, 4, 5, 8, 5, 3, 3, 5, 1, -1, -1, -1, -1, -1, -1, -1},
-	{0, 4, 5, 1, 0, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5, -1, -1, -1, -1},
-	{9, 4, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{4, 11, 7, 4, 9, 11, 9, 10, 11, -1, -1, -1, -1, -1, -1, -1},
-	{0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11, -1, -1, -1, -1},
-	{1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11, -1, -1, -1, -1},
-	{3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4, -1},
-	{4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2, -1, -1, -1, -1},
-	{9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3, -1},
-	{11, 7, 4, 11, 4, 2, 2, 4, 0, -1, -1, -1, -1, -1, -1, -1},
-	{11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4, -1, -1, -1, -1},
-	{2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9, -1, -1, -1, -1},
-	{9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7, -1},
-	{3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10, -1},
-	{1, 10, 2, 8, 7, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{4, 9, 1, 4, 1, 7, 7, 1, 3, -1, -1, -1, -1, -1, -1, -1},
-	{4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1, -1, -1, -1, -1},
-	{4, 0, 3, 7, 4, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{4, 8, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{9, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{3, 0, 9, 3, 9, 11, 11, 9, 10, -1, -1, -1, -1, -1, -1, -1},
-	{0, 1, 10, 0, 10, 8, 8, 10, 11, -1, -1, -1, -1, -1, -1, -1},
-	{3, 1, 10, 11, 3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{1, 2, 11, 1, 11, 9, 9, 11, 8, -1, -1, -1, -1, -1, -1, -1},
-	{3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9, -1, -1, -1, -1},
-	{0, 2, 11, 8, 0, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{3, 2, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{2, 3, 8, 2, 8, 10, 10, 8, 9, -1, -1, -1, -1, -1, -1, -1},
-	{9, 10, 2, 0, 9, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8, -1, -1, -1, -1},
-	{1, 10, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{1, 3, 8, 9, 1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{0, 9, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
-	{0, 3, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  8,  3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  1,  9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  8,  3,  9,  8,  1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  8,  3,  1,  2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 9,  2, 10,  0,  2,  9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 2,  8,  3,  2, 10,  8, 10,  9,  8, -1, -1, -1, -1, -1, -1, -1},
+	{ 3, 11,  2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 0, 11,  2,  8, 11,  0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  9,  0,  2,  3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 1, 11,  2,  1,  9, 11,  9,  8, 11, -1, -1, -1, -1, -1, -1, -1},
+	{ 3, 10,  1, 11, 10,  3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 0, 10,  1,  0,  8, 10,  8, 11, 10, -1, -1, -1, -1, -1, -1, -1},
+	{ 3,  9,  0,  3, 11,  9, 11, 10,  9, -1, -1, -1, -1, -1, -1, -1},
