Jiaming Guo / flow3

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Commit 9191c39e5a985e1a2d988537802f95dbcfe5e9d2

Authored by Jiaming Guo 2017-03-29 09:51:09 -0500

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first version of flow3

Showing 8 changed files with 19211 additions and 0 deletions Show diff stats

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CMakeLists.txt 0 → 100644

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	1	+++ a/CMakeLists.txt
	1	+#Specify the version being used as well as the language
	2	+cmake_minimum_required(VERSION 2.8.11)
	3	+
	4	+#Name your project here
	5	+project(flow3)
	6	+
	7	+#set the module directory
	8	+set(CMAKE_MODULE_PATH ${CMAKE_MODULE_PATH} "${CMAKE_SOURCE_DIR}")
	9	+
	10	+#find the STIM library
	11	+find_package(STIM)
	12	+
	13	+#if the STIM library isn't found, download it
	14	+if(NOT STIM_INCLUDE_DIRS)
	15	+ file(REMOVE_RECURSE ${CMAKE_BINARY_DIR}/stimlib) #remove the stimlib directory if it exists
	16	+ set(STIM_GIT "https://git.stim.ee.uh.edu/codebase/stimlib.git")
	17	+ execute_process(COMMAND git clone --depth 1 ${STIM_GIT} WORKING_DIRECTORY ${CMAKE_BINARY_DIR})
	18	+ set(STIM_INCLUDE_DIRS "${CMAKE_BINARY_DIR}/stimlib" CACHE TYPE PATH)
	19	+endif(NOT STIM_INCLUDE_DIRS)
	20	+
	21	+#find BOOST
	22	+find_package(Boost REQUIRED)
	23	+
	24	+#find cuda
	25	+find_package(CUDA REQUIRED)
	26	+
	27	+#find the GLUT library for visualization
	28	+find_package(OpenGL REQUIRED)
	29	+
	30	+find_package(GLUT REQUIRED)
	31	+
	32	+#find OpenCV
	33	+find_package(OpenCV REQUIRED)
	34	+add_definitions(-DUSING_OPENCV)
	35	+
	36	+#find the pthreads package
	37	+find_package(Threads)
	38	+
	39	+#find the X11 package
	40	+find_package(X11)
	41	+
	42	+#find the Approximate Nearest Neighbor Library
	43	+#find_package(ANN REQUIRED)
	44	+
	45	+#build the executable in the binary directory on MS Visual Studio
	46	+if ( MSVC )
	47	+ SET( CMAKE_RUNTIME_OUTPUT_DIRECTORY_DEBUG "${OUTPUT_DIRECTORY}")
	48	+ SET( CMAKE_RUNTIME_OUTPUT_DIRECTORY_RELEASE "${OUTPUT_DIRECTORY}")
	49	+endif ( MSVC )
	50	+
	51	+include_directories(
	52	+ ${OPENGL_INCLUDE_DIRS}
	53	+ ${GLUT_INCLUDE_DIR}
	54	+ ${STIM_INCLUDE_DIRS}
	55	+ #${ANN_INCLUDE_DIR}
	56	+ ${Boost_INCLUDE_DIR}
	57	+ ${CUDA_INCLUDE_DIRS}
	58	+ ${OpenCV_INCLUDE_DIRS}
	59	+ )
	60	+
	61	+#Assign source files to the appropriate variables
	62	+#file(GLOB SRC_CU "*.cu")
	63	+#file(GLOB SRC_H "*.h")
	64	+#file(GLOB SRC_CUH "*.h")
	65	+
	66	+#create an executable file
	67	+cuda_add_executable(flow3
	68	+ main.cu
	69	+ #${SRC_CUH}
	70	+ )
	71	+
	72	+#set the link libraries
	73	+target_link_libraries(flow3
	74	+# ${OpenGL_LIBRARIES}
	75	+ ${OPENGL_gl_LIBRARY}
	76	+ ${OPENGL_glu_LIBRARY}
	77	+ ${GLUT_LIBRARIES}
	78	+ ${CMAKE_THREAD_LIBS_INIT}
	79	+ #${ANN_LIBRARY}
	80	+ ${X11_LIBRARIES}
	81	+ ${CUDA_cublas_LIBRARY}
	82	+ ${OpenCV_LIBS}
	83	+ )
	84	+
	85	+#set up copying data files
	86	+configure_file(data/h1_GT.obj ${CMAKE_CURRENT_BINARY_DIR}/h1_GT.obj @ONLY)
	87	+configure_file(data/h2_GT.obj ${CMAKE_CURRENT_BINARY_DIR}/h2_GT.obj @ONLY)
	88	+configure_file(data/00_GT.obj ${CMAKE_CURRENT_BINARY_DIR}/00_GT.obj @ONLY)
...	...

