diff --git a/example/cube_vq.cpp b/example/cube_vq.cpp
index 6483418..9c58518 100644
--- a/example/cube_vq.cpp
+++ b/example/cube_vq.cpp
@@ -231,6 +231,6 @@ void main()
 			       tile_width,
 			       tile_height);
     transfer_scene(theta);
-    //theta += degree;
+    theta += degree;
   }
 }
diff --git a/example/cube_vq_rectangular.cpp b/example/cube_vq_rectangular.cpp
new file mode 100644
index 0000000..a063b53
--- /dev/null
+++ b/example/cube_vq_rectangular.cpp
@@ -0,0 +1,235 @@
+#include <cstdint>
+
+#include "holly/isp_tsp.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/ta_fifo_polygon_converter.hpp"
+#include "holly/holly.hpp"
+#include "holly/core_bits.hpp"
+#include "holly/core.hpp"
+#include "holly/region_array.hpp"
+#include "holly/background.hpp"
+#include "holly/video_output.hpp"
+#include "holly/texture_memory_alloc2.hpp"
+#include "sh7091/store_queue.hpp"
+#include "sh7091/serial.hpp"
+
+#include "twiddle.hpp"
+
+#include "math/vec2.hpp"
+
+#include "texture/panda/panda_rectangular.vq.h"
+
+enum material {
+  Material,
+};
+
+#include "model/prism.h"
+
+void transfer_scene(float theta)
+{
+  const uint32_t parameter_control_word = para_control::para_type::polygon_or_modifier_volume
+                                        | para_control::list_type::opaque
+                                        | obj_control::col_type::intensity_mode_1
+                                        | obj_control::texture
+                                        | obj_control::gouraud;
+
+  const uint32_t isp_tsp_instruction_word = isp_tsp_instruction_word::depth_compare_mode::greater
+                                          | isp_tsp_instruction_word::culling_mode::cull_if_positive;
+
+  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
+                                      | tsp_instruction_word::texture_shading_instruction::modulate
+                                      | tsp_instruction_word::texture_u_size::from_int(512)
+                                      | tsp_instruction_word::texture_v_size::from_int(256);
+
+  const uint32_t texture_address = texture_memory_alloc::texture.start;
+  const uint32_t texture_control_word = texture_control_word::vq_compressed
+                                      | texture_control_word::pixel_format::_565
+                                      | texture_control_word::scan_order::twiddled
+                                      | texture_control_word::texture_address(texture_address / 8);
+
+  for (int j = 0; j < prism_model.object_count; j++) {
+    *reinterpret_cast<ta_global_parameter::polygon_type_1 *>(store_queue) =
+      ta_global_parameter::polygon_type_1(parameter_control_word,
+					  isp_tsp_instruction_word,
+					  tsp_instruction_word,
+					  texture_control_word, // texture_control_word
+					  1.0, // face color alpha
+					  1.0, // face color r
+					  1.0, // face color g
+					  1.0  // face color b
+					  );
+    sq_transfer_32byte(ta_fifo_polygon_converter);
+
+    struct object * object = prism_model.object[j];
+    for (int i = 0; i < object->triangle_count; i++) {
+      for (int k = 0; k < 3; k++) {
+	int position_ix = object->triangle[i].v[k].position;
+	float x0 = prism_model.position[position_ix].x;
+	float y0 = prism_model.position[position_ix].y;
+	float z0 = prism_model.position[position_ix].z;
+
+	float x1 = x0 * cos(theta) - z0 * sin(theta);
+	float y1 = y0;
+	float z1 = x0 * sin(theta) + z0 * cos(theta);
+
+	float x = x1;
+	float y = y1 * cos(theta) - z1 * sin(theta);
+	float z = y1 * sin(theta) + z1 * cos(theta);
+
+	z += 2.0;
+
+	x /= z;
+	y /= z;
+
+	// do rotation
+	x = x * 240 + 320;
+	y = y * 240 + 240;
+
+	z = 1/z;
+
+	bool end_of_strip = k == 2;
+
+	int texture_ix = object->triangle[i].v[k].texture;
+	float u = 1.0 - prism_model.texture[texture_ix].u;
+	float v = prism_model.texture[texture_ix].v;