+	{ 9,  8, 10, 10,  8, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 4,  7,  8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 4,  3,  0,  7,  3,  4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  1,  9,  8,  4,  7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 4,  1,  9,  4,  7,  1,  7,  3,  1, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  2, 10,  8,  4,  7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 3,  4,  7,  3,  0,  4,  1,  2, 10, -1, -1, -1, -1, -1, -1, -1},
+	{ 9,  2, 10,  9,  0,  2,  8,  4,  7, -1, -1, -1, -1, -1, -1, -1},
+	{ 2, 10,  9,  2,  9,  7,  2,  7,  3,  7,  9,  4, -1, -1, -1, -1},
+	{ 8,  4,  7,  3, 11,  2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{11,  4,  7, 11,  2,  4,  2,  0,  4, -1, -1, -1, -1, -1, -1, -1},
+	{ 9,  0,  1,  8,  4,  7,  2,  3, 11, -1, -1, -1, -1, -1, -1, -1},
+	{ 4,  7, 11,  9,  4, 11,  9, 11,  2,  9,  2,  1, -1, -1, -1, -1},
+	{ 3, 10,  1,  3, 11, 10,  7,  8,  4, -1, -1, -1, -1, -1, -1, -1},
+	{ 1, 11, 10,  1,  4, 11,  1,  0,  4,  7, 11,  4, -1, -1, -1, -1},
+	{ 4,  7,  8,  9,  0, 11,  9, 11, 10, 11,  0,  3, -1, -1, -1, -1},
+	{ 4,  7, 11,  4, 11,  9,  9, 11, 10, -1, -1, -1, -1, -1, -1, -1},
+	{ 9,  5,  4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 9,  5,  4,  0,  8,  3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  5,  4,  1,  5,  0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 8,  5,  4,  8,  3,  5,  3,  1,  5, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  2, 10,  9,  5,  4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 3,  0,  8,  1,  2, 10,  4,  9,  5, -1, -1, -1, -1, -1, -1, -1},
+	{ 5,  2, 10,  5,  4,  2,  4,  0,  2, -1, -1, -1, -1, -1, -1, -1},
+	{ 2, 10,  5,  3,  2,  5,  3,  5,  4,  3,  4,  8, -1, -1, -1, -1},
+	{ 9,  5,  4,  2,  3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 0, 11,  2,  0,  8, 11,  4,  9,  5, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  5,  4,  0,  1,  5,  2,  3, 11, -1, -1, -1, -1, -1, -1, -1},
+	{ 2,  1,  5,  2,  5,  8,  2,  8, 11,  4,  8,  5, -1, -1, -1, -1},
+	{10,  3, 11, 10,  1,  3,  9,  5,  4, -1, -1, -1, -1, -1, -1, -1},
+	{ 4,  9,  5,  0,  8,  1,  8, 10,  1,  8, 11, 10, -1, -1, -1, -1},
+	{ 5,  4,  0,  5,  0, 11,  5, 11, 10, 11,  0,  3, -1, -1, -1, -1},
+	{ 5,  4,  8,  5,  8, 10, 10,  8, 11, -1, -1, -1, -1, -1, -1, -1},
+	{ 9,  7,  8,  5,  7,  9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 9,  3,  0,  9,  5,  3,  5,  7,  3, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  7,  8,  0,  1,  7,  1,  5,  7, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  5,  3,  3,  5,  7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 9,  7,  8,  9,  5,  7, 10,  1,  2, -1, -1, -1, -1, -1, -1, -1},
+	{10,  1,  2,  9,  5,  0,  5,  3,  0,  5,  7,  3, -1, -1, -1, -1},
+	{ 8,  0,  2,  8,  2,  5,  8,  5,  7, 10,  5,  2, -1, -1, -1, -1},
+	{ 2, 10,  5,  2,  5,  3,  3,  5,  7, -1, -1, -1, -1, -1, -1, -1},
+	{ 7,  9,  5,  7,  8,  9,  3, 11,  2, -1, -1, -1, -1, -1, -1, -1},
+	{ 9,  5,  7,  9,  7,  2,  9,  2,  0,  2,  7, 11, -1, -1, -1, -1},
+	{ 2,  3, 11,  0,  1,  8,  1,  7,  8,  1,  5,  7, -1, -1, -1, -1},
+	{11,  2,  1, 11,  1,  7,  7,  1,  5, -1, -1, -1, -1, -1, -1, -1},
+	{ 9,  5,  8,  8,  5,  7, 10,  1,  3, 10,  3, 11, -1, -1, -1, -1},
