diff --git a/example/cube.cpp b/example/cube.cpp
index 83e143e..70b998c 100644
--- a/example/cube.cpp
+++ b/example/cube.cpp
@@ -17,11 +17,10 @@
 #include "holly/texture_memory_alloc.hpp"
 #include "memorymap.hpp"
 
+#include "geometry/geometry.hpp"
 #include "geometry/cube.hpp"
 #include "math/vec4.hpp"
 
-using vec4 = vec<4, float>;
-
 constexpr float half_degree = 0.01745329f / 2;
 
 vec3 rotate(const vec3& vertex, float theta)
diff --git a/example/example.mk b/example/example.mk
index 1b2bd7a..3b89c59 100644
--- a/example/example.mk
+++ b/example/example.mk
@@ -163,6 +163,18 @@ HEART_OBJ = \
 example/heart.elf: LDSCRIPT = $(LIB)/alt.lds
 example/heart.elf: $(START_OBJ) $(HEART_OBJ)
 
+VIEWING_SYSTEM_OBJ = \
+	example/viewing_system.o \
+	vga.o \
+	holly/core.o \
+	holly/region_array.o \
+	holly/background.o \
+	holly/ta_fifo_polygon_converter.o \
+	$(LIBGCC)
+
+example/viewing_system.elf: LDSCRIPT = $(LIB)/alt.lds
+example/viewing_system.elf: $(START_OBJ) $(VIEWING_SYSTEM_OBJ)
+
 MACAW_CUBE_OBJ = \
 	example/macaw_cube.o \
 	vga.o \
diff --git a/example/viewing_system.cpp b/example/viewing_system.cpp
new file mode 100644
index 0000000..5464da7
--- /dev/null
+++ b/example/viewing_system.cpp
@@ -0,0 +1,202 @@
+#include <cstdint>
+
+#include "align.hpp"
+
+#include "vga.hpp"
+#include "holly/texture_memory_alloc.hpp"
+#include "holly/holly.hpp"
+#include "holly/core.hpp"
+#include "holly/core_bits.hpp"
+#include "holly/ta_fifo_polygon_converter.hpp"
+#include "holly/ta_parameter.hpp"
+#include "holly/ta_global_parameter.hpp"
+#include "holly/ta_vertex_parameter.hpp"
+#include "holly/ta_bits.hpp"
+#include "holly/region_array.hpp"
+#include "holly/background.hpp"
+#include "holly/isp_tsp.hpp"
+#include "memorymap.hpp"
+
+#include "geometry/geometry.hpp"
+#include "geometry/suzanne2.hpp"
+
+#include "viewing_system/view_space.hpp"
+#include "viewing_system/screen_space.hpp"
+
+uint32_t _ta_parameter_buf[((32 * 8192) + 32) / 4];
+
+struct viewer {
+  vec3 position;
+  vec3 orientation;
+};
+
+constexpr mat4x4 world_transform = { 1.f, 0.f, 0.f, 0.f,
+                                     0.f, 1.f, 0.f, 0.f,
+                                     0.f, 0.f, 1.f, 3.f,
+                                     0.f, 0.f, 0.f, 1.f };
+
+void ta_upload(ta_parameter_writer& parameter,
+               const position__color * vertices,
+               const face_vtn * faces,
+               const uint32_t num_faces,
+               const mat4x4 screen_transform
+               )
+{
+  const uint32_t parameter_control_word = para_control::para_type::polygon_or_modifier_volume
+                                        | para_control::list_type::opaque
+                                        | obj_control::col_type::floating_color
+					| obj_control::gouraud;
+
+  const uint32_t isp_tsp_instruction_word = isp_tsp_instruction_word::depth_compare_mode::greater
+                                          | isp_tsp_instruction_word::culling_mode::no_culling;
+
+  const uint32_t tsp_instruction_word = tsp_instruction_word::src_alpha_instr::one
+                                      | tsp_instruction_word::dst_alpha_instr::zero
+                                      | tsp_instruction_word::fog_control::no_fog;
+
+  for (uint32_t face_ix = 0; face_ix < num_faces; face_ix++) {
+    parameter.append<ta_global_parameter::polygon_type_0>() =
+      ta_global_parameter::polygon_type_0(parameter_control_word,
+					  isp_tsp_instruction_word,
+					  tsp_instruction_word,
+					  0, // texture_control_word
+					  0, // data_size_for_sort_dma
+					  0  // next_address_for_sort_dma
+					  );
+
+    auto& face = faces[face_ix];
+    constexpr uint32_t strip_length = 3;
+    mat4x4 transform = screen_transform * world_transform;
+    for (uint32_t i = 0; i < strip_length; i++) {
+      const uint32_t vertex_ix = face[i].vertex;
+      auto& position = vertices[vertex_ix].position;
+      auto& color = vertices[vertex_ix].color;
+      vec4 vertex = { position.x,
+                      position.y,
+                      position.z,
+                      1.0f       };
+
+      // in three-dimensional screen space
+      vec4 v = transform * vertex;
+
+      float x = v.x / v.w;
+      float y = v.y / v.w;
+      float z = v.w / v.z;
+
+      x = x * 240.f + 320.f;
+      y = y * 240.f + 240.f;
+
+      // perspective divide
+      bool end_of_strip = i == strip_length - 1;
+      parameter.append<ta_vertex_parameter::polygon_type_1>() =
+	ta_vertex_parameter::polygon_type_1(polygon_vertex_parameter_control_word(end_of_strip),
+					    x,
+					    y,
+					    z,
+					    1.0f, // alpha
+					    color.r, // red
+					    color.g, // green
+					    color.b  // blue
+					    );
+    }
+  }
+}
+
+void init_texture_memory(const struct opb_size& opb_size)
+{
+  auto mem = reinterpret_cast<volatile texture_memory_alloc *>(texture_memory32);
+
+  background_parameter(mem->background, 0xff220000);
+  holly.VO_BORDER_COL = 0x00220000;
+
+  region_array2(mem->region_array,
+	        (offsetof (struct texture_memory_alloc, object_list)),
+		640 / 32, // width
+		480 / 32, // height
+		opb_size
+		);
+}
+
+void main()
+{
+  vga();
+
+  // The address of `ta_parameter_buf` must be a multiple of 32 bytes.
+  // This is mandatory for ch2-dma to the ta fifo polygon converter.