FindGLUT.cmake 0 → 100644

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	1	+++ a/FindGLUT.cmake
	1	+#.rst:
	2	+# FindGLUT
	3	+# --------
	4	+#
	5	+# try to find glut library and include files.
	6	+#
	7	+# IMPORTED Targets
	8	+# ^^^^^^^^^^^^^^^^
	9	+#
	10	+# This module defines the :prop_tgt:`IMPORTED` targets:
	11	+#
	12	+# ``GLUT::GLUT``
	13	+# Defined if the system has GLUT.
	14	+#
	15	+# Result Variables
	16	+# ^^^^^^^^^^^^^^^^
	17	+#
	18	+# This module sets the following variables:
	19	+#
	20	+# ::
	21	+#
	22	+# GLUT_INCLUDE_DIR, where to find GL/glut.h, etc.
	23	+# GLUT_LIBRARIES, the libraries to link against
	24	+# GLUT_FOUND, If false, do not try to use GLUT.
	25	+#
	26	+# Also defined, but not for general use are:
	27	+#
	28	+# ::
	29	+#
	30	+# GLUT_glut_LIBRARY = the full path to the glut library.
	31	+# GLUT_Xmu_LIBRARY = the full path to the Xmu library.
	32	+# GLUT_Xi_LIBRARY = the full path to the Xi Library.
	33	+
	34	+#=============================================================================
	35	+# Copyright 2001-2009 Kitware, Inc.
	36	+#
	37	+# Distributed under the OSI-approved BSD License (the "License");
	38	+# see accompanying file Copyright.txt for details.
	39	+#
	40	+# This software is distributed WITHOUT ANY WARRANTY; without even the
	41	+# implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
	42	+# See the License for more information.
	43	+#=============================================================================
	44	+# (To distribute this file outside of CMake, substitute the full
	45	+# License text for the above reference.)
	46	+
	47	+if (WIN32)
	48	+ find_path( GLUT_INCLUDE_DIR NAMES GL/glut.h
	49	+ PATHS $ENV{GLUT_ROOT_PATH}/include )
	50	+
	51	+ if( CMAKE_SIZEOF_VOID_P EQUAL 8 )
	52	+ find_library( GLUT_glut_LIBRARY NAMES freeglut
	53	+ PATHS
	54	+ $ENV{GLUT_ROOT_PATH}/lib/x64
	55	+
	56	+ NO_DEFAULT_PATH
	57	+ )
	58	+ else( CMAKE_SIZEOF_VOID_P EQUAL 8 )
	59	+ find_library( GLUT_glut_LIBRARY NAMES glut glut32 freeglut
	60	+ PATHS
	61	+ ${OPENGL_LIBRARY_DIR}
	62	+ $ENV{GLUT_ROOT_PATH}/lib
	63	+ )
	64	+ endif( CMAKE_SIZEOF_VOID_P EQUAL 8 )
	65	+
	66	+else ()
	67	+
	68	+ if (APPLE)
	69	+ find_path(GLUT_INCLUDE_DIR glut.h ${OPENGL_LIBRARY_DIR})
	70	+ find_library(GLUT_glut_LIBRARY GLUT DOC "GLUT library for OSX")
	71	+ find_library(GLUT_cocoa_LIBRARY Cocoa DOC "Cocoa framework for OSX")
	72	+
	73	+ if(GLUT_cocoa_LIBRARY AND NOT TARGET GLUT::Cocoa)
	74	+ add_library(GLUT::Cocoa UNKNOWN IMPORTED)
	75	+ # Cocoa should always be a Framework, but we check to make sure.
	76	+ if(GLUT_cocoa_LIBRARY MATCHES "/([^/]+)\\.framework$")
	77	+ set_target_properties(GLUT::Cocoa PROPERTIES
	78	+ IMPORTED_LOCATION "${GLUT_cocoa_LIBRARY}/${CMAKE_MATCH_1}")
	79	+ else()
	80	+ set_target_properties(GLUT::Cocoa PROPERTIES
	81	+ IMPORTED_LOCATION "${GLUT_cocoa_LIBRARY}")
	82	+ endif()
	83	+ endif()
	84	+ else ()
	85	+
	86	+ if (BEOS)
	87	+
	88	+ set(_GLUT_INC_DIR /boot/develop/headers/os/opengl)
	89	+ set(_GLUT_glut_LIB_DIR /boot/develop/lib/x86)
	90	+
	91	+ else()
	92	+
	93	+ find_library( GLUT_Xi_LIBRARY Xi
	94	+ /usr/openwin/lib
	95	+ )
	96	+
	97	+ find_library( GLUT_Xmu_LIBRARY Xmu
	98	+ /usr/openwin/lib
	99	+ )
	100	+
	101	+ if(GLUT_Xi_LIBRARY AND NOT TARGET GLUT::Xi)
	102	+ add_library(GLUT::Xi UNKNOWN IMPORTED)
	103	+ set_target_properties(GLUT::Xi PROPERTIES
	104	+ IMPORTED_LOCATION "${GLUT_Xi_LIBRARY}")
	105	+ endif()
	106	+
	107	+ if(GLUT_Xmu_LIBRARY AND NOT TARGET GLUT::Xmu)
	108	+ add_library(GLUT::Xmu UNKNOWN IMPORTED)
	109	+ set_target_properties(GLUT::Xmu PROPERTIES
	110	+ IMPORTED_LOCATION "${GLUT_Xmu_LIBRARY}")
	111	+ endif()
	112	+
	113	+ endif ()
	114	+
	115	+ find_path( GLUT_INCLUDE_DIR GL/glut.h
	116	+ /usr/include/GL
	117	+ /usr/openwin/share/include
	118	+ /usr/openwin/include
	119	+ /opt/graphics/OpenGL/include
	120	+ /opt/graphics/OpenGL/contrib/libglut
	121	+ ${_GLUT_INC_DIR}
	122	+ )
	123	+
	124	+ find_library( GLUT_glut_LIBRARY glut
	125	+ /usr/openwin/lib
	126	+ ${_GLUT_glut_LIB_DIR}
	127	+ )
	128	+
	129	+ unset(_GLUT_INC_DIR)
	130	+ unset(_GLUT_glut_LIB_DIR)
	131	+
	132	+ endif ()
	133	+
	134	+endif ()
	135	+
	136	+FIND_PACKAGE_HANDLE_STANDARD_ARGS(GLUT REQUIRED_VARS GLUT_glut_LIBRARY GLUT_INCLUDE_DIR)
	137	+
	138	+if (GLUT_FOUND)
	139	+ # Is -lXi and -lXmu required on all platforms that have it?
	140	+ # If not, we need some way to figure out what platform we are on.
	141	+ set( GLUT_LIBRARIES
	142	+ ${GLUT_glut_LIBRARY}
	143	+ ${GLUT_Xmu_LIBRARY}
	144	+ ${GLUT_Xi_LIBRARY}
	145	+ ${GLUT_cocoa_LIBRARY}
	146	+ )
	147	+
	148	+ if(NOT TARGET GLUT::GLUT)
	149	+ add_library(GLUT::GLUT UNKNOWN IMPORTED)
	150	+ set_target_properties(GLUT::GLUT PROPERTIES
	151	+ INTERFACE_INCLUDE_DIRECTORIES "${GLUT_INCLUDE_DIR}")
	152	+ if(GLUT_glut_LIBRARY MATCHES "/([^/]+)\\.framework$")
	153	+ set_target_properties(GLUT::GLUT PROPERTIES
	154	+ IMPORTED_LOCATION "${GLUT_glut_LIBRARY}/${CMAKE_MATCH_1}")
	155	+ else()
	156	+ set_target_properties(GLUT::GLUT PROPERTIES
	157	+ IMPORTED_LOCATION "${GLUT_glut_LIBRARY}")
	158	+ endif()
	159	+
	160	+ if(TARGET GLUT::Xmu)
	161	+ set_property(TARGET GLUT::GLUT APPEND
	162	+ PROPERTY INTERFACE_LINK_LIBRARIES GLUT::Xmu)
	163	+ endif()
	164	+
	165	+ if(TARGET GLUT::Xi)
	166	+ set_property(TARGET GLUT::GLUT APPEND
	167	+ PROPERTY INTERFACE_LINK_LIBRARIES GLUT::Xi)
	168	+ endif()
	169	+
	170	+ if(TARGET GLUT::Cocoa)
	171	+ set_property(TARGET GLUT::GLUT APPEND
	172	+ PROPERTY INTERFACE_LINK_LIBRARIES GLUT::Cocoa)
	173	+ endif()
	174	+ endif()
	175	+
	176	+ #The following deprecated settings are for backwards compatibility with CMake1.4
	177	+ set (GLUT_LIBRARY ${GLUT_LIBRARIES})
	178	+ set (GLUT_INCLUDE_PATH ${GLUT_INCLUDE_DIR})
	179	+endif()
	180	+
	181	+mark_as_advanced(
	182	+ GLUT_INCLUDE_DIR
	183	+ GLUT_glut_LIBRARY
	184	+ GLUT_Xmu_LIBRARY
	185	+ GLUT_Xi_LIBRARY
	186	+ )
...	...