+	{ 5,  7,  0,  5,  0,  9,  7, 11,  0,  1,  0, 10, 11, 10,  0, -1},
+	{11, 10,  0, 11,  0,  3, 10,  5,  0,  8,  0,  7,  5,  7,  0, -1},
+	{11, 10,  5,  7, 11,  5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{10,  6,  5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  8,  3,  5, 10,  6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 9,  0,  1,  5, 10,  6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  8,  3,  1,  9,  8,  5, 10,  6, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  6,  5,  2,  6,  1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  6,  5,  1,  2,  6,  3,  0,  8, -1, -1, -1, -1, -1, -1, -1},
+	{ 9,  6,  5,  9,  0,  6,  0,  2,  6, -1, -1, -1, -1, -1, -1, -1},
+	{ 5,  9,  8,  5,  8,  2,  5,  2,  6,  3,  2,  8, -1, -1, -1, -1},
+	{ 2,  3, 11, 10,  6,  5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{11,  0,  8, 11,  2,  0, 10,  6,  5, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  1,  9,  2,  3, 11,  5, 10,  6, -1, -1, -1, -1, -1, -1, -1},
+	{ 5, 10,  6,  1,  9,  2,  9, 11,  2,  9,  8, 11, -1, -1, -1, -1},
+	{ 6,  3, 11,  6,  5,  3,  5,  1,  3, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  8, 11,  0, 11,  5,  0,  5,  1,  5, 11,  6, -1, -1, -1, -1},
+	{ 3, 11,  6,  0,  3,  6,  0,  6,  5,  0,  5,  9, -1, -1, -1, -1},
+	{ 6,  5,  9,  6,  9, 11, 11,  9,  8, -1, -1, -1, -1, -1, -1, -1},
+	{ 5, 10,  6,  4,  7,  8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 4,  3,  0,  4,  7,  3,  6,  5, 10, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  9,  0,  5, 10,  6,  8,  4,  7, -1, -1, -1, -1, -1, -1, -1},
+	{10,  6,  5,  1,  9,  7,  1,  7,  3,  7,  9,  4, -1, -1, -1, -1},
+	{ 6,  1,  2,  6,  5,  1,  4,  7,  8, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  2,  5,  5,  2,  6,  3,  0,  4,  3,  4,  7, -1, -1, -1, -1},
+	{ 8,  4,  7,  9,  0,  5,  0,  6,  5,  0,  2,  6, -1, -1, -1, -1},
+	{ 7,  3,  9,  7,  9,  4,  3,  2,  9,  5,  9,  6,  2,  6,  9, -1},
+	{ 3, 11,  2,  7,  8,  4, 10,  6,  5, -1, -1, -1, -1, -1, -1, -1},
+	{ 5, 10,  6,  4,  7,  2,  4,  2,  0,  2,  7, 11, -1, -1, -1, -1},
+	{ 0,  1,  9,  4,  7,  8,  2,  3, 11,  5, 10,  6, -1, -1, -1, -1},
+	{ 9,  2,  1,  9, 11,  2,  9,  4, 11,  7, 11,  4,  5, 10,  6, -1},
+	{ 8,  4,  7,  3, 11,  5,  3,  5,  1,  5, 11,  6, -1, -1, -1, -1},
+	{ 5,  1, 11,  5, 11,  6,  1,  0, 11,  7, 11,  4,  0,  4, 11, -1},
+	{ 0,  5,  9,  0,  6,  5,  0,  3,  6, 11,  6,  3,  8,  4,  7, -1},
+	{ 6,  5,  9,  6,  9, 11,  4,  7,  9,  7, 11,  9, -1, -1, -1, -1},
+	{10,  4,  9,  6,  4, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 4, 10,  6,  4,  9, 10,  0,  8,  3, -1, -1, -1, -1, -1, -1, -1},
+	{10,  0,  1, 10,  6,  0,  6,  4,  0, -1, -1, -1, -1, -1, -1, -1},
+	{ 8,  3,  1,  8,  1,  6,  8,  6,  4,  6,  1, 10, -1, -1, -1, -1},
+	{ 1,  4,  9,  1,  2,  4,  2,  6,  4, -1, -1, -1, -1, -1, -1, -1},
+	{ 3,  0,  8,  1,  2,  9,  2,  4,  9,  2,  6,  4, -1, -1, -1, -1},
+	{ 0,  2,  4,  4,  2,  6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 8,  3,  2,  8,  2,  4,  4,  2,  6, -1, -1, -1, -1, -1, -1, -1},
+	{10,  4,  9, 10,  6,  4, 11,  2,  3, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  8,  2,  2,  8, 11,  4,  9, 10,  4, 10,  6, -1, -1, -1, -1},