+
+	*reinterpret_cast<ta_vertex_parameter::polygon_type_7 *>(store_queue) =
+	  ta_vertex_parameter::polygon_type_7(polygon_vertex_parameter_control_word(end_of_strip),
+					      x, y, z,
+					      u, v,
+					      1.0, // base intensity
+					      1.0  // offset intensity
+					      );
+	sq_transfer_32byte(ta_fifo_polygon_converter);
+      }
+    }
+  }
+
+  *reinterpret_cast<ta_global_parameter::end_of_list *>(store_queue) =
+    ta_global_parameter::end_of_list(para_control::para_type::end_of_list);
+  sq_transfer_32byte(ta_fifo_polygon_converter);
+}
+
+template <typename T>
+inline void copy(T * dst, const T * src, const int32_t n) noexcept
+{
+  int32_t n_t = n / (sizeof (T));
+  while (n_t > 0) {
+    *dst++ = *src++;
+    n_t--;
+  }
+}
+
+void texture_init()
+{
+  uint32_t offset = texture_memory_alloc::texture.start;
+  copy<volatile uint32_t>(&texture_memory64[offset / 4],
+			  reinterpret_cast<uint32_t *>(&_binary_texture_panda_panda_rectangular_vq_start),
+			  reinterpret_cast<int>(&_binary_texture_panda_panda_rectangular_vq_size));
+}
+
+void main()
+{
+  serial::init(4);
+  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 int render_passes = 1;
+  constexpr struct opb_size opb_size[render_passes] = {
+    {
+      .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();
+
+  video_output::set_mode_vga();
+
+  constexpr int framebuffer_width = 640;
+  constexpr int framebuffer_height = 480;
+  constexpr int tile_width = framebuffer_width / 32;
+  constexpr int tile_height = framebuffer_height / 32;
+
+  region_array_multipass(tile_width,
+			 tile_height,
+			 opb_size,
+			 render_passes,
+			 texture_memory_alloc::region_array[0].start,
+			 texture_memory_alloc::object_list[0].start);
+  region_array_multipass(tile_width,
+			 tile_height,
+			 opb_size,
+			 render_passes,
+			 texture_memory_alloc::region_array[1].start,
+			 texture_memory_alloc::object_list[1].start);
+
+  background_parameter2(texture_memory_alloc::background[0].start,
+			0xff220033);
+  background_parameter2(texture_memory_alloc::background[1].start,
+			0xff220033);
+
+  texture_init();
+
+  const float degree = 0.017453292519943295;
+  float theta = 0;
+  int ta = -1;
+  int core = -2;
+  while (1) {
+    if (core >= 0) {
+      // core = 0  ; core = 1
+      // ta = 1    ; ta = 0
+      core_wait_end_of_render_video();
+      while (!spg_status::vsync(holly.SPG_STATUS));
+      holly.FB_R_SOF1 = texture_memory_alloc::framebuffer[core].start;
+      while (spg_status::vsync(holly.SPG_STATUS));
+    }
+
+    // core = -2 ; core = 1 ; core = 0
+    // ta = -1   ; ta = 0   ; ta = 1
+    core += 1;
+    ta += 1;
+    if (core > 1) core = 0;
+    if (ta > 1) ta = 0;
+
+    if (core >= 0) {
+      // core = 1 ; core = 0
+      // ta = 0   ; ta = 1
+      ta_wait_opaque_list();
+      core_start_render2(texture_memory_alloc::region_array[core].start,
+			 texture_memory_alloc::isp_tsp_parameters[core].start,
+			 texture_memory_alloc::background[core].start,
+			 texture_memory_alloc::framebuffer[core].start,
+			 framebuffer_width);
+    }
+
+
+    // core = -1 ; core = 1 ; core = 0
+    // ta = 0    ; ta = 0   ; ta = 1
+    ta_polygon_converter_init2(texture_memory_alloc::isp_tsp_parameters[ta].start,
+			       texture_memory_alloc::isp_tsp_parameters[ta].end,
+			       texture_memory_alloc::object_list[ta].start,
+			       texture_memory_alloc::object_list[ta].end,
+			       opb_size[0].total(),
+			       ta_alloc,
+			       tile_width,
+			       tile_height);
+    transfer_scene(theta);
+    theta += degree;
+  }
+}
diff --git a/example/example.mk b/example/example.mk
index ea74607..fcf269d 100644
--- a/example/example.mk
+++ b/example/example.mk
@@ -582,6 +582,19 @@ CUBE_VQ_OBJ = \
 example/cube_vq.elf: LDSCRIPT = $(LIB)/alt.lds
 example/cube_vq.elf: $(START_OBJ) $(CUBE_VQ_OBJ)
 