+  uint32_t * ta_parameter_buf = align_32byte(_ta_parameter_buf);
+
+  constexpr uint32_t ta_alloc = ta_alloc_ctrl::pt_opb::no_list
+			      | ta_alloc_ctrl::tm_opb::no_list
+			      | ta_alloc_ctrl::t_opb::no_list
+			      | ta_alloc_ctrl::om_opb::no_list
+                              | ta_alloc_ctrl::o_opb::_16x4byte;
+
+  constexpr struct opb_size opb_size = { .opaque = 16 * 4
+				       , .opaque_modifier = 0
+				       , .translucent = 0
+				       , .translucent_modifier = 0
+				       , .punch_through = 0
+				       };
+
+  holly.SOFTRESET = softreset::pipeline_soft_reset
+		  | softreset::ta_soft_reset;
+  holly.SOFTRESET = 0;
+
+  core_init();
+  init_texture_memory(opb_size);
+
+  viewer viewer {
+    .position    = {0.f, -3.f, 0.f},
+    .orientation = {0.f, -1.f, 0.f}, // approximate "up" orientation
+  };
+
+  vec3 plane_normal = view_space::viewing_direction(pi / 2.f, // azimuth
+                                                    pi / 4.f  // colatitude
+                                                    );
+  vec3 up_vector = view_space::project_vector_to_plane(plane_normal,
+                                                       viewer.orientation
+                                                       );
+
+  const mat4x4 view_space_transform = view_space::transformation_matrix(viewer.position,
+                                                                        plane_normal,
+                                                                        up_vector);
+
+  const mat4x4 perspective_transform = screen_space::transformation_matrix(1.f,   // the z-coordinate of the view window
+                                                                           100.f, // the z-coordinate of the far clip plane
+                                                                           1.f    // the dimension of the square view window
+                                                                           );
+
+  const mat4x4 screen_transform = perspective_transform * view_space_transform;
+
+
+  uint32_t frame_ix = 0;
+  constexpr uint32_t num_frames = 1;
+
+  while (true) {
+    ta_polygon_converter_init(opb_size.total(),
+			      ta_alloc,
+			      640 / 32,
+			      480 / 32);
+    auto parameter = ta_parameter_writer(ta_parameter_buf);
+
+    ta_upload(parameter,
+              suzanne::vertices,
+              suzanne::faces,
+              suzanne::num_faces,
+              screen_transform
+              );
+
+    // end of opaque list
+    parameter.append<ta_global_parameter::end_of_list>() = ta_global_parameter::end_of_list(para_control::para_type::end_of_list);
+
+    ta_polygon_converter_transfer(ta_parameter_buf, parameter.offset);
+    ta_wait_opaque_list();
+
+    core_start_render(frame_ix, num_frames);
+
+    v_sync_in();
+    core_wait_end_of_render_video(frame_ix, num_frames);
+
+    frame_ix += 1;
+  }
+}
diff --git a/geometry/geometry.hpp b/geometry/geometry.hpp
index 25f89da..c511b09 100644
--- a/geometry/geometry.hpp
+++ b/geometry/geometry.hpp
@@ -5,11 +5,14 @@
 #include "math/vec2.hpp"
 #include "math/vec3.hpp"
 #include "math/vec4.hpp"
+#include "math/mat4x4.hpp"
 
 using vec2 = vec<2, float>;
 using vec3 = vec<3, float>;
 using vec4 = vec<4, float>;
 
+using mat4x4 = mat<4, 4, float>;
+
 struct vertex__texture__normal {
   uint16_t vertex;
   uint16_t texture;
diff --git a/geometry/suzanne2.hpp b/geometry/suzanne2.hpp
new file mode 100644
index 0000000..b627c43
--- /dev/null
+++ b/geometry/suzanne2.hpp
@@ -0,0 +1,2992 @@
+#pragma once
+
+#include "geometry.hpp"
+
+namespace suzanne {
+  constexpr position__color vertices[] = {
+    { { 0.437500f, -0.164062f, -0.765625f}, { 1.000000f,  0.709800f,  0.015700f} },
+    { {-0.437500f, -0.164062f, -0.765625f}, { 0.019600f,  1.000000f,  0.831300f} },
+    { { 0.500000f, -0.093750f, -0.687500f}, { 0.929400f,  0.725500f,  0.490200f} },
+    { {-0.500000f, -0.093750f, -0.687500f}, { 0.133300f,  0.996000f,  0.827400f} },
+    { { 0.546875f, -0.054688f, -0.578125f}, { 0.619700f,  0.721600f,  1.000000f} },
+    { {-0.546875f, -0.054688f, -0.578125f}, { 0.078400f,  0.501900f,  0.862700f} },
+    { { 0.351562f,  0.023438f, -0.617188f}, { 0.137300f,  0.164700f,  1.000000f} },
+    { {-0.351562f,  0.023438f, -0.617188f}, { 0.239200f,  0.545100f,  0.882300f} },
+    { { 0.351562f, -0.031250f, -0.718750f}, { 0.537300f,  0.627600f,  1.000000f} },
+    { {-0.351562f, -0.031250f, -0.718750f}, { 0.164700f,  0.631500f,  0.941100f} },
+    { { 0.351562f, -0.132812f, -0.781250f}, { 0.996000f,  0.709800f,  0.113700f} },
+    { {-0.351562f, -0.132812f, -0.781250f}, { 0.019600f,  1.000000f,  0.831300f} },
+    { { 0.273438f, -0.164062f, -0.796875f}, { 0.996000f,  0.709800f,  0.098000f} },
+    { {-0.273438f, -0.164062f, -0.796875f}, { 0.019600f,  1.000000f,  0.831300f} },
+    { { 0.203125f, -0.093750f, -0.742188f}, { 0.658900f,  0.768600f,  1.000000f} },
+    { {-0.203125f, -0.093750f, -0.742188f}, { 0.262700f,  0.968600f,  0.858800f} },
+    { { 0.156250f, -0.054688f, -0.648438f}, { 0.639300f,  0.749000f,  1.000000f} },
+    { {-0.156250f, -0.054688f, -0.648438f}, { 0.698000f,  0.776400f,  1.000000f} },
+    { { 0.078125f, -0.242188f, -0.656250f}, { 0.776400f,  0.796000f,  0.862700f} },
+    { {-0.078125f, -0.242188f, -0.656250f}, { 0.780400f,  0.796000f,  0.933300f} },
+    { { 0.140625f, -0.242188f, -0.742188f}, { 0.956800f,  0.756800f,  0.388200f} },
+    { {-0.140625f, -0.242188f, -0.742188f}, { 0.321600f,  0.933300f,  0.866600f} },
+    { { 0.242188f, -0.242188f, -0.796875f}, { 1.000000f,  0.713700f,  0.023500f} },