FindSTIM.cmake 0 → 100644

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	1	+++ a/FindSTIM.cmake
	1	+include(FindPackageHandleStandardArgs)
	2	+
	3	+set(STIM_INCLUDE_DIR $ENV{STIMLIB_PATH})
	4	+
	5	+find_package_handle_standard_args(STIM DEFAULT_MSG STIM_INCLUDE_DIR)
	6	+
	7	+if(STIM_FOUND)
	8	+ set(STIM_INCLUDE_DIRS ${STIM_INCLUDE_DIR})
	9	+endif()
0	10	\ No newline at end of file
...	...

data/00_GT.obj 0 → 100644

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	1	+++ a/data/00_GT.obj
	1	+v 99 677 -55
	2	+v 229 510 -30
	3	+v 57 347 50
	4	+v 344 724 5
	5	+v 581 361 0
	6	+v 341 199 0
	7	+v 757 377 -10
	8	+v 981 152 40
	9	+v 793 508 -30
	10	+v 941 600 30
	11	+v 647 738 20
	12	+v 88 563 0
	13	+v 181 372 0
	14	+v 316 596 -5
	15	+v 385 425 0
	16	+v 481 165 7
	17	+v 574 223 -8
	18	+v 818 229 0
	19	+v 679 601 -11
	20	+v 400 500 50
	21	+l 1 12 2
	22	+l 3 13 2
	23	+l 2 14
	24	+l 14 4
	25	+l 2 15 5
	26	+l 6 16 17 5
	27	+l 5 7
	28	+l 8 18 7
	29	+l 7 9
	30	+l 9 10
	31	+l 9 19 11
	32	+l 14 20 5
...	...

data/h1_GT.obj 0 → 100644

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Changes suppressed. Click to show