+	{ 3, 11,  2,  0,  1,  6,  0,  6,  4,  6,  1, 10, -1, -1, -1, -1},
+	{ 6,  4,  1,  6,  1, 10,  4,  8,  1,  2,  1, 11,  8, 11,  1, -1},
+	{ 9,  6,  4,  9,  3,  6,  9,  1,  3, 11,  6,  3, -1, -1, -1, -1},
+	{ 8, 11,  1,  8,  1,  0, 11,  6,  1,  9,  1,  4,  6,  4,  1, -1},
+	{ 3, 11,  6,  3,  6,  0,  0,  6,  4, -1, -1, -1, -1, -1, -1, -1},
+	{ 6,  4,  8, 11,  6,  8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 7, 10,  6,  7,  8, 10,  8,  9, 10, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  7,  3,  0, 10,  7,  0,  9, 10,  6,  7, 10, -1, -1, -1, -1},
+	{10,  6,  7,  1, 10,  7,  1,  7,  8,  1,  8,  0, -1, -1, -1, -1},
+	{10,  6,  7, 10,  7,  1,  1,  7,  3, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  2,  6,  1,  6,  8,  1,  8,  9,  8,  6,  7, -1, -1, -1, -1},
+	{ 2,  6,  9,  2,  9,  1,  6,  7,  9,  0,  9,  3,  7,  3,  9, -1},
+	{ 7,  8,  0,  7,  0,  6,  6,  0,  2, -1, -1, -1, -1, -1, -1, -1},
+	{ 7,  3,  2,  6,  7,  2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 2,  3, 11, 10,  6,  8, 10,  8,  9,  8,  6,  7, -1, -1, -1, -1},
+	{ 2,  0,  7,  2,  7, 11,  0,  9,  7,  6,  7, 10,  9, 10,  7, -1},
+	{ 1,  8,  0,  1,  7,  8,  1, 10,  7,  6,  7, 10,  2,  3, 11, -1},
+	{11,  2,  1, 11,  1,  7, 10,  6,  1,  6,  7,  1, -1, -1, -1, -1},
+	{ 8,  9,  6,  8,  6,  7,  9,  1,  6, 11,  6,  3,  1,  3,  6, -1},
+	{ 0,  9,  1, 11,  6,  7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 7,  8,  0,  7,  0,  6,  3, 11,  0, 11,  6,  0, -1, -1, -1, -1},
+	{ 7, 11,  6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 7,  6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 3,  0,  8, 11,  7,  6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  1,  9, 11,  7,  6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 8,  1,  9,  8,  3,  1, 11,  7,  6, -1, -1, -1, -1, -1, -1, -1},
+	{10,  1,  2,  6, 11,  7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  2, 10,  3,  0,  8,  6, 11,  7, -1, -1, -1, -1, -1, -1, -1},
+	{ 2,  9,  0,  2, 10,  9,  6, 11,  7, -1, -1, -1, -1, -1, -1, -1},
+	{ 6, 11,  7,  2, 10,  3, 10,  8,  3, 10,  9,  8, -1, -1, -1, -1},
+	{ 7,  2,  3,  6,  2,  7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 7,  0,  8,  7,  6,  0,  6,  2,  0, -1, -1, -1, -1, -1, -1, -1},
+	{ 2,  7,  6,  2,  3,  7,  0,  1,  9, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  6,  2,  1,  8,  6,  1,  9,  8,  8,  7,  6, -1, -1, -1, -1},
+	{10,  7,  6, 10,  1,  7,  1,  3,  7, -1, -1, -1, -1, -1, -1, -1},
+	{10,  7,  6,  1,  7, 10,  1,  8,  7,  1,  0,  8, -1, -1, -1, -1},
+	{ 0,  3,  7,  0,  7, 10,  0, 10,  9,  6, 10,  7, -1, -1, -1, -1},
+	{ 7,  6, 10,  7, 10,  8,  8, 10,  9, -1, -1, -1, -1, -1, -1, -1},
+	{ 6,  8,  4, 11,  8,  6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 3,  6, 11,  3,  0,  6,  0,  4,  6, -1, -1, -1, -1, -1, -1, -1},
+	{ 8,  6, 11,  8,  4,  6,  9,  0,  1, -1, -1, -1, -1, -1, -1, -1},
+	{ 9,  4,  6,  9,  6,  3,  9,  3,  1, 11,  3,  6, -1, -1, -1, -1},
+	{ 6,  8,  4,  6, 11,  8,  2, 10,  1, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  2, 10,  3,  0, 11,  0,  6, 11,  0,  4,  6, -1, -1, -1, -1},