+CUBE_VQ_RECTANGULAR_OBJ = \
+	example/cube_vq_rectangular.o \
+	holly/core.o \
+	holly/region_array.o \
+	holly/background.o \
+	holly/ta_fifo_polygon_converter.o \
+	holly/video_output.o \
+	sh7091/serial.o \
+	texture/panda/panda_rectangular.vq.o
+
+example/cube_vq_rectangular.elf: LDSCRIPT = $(LIB)/alt.lds
+example/cube_vq_rectangular.elf: $(START_OBJ) $(CUBE_VQ_RECTANGULAR_OBJ)
+
 SHEIK_OBJ = \
 	example/sheik.o \
 	holly/core.o \
diff --git a/model/prism.h b/model/prism.h
new file mode 100644
index 0000000..c4a9774
--- /dev/null
+++ b/model/prism.h
@@ -0,0 +1,124 @@
+#include <stddef.h>
+
+#include "model.h"
+
+// floating-point
+vertex_position prism_position[] = {
+  {1.0, 0.5, -0.5},
+  {1.0, -0.5, -0.5},
+  {1.0, 0.5, 0.5},
+  {1.0, -0.5, 0.5},
+  {-1.0, 0.5, -0.5},
+  {-1.0, -0.5, -0.5},
+  {-1.0, 0.5, 0.5},
+  {-1.0, -0.5, 0.5},
+};
+
+// floating-point
+vertex_texture prism_texture[] = {
+  {0.0, 1.0},
+  {1.0, 0.0},
+  {1.0, 1.0},
+  {0.0, 0.0},
+  {1.0, 1.0},
+  {0.0, 1.0},
+  {0.75, 0.0},
+  {0.25, 1.0},
+  {0.25, 0.0},
+  {0.0, 0.0},
+  {0.75, 1.0},
+};
+
+// floating-point
+vertex_normal prism_normal[] = {
+  {0.0, 1.0, 0.0},
+  {0.0, 0.0, 1.0},
+  {-1.0, 0.0, 0.0},
+  {0.0, -1.0, 0.0},
+  {1.0, 0.0, 0.0},
+  {0.0, 0.0, -1.0},
+};
+
+union triangle prism_Cube_triangle[] = {
+  { .v = {
+    {4, 0, 0},
+    {2, 1, 0},
+    {0, 2, 0},
+  }},
+  { .v = {
+    {2, 3, 1},
+    {7, 4, 1},
+    {3, 5, 1},
+  }},
+  { .v = {
+    {6, 6, 2},
+    {5, 7, 2},
+    {7, 8, 2},
+  }},
+  { .v = {
+    {1, 0, 3},
+    {7, 1, 3},
+    {5, 2, 3},
+  }},
+  { .v = {
+    {0, 6, 4},
+    {3, 7, 4},
+    {1, 8, 4},
+  }},
+  { .v = {
+    {4, 3, 5},
+    {1, 4, 5},
+    {5, 5, 5},
+  }},
+  { .v = {
+    {4, 0, 0},
+    {6, 9, 0},
+    {2, 1, 0},
+  }},
+  { .v = {
+    {2, 3, 1},
+    {6, 1, 1},
+    {7, 4, 1},
+  }},
+  { .v = {
+    {6, 6, 2},
+    {4, 10, 2},
+    {5, 7, 2},
+  }},
+  { .v = {
+    {1, 0, 3},
+    {3, 9, 3},
+    {7, 1, 3},
+  }},
+  { .v = {
+    {0, 6, 4},
+    {2, 10, 4},
+    {3, 7, 4},
+  }},
+  { .v = {
+    {4, 3, 5},
+    {0, 1, 5},
+    {1, 4, 5},
+  }},
+};
+
+struct object prism_Cube = {
+  .triangle = &prism_Cube_triangle[0],
+  .quadrilateral = NULL,
+  .triangle_count = 12,
+  .quadrilateral_count = 0,
+  .material = Material,
+};
+
+struct object * prism_object_list[] = {
+  &prism_Cube,
+};
+
+struct model prism_model = {
+  .position = &prism_position[0],
+  .texture = &prism_texture[0],
+  .normal = &prism_normal[0],
+  .object = &prism_object_list[0],
+  .object_count = 1,
+};
+
diff --git a/model/prism.mtl b/model/prism.mtl
new file mode 100644
index 0000000..4d490e8
--- /dev/null
+++ b/model/prism.mtl
@@ -0,0 +1,12 @@
+# Blender 4.1.1 MTL File: 'None'
+# www.blender.org
+
+newmtl Material
+Ns 250.000000
+Ka 1.000000 1.000000 1.000000
+Kd 0.800000 0.800000 0.800000
+Ks 0.500000 0.500000 0.500000
+Ke 0.000000 0.000000 0.000000
+Ni 1.450000
+d 1.000000
+illum 2
diff --git a/texture/panda/panda.vq b/texture/panda/panda.vq
index 0362f18..84bdee0 100644
Binary files a/texture/panda/panda.vq and b/texture/panda/panda.vq differ
diff --git a/texture/panda/panda_rectangular.vq b/texture/panda/panda_rectangular.vq
new file mode 100644
index 0000000..5602e26
Binary files /dev/null and b/texture/panda/panda_rectangular.vq differ
diff --git a/texture/panda/panda_rectangular.vq.h b/texture/panda/panda_rectangular.vq.h
new file mode 100644
index 0000000..22d0e39
--- /dev/null
+++ b/texture/panda/panda_rectangular.vq.h
@@ -0,0 +1,5 @@
+#pragma once
+#include <cstdint>
+extern uint32_t _binary_texture_panda_panda_rectangular_vq_start __asm("_binary_texture_panda_panda_rectangular_vq_start");
+extern uint32_t _binary_texture_panda_panda_rectangular_vq_end __asm("_binary_texture_panda_panda_rectangular_vq_end");
+extern uint32_t _binary_texture_panda_panda_rectangular_vq_size __asm("_binary_texture_panda_panda_rectangular_vq_size");
diff --git a/twiddle.hpp b/twiddle.hpp
index 7c521aa..170c7c9 100644
--- a/twiddle.hpp
+++ b/twiddle.hpp
@@ -26,37 +26,75 @@ alternately, in verilog syntax:
   assign t = {x[2], y[2], x[1], y[1], x[0], y[0]};
 */
 