	1	+++ a/data/h1_GT.obj
	1	+#vertex positions
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	1788	+v 218.399 251.329 276.421
	1789	+v 220.799 254.81 277.974
	1790	+v 225.599 258.013 281.041
	1791	+v 229.199 259.201 279.381
	1792	+v 233.999 259.727 277.464
	1793	+v 238.799 262.533 277.932
	1794	+v 243.599 265.043 278.941
	1795	+v 248.399 266.686 278.925
	1796	+v 252.599 269.376 283.183
	1797	+v 258 272.318 285.336
	1798	+v 262.2 276.096 287.673
	1799	+v 267.6 279.719 288.213
	1800	+v 273.6 281.825 287.13
	1801	+v 278.4 283.942 286.575
	1802	+v 285 286.769 286.336
	1803	+v 286.2 295.525 283.234
	1804	+v 289.8 300.026 282.112
	1805	+v 292.8 301.961 278.91
	1806	+v 295.8 304.894 278.521
	1807	+v 275.4 279.312 289.238
	1808	+v 275.4 275.408 294.023
	1809	+v 277.2 272.942 295.368
	1810	+v 185.148 264.303 252
	1811	+v 182.382 268.783 247
	1812	+v 179.495 271.068 242
	1813	+v 176.027 273.553 237
	1814	+v 173.066 273.658 232
	1815	+v 168.286 276.178 225
	1816	+v 161.323 276.51 217
	1817	+v 151.378 280.806 209
	1818	+v 144.16 282.82 202
	1819	+v 138.055 287.064 195
	1820	+v 128.332 287.139 190
	1821	+v 120.514 289.804 185
	1822	+v 111.858 294.754 180
	1823	+v 107.998 296.593 178.947
	1824	+v 103.798 298.984 175.494
	1825	+v 98.9982 301.485 173.081
	1826	+v 86.3983 304.498 173.245
	1827	+v 80.9983 305.084 172.702
	1828	+v 74.3983 304.212 170.259
	1829	+v 68.9984 305.777 170.176
	1830	+v 61.7984 306.044 167.592
	1831	+v 122.949 284.401 185.614
	1832	+v 122.19 280.801 177.853
	1833	+v 117.582 277.201 170.403
	1834	+v 116.973 275.143 167
	1835	+v 116.221 275.062 162
	1836	+v 112.601 273.7 157
	1837	+v 110.993 274.103 152
	1838	+v 108.193 273.163 145
	1839	+v 106.105 272.59 139
	1840	+v 102.968 271.683 133
	1841	+v 101.396 270.26 125
	1842	+v 99.3167 270.897 117
	1843	+v 95.1954 267.206 110
	1844	+v 92.6608 266.918 104
	1845	+v 89.2568 266.264 95
	1846	+v 85.5769 264.928 86
	1847	+v 82.0056 261.512 77
	1848	+v 77.671 260.11 69
	1849	+v 73.8516 260.579 60
	1850	+v 71.6249 260.903 51
	1851	+v 69.0208 259.097 42
	1852	+v 67.7465 260.215 34
	1853	+v 64.9391 260.503 23
	1854	+v 62.5528 260.33 14
	1855	+v 60.5939 262.617 6
	1856	+v 60.5357 256.379 15
	1857	+v 57.4051 255.171 12
	1858	+v 53.8174 252.497 9
	1859	+v 51.3963 250.627 6
	1860	+v 49.2098 249.701 3
	1861	+v 47.5727 248.739 1
	1862	+v 68.3956 258.709 11
	1863	+v 71.5256 258.269 7
	1864	+v 76.346 257.908 3
	1865	+v 77.8084 257.883 1
	1866	+v 77.9768 257.316 4
	1867	+v 81.0428 256.497 8
	1868	+v 82.7989 253.885 12
	1869	+v 84.0428 252.159 17
	1870	+v 87.4628 249.165 22
	1871	+v 93.0049 247.035 24
	1872	+v 96.4206 246.089 26
	1873	+v 100.805 244.818 30
	1874	+v 106.745 244.247 32
	1875	+v 114.319 244.708 33
	1876	+v 119.015 243.966 34
	1877	+v 123.199 243.542 35
	1878	+v 127.286 239.718 37
	1879	+v 129.564 235.835 39
	1880	+v 131.983 231.31 42
	1881	+v 130.666 225.436 41
	1882	+v 128.791 221.791 40
	1883	+v 124.658 217.027 42
	1884	+v 119.465 212.43 44
	1885	+v 114.976 206.401 43.4292
	1886	+v 111.612 202.201 43.9975
	1887	+v 107.515 196.8 42.3773
	1888	+v 103.786 192 40.8822
	1889	+v 99.2483 188.4 36.4456
	1890	+v 93.5752 183.6 32.1504
	1891	+v 88.6246 179.4 29.2641
	1892	+v 82.0981 175.2 26.1755
	1893	+v 77.0029 171.996 24
	1894	+v 71.212 167.739 20
	1895	+v 65.0263 165.258 16
	1896	+v 60.8201 163.05 12
	1897	+v 58.4613 163.427 9
	1898	+v 49.1133 154.364 3
	1899	+v 42.6667 147.903 1
	1900	+v 40.2279 141.793 5
	1901	+v 36.8895 136.215 8
	1902	+v 32.1676 132.275 12
	1903	+v 27.3792 129.539 16
	1904	+v 19.3056 124.751 19
	1905	+v 10.6013 119.029 21
	1906	+v 5.17508 116.428 23
	1907	+v 3.30234 111.95 26
	1908	+v 9.21675 109.293 25
	1909	+v 10.6558 107.406 27
	1910	+v 14.0942 105.271 32
	1911	+v 17.5952 102.478 37
	1912	+v 19.864 96.1645 39
	1913	+v 23.0934 91.6027 43
	1914	+v 25.3288 83.7556 48
	1915	+v 29.1809 76.6086 53
	1916	+v 32.2133 69.4116 59
	1917	+v 28.0855 64.3669 65
	1918	+v 23.1172 60.7388 70
	1919	+v 23.5734 62.1096 75
	1920	+v 23.7443 65.0447 82
	1921	+v 21.6709 67.2925 89
	1922	+v 19.7961 70.7334 92
	1923	+v 18.2902 75.3554 94
	1924	+v 23.2526 79.6358 94
	1925	+v 31.0674 81.2472 95
	1926	+v 42.7256 85.9956 98
	1927	+v 47.2457 89.4619 104
	1928	+v 50.3099 96.8022 109
	1929	+v 50.7873 103.761 114
	1930	+v 51.783 108.646 119
	1931	+v 51.3476 112.457 123
	1932	+v 46.9875 114.746 125
	1933	+v 293.956 169.117 117
	1934	+v 293.448 172.749 122
	1935	+v 292.714 179.238 127
	1936	+v 289.019 181.432 128
	1937	+v 280.559 183.853 130
	1938	+v 271.488 184.35 132
	1939	+v 265.8 184.505 133.822
	1940	+v 258 183.401 135.672
	1941	+v 252.599 180.135 134.477
	1942	+v 244.799 175.103 135.03
	1943	+v 239.999 168.18 132.079
	1944	+v 239.399 164.375 128.156
	1945	+v 238.199 160.64 126.847
	1946	+v 236.999 157.089 123.199
	1947	+v 235.199 153.936 120.545
	1948	+v 233.399 151.948 118.12
	1949	+v 264.6 204.084 142.76
	1950	+v 267 202.736 141.92
	1951	+v 270 204.066 142.025
	1952	+v 273 203.075 140.712
	1953	+v 276 202.796 139.549