+	{ 4, 11,  8,  4,  6, 11,  0,  2,  9,  2, 10,  9, -1, -1, -1, -1},
+	{10,  9,  3, 10,  3,  2,  9,  4,  3, 11,  3,  6,  4,  6,  3, -1},
+	{ 8,  2,  3,  8,  4,  2,  4,  6,  2, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  4,  2,  4,  6,  2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  9,  0,  2,  3,  4,  2,  4,  6,  4,  3,  8, -1, -1, -1, -1},
+	{ 1,  9,  4,  1,  4,  2,  2,  4,  6, -1, -1, -1, -1, -1, -1, -1},
+	{ 8,  1,  3,  8,  6,  1,  8,  4,  6,  6, 10,  1, -1, -1, -1, -1},
+	{10,  1,  0, 10,  0,  6,  6,  0,  4, -1, -1, -1, -1, -1, -1, -1},
+	{ 4,  6,  3,  4,  3,  8,  6, 10,  3,  0,  3,  9, 10,  9,  3, -1},
+	{10,  9,  4,  6, 10,  4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 4,  9,  5,  7,  6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  8,  3,  4,  9,  5, 11,  7,  6, -1, -1, -1, -1, -1, -1, -1},
+	{ 5,  0,  1,  5,  4,  0,  7,  6, 11, -1, -1, -1, -1, -1, -1, -1},
+	{11,  7,  6,  8,  3,  4,  3,  5,  4,  3,  1,  5, -1, -1, -1, -1},
+	{ 9,  5,  4, 10,  1,  2,  7,  6, 11, -1, -1, -1, -1, -1, -1, -1},
+	{ 6, 11,  7,  1,  2, 10,  0,  8,  3,  4,  9,  5, -1, -1, -1, -1},
+	{ 7,  6, 11,  5,  4, 10,  4,  2, 10,  4,  0,  2, -1, -1, -1, -1},
+	{ 3,  4,  8,  3,  5,  4,  3,  2,  5, 10,  5,  2, 11,  7,  6, -1},
+	{ 7,  2,  3,  7,  6,  2,  5,  4,  9, -1, -1, -1, -1, -1, -1, -1},
+	{ 9,  5,  4,  0,  8,  6,  0,  6,  2,  6,  8,  7, -1, -1, -1, -1},
+	{ 3,  6,  2,  3,  7,  6,  1,  5,  0,  5,  4,  0, -1, -1, -1, -1},
+	{ 6,  2,  8,  6,  8,  7,  2,  1,  8,  4,  8,  5,  1,  5,  8, -1},
+	{ 9,  5,  4, 10,  1,  6,  1,  7,  6,  1,  3,  7, -1, -1, -1, -1},
+	{ 1,  6, 10,  1,  7,  6,  1,  0,  7,  8,  7,  0,  9,  5,  4, -1},
+	{ 4,  0, 10,  4, 10,  5,  0,  3, 10,  6, 10,  7,  3,  7, 10, -1},
+	{ 7,  6, 10,  7, 10,  8,  5,  4, 10,  4,  8, 10, -1, -1, -1, -1},
+	{ 6,  9,  5,  6, 11,  9, 11,  8,  9, -1, -1, -1, -1, -1, -1, -1},
+	{ 3,  6, 11,  0,  6,  3,  0,  5,  6,  0,  9,  5, -1, -1, -1, -1},
+	{ 0, 11,  8,  0,  5, 11,  0,  1,  5,  5,  6, 11, -1, -1, -1, -1},
+	{ 6, 11,  3,  6,  3,  5,  5,  3,  1, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  2, 10,  9,  5, 11,  9, 11,  8, 11,  5,  6, -1, -1, -1, -1},
+	{ 0, 11,  3,  0,  6, 11,  0,  9,  6,  5,  6,  9,  1,  2, 10, -1},
+	{11,  8,  5, 11,  5,  6,  8,  0,  5, 10,  5,  2,  0,  2,  5, -1},
+	{ 6, 11,  3,  6,  3,  5,  2, 10,  3, 10,  5,  3, -1, -1, -1, -1},
+	{ 5,  8,  9,  5,  2,  8,  5,  6,  2,  3,  8,  2, -1, -1, -1, -1},
+	{ 9,  5,  6,  9,  6,  0,  0,  6,  2, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  5,  8,  1,  8,  0,  5,  6,  8,  3,  8,  2,  6,  2,  8, -1},
+	{ 1,  5,  6,  2,  1,  6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  3,  6,  1,  6, 10,  3,  8,  6,  5,  6,  9,  8,  9,  6, -1},
+	{10,  1,  0, 10,  0,  6,  9,  5,  0,  5,  6,  0, -1, -1, -1, -1},
+	{ 0,  3,  8,  5,  6, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{10,  5,  6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{11,  5, 10,  7,  5, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{11,  5, 10, 11,  7,  5,  8,  3,  0, -1, -1, -1, -1, -1, -1, -1},
+	{ 5, 11,  7,  5, 10, 11,  1,  9,  0, -1, -1, -1, -1, -1, -1, -1},
+	{10,  7,  5, 10, 11,  7,  9,  8,  1,  8,  3,  1, -1, -1, -1, -1},