+    { {-0.242188f, -0.242188f, -0.796875f}, { 0.090200f,  1.000000f,  0.827400f} },
+    { { 0.273438f, -0.328125f, -0.796875f}, { 1.000000f,  0.725500f,  0.047100f} },
+    { {-0.273438f, -0.328125f, -0.796875f}, { 0.396100f,  1.000000f,  0.768600f} },
+    { { 0.203125f, -0.390625f, -0.742188f}, { 0.913700f,  0.933300f,  0.572500f} },
+    { {-0.203125f, -0.390625f, -0.742188f}, { 0.780400f,  1.000000f,  0.553000f} },
+    { { 0.156250f, -0.437500f, -0.648438f}, { 1.000000f,  1.000000f,  0.203900f} },
+    { {-0.156250f, -0.437500f, -0.648438f}, { 1.000000f,  1.000000f,  0.231400f} },
+    { { 0.351562f, -0.515625f, -0.617188f}, { 1.000000f,  1.000000f,  0.200000f} },
+    { {-0.351562f, -0.515625f, -0.617188f}, { 1.000000f,  1.000000f,  0.200000f} },
+    { { 0.351562f, -0.453125f, -0.718750f}, { 0.898000f,  0.921500f,  0.568600f} },
+    { {-0.351562f, -0.453125f, -0.718750f}, { 0.996000f,  1.000000f,  0.231400f} },
+    { { 0.351562f, -0.359375f, -0.781250f}, { 0.996000f,  0.733300f,  0.113700f} },
+    { {-0.351562f, -0.359375f, -0.781250f}, { 0.651000f,  1.000000f,  0.651000f} },
+    { { 0.437500f, -0.328125f, -0.765625f}, { 0.964700f,  0.721600f,  0.356800f} },
+    { {-0.437500f, -0.328125f, -0.765625f}, { 0.623600f,  1.000000f,  0.658900f} },
+    { { 0.500000f, -0.390625f, -0.687500f}, { 0.811700f,  0.866600f,  0.772500f} },
+    { {-0.500000f, -0.390625f, -0.687500f}, { 0.992100f,  0.996000f,  0.231400f} },
+    { { 0.546875f, -0.437500f, -0.578125f}, { 1.000000f,  1.000000f,  0.251000f} },
+    { {-0.546875f, -0.437500f, -0.578125f}, { 1.000000f,  1.000000f,  0.200000f} },
+    { { 0.625000f, -0.242188f, -0.562500f}, { 0.760800f,  0.823500f,  0.964700f} },
+    { {-0.625000f, -0.242188f, -0.562500f}, { 0.894100f,  0.894100f,  0.549000f} },
+    { { 0.562500f, -0.242188f, -0.671875f}, { 0.776400f,  0.752900f,  0.835300f} },
+    { {-0.562500f, -0.242188f, -0.671875f}, { 0.600000f,  1.000000f,  0.674500f} },
+    { { 0.468750f, -0.242188f, -0.757812f}, { 0.996000f,  0.709800f,  0.058800f} },
+    { {-0.468750f, -0.242188f, -0.757812f}, { 0.215700f,  1.000000f,  0.815700f} },
+    { { 0.476562f, -0.242188f, -0.773438f}, { 0.996000f,  0.709800f,  0.054900f} },
+    { {-0.476562f, -0.242188f, -0.773438f}, { 0.153000f,  1.000000f,  0.823500f} },
+    { { 0.445312f, -0.335938f, -0.781250f}, { 0.945100f,  0.725500f,  0.435300f} },
+    { {-0.445312f, -0.335938f, -0.781250f}, { 0.588200f,  1.000000f,  0.686300f} },
+    { { 0.351562f, -0.375000f, -0.804688f}, { 0.988200f,  0.725500f,  0.211800f} },
+    { {-0.351562f, -0.375000f, -0.804688f}, { 0.572500f,  1.000000f,  0.690200f} },
+    { { 0.265625f, -0.335938f, -0.820312f}, { 1.000000f,  0.721600f,  0.039200f} },
+    { {-0.265625f, -0.335938f, -0.820312f}, { 0.301900f,  1.000000f,  0.796000f} },
+    { { 0.226562f, -0.242188f, -0.820312f}, { 1.000000f,  0.713700f,  0.015700f} },
+    { {-0.226562f, -0.242188f, -0.820312f}, { 0.019600f,  1.000000f,  0.831300f} },
+    { { 0.265625f, -0.156250f, -0.820312f}, { 0.992100f,  0.713700f,  0.188200f} },
+    { {-0.265625f, -0.156250f, -0.820312f}, { 0.019600f,  1.000000f,  0.831300f} },
+    { { 0.351562f, -0.242188f, -0.828125f}, { 0.125500f,  0.090200f,  0.000000f} },
+    { {-0.351562f, -0.242188f, -0.828125f}, { 0.000000f,  0.109800f,  0.090200f} },
+    { { 0.351562f, -0.117188f, -0.804688f}, { 0.984300f,  0.713700f,  0.203900f} },
+    { {-0.351562f, -0.117188f, -0.804688f}, { 0.019600f,  1.000000f,  0.831300f} },
+    { { 0.445312f, -0.156250f, -0.781250f}, { 1.000000f,  0.709800f,  0.019600f} },
+    { {-0.445312f, -0.156250f, -0.781250f}, { 0.019600f,  1.000000f,  0.831300f} },
+    { { 0.000000f, -0.429688f, -0.742188f}, { 0.980400f,  0.980400f,  0.419600f} },
+    { { 0.000000f, -0.351562f, -0.820312f}, { 0.607900f,  0.662800f,  0.913700f} },
+    { { 0.000000f,  0.679688f, -0.734375f}, { 0.952900f,  0.607900f,  0.603900f} },
+    { { 0.000000f,  0.320312f, -0.781250f}, { 0.431400f,  0.117600f,  0.184300f} },
+    { { 0.000000f,  0.187500f, -0.796875f}, { 0.894100f,  0.251000f,  0.376500f} },
+    { { 0.000000f,  0.773438f, -0.718750f}, { 0.647100f,  0.835300f,  0.411800f} },
+    { { 0.000000f, -0.406250f, -0.601562f}, { 1.000000f,  1.000000f,  0.207800f} },
+    { { 0.000000f, -0.570312f, -0.570312f}, { 1.000000f,  1.000000f,  0.200000f} },
+    { { 0.000000f, -0.898438f,  0.546875f}, { 1.000000f,  0.898000f,  0.933300f} },
+    { { 0.000000f, -0.562500f,  0.851562f}, { 1.000000f,  0.317600f,  0.674500f} },
+    { { 0.000000f, -0.070312f,  0.828125f}, { 0.603900f,  0.866600f,  0.545100f} },
+    { { 0.000000f,  0.382812f,  0.351562f}, { 0.078400f,  1.000000f,  0.000000f} },
+    { { 0.203125f,  0.187500f, -0.562500f}, { 0.352900f,  0.988200f,  0.058800f} },
+    { {-0.203125f,  0.187500f, -0.562500f}, { 0.839200f,  0.545100f,  0.000000f} },
+    { { 0.312500f,  0.437500f, -0.570312f}, { 0.839200f,  0.580400f,  0.000000f} },
+    { {-0.312500f,  0.437500f, -0.570312f}, { 0.882300f,  0.486300f,  0.039200f} },
+    { { 0.351562f,  0.695312f, -0.570312f}, { 1.000000f,  0.003900f,  0.023500f} },
+    { {-0.351562f,  0.695312f, -0.570312f}, { 1.000000f,  0.039200f,  0.192200f} },
+    { { 0.367188f,  0.890625f, -0.531250f}, { 0.964700f,  0.262700f,  0.200000f} },
+    { {-0.367188f,  0.890625f, -0.531250f}, { 0.976400f,  0.211800f,  0.211800f} },
+    { { 0.328125f,  0.945312f, -0.523438f}, { 0.980400f,  0.196100f,  0.211800f} },
+    { {-0.328125f,  0.945312f, -0.523438f}, { 0.996000f,  0.102000f,  0.215700f} },