-constexpr inline uint32_t from_xy(uint32_t x, uint32_t y)
+constexpr inline int log2(uint32_t n)
+{
+  switch (n) {
+  default:
+  case 8: return 3;
+  case 16: return 4;
+  case 32: return 5;
+  case 64: return 6;
+  case 128: return 7;
+  case 256: return 8;
+  case 512: return 9;
+  case 1024: return 10;
+  }
+}
+
+constexpr inline uint32_t from_xy(uint32_t x, uint32_t y, uint32_t width, uint32_t height)
 {
   // maximum texture size       : 1024x1024
   // maximum 1-dimensional index: 0xfffff
   // bits                       : 19-0
 
+  // y bits: 0, 2, 4, 6, 8, 10, 12, 14, 16, 18
+  // x bits: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
+
+  int width_max = log2(width);
+  int height_max = log2(height);
+
   uint32_t twiddle_ix = 0;
-  for (int i = 0; i <= (20 / 2); i++) {
-    twiddle_ix |= ((y >> i) & 1) << (i * 2 + 0);
-    twiddle_ix |= ((x >> i) & 1) << (i * 2 + 1);
+  for (int i = 0; i < (20 / 2); i++) {
+    if (i < width_max && i < height_max) {
+      twiddle_ix |= ((y >> i) & 1) << (i * 2 + 0);
+      twiddle_ix |= ((x >> i) & 1) << (i * 2 + 1);
+    } else if (i < width_max) {
+      twiddle_ix |= ((x >> i) & 1) << (i + height_max);
+    } else if (i < height_max) {
+      twiddle_ix |= ((y >> i) & 1) << (i + width_max);
+    } else {
+      break;
+    }
   }
 