+	{11,  1,  2, 11,  7,  1,  7,  5,  1, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  8,  3,  1,  2,  7,  1,  7,  5,  7,  2, 11, -1, -1, -1, -1},
+	{ 9,  7,  5,  9,  2,  7,  9,  0,  2,  2, 11,  7, -1, -1, -1, -1},
+	{ 7,  5,  2,  7,  2, 11,  5,  9,  2,  3,  2,  8,  9,  8,  2, -1},
+	{ 2,  5, 10,  2,  3,  5,  3,  7,  5, -1, -1, -1, -1, -1, -1, -1},
+	{ 8,  2,  0,  8,  5,  2,  8,  7,  5, 10,  2,  5, -1, -1, -1, -1},
+	{ 9,  0,  1,  5, 10,  3,  5,  3,  7,  3, 10,  2, -1, -1, -1, -1},
+	{ 9,  8,  2,  9,  2,  1,  8,  7,  2, 10,  2,  5,  7,  5,  2, -1},
+	{ 1,  3,  5,  3,  7,  5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  8,  7,  0,  7,  1,  1,  7,  5, -1, -1, -1, -1, -1, -1, -1},
+	{ 9,  0,  3,  9,  3,  5,  5,  3,  7, -1, -1, -1, -1, -1, -1, -1},
+	{ 9,  8,  7,  5,  9,  7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 5,  8,  4,  5, 10,  8, 10, 11,  8, -1, -1, -1, -1, -1, -1, -1},
+	{ 5,  0,  4,  5, 11,  0,  5, 10, 11, 11,  3,  0, -1, -1, -1, -1},
+	{ 0,  1,  9,  8,  4, 10,  8, 10, 11, 10,  4,  5, -1, -1, -1, -1},
+	{10, 11,  4, 10,  4,  5, 11,  3,  4,  9,  4,  1,  3,  1,  4, -1},
+	{ 2,  5,  1,  2,  8,  5,  2, 11,  8,  4,  5,  8, -1, -1, -1, -1},
+	{ 0,  4, 11,  0, 11,  3,  4,  5, 11,  2, 11,  1,  5,  1, 11, -1},
+	{ 0,  2,  5,  0,  5,  9,  2, 11,  5,  4,  5,  8, 11,  8,  5, -1},
+	{ 9,  4,  5,  2, 11,  3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 2,  5, 10,  3,  5,  2,  3,  4,  5,  3,  8,  4, -1, -1, -1, -1},
+	{ 5, 10,  2,  5,  2,  4,  4,  2,  0, -1, -1, -1, -1, -1, -1, -1},
+	{ 3, 10,  2,  3,  5, 10,  3,  8,  5,  4,  5,  8,  0,  1,  9, -1},
+	{ 5, 10,  2,  5,  2,  4,  1,  9,  2,  9,  4,  2, -1, -1, -1, -1},
+	{ 8,  4,  5,  8,  5,  3,  3,  5,  1, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  4,  5,  1,  0,  5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 8,  4,  5,  8,  5,  3,  9,  0,  5,  0,  3,  5, -1, -1, -1, -1},
+	{ 9,  4,  5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 4, 11,  7,  4,  9, 11,  9, 10, 11, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  8,  3,  4,  9,  7,  9, 11,  7,  9, 10, 11, -1, -1, -1, -1},
+	{ 1, 10, 11,  1, 11,  4,  1,  4,  0,  7,  4, 11, -1, -1, -1, -1},
+	{ 3,  1,  4,  3,  4,  8,  1, 10,  4,  7,  4, 11, 10, 11,  4, -1},
+	{ 4, 11,  7,  9, 11,  4,  9,  2, 11,  9,  1,  2, -1, -1, -1, -1},
+	{ 9,  7,  4,  9, 11,  7,  9,  1, 11,  2, 11,  1,  0,  8,  3, -1},
+	{11,  7,  4, 11,  4,  2,  2,  4,  0, -1, -1, -1, -1, -1, -1, -1},
+	{11,  7,  4, 11,  4,  2,  8,  3,  4,  3,  2,  4, -1, -1, -1, -1},
+	{ 2,  9, 10,  2,  7,  9,  2,  3,  7,  7,  4,  9, -1, -1, -1, -1},
+	{ 9, 10,  7,  9,  7,  4, 10,  2,  7,  8,  7,  0,  2,  0,  7, -1},
+	{ 3,  7, 10,  3, 10,  2,  7,  4, 10,  1, 10,  0,  4,  0, 10, -1},
+	{ 1, 10,  2,  8,  7,  4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 4,  9,  1,  4,  1,  7,  7,  1,  3, -1, -1, -1, -1, -1, -1, -1},
+	{ 4,  9,  1,  4,  1,  7,  0,  8,  1,  8,  7,  1, -1, -1, -1, -1},
+	{ 4,  0,  3,  7,  4,  3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 4,  8,  7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 9, 10,  8, 10, 11,  8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 3,  0,  9,  3,  9, 11, 11,  9, 10, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  1, 10,  0, 10,  8,  8, 10, 11, -1, -1, -1, -1, -1, -1, -1},