+    { { 0.179688f,  0.968750f, -0.554688f}, { 1.000000f,  0.019600f,  0.215700f} },
+    { {-0.179688f,  0.968750f, -0.554688f}, { 1.000000f,  0.011800f,  0.211800f} },
+    { { 0.000000f,  0.984375f, -0.578125f}, { 1.000000f,  0.000000f,  0.215700f} },
+    { { 0.437500f,  0.140625f, -0.531250f}, { 0.313700f,  1.000000f,  0.015700f} },
+    { {-0.437500f,  0.140625f, -0.531250f}, { 0.415700f,  1.000000f,  0.407800f} },
+    { { 0.632812f,  0.039062f, -0.539062f}, { 0.003900f,  0.047100f,  1.000000f} },
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+    {  0.677256f,  0.670436f },
+    {  0.745511f,  0.652100f },
+    {  0.049526f,  0.748824f },
+    {  0.083564f,  0.662038f },
+    {  0.671403f,  0.592656f },
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+    {  0.019409f,  0.639749f },
+    {  0.092820f,  0.589862f },
+    {  0.834705f,  0.206959f },
+    {  0.051216f,  0.522659f },
+    {  0.033664f,  0.564403f },
+    {  0.620420f,  0.565675f },
+    {  0.498072f,  0.552315f },
+    {  0.145041f,  0.562595f },
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+    {  0.271364f,  0.473316f },
+    {  0.488870f,  0.770464f },
+    {  0.834578f,  0.206879f },
+  };
+
+  constexpr vec3 normals[] = {
+    {  0.661700f,  0.202600f, -0.721900f },
+    { -0.661700f,  0.202600f, -0.721900f },
+    {  0.826800f,  0.305100f, -0.472500f },
+    { -0.826800f,  0.305100f, -0.472500f },
+    {  0.407600f,  0.790500f, -0.457000f },
+    { -0.407600f,  0.790500f, -0.457000f },
+    {  0.379100f,  0.516300f, -0.767900f },
+    { -0.379100f,  0.516300f, -0.767900f },
+    { -0.085900f,  0.522200f, -0.848500f },
+    {  0.085900f,  0.522200f, -0.848500f },
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+    { -0.104600f, -0.039200f, -0.993700f },
+    {  0.413400f, -0.041300f, -0.909600f },
+    { -0.246100f, -0.085200f, -0.965500f },
+    {  0.322800f,  0.046100f, -0.945300f },
+    { -0.322800f,  0.046100f, -0.945300f },
+    {  0.122000f, -0.045800f, -0.991500f },
+    { -0.210400f, -0.012400f, -0.977500f },
+    {  0.567900f, -0.191600f, -0.800500f },
+    { -0.567900f, -0.191600f, -0.800500f },
+    {  0.424400f,  0.032000f, -0.904900f },
+    { -0.378700f,  0.036400f, -0.924800f },
+    {  0.257000f, -0.072300f, -0.963700f },
+    { -0.253000f,  0.189700f, -0.948700f },
+    {  0.135100f,  0.022500f, -0.990600f },
+    { -0.135100f,  0.022500f, -0.990600f },
+    { -0.298100f, -0.745400f, -0.596300f },
+    {  0.487000f, -0.608800f, -0.626200f },
+    {  0.557100f,  0.148600f, -0.817100f },
+    { -0.557100f,  0.148600f, -0.817100f },
+    {  0.472300f,  0.198600f, -0.858800f },
+    { -0.438800f,  0.200800f, -0.875900f },
+    {  0.297500f,  0.406200f, -0.864000f },
+    { -0.578600f,  0.133400f, -0.804600f },
+    {  0.577100f, -0.216400f, -0.787500f },
+    { -0.577100f, -0.216400f, -0.787500f },
+    {  0.093100f,  0.993200f,  0.069200f },
+    { -0.093100f,  0.993200f,  0.069200f },
+    {  0.516100f,  0.852700f,  0.081200f },
+    { -0.516100f,  0.852700f,  0.081200f },
+    {  0.926400f,  0.246000f, -0.285100f },
+    { -0.930900f,  0.254100f, -0.262400f },
+    {  0.826700f, -0.562700f,  0.003500f },
+    { -0.846500f, -0.529100f,  0.059500f },
+    { -0.214600f, -0.924300f,  0.315700f },
+    {  0.251100f, -0.943900f,  0.214500f },
+    { -0.419600f, -0.885100f,  0.201200f },
+    {  0.484100f, -0.874300f,  0.036100f },
+    { -0.547000f,  0.014400f,  0.837000f },
+    {  0.525600f,  0.003000f,  0.850700f },
+    { -0.255600f,  0.074900f,  0.963900f },
+    {  0.255600f,  0.074900f,  0.963900f },
+    { -0.733000f, -0.678600f, -0.047200f },
+    {  0.807300f, -0.590100f, -0.004100f },
+    {  0.684400f,  0.171100f,  0.708800f },
+    { -0.684400f,  0.171100f,  0.708800f },
+    { -0.360400f,  0.828300f,  0.429000f },
+    {  0.360400f,  0.828300f,  0.429000f },
+  };
+
+  constexpr face_vtn faces[] = {
+    {{ 46,   0,   0}, {  2,   1,   0}, { 44,   2,   0}},
+    {{  3,   3,   1}, { 47,   4,   1}, { 45,   5,   1}},
+    {{ 44,   2,   2}, {  4,   6,   2}, { 42,   7,   2}},
+    {{  5,   8,   3}, { 45,   5,   3}, { 43,   9,   3}},
+    {{  2,   1,   4}, {  6,  10,   4}, {  4,   6,   4}},
+    {{  7,  11,   5}, {  3,   3,   5}, {  5,   8,   5}},
+    {{  0,  12,   6}, {  8,  13,   6}, {  2,   1,   6}},
+    {{  9,  14,   7}, {  1,  15,   7}, {  3,   3,   7}},
+    {{ 10,  16,   8}, { 14,  17,   8}, {  8,  13,   8}},
+    {{ 15,  18,   9}, { 11,  19,   9}, {  9,  14,   9}},
+    {{  8,  13,  10}, { 16,  20,  10}, {  6,  10,  10}},
+    {{ 17,  21,  11}, {  9,  14,  11}, {  7,  11,  11}},
+    {{ 20,  22,  12}, { 16,  20,  12}, { 14,  17,  12}},
+    {{ 21,  23,  13}, { 17,  21,  13}, { 19,  24,  13}},
+    {{ 12,  25,  14}, { 20,  22,  14}, { 14,  17,  14}},
+    {{ 21,  23,  15}, { 13,  26,  15}, { 15,  18,  15}},
+    {{ 22,  27,  16}, { 26,  28,  16}, { 20,  22,  16}},
+    {{ 27,  29,  17}, { 23,  30,  17}, { 21,  23,  17}},
+    {{ 26,  28,  18}, { 18,  31,  18}, { 20,  22,  18}},
+    {{ 27,  29,  19}, { 19,  24,  19}, { 29,  32,  19}},
+    {{ 32,  33,  20}, { 28,  34,  20}, { 26,  28,  20}},
+    {{ 33,  35,  21}, { 29,  32,  21}, { 31,  36,  21}},
+    {{ 34,  37,  22}, { 26,  28,  22}, { 24,  38,  22}},
+    {{ 35,  39,  23}, { 27,  29,  23}, { 33,  35,  23}},
+    {{ 36,  40,  24}, { 32,  33,  24}, { 34,  37,  24}},
+    {{ 37,  41,  25}, { 33,  35,  25}, { 39,  42,  25}},
+    {{ 38,  43,  26}, { 30,  44,  26}, { 32,  33,  26}},
+    {{ 39,  42,  27}, { 31,  36,  27}, { 41,  45,  27}},
+    {{ 44,   2,  28}, { 40,  46,  28}, { 38,  43,  28}},