	1954	+v 279 203.601 138.282
	1955	+v 282 200.913 137.02
	1956	+v 285 201.133 135.028
	1957	+v 288 200.615 133.567
	1958	+v 291 199.875 131.113
	1959	+v 294 197.37 125.747
	1960	+v 297 193.384 121.386
	1961	+v 300 190.033 117.815
	1962	+v 303 184.507 115.083
	1963	+v 306 182.768 113.492
	1964	+v 248.999 222.344 124.697
	1965	+v 251.999 223.181 125.181
	1966	+v 254.999 222.614 125.193
	1967	+v 258 225.178 124.012
	1968	+v 261 226.335 122.377
	1969	+v 264 227.177 122.948
	1970	+v 267 227.937 121.613
	1971	+v 270 229.88 119.603
	1972	+v 272.4 230.619 119.163
	1973	+v 274.8 230.682 118.492
	1974	+v 277.2 232.876 117.872
	1975	+v 279.6 236.082 119.889
	1976	+v 282.6 237.848 121.315
	1977	+v 285 240.357 123.081
	1978	+v 286.2 244.646 132.11
	1979	+v 288 250.298 135.246
	1980	+v 290.4 254.308 135.356
	1981	+v 285.6 199.131 208.212
	1982	+v 280.8 200.957 209.486
	1983	+v 277.2 200.441 206.509
	1984	+v 274.2 198.244 205.012
	1985	+v 270 199.849 206.114
	1986	+v 273.054 195.599 202.869
	1987	+v 274.852 192.599 202.831
	1988	+v 274.713 188.399 201.572
	1989	+v 274.787 184.199 201.162
	1990	+v 276.997 179.999 198.793
	1991	+v 277.888 175.199 199.725
	1992	+v 276.62 170.999 198.749
	1993	+v 280.8 167.372 197.929
	1994	+v 283.8 165.919 196.817
	1995	+v 288 163.925 193.593
	1996	+v 289.2 161.752 185.894
	1997	+v 290.4 159.669 177.289
	1998	+v 289.2 158.829 171.515
	1999	+v 291.6 156.101 165.746
	2000	+v 294 155.259 163.425
	2001	+v 297 152.613 157.863
	2002	+v 299.4 153.586 155.382
	2003	+v 301.2 152.56 154.996
	2004	+v 304.2 152.153 157.037
	2005	+v 306.6 150.332 159.468
	2006	+v 300 155.728 157.483
	2007	+v 301.8 159.278 157.773
	2008	+v 304.2 159.117 158.344
	2009	+v 306.6 159.698 157.441
	2010	+v 300.6 151.391 151.943
	2011	+v 303.6 149.302 149.301
	2012	+v 306 146.466 145.885
	2013	+v 306.6 140.92 145.07
	2014	+v 281.4 168.767 200.034
	2015	+v 283.8 170.614 201.122
	2016	+v 286.2 169.321 202.232
	2017	+v 288.6 169.23 200.73
	2018	+v 291 166.594 202.194
	2019	+v 293.4 164.662 201.531
	2020	+v 295.8 163.115 201.517
	2021	+v 298.2 161.893 202.699
	2022	+v 300 161.049 204.022
	2023	+v 301.8 159.791 205.271
	2024	+v 304.2 158.079 207.481
	2025	+v 306.6 156.756 210.298
	2026	+v 272.4 185.021 203.327
	2027	+v 270 185.594 205.031
	2028	+v 266.4 184.821 206.189
	2029	+v 262.8 183.513 207.867
	2030	+v 258 181.039 207.365
	2031	+v 254.399 177.882 212.261
	2032	+v 249.599 173.596 214.447
	2033	+v 248.399 172.614 221.356
	2034	+v 245.999 172.989 226.914
	2035	+v 243.599 171.001 233.234
	2036	+v 242.999 171.757 242.674
	2037	+v 245.399 175.758 249.567
	2038	+v 247.199 180.286 260.891
	2039	+v 249.599 182.754 267.289
	2040	+v 251.399 183.333 266.549
	2041	+v 253.799 185.12 267.999
	2042	+v 256.199 185.756 266.675
	2043	+v 258.6 185.068 266.317
	2044	+v 261.6 185.996 268.199
	2045	+v 265.8 187.451 270.774
	2046	+v 269.4 191.905 272.07
	2047	+v 274.2 193.585 275.396
	2048	+v 278.4 194.553 283.142
	2049	+v 282.6 194.858 287.749
	2050	+v 286.8 194.172 295.085
	2051	+v 248.999 171.611 211.439
	2052	+v 247.199 166.917 211.496
	2053	+v 244.199 164.519 211.633
	2054	+v 239.399 160.665 210.434
	2055	+v 235.199 154.879 206.825
	2056	+v 229.199 151.274 206.192
	2057	+v 223.799 144.166 205.741
	2058	+v 218.999 136.952 205.584
	2059	+v 214.199 134.804 208.202
	2060	+v 209.999 130.948 211.342
	2061	+v 206.399 126.608 216.406
	2062	+v 246.599 165.651 208.824
	2063	+v 248.399 165.207 206.53
	2064	+v 250.799 161.959 203.48
	2065	+v 252.599 161.55 203.256
	2066	+v 253.799 160.177 202.256
	2067	+v 256.799 157.491 201.563
	2068	+v 259.8 154.4 202.413
	2069	+v 262.8 153.658 203.779
	2070	+v 265.8 152.062 207.14
	2071	+v 268.2 151.812 210.202
	2072	+v 270 151.562 214.436
	2073	+v 272.4 152.258 219.362
	2074	+v 275.4 154.72 223.517
	2075	+v 277.8 156.213 226.421
	2076	+v 280.8 156.826 228.141
	2077	+v 285.6 157.547 231.524
	2078	+v 290.4 157.818 233.961
	2079	+v 295.2 156.82 235.486
	2080	+v 300 157.921 237.468
	2081	+v 303.6 158.096 237.631
	2082	+v 268.2 86.9667 76.6378
	2083	+v 270.6 85.3182 77.3077
	2084	+v 273 87.4782 75.6635
	2085	+v 275.4 88.3456 75.8503
	2086	+v 278.4 88.714 76.7204
	2087	+v 281.4 87.4129 76.2088
	2088	+v 284.4 87.79 77.1006
	2089	+v 286.8 88.0237 78.2113
	2090	+v 289.2 88.2574 79.3221
	2091	+v 291.6 88.8573 81.0148
	2092	+v 294 90.0653 81.8321
	2093	+v 296.4 91.9862 83.8035
	2094	+v 298.8 91.6789 85.2896
	2095	+v 301.2 94.1769 86.3903
	2096	+v 303.6 96.2954 86.9252
	2097	+v 306 97.6891 86.3396
	2098	+v 262.2 76.4817 73.9553
	2099	+v 264.6 74.3001 75.0297
	2100	+v 267 73.9859 73.862
	2101	+v 269.4 71.4869 71.1886
	2102	+v 271.8 70.8054 69.4557
	2103	+v 274.2 66.6119 68.5593
	2104	+v 276 65.6319 68.0986
	2105	+v 278.4 268.991 170.522
	2106	+v 280.2 264.895 169.797
	2107	+v 281.4 264.56 167.233
	2108	+v 271.8 104.795 164.526
	2109	+v 273.6 105.702 164.403
	2110	+v 275.4 106.042 164.616
	2111	+v 277.8 106.571 164.593
	2112	+v 280.2 106.302 167.842