+	{ 3,  1, 10, 11,  3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  2, 11,  1, 11,  9,  9, 11,  8, -1, -1, -1, -1, -1, -1, -1},
+	{ 3,  0,  9,  3,  9, 11,  1,  2,  9,  2, 11,  9, -1, -1, -1, -1},
+	{ 0,  2, 11,  8,  0, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 3,  2, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 2,  3,  8,  2,  8, 10, 10,  8,  9, -1, -1, -1, -1, -1, -1, -1},
+	{ 9, 10,  2,  0,  9,  2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 2,  3,  8,  2,  8, 10,  0,  1,  8,  1, 10,  8, -1, -1, -1, -1},
+	{ 1, 10,  2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 1,  3,  8,  9,  1,  8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  9,  1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
+	{ 0,  3,  8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
 	{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}
 };
 

src/geom/marching-cubes.hpp

@@ -56,4 +56,3 @@ constexpr float unit_cube[8][3] =
 } // namespace geom
 
 #endif // ANTKEEPER_GEOM_MARCHING_CUBES_HPP
-

src/geom/mesh-accelerator.hpp

@@ -54,7 +54,7 @@ public:
 	 * Finds the first intersection between a ray and a triangle in the mesh.
 	 *
 	 * @param ray Ray to test for intersection.
-	 * @return Ray query result on intersection, and `std::nullopt` if no intersection occurreda.
+	 * @return Ray query result on intersection, and `std::nullopt` if no intersection occurred.
 	 */
 	std::optional<ray_query_result> query_nearest(const ray<float>& ray) const;
 	

src/math/math.hpp

@@ -48,5 +48,6 @@ namespace math {}
 #include "math/interpolation.hpp"
 #include "math/random.hpp"
 #include "math/map.hpp"
+#include "math/projection.hpp"
 
 #endif // ANTKEEPER_MATH_HPP

src/math/projection.hpp

@@ -0,0 +1,61 @@
+/*
+ * Copyright (C) 2021  Christopher J. Howard
+ *
+ * This file is part of Antkeeper source code.
+ *
+ * Antkeeper source code is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * Antkeeper source code is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with Antkeeper source code.  If not, see <http://www.gnu.org/licenses/>.
+ */
+
+#ifndef ANTKEEPER_MATH_PROJECTION_HPP
+#define ANTKEEPER_MATH_PROJECTION_HPP
+
+#include <cmath>
+
+namespace math {
+
+/**
+ * Calculates a horizontal FoV given a vertical FoV and aspect ratio.
+ *
+ * @param v Vertical FoV, in radians.
+ * @param r Ratio of width to height.
+ *
+ * @return Horizontal FoV, in radians.
+ *
+ * @see https://en.wikipedia.org/wiki/Field_of_view_in_video_games
+ */
+template <class T>
+T horizontal_fov(T v, T r)
+{
+	return T{2} * std::atan(std::tan(v * T{0.5}) * r);
+}
+
+/**
+ * Calculates a vertical FoV given a horizontal FoV and aspect ratio.
+ *
+ * @param h Horizontal FoV, in radians.
+ * @param r Ratio of width to height.
+ *
+ * @return Vertical FoV, in radians.
+ *
+ * @see https://en.wikipedia.org/wiki/Field_of_view_in_video_games
+ */
+template <class T>
+T vertical_fov(T h, T r)
+{
+	return T{2} * std::atan(std::tan(h * T{0.5}) / r);
+}
+
+} // namespace math
+
+#endif // ANTKEEPER_MATH_PROJECTION_HPP