+    {{ 45,   5,  29}, { 41,  45,  29}, { 43,   9,  29}},
+    {{ 46,   0,  30}, { 38,  43,  30}, { 36,  40,  30}},
+    {{ 47,   4,  31}, { 39,  42,  31}, { 45,   5,  31}},
+    {{ 36,  40,  32}, { 48,  47,  32}, { 46,   0,  32}},
+    {{ 37,  41,  33}, { 49,  48,  33}, { 51,  49,  33}},
+    {{ 34,  37,  34}, { 50,  50,  34}, { 36,  40,  34}},
+    {{ 35,  39,  35}, { 51,  49,  35}, { 53,  51,  35}},
+    {{ 24,  38,  36}, { 52,  52,  36}, { 34,  37,  36}},
+    {{ 25,  53,  37}, { 53,  51,  37}, { 55,  54,  37}},
+    {{ 22,  27,  38}, { 54,  55,  38}, { 24,  38,  38}},
+    {{ 23,  30,  39}, { 55,  54,  39}, { 57,  56,  39}},
+    {{ 22,  27,  40}, { 58,  57,  40}, { 56,  58,  40}},
+    {{ 59,  59,  41}, { 23,  30,  41}, { 57,  56,  41}},
+    {{ 12,  25,  42}, { 62,  60,  42}, { 58,  57,  42}},
+    {{ 63,  61,  43}, { 13,  26,  43}, { 59,  59,  43}},
+    {{ 10,  16,  44}, { 64,  62,  44}, { 62,  60,  44}},
+    {{ 65,  63,  45}, { 11,  19,  45}, { 63,  61,  45}},
+    {{  0,  12,  46}, { 48,  47,  46}, { 64,  62,  46}},
+    {{ 49,  48,  47}, {  1,  15,  47}, { 65,  63,  47}},
+    {{ 60,  64,  48}, { 64,  62,  48}, { 48,  47,  48}},
+    {{ 49,  48,  49}, { 65,  63,  49}, { 61,  65,  49}},
+    {{ 62,  60,  50}, { 64,  62,  50}, { 60,  64,  50}},
+    {{ 61,  65,  51}, { 65,  63,  51}, { 63,  61,  51}},
+    {{ 60,  64,  52}, { 58,  57,  52}, { 62,  60,  52}},
+    {{ 63,  61,  53}, { 59,  59,  53}, { 61,  65,  53}},
+    {{ 60,  64,  54}, { 56,  58,  54}, { 58,  57,  54}},
+    {{ 59,  59,  55}, { 57,  56,  55}, { 61,  65,  55}},
+    {{ 60,  64,  56}, { 54,  55,  56}, { 56,  58,  56}},
+    {{ 57,  56,  57}, { 55,  54,  57}, { 61,  65,  57}},
+    {{ 60,  64,  58}, { 52,  52,  58}, { 54,  55,  58}},
+    {{ 55,  54,  59}, { 53,  51,  59}, { 61,  65,  59}},
+    {{ 60,  64,  60}, { 50,  50,  60}, { 52,  52,  60}},
+    {{ 53,  51,  61}, { 51,  49,  61}, { 61,  65,  61}},
+    {{ 60,  64,  62}, { 48,  47,  62}, { 50,  50,  62}},
+    {{ 51,  49,  63}, { 49,  48,  63}, { 61,  65,  63}},
+    {{173,  66,  64}, { 90,  67,  64}, { 88,  68,  64}},
+    {{174,  69,  65}, { 90,  67,  65}, {175,  70,  65}},
+    {{171,  71,  66}, { 88,  68,  66}, { 86,  72,  66}},
+    {{172,  73,  67}, { 89,  74,  67}, {174,  69,  67}},
+    {{ 84,  75,  68}, {171,  71,  68}, { 86,  72,  68}},
+    {{172,  73,  69}, { 85,  76,  69}, { 87,  77,  69}},
+    {{ 82,  78,  70}, {169,  79,  70}, { 84,  75,  70}},
+    {{170,  80,  71}, { 83,  81,  71}, { 85,  76,  71}},
+    {{ 80,  82,  72}, {167,  83,  72}, { 82,  78,  72}},
+    {{168,  84,  73}, { 81,  85,  73}, { 83,  81,  73}},
+    {{ 78,  86,  74}, {145,  87,  74}, {163,  88,  74}},
+    {{146,  89,  75}, { 79,  90,  75}, {164,  91,  75}},
+    {{ 93,  92,  76}, {145,  87,  76}, { 91,  93,  76}},
+    {{ 94,  94,  77}, {146,  89,  77}, {148,  95,  77}},
+    {{ 93,  92,  78}, {149,  96,  78}, {147,  97,  78}},
+    {{150,  98,  79}, { 94,  94,  79}, {148,  95,  79}},
+    {{ 97,  99,  80}, {149,  96,  80}, { 95, 100,  80}},
+    {{ 98, 101,  81}, {150,  98,  81}, {152, 102,  81}},
+    {{ 99, 103,  82}, {151, 104,  82}, { 97,  99,  82}},
+    {{100, 105,  83}, {152, 102,  83}, {154, 106,  83}},
+    {{101, 107,  84}, {153, 108,  84}, { 99, 103,  84}},
+    {{102, 109,  85}, {154, 106,  85}, {156, 110,  85}},
+    {{101, 107,  86}, {157, 111,  86}, {155, 112,  86}},
+    {{158, 113,  87}, {102, 109,  87}, {156, 110,  87}},
+    {{105, 114,  88}, {157, 111,  88}, {103, 115,  88}},
+    {{106, 116,  89}, {158, 113,  89}, {160, 117,  89}},
+    {{107, 118,  90}, {159, 119,  90}, {105, 114,  90}},
+    {{108, 120,  91}, {160, 117,  91}, {162, 121,  91}},
+    {{ 66, 122,  92}, {161, 123,  92}, {107, 118,  92}},
+    {{ 66, 122,  93}, {162, 121,  93}, { 67, 124,  93}},
+    {{127, 125,  94}, {161, 123,  94}, {109, 126,  94}},
+    {{128, 127,  95}, {162, 121,  95}, {160, 117,  95}},
+    {{127, 125,  96}, {157, 111,  96}, {159, 119,  96}},
+    {{158, 113,  97}, {128, 127,  97}, {160, 117,  97}},
+    {{155, 112,  98}, {178, 128,  98}, {125, 129,  98}},
+    {{156, 110,  99}, {179, 130,  99}, {158, 113,  99}},
+    {{153, 108, 100}, {125, 129, 100}, {123, 131, 100}},
+    {{154, 106, 101}, {126, 132, 101}, {156, 110, 101}},
+    {{151, 104, 102}, {123, 131, 102}, {121, 133, 102}},
+    {{152, 102, 103}, {124, 134, 103}, {154, 106, 103}},
+    {{149,  96, 104}, {121, 133, 104}, {119, 135, 104}},
+    {{150,  98, 105}, {122, 136, 105}, {152, 102, 105}},
+    {{147,  97, 106}, {119, 135, 106}, {117, 137, 106}},
+    {{148,  95, 107}, {120, 138, 107}, {150,  98, 107}},
+    {{145,  87, 108}, {117, 137, 108}, {115, 139, 108}},
+    {{146,  89, 109}, {118, 140, 109}, {148,  95, 109}},
+    {{163,  88, 110}, {115, 139, 110}, {113, 141, 110}},
+    {{164,  91, 111}, {116, 142, 111}, {146,  89, 111}},
+    {{113, 141, 112}, {176, 143, 112}, {163,  88, 112}},
+    {{176, 143, 113}, {114, 144, 113}, {164,  91, 113}},
+    {{161, 123, 114}, {111, 145, 114}, {109, 126, 114}},
+    {{162, 121, 115}, {112, 146, 115}, { 67, 124, 115}},
+    {{111, 145, 116}, {177, 147, 116}, {182, 148, 116}},
+    {{177, 147, 117}, {112, 146, 117}, {183, 149, 117}},
+    {{180, 150, 118}, {177, 147, 118}, {176, 143, 118}},
+    {{181, 151, 119}, {177, 147, 119}, {183, 149, 119}},
+    {{134, 152, 120}, {175,  70, 120}, {173,  66, 120}},
+    {{175,  70, 121}, {135, 153, 121}, {174,  69, 121}},
+    {{132, 154, 122}, {173,  66, 122}, {171,  71, 122}},
+    {{174,  69, 123}, {133, 155, 123}, {172,  73, 123}},
+    {{132, 154, 124}, {169,  79, 124}, {130, 156, 124}},