	2113	+v 282.6 107.256 169.951
	2114	+v 285 104.054 171.725
	2115	+v 287.4 103.615 171.891
	2116	+v 289.8 102.97 171.018
	2117	+v 292.2 100.931 172.155
	2118	+v 294.6 100.417 172.793
	2119	+v 297 104.373 175.801
	2120	+v 299.4 111.64 179.836
	2121	+v 301.8 114.411 183.387
	2122	+v 304.2 116.556 183.901
	2123	+v 306.6 118.05 185.155
	2124	+v 291 97.0917 171.521
	2125	+v 288.6 91.2891 167.917
	2126	+v 286.2 87.3878 165.887
	2127	+v 283.2 84.968 163.595
	2128	+v 279 82.8963 161.894
	2129	+v 276 80.0948 159.307
	2130	+v 271.8 77.2644 155.36
	2131	+v 267.6 75.8257 151.364
	2132	+v 263.4 73.65 146.557
	2133	+v 259.2 71.1575 141.08
	2134	+v 257.4 69.7224 135.264
	2135	+v 255.763 66.3391 129
	2136	+v 255.696 62.5175 124
	2137	+v 256.174 59.8454 120
	2138	+v 255.977 57.6535 116
	2139	+v 257.105 52.8438 112
	2140	+v 258.6 49.4926 108.821
	2141	+v 261 46.6326 109.167
	2142	+v 263.4 43.0326 108.472
	2143	+v 266.4 42.5532 108.699
	2144	+v 268.8 41.0145 109.507
	2145	+v 271.2 38.1672 109.451
	2146	+v 269.4 32.5938 103.992
	2147	+v 266.4 31.5008 96.0399
	2148	+v 262.8 29.5445 89.4406
	2149	+v 260.4 28.827 82.3549
	2150	+v 258.6 24.1284 76.1159
	2151	+v 261.6 19.4328 70.5552
	2152	+v 264 14.7927 68.663
	2153	+v 266.4 12.6854 67.6084
	2154	+v 269.4 10.7503 66.4156
	2155	+v 272.4 11.4958 65.6128
	2156	+v 275.4 12.8193 64.6095
	2157	+v 277.8 14.1293 64.3975
	2158	+v 280.8 13.8768 66.3629
	2159	+v 283.2 16.9576 72.4747
	2160	+v 285.6 17.5615 73.5024
	2161	+v 288 20.5218 77.9207
	2162	+v 290.4 21.0948 78.9315
	2163	+v 292.8 22.2941 81.331
	2164	+v 295.2 22.7467 85.9124
	2165	+v 297.6 24.4845 88.0638
	2166	+v 300 25.2021 91.1979
	2167	+v 301.2 28.8964 97.8924
	2168	+v 302.4 29.4392 100.301
	2169	+v 303.6 29.5206 99.4083
	2170	+v 305.4 31.0971 105.689
	2171	+v 306.6 31.1637 111.307
	2172	+v 243.38 9.16297 103
	2173	+v 245.244 6.62384 107
	2174	+v 246.632 8.86877 111
	2175	+v 247.107 7.52203 115
	2176	+v 248.828 8.89141 119
	2177	+v 250.534 9.15767 123
	2178	+v 251.098 7.85085 127
	2179	+v 254.273 9.28031 131
	2180	+v 257.481 11.7513 135
	2181	+v 256.867 12.0133 137
	2182	+v 258.531 16.8922 141
	2183	+v 258.757 18.5089 145
	2184	+v 258.08 25.9423 149
	2185	+v 256.807 30.5722 151
	2186	+v 256.383 35.8497 152
	2187	+v 257.314 40.0965 153
	2188	+v 255.687 41.7751 154
	2189	+v 254.76 44.5939 156
	2190	+v 255.958 46.6611 158
	2191	+v 255.035 47.4743 160
	2192	+v 255.444 50.0582 163
	2193	+v 255.855 52.6198 166
	2194	+v 255.005 54.9322 169
	2195	+v 251.53 56.8112 172
	2196	+v 247.559 59.7063 176
	2197	+v 244.776 58.7671 180
	2198	+v 242.895 57.5039 183
	2199	+v 242.803 57.093 186
	2200	+v 240.838 59.6884 190
	2201	+v 241.351 61.4287 194
	2202	+v 241.024 63.7351 197
	2203	+v 241.978 63.9453 201
	2204	+v 243.558 62.9749 205
	2205	+v 242.897 61.4343 209
	2206	+v 243.594 59.793 212
	2207	+v 242.313 56.0703 215
	2208	+v 241.523 52.5404 218
	2209	+v 239.711 48.1638 220
	2210	+v 238.033 43.9624 217
	2211	+v 235.637 39.5639 213
	2212	+v 234.083 35.4288 209
	2213	+v 230.928 32.8404 205
	2214	+v 229.226 29.039 201
	2215	+v 227.218 26.0825 197
	2216	+v 227.581 24.0301 193
	2217	+v 228.696 15.7205 189
	2218	+v 226.453 11.5109 185
	2219	+v 226.451 7.89009 181
	2220	+v 224.687 3.65469 177
	2221	+v 224.882 0.972435 177
	2222	+v 260.4 10.6487 139.867
	2223	+v 262.8 10.0331 143.057
	2224	+v 265.2 9.51656 146.906
	2225	+v 267.6 10.1377 151.436
	2226	+v 270 6.29838 156.953
	2227	+v 272.4 5.14353 162.588
	2228	+v 274.8 4.87732 168.419
	2229	+v 277.2 8.37682 174.968
	2230	+v 279.6 8.38372 180.948
	2231	+v 282 8.89115 184.508
	2232	+v 284.4 10.7278 189.079
	2233	+v 286.8 10.5771 191.51
	2234	+v 289.2 12.2889 194.757
	2235	+v 291.6 16.8861 200.17
	2236	+v 294 17.739 211.245
	2237	+v 292.886 16.0831 215
	2238	+v 292.998 15.4288 219
	2239	+v 292.13 14.6889 223
	2240	+v 292.647 14.4383 226
	2241	+v 297.316 15.8786 230
	2242	+v 302.042 18.7122 234
	2243	+v 306 20.2686 236.799
	2244	+v 289.8 12.2596 222.266
	2245	+v 287.4 9.65829 222.961
	2246	+v 285 8.61662 220.685
	2247	+v 282.6 6.58747 217.905
	2248	+v 280.2 6.1481 216.47
	2249	+v 277.8 6.60841 214.232
	2250	+v 275.4 2.07591 212.15
	2251	+v 273 1.96164 210.353
	2252	+v 257.4 52.8439 259.373
	2253	+v 256.695 51.3034 261
	2254	+v 259.249 49.4048 264
	2255	+v 261.803 47.5186 267
	2256	+v 263.045 45.7757 271
	2257	+v 265.361 42.9142 275
	2258	+v 268.458 40.4525 279
	2259	+v 270.05 36.7398 283
	2260	+v 273.752 30.9917 284
	2261	+v 276.446 27.5733 283
	2262	+v 274.158 30.264 297
	2263	+v 276.133 27.1189 293
	2264	+v 275.672 26.5685 288
	2265	+v 277.308 27.1853 284
	2266	+v 279.577 24.4832 280
	2267	+v 283.744 22.0512 275
	2268	+v 286.164 17.7417 271
	2269	+v 288.438 12.6 267
	2270	+v 286.339 9.09343 263
	2271	+v 286.051 5.6373 259
	2272	+v 288.044 2.82865 255
	2273	+v 286.203 98.6413 126
	2274	+v 290.566 97.3652 122
	2275	+v 294.886 96.1022 118
	2276	+v 300.468 94.5307 114
	2277	+v 303.577 92.6265 110
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...	...

