 				{ 0.0f, 0.0f, 0.0f, 0.0f, 0.0f }
 			} };
 
-			/// ゼロベクトル
+			/// zero vector
 			static const float5 ZERO_5x1 = { {0.0f, 0.0f, 0.0f, 0.0f, 0.0f} };
 			static const float4 ONE_4x1 = float4(1.0f, 1.0f, 1.0f, 1.0f);
 
-			/// 5次元ベクトルに変換する
+			/// to 5D vector from 4D vector 
 			float5 toFloat5(const float4 v)
 			{
 				const float5 result = { {v.x, v.y, v.z, v.w, 1.0f} };
 				return result;
 			}
 
-			/// 4次元ベクトルに変換する
+			/// to 4D vector from 5D vector
 			float4 toFloat4(const float5 v)
 			{
 				return float4(v.values[0], v.values[1], v.values[2], v.values[3]);
 			}
 
-			/// 5x5行列の乗算
+			/// multiply 5D matricies
 			float5x5 mul5x5(const float5x5 lhs, const float5x5 rhs)
 			{
 				float5x5 result;

				return result;
			}

			/// YW平面回転行列を生成する(XZ座標が変化)
			float5x5 makeRotateYW(float theta)
			{
				float c = cos(theta);

				float2 uv : TEXCOORD0;
			};

			/// fragment shader input.
			struct v2f
			{
				float4 vertex : SV_POSITION;
				float4 color : COLOR0;
			};

			/// vertex shader function.
			v2f vert(appdata v)
			{
				v2f o;