+    {{133, 155, 125}, {170,  80, 125}, {172,  73, 125}},
+    {{165, 157, 126}, {184, 158, 126}, {167,  83, 126}},
+    {{185, 159, 127}, {166, 160, 127}, {168,  84, 127}},
+    {{130, 156, 128}, {167,  83, 128}, {184, 158, 128}},
+    {{168,  84, 129}, {131, 161, 129}, {185, 159, 129}},
+    {{189, 162, 130}, {186, 163, 130}, {143, 164, 130}},
+    {{189, 162, 131}, {187, 165, 131}, {188, 166, 131}},
+    {{186, 163, 132}, { 68, 167, 132}, {184, 158, 132}},
+    {{187, 165, 133}, { 68, 167, 133}, {188, 166, 133}},
+    {{130, 156, 134}, { 68, 167, 134}, {129, 168, 134}},
+    {{131, 161, 134}, { 68, 167, 134}, {185, 159, 134}},
+    {{141, 169, 135}, {190, 170, 135}, {143, 164, 135}},
+    {{191, 171, 136}, {142, 172, 136}, {144, 173, 136}},
+    {{139, 174, 137}, {192, 175, 137}, {141, 169, 137}},
+    {{193, 176, 138}, {140, 177, 138}, {142, 172, 138}},
+    {{196, 178, 139}, {139, 174, 139}, {138, 179, 139}},
+    {{197, 180, 140}, {140, 177, 140}, {195, 181, 140}},
+    {{ 70, 182, 141}, {138, 179, 141}, {137, 183, 141}},
+    {{ 70, 182, 142}, {138, 179, 142}, {197, 180, 142}},
+    {{143, 164, 143}, { 69, 184, 143}, {189, 162, 143}},
+    {{144, 173, 144}, { 69, 184, 144}, {191, 171, 144}},
+    {{190, 170, 145}, {207, 185, 145}, { 69, 184, 145}},
+    {{191, 171, 146}, {207, 185, 146}, {206, 186, 146}},
+    {{ 70, 182, 147}, {199, 187, 147}, {196, 178, 147}},
+    {{200, 188, 148}, { 70, 182, 148}, {197, 180, 148}},
+    {{196, 178, 149}, {201, 189, 149}, {194, 190, 149}},
+    {{202, 191, 150}, {197, 180, 150}, {195, 181, 150}},
+    {{201, 189, 151}, {192, 175, 151}, {194, 190, 151}},
+    {{202, 191, 152}, {193, 176, 152}, {204, 192, 152}},
+    {{192, 175, 153}, {205, 193, 153}, {190, 170, 153}},
+    {{206, 186, 154}, {193, 176, 154}, {191, 171, 154}},
+    {{203, 194, 155}, {199, 187, 155}, {198, 195, 155}},
+    {{204, 192, 156}, {200, 188, 156}, {202, 191, 156}},
+    {{198, 195, 157}, {205, 193, 157}, {203, 194, 157}},
+    {{206, 186, 158}, {198, 195, 158}, {204, 192, 158}},
+    {{138, 179, 159}, {163,  88, 159}, {176, 143, 159}},
+    {{164,  91, 160}, {138, 179, 160}, {176, 143, 160}},
+    {{139, 174, 161}, {210, 196, 161}, {163,  88, 161}},
+    {{211, 197, 162}, {140, 177, 162}, {164,  91, 162}},
+    {{143, 164, 163}, {210, 196, 163}, {141, 169, 163}},
+    {{144, 173, 164}, {211, 197, 164}, {213, 198, 164}},
+    {{186, 163, 165}, {212, 199, 165}, {143, 164, 165}},
+    {{187, 165, 166}, {213, 198, 166}, {166, 160, 166}},
+    {{208, 200, 167}, {165, 157, 167}, { 80,  82, 167}},
+    {{209, 201, 168}, {166, 160, 168}, {213, 198, 168}},
+    {{214, 202, 169}, {212, 199, 169}, {208, 200, 169}},
+    {{215, 203, 170}, {213, 198, 170}, {211, 197, 170}},
+    {{ 78,  86, 171}, {210, 196, 171}, {214, 202, 171}},
+    {{211, 197, 172}, { 79,  90, 172}, {215, 203, 172}},
+    {{129, 168, 173}, {221, 204, 173}, {130, 156, 173}},
+    {{129, 168, 174}, {222, 205, 174}, { 71, 206, 174}},
+    {{132, 154, 175}, {221, 204, 175}, {219, 207, 175}},
+    {{222, 205, 176}, {133, 155, 176}, {220, 208, 176}},
+    {{134, 152, 177}, {219, 207, 177}, {217, 209, 177}},
+    {{220, 208, 178}, {135, 153, 178}, {218, 210, 178}},
+    {{136, 211, 134}, {217, 209, 134}, {216, 212, 134}},
+    {{218, 210, 134}, {136, 211, 134}, {216, 212, 134}},
+    {{217, 209, 179}, {230, 213, 179}, {216, 212, 179}},
+    {{218, 210, 180}, {230, 213, 180}, {229, 214, 180}},
+    {{217, 209, 181}, {226, 215, 181}, {228, 216, 181}},
+    {{227, 217, 182}, {218, 210, 182}, {229, 214, 182}},
+    {{219, 207, 141}, {224, 218, 141}, {226, 215, 141}},
+    {{225, 219, 183}, {220, 208, 183}, {227, 217, 183}},
+    {{ 71, 206, 184}, {224, 218, 184}, {221, 204, 184}},
+    {{ 71, 206, 185}, {225, 219, 185}, {223, 220, 185}},
+    {{223, 220, 186}, {228, 216, 186}, {224, 218, 186}},
+    {{229, 214, 187}, {223, 220, 187}, {225, 219, 187}},
+    {{224, 218, 188}, {228, 216, 188}, {226, 215, 188}},
+    {{227, 217, 189}, {229, 214, 189}, {225, 219, 189}},
+    {{182, 148, 190}, {233, 221, 190}, {231, 222, 190}},
+    {{234, 223, 191}, {183, 149, 191}, {232, 224, 191}},
+    {{111, 145, 192}, {231, 222, 192}, {253, 225, 192}},
+    {{232, 224, 193}, {112, 146, 193}, {254, 226, 193}},
+    {{111, 145, 194}, {255, 227, 194}, {109, 126, 194}},
+    {{112, 146, 195}, {256, 228, 195}, {254, 226, 195}},
+    {{113, 141, 196}, {233, 221, 196}, {180, 150, 196}},
+    {{114, 144, 197}, {234, 223, 197}, {252, 229, 197}},
+    {{113, 141, 198}, {249, 230, 198}, {251, 231, 198}},
+    {{250, 232, 199}, {114, 144, 199}, {252, 229, 199}},
+    {{115, 139, 200}, {247, 233, 200}, {249, 230, 200}},
+    {{248, 234, 201}, {116, 142, 201}, {250, 232, 201}},
+    {{117, 137, 202}, {245, 235, 202}, {247, 233, 202}},
+    {{246, 236, 203}, {118, 140, 203}, {248, 234, 203}},
+    {{119, 135, 204}, {243, 237, 204}, {245, 235, 204}},
+    {{244, 238, 205}, {120, 138, 205}, {246, 236, 205}},
+    {{123, 131, 206}, {243, 237, 206}, {121, 133, 206}},
+    {{124, 134, 207}, {244, 238, 207}, {242, 239, 207}},
+    {{125, 129, 208}, {241, 240, 208}, {123, 131, 208}},
+    {{126, 132, 209}, {242, 239, 209}, {240, 241, 209}},
+    {{125, 129, 210}, {235, 242, 210}, {239, 243, 210}},
+    {{236, 244, 211}, {126, 132, 211}, {240, 241, 211}},
+    {{178, 128, 212}, {237, 245, 212}, {235, 242, 212}},
+    {{238, 246, 213}, {179, 130, 213}, {236, 244, 213}},
+    {{127, 125, 214}, {255, 227, 214}, {237, 245, 214}},
+    {{256, 228, 215}, {128, 127, 215}, {238, 246, 215}},
+    {{255, 227, 216}, {275, 247, 216}, {237, 245, 216}},