data/h2_GT.obj 0 → 100644

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	1680	+v 270.813 298.792 103
	1681	+v 269.336 299.076 108
	1682	+v 269.861 300.587 113
	1683	+v 270.186 299.578 120
	1684	+v 272.672 298.039 127
	1685	+v 275.563 296.965 133
	1686	+v 273.74 296.385 140
	1687	+v 272.11 298.645 146
	1688	+v 268.781 300.138 153
	1689	+v 264.989 301.48 161
	1690	+v 259.713 303.882 168
	1691	+v 258.348 305.748 170
	1692	+v 287.307 265.091 108
	1693	+v 288.065 261.655 106
	1694	+v 289.521 256.281 105
	1695	+v 288.696 254.655 103
	1696	+v 289.047 252.491 99
	1697	+v 288.061 250.257 96
	1698	+v 285.639 246.739 92
	1699	+v 281.627 243.171 87
	1700	+v 277.478 238.487 83
	1701	+v 276.06 234.271 79
	1702	+v 276.296 231.466 76
	1703	+v 292.167 256.069 107
	1704	+v 294.484 255.27 114
	1705	+v 295.052 253.215 122
	1706	+v 293.505 254.333 129
	1707	+v 290.73 257.362 139
	1708	+v 288.281 260.111 146
	1709	+v 286.085 262.932 157
	1710	+v 283.717 263.294 165
	1711	+v 283.964 261.342 173
	1712	+v 283.837 258.591 180
	1713	+v 284.64 256.068 187
	1714	+v 282.783 254.317 193
	1715	+v 282.249 248.872 196
	1716	+v 277.25 239.505 199
	1717	+v 279.371 230.165 199
	1718	+v 280.925 225.205 197
	1719	+v 282.273 218.97 195
	1720	+v 285.604 210.304 193
	1721	+v 289.259 202.632 191
	1722	+v 290.657 200.227 186
	1723	+v 290.894 198.783 181
	1724	+v 295.817 195.829 177
	1725	+v 300.739 193.752 181
	1726	+v 303.042 194.333 183
	1727	+v 305.315 192.994 186
	1728	+v 290.178 201.207 193
	1729	+v 290.23 200.05 197
	1730	+v 290.017 198.563 202
	1731	+v 290.964 197.149 207
	1732	+v 295.46 197.889 209
	1733	+v 300.453 199.301 212
	1734	+v 306.223 202.644 214
	1735	+v 306.611 206.569 217
	1736	+v 301.231 219.531 224
	1737	+v 304.404 215.874 221
	1738	+v 293.707 247.73 96
	1739	+v 298.247 247.913 99
	1740	+v 301.552 245.794 101
	1741	+v 304.928 245.02 103
	1742	+v 305.772 245.066 105
	1743	+v 275.928 200.519 97
	1744	+v 271.863 202.921 94
	1745	+v 265.801 204.202 91
	1746	+v 261.298 208.104 94
	1747	+v 258.054 209.528 98
	1748	+v 255.586 210.606 102
	1749	+v 247.933 214.113 106
	1750	+v 242.219 218.801 108
	1751	+v 237.853 223.332 110
	1752	+v 242.288 227.568 112
	1753	+v 207.678 279.364 9
	1754	+v 209.249 279.573 4
	1755	+v 211.785 278.408 1
	1756	+v 261.995 211.436 161
	1757	+v 262.246 215.377 163
	1758	+v 260.754 220.016 165
	1759	+v 259.965 226.357 168
	1760	+v 259.987 233.775 172
	1761	+v 263.63 240.376 175
	1762	+v 265.093 246.505 173
	1763	+v 264.918 248.7 169
	1764	+v 264.189 250.966 164
	1765	+v 261.764 251.469 157
	1766	+v 259.64 251.476 151
	1767	+v 256.343 251.546 145
	1768	+v 252.722 253.019 143
	1769	+v 249.64 253.97 147
	1770	+v 245.422 255.822 152
	1771	+v 241.41 257.135 157
	1772	+v 241.844 259.076 162
	1773	+v 241.653 260.834 165
	1774	+v 243.375 264.855 168
	1775	+v 245.801 266.185 172
	1776	+v 247.188 270.596 173
	1777	+v 251.232 272.314 175
	1778	+v 252.599 272.993 176.488
	1779	+v 257.4 274.923 176.807
	1780	+v 262.8 275.655 176.514
	1781	+v 270 274.99 175.164
	1782	+v 277.8 269.662 169.725
	1783	+v 254.001 251.18 139
	1784	+v 254.421 248.7 131
	1785	+v 252.839 245.894 122
	1786	+v 251.532 242.478 113
	1787	+v 251.904 234.807 108
	1788	+v 218.399 251.329 276.421
	1789	+v 220.799 254.81 277.974
	1790	+v 225.599 258.013 281.041
	1791	+v 229.199 259.201 279.381
	1792	+v 233.999 259.727 277.464
	1793	+v 238.799 262.533 277.932
	1794	+v 243.599 265.043 278.941
	1795	+v 248.399 266.686 278.925
	1796	+v 252.599 269.376 283.183
	1797	+v 258 272.318 285.336
	1798	+v 262.2 276.096 287.673
	1799	+v 267.6 279.719 288.213
	1800	+v 273.6 281.825 287.13