   return twiddle_ix;
 }
 
-static_assert(from_xy(0b000, 0b000) == 0);
-static_assert(from_xy(0b001, 0b000) == 2);
-static_assert(from_xy(0b010, 0b000) == 8);
-static_assert(from_xy(0b011, 0b000) == 10);
-static_assert(from_xy(0b100, 0b000) == 32);
-static_assert(from_xy(0b101, 0b000) == 34);
-static_assert(from_xy(0b110, 0b000) == 40);
-static_assert(from_xy(0b111, 0b000) == 42);
+static_assert(from_xy(0b000, 0b000, 8, 8) == 0);
+static_assert(from_xy(0b001, 0b000, 8, 8) == 2);
+static_assert(from_xy(0b010, 0b000, 8, 8) == 8);
+static_assert(from_xy(0b011, 0b000, 8, 8) == 10);
+static_assert(from_xy(0b100, 0b000, 8, 8) == 32);
+static_assert(from_xy(0b101, 0b000, 8, 8) == 34);
+static_assert(from_xy(0b110, 0b000, 8, 8) == 40);
+static_assert(from_xy(0b111, 0b000, 8, 8) == 42);
 
-static_assert(from_xy(0b000, 0b001) == 1);
-static_assert(from_xy(0b000, 0b010) == 4);
-static_assert(from_xy(0b000, 0b011) == 5);
-static_assert(from_xy(0b000, 0b100) == 16);
-static_assert(from_xy(0b000, 0b101) == 17);
-static_assert(from_xy(0b000, 0b110) == 20);
-static_assert(from_xy(0b000, 0b111) == 21);
+static_assert(from_xy(0b000, 0b001, 8, 8) == 1);
+static_assert(from_xy(0b000, 0b010, 8, 8) == 4);
+static_assert(from_xy(0b000, 0b011, 8, 8) == 5);
+static_assert(from_xy(0b000, 0b100, 8, 8) == 16);
+static_assert(from_xy(0b000, 0b101, 8, 8) == 17);
+static_assert(from_xy(0b000, 0b110, 8, 8) == 20);
+static_assert(from_xy(0b000, 0b111, 8, 8) == 21);
+
+//                                1  0  0  0
+// x bits: 19, 17, 15, 13, 11, 9, 7, 5, 3, 1
+// y bits: 18, 16, 14, 12, 10, 8, 6, 4, 2, 0
+static_assert(from_xy(0b1000, 0b001, 16, 8) == 65);
+static_assert(from_xy(0b1010, 0b001, 16, 8) == 73);
+
+static_assert(from_xy(0b000, 0b1001, 8, 16) == 65);
+static_assert(from_xy(0b010, 0b1001, 8, 16) == 73);
 
 /*
 constexpr inline std::array<uint32_t, 2>
@@ -73,7 +111,6 @@ from_ix(uint32_t curve_ix)
 
   return x_y;
 }
-*/
 
 constexpr inline std::tuple<uint32_t, uint32_t>
 from_ix(uint32_t curve_ix)
@@ -110,13 +147,14 @@ static_assert(from_ix(16) == xy_type{0b000, 0b100});
 static_assert(from_ix(17) == xy_type{0b000, 0b101});
 static_assert(from_ix(20) == xy_type{0b000, 0b110});
 static_assert(from_ix(21) == xy_type{0b000, 0b111});
+*/
 
 template <typename T>
 void texture(volatile T * dst, const T * src, const uint32_t width, const uint32_t height)
 {
   for (uint32_t y = 0; y < height; y++) {
     for (uint32_t x = 0; x < width; x++) {
-      uint32_t twiddle_ix = from_xy(x, y);
+      uint32_t twiddle_ix = from_xy(x, y, width, height);
       T value = src[y * width + x];
       dst[twiddle_ix] = value;
     }
@@ -128,7 +166,7 @@ void texture_4bpp(volatile T * dst, const T * src, const uint32_t width, const u
 {
   for (uint32_t y = 0; y < height; y++) {
     for (uint32_t x = 0; x < width; x++) {
-      uint32_t twiddle_ix = from_xy(x, y);
+      uint32_t twiddle_ix = from_xy(x, y, width, height);
       T value = src[y * width + x];
       uint32_t shift = (4 * (twiddle_ix & 1));
       dst[twiddle_ix / 2] &= ~(0b1111 << shift);
@@ -137,6 +175,9 @@ void texture_4bpp(volatile T * dst, const T * src, const uint32_t width, const u
   }
 }
 
+/*
+  the following code is not correct
+
 template <uint32_t dst_bits_per_pixel, typename T, typename U>
 void texture2(volatile T * dst, const U * src,
 	      const uint32_t src_stride,
@@ -206,5 +247,6 @@ void texture3(volatile T * dst, const U * src,
     }
   }
 }
+*/
 
 }