+    {{256, 228, 217}, {276, 248, 217}, {258, 249, 217}},
+    {{235, 242, 218}, {275, 247, 218}, {277, 250, 218}},
+    {{276, 248, 219}, {236, 244, 219}, {278, 251, 219}},
+    {{235, 242, 220}, {273, 252, 220}, {239, 243, 220}},
+    {{236, 244, 221}, {274, 253, 221}, {278, 251, 221}},
+    {{239, 243, 222}, {271, 254, 222}, {241, 240, 222}},
+    {{240, 241, 223}, {272, 255, 223}, {274, 253, 223}},
+    {{243, 237, 224}, {271, 254, 224}, {269, 256, 224}},
+    {{272, 255, 225}, {244, 238, 225}, {270, 257, 225}},
+    {{243, 237, 226}, {267, 258, 226}, {245, 235, 226}},
+    {{244, 238, 227}, {268, 259, 227}, {270, 257, 227}},
+    {{247, 233, 228}, {267, 258, 228}, {265, 260, 228}},
+    {{268, 259, 229}, {248, 234, 229}, {266, 261, 229}},
+    {{247, 233, 230}, {263, 262, 230}, {249, 230, 230}},
+    {{248, 234, 231}, {264, 263, 231}, {266, 261, 231}},
+    {{249, 230, 232}, {261, 264, 232}, {251, 231, 232}},
+    {{250, 232, 233}, {262, 265, 233}, {264, 263, 233}},
+    {{233, 221, 234}, {261, 264, 234}, {279, 266, 234}},
+    {{262, 265, 235}, {234, 223, 235}, {280, 267, 235}},
+    {{255, 227, 236}, {259, 268, 236}, {257, 269, 236}},
+    {{260, 270, 237}, {256, 228, 237}, {258, 249, 237}},
+    {{253, 225, 238}, {281, 271, 238}, {259, 268, 238}},
+    {{282, 272, 239}, {254, 226, 239}, {260, 270, 239}},
+    {{231, 222, 240}, {279, 266, 240}, {281, 271, 240}},
+    {{280, 267, 241}, {232, 224, 241}, {282, 272, 241}},
+    {{ 66, 122, 242}, {283, 273, 242}, { 72, 274, 242}},
+    {{284, 275, 243}, { 66, 122, 243}, { 72, 274, 243}},
+    {{107, 118, 244}, {285, 276, 244}, {283, 273, 244}},
+    {{286, 277, 245}, {108, 120, 245}, {284, 275, 245}},
+    {{103, 115, 246}, {285, 276, 246}, {105, 114, 246}},
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+    {{427, 443, 842}, {425, 441, 842}, {403, 413, 842}},
+    {{428, 444, 843}, {402, 411, 843}, {404, 415, 843}},
+    {{401, 408, 844}, {413, 454, 844}, {415, 445, 844}},
+    {{416, 446, 845}, {414, 412, 845}, {402, 411, 845}},
+    {{319, 399, 846}, {443, 479, 846}, {441, 447, 846}},
+    {{320, 400, 847}, {318, 339, 847}, {442, 448, 847}},
+    {{389, 430, 848}, {411, 429, 848}, {443, 450, 848}},
+    {{390, 432, 849}, {320, 549, 849}, {444, 452, 849}},
+    {{309, 338, 850}, {317, 337, 850}, {441, 447, 850}},
+    {{442, 448, 851}, {318, 339, 851}, {310, 340, 851}},
+    {{381, 453, 852}, {429, 470, 852}, {413, 454, 852}},
+    {{414, 412, 853}, {430, 473, 853}, {382, 455, 853}},
+    {{411, 429, 854}, {417, 434, 854}, {439, 456, 854}},
+    {{440, 457, 855}, {418, 435, 855}, {412, 431, 855}},
+    {{445, 458, 856}, {443, 450, 856}, {439, 456, 856}},
+    {{446, 460, 857}, {438, 463, 857}, {440, 457, 857}},
+    {{433, 461, 858}, {445, 458, 858}, {437, 459, 858}},
+    {{438, 463, 859}, {446, 460, 859}, {434, 464, 859}},
+    {{447, 466, 860}, {445, 458, 860}, {433, 461, 860}},
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+    {{447, 466, 862}, {431, 467, 862}, {449, 469, 862}},
+    {{448, 468, 863}, {430, 473, 863}, {450, 471, 863}},
+    {{429, 470, 864}, {449, 469, 864}, {415, 445, 864}},
+    {{430, 473, 865}, {414, 412, 865}, {416, 446, 865}},
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+    {{430, 475, 867}, {448, 477, 867}, {312, 392, 867}},
+    {{441, 447, 868}, {445, 480, 868}, {447, 476, 868}},
+    {{442, 448, 869}, {312, 392, 869}, {448, 477, 869}},
+    {{415, 445, 870}, {449, 469, 870}, {451, 481, 870}},
+    {{452, 483, 871}, {450, 471, 871}, {416, 446, 871}},
+    {{431, 467, 872}, {461, 487, 872}, {451, 481, 872}},
+    {{432, 472, 873}, {450, 471, 873}, {452, 483, 873}},
+    {{431, 467, 420}, {433, 461, 420}, {459, 486, 420}},
+    {{460, 488, 421}, {434, 464, 421}, {432, 472, 421}},
+    {{435, 462, 874}, {457, 490, 874}, {459, 486, 874}},
+    {{436, 465, 875}, {434, 464, 875}, {460, 488, 875}},
+    {{437, 459, 876}, {455, 493, 876}, {457, 490, 876}},
+    {{438, 463, 877}, {436, 465, 877}, {458, 489, 877}},
+    {{437, 459, 878}, {439, 456, 878}, {453, 492, 878}},
+    {{454, 494, 879}, {440, 457, 879}, {438, 463, 879}},
+    {{439, 456, 880}, {417, 434, 880}, {473, 495, 880}},
+    {{474, 496, 881}, {418, 435, 881}, {440, 457, 881}},
+    {{427, 443, 882}, {415, 445, 882}, {475, 482, 882}},
+    {{476, 484, 883}, {416, 446, 883}, {428, 444, 883}},
+    {{425, 441, 884}, {427, 443, 884}, {463, 497, 884}},
+    {{464, 498, 885}, {428, 444, 885}, {426, 442, 885}},
+    {{423, 438, 886}, {425, 441, 886}, {465, 499, 886}},
+    {{466, 500, 887}, {426, 442, 887}, {424, 439, 887}},
+    {{423, 438, 888}, {467, 501, 888}, {469, 503, 888}},
+    {{424, 439, 889}, {422, 440, 889}, {470, 505, 889}},
+    {{421, 504, 890}, {469, 503, 890}, {471, 506, 890}},
+    {{422, 440, 891}, {420, 437, 891}, {472, 507, 891}},
+    {{419, 436, 892}, {471, 506, 892}, {473, 495, 892}},
+    {{420, 437, 893}, {418, 435, 893}, {474, 496, 893}},
+    {{455, 493, 894}, {479, 511, 894}, {477, 508, 894}},
+    {{456, 491, 895}, {458, 489, 895}, {478, 509, 895}},
+    {{479, 511, 896}, {481, 554, 896}, {483, 512, 896}},
+    {{480, 510, 897}, {478, 509, 897}, {484, 513, 897}},
+    {{483, 512, 898}, {481, 554, 898}, {487, 515, 898}},
+    {{488, 517, 899}, {482, 514, 899}, {484, 513, 899}},
+    {{487, 515, 900}, {489, 522, 900}, {491, 519, 900}},
+    {{488, 517, 901}, {486, 518, 901}, {492, 520, 901}},
+    {{463, 497, 902}, {475, 482, 902}, {485, 516, 902}},
+    {{486, 518, 903}, {476, 484, 903}, {464, 498, 903}},
+    {{483, 512, 904}, {485, 516, 904}, {475, 482, 904}},
+    {{484, 513, 905}, {452, 483, 905}, {476, 484, 905}},
+    {{461, 487, 906}, {477, 508, 906}, {483, 512, 906}},
+    {{462, 485, 907}, {452, 483, 907}, {484, 513, 907}},
+    {{457, 490, 908}, {477, 508, 908}, {461, 487, 908}},
+    {{462, 485, 909}, {478, 509, 909}, {458, 489, 909}},
+    {{473, 495, 910}, {479, 511, 910}, {455, 493, 910}},
+    {{474, 496, 911}, {454, 494, 911}, {456, 491, 911}},
+    {{471, 506, 912}, {481, 554, 912}, {479, 511, 912}},
+    {{480, 510, 913}, {482, 514, 913}, {472, 507, 913}},
+    {{487, 515, 914}, {481, 554, 914}, {471, 506, 914}},
+    {{488, 517, 915}, {470, 505, 915}, {472, 507, 915}},
+    {{489, 522, 916}, {487, 515, 916}, {469, 503, 916}},
+    {{490, 521, 917}, {468, 502, 917}, {470, 505, 917}},
+    {{465, 499, 918}, {491, 519, 918}, {489, 522, 918}},
+    {{490, 521, 919}, {492, 520, 919}, {466, 500, 919}},
+    {{391, 426, 920}, {389, 430, 920}, {503, 523, 920}},
+    {{504, 525, 921}, {390, 432, 921}, {392, 427, 921}},
+    {{393, 422, 922}, {391, 426, 922}, {501, 524, 922}},
+    {{502, 526, 923}, {392, 427, 923}, {394, 423, 923}},
+    {{393, 422, 924}, {499, 527, 924}, {497, 529, 924}},
+    {{394, 423, 925}, {396, 419, 925}, {498, 530, 925}},
+    {{395, 418, 926}, {497, 529, 926}, {495, 531, 926}},
+    {{396, 419, 927}, {398, 536, 927}, {496, 533, 927}},
+    {{397, 532, 928}, {495, 531, 928}, {493, 534, 928}},
+    {{398, 536, 929}, {400, 540, 929}, {494, 537, 929}},
+    {{399, 535, 930}, {493, 534, 930}, {505, 538, 930}},
+    {{400, 540, 931}, {388, 544, 931}, {506, 541, 931}},
+    {{501, 524, 932}, {503, 523, 932}, {505, 538, 932}},
+    {{502, 526, 933}, {494, 537, 933}, {506, 541, 933}},
+    {{493, 534, 934}, {495, 531, 934}, {499, 527, 934}},
+    {{500, 528, 935}, {496, 533, 935}, {494, 537, 935}},
+    {{381, 393, 936}, {387, 555, 936}, {505, 542, 936}},
+    {{382, 543, 937}, {314, 547, 937}, {506, 541, 937}},
+    {{313, 545, 938}, {505, 538, 938}, {503, 523, 938}},
+    {{504, 525, 939}, {506, 541, 939}, {314, 547, 939}},
+    {{319, 451, 940}, {321, 546, 940}, {503, 523, 940}},
+    {{504, 525, 941}, {322, 548, 941}, {320, 549, 941}},
+  };
+
+  constexpr uint32_t num_faces = (sizeof (faces)) / (sizeof (face_vtn));
+
+}
diff --git a/geometry/suzanne2.obj b/geometry/suzanne2.obj
new file mode 100644
index 0000000..638208b
--- /dev/null
+++ b/geometry/suzanne2.obj
@@ -0,0 +1,2976 @@
+# Blender 3.3.6
+# www.blender.org
+o Suzanne
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diff --git a/math/vec3.hpp b/math/vec3.hpp
index e440cae..13d8241 100644
--- a/math/vec3.hpp
+++ b/math/vec3.hpp
@@ -139,6 +139,14 @@ inline constexpr T dot(vec<3, T> const& v1, vec<3, T> const& v2)
   return tmp.x + tmp.y + tmp.z;
 }
 
+template <typename T>
+inline constexpr vec<3, T> cross(vec<3, T> const& v1, vec<3, T> const& v2)
+{
+  return vec<3, T>(v1.y * v2.z - v2.y * v1.z,
+                   v1.z * v2.x - v2.z * v1.x,
+                   v1.x * v2.y - v2.x * v1.y);
+}
+
 template <typename T>
 inline constexpr vec<3, T> functor1(T (&func) (T const& x), vec<3, T> const& v)
 {
diff --git a/viewing_system/screen_space.hpp b/viewing_system/screen_space.hpp
new file mode 100644
index 0000000..72cfce6
--- /dev/null
+++ b/viewing_system/screen_space.hpp
@@ -0,0 +1,15 @@
+#include "geometry/geometry.hpp"
+
+namespace screen_space {
+
+  constexpr mat4x4 transformation_matrix(const float d, // the z-coordinate of the view window and the near clip plane
+                                         const float f, // the z-coordnate of the far clip plane
+                                         const float h  // the dimension of the square view window
+                                         )
+  {
+    return { d/h, 0.f, 0.f    , 0.f       ,
+             0.f, d/h, 0.f    , 0.f       ,
+             0.f, 0.f, f/(f-d), -d*f/(f-d),
+             0.f, 0.f, 1.f    , 0.f        };
+  }
+}
diff --git a/viewing_system/view_space.hpp b/viewing_system/view_space.hpp
new file mode 100644
index 0000000..a38ffb3
--- /dev/null
+++ b/viewing_system/view_space.hpp
@@ -0,0 +1,44 @@
+#include "geometry/geometry.hpp"
+
+namespace view_space {
+
+  constexpr vec3 viewing_direction(const float azimuth,
+                                   const float colatitude
+                                   )
+  {
+    const float x = sin(colatitude) * cos(azimuth);
+    const float y = sin(colatitude) * sin(azimuth);
+    const float z = cos(colatitude);
+    return {x, y, z};
+  }
+
+
+  constexpr vec3 project_vector_to_plane(const vec3& n,  // N: plane normal
+                                         const vec3& v_  // V': approximate "up" orientation
+                                         )
+  {
+    return v_ - dot(v_, n) * n;
+  }
+
+  constexpr mat4x4 transformation_matrix(const vec3& c,  // C: in world space, the position of the viewer
+                                         const vec3& n,  // N: in world space, the viewing direction
+                                         const vec3& v_  // V': approximate "up" orientation
+                                         )
+  {
+    const vec3 v = project_vector_to_plane(n, v_);
+    const vec3 u = cross(n, v);
+
+    const mat4x4 t = { 1.f, 0.f, 0.f, -c.x,
+                       0.f, 1.f, 0.f, -c.y,
+                       0.f, 0.f, 1.f, -c.z,
+                       0.f, 0.f, 0.f,  1.f };
+
+    const mat4x4 r = { u.x, u.y, u.z, 0.f,
+                       v.x, v.y, v.z, 0.f,
+                       n.x, n.y, n.z, 0.f,
+                       0.f, 0.f, 0.f, 1.f };
+
+    return r * t;
+  }
+
+}