	1801	+v 278.4 283.942 286.575
	1802	+v 285 286.769 286.336
	1803	+v 286.2 295.525 283.234
	1804	+v 289.8 300.026 282.112
	1805	+v 292.8 301.961 278.91
	1806	+v 295.8 304.894 278.521
	1807	+v 275.4 279.312 289.238
	1808	+v 275.4 275.408 294.023
	1809	+v 277.2 272.942 295.368
	1810	+v 185.148 264.303 252
	1811	+v 182.382 268.783 247
	1812	+v 179.495 271.068 242
	1813	+v 176.027 273.553 237
	1814	+v 173.066 273.658 232
	1815	+v 168.286 276.178 225
	1816	+v 161.323 276.51 217
	1817	+v 151.378 280.806 209
	1818	+v 144.16 282.82 202
	1819	+v 138.055 287.064 195
	1820	+v 128.332 287.139 190
	1821	+v 120.514 289.804 185
	1822	+v 111.858 294.754 180
	1823	+v 107.998 296.593 178.947
	1824	+v 103.798 298.984 175.494
	1825	+v 98.9982 301.485 173.081
	1826	+v 86.3983 304.498 173.245
	1827	+v 80.9983 305.084 172.702
	1828	+v 74.3983 304.212 170.259
	1829	+v 68.9984 305.777 170.176
	1830	+v 61.7984 306.044 167.592
	1831	+v 122.949 284.401 185.614
	1832	+v 122.19 280.801 177.853
	1833	+v 117.582 277.201 170.403
	1834	+v 116.973 275.143 167
	1835	+v 116.221 275.062 162
	1836	+v 112.601 273.7 157
	1837	+v 110.993 274.103 152
	1838	+v 108.193 273.163 145
	1839	+v 106.105 272.59 139
	1840	+v 102.968 271.683 133
	1841	+v 101.396 270.26 125
	1842	+v 99.3167 270.897 117
	1843	+v 95.1954 267.206 110
	1844	+v 92.6608 266.918 104
	1845	+v 89.2568 266.264 95
	1846	+v 85.5769 264.928 86
	1847	+v 82.0056 261.512 77
	1848	+v 77.671 260.11 69
	1849	+v 73.8516 260.579 60
	1850	+v 71.6249 260.903 51
	1851	+v 69.0208 259.097 42
	1852	+v 67.7465 260.215 34
	1853	+v 64.9391 260.503 23
	1854	+v 62.5528 260.33 14
	1855	+v 60.5939 262.617 6
	1856	+v 60.5357 256.379 15
	1857	+v 57.4051 255.171 12
	1858	+v 53.8174 252.497 9
	1859	+v 51.3963 250.627 6
	1860	+v 49.2098 249.701 3
	1861	+v 47.5727 248.739 1
	1862	+v 68.3956 258.709 11
	1863	+v 71.5256 258.269 7
	1864	+v 76.346 257.908 3
	1865	+v 77.8084 257.883 1
	1866	+v 77.9768 257.316 4
	1867	+v 81.0428 256.497 8
	1868	+v 82.7989 253.885 12
	1869	+v 84.0428 252.159 17
	1870	+v 87.4628 249.165 22
	1871	+v 93.0049 247.035 24
	1872	+v 96.4206 246.089 26
	1873	+v 100.805 244.818 30
	1874	+v 106.745 244.247 32
	1875	+v 114.319 244.708 33
	1876	+v 119.015 243.966 34
	1877	+v 123.199 243.542 35
	1878	+v 127.286 239.718 37
	1879	+v 129.564 235.835 39
	1880	+v 131.983 231.31 42
	1881	+v 130.666 225.436 41
	1882	+v 128.791 221.791 40
	1883	+v 124.658 217.027 42
	1884	+v 119.465 212.43 44
	1885	+v 114.976 206.401 43.4292
	1886	+v 111.612 202.201 43.9975
	1887	+v 107.515 196.8 42.3773
	1888	+v 103.786 192 40.8822
	1889	+v 99.2483 188.4 36.4456
	1890	+v 93.5752 183.6 32.1504
	1891	+v 88.6246 179.4 29.2641
	1892	+v 82.0981 175.2 26.1755
	1893	+v 77.0029 171.996 24
	1894	+v 71.212 167.739 20
	1895	+v 65.0263 165.258 16
	1896	+v 60.8201 163.05 12
	1897	+v 58.4613 163.427 9
	1898	+v 49.1133 154.364 3
	1899	+v 42.6667 147.903 1
	1900	+v 40.2279 141.793 5
	1901	+v 36.8895 136.215 8
	1902	+v 32.1676 132.275 12
	1903	+v 27.3792 129.539 16
	1904	+v 19.3056 124.751 19
	1905	+v 10.6013 119.029 21
	1906	+v 5.17508 116.428 23
	1907	+v 3.30234 111.95 26
	1908	+v 9.21675 109.293 25
	1909	+v 10.6558 107.406 27
	1910	+v 14.0942 105.271 32
	1911	+v 17.5952 102.478 37
	1912	+v 19.864 96.1645 39
	1913	+v 23.0934 91.6027 43
	1914	+v 25.3288 83.7556 48
	1915	+v 29.1809 76.6086 53
	1916	+v 32.2133 69.4116 59
	1917	+v 28.0855 64.3669 65
	1918	+v 23.1172 60.7388 70
	1919	+v 23.5734 62.1096 75
	1920	+v 23.7443 65.0447 82
	1921	+v 21.6709 67.2925 89
	1922	+v 19.7961 70.7334 92
	1923	+v 18.2902 75.3554 94
	1924	+v 23.2526 79.6358 94
	1925	+v 31.0674 81.2472 95
	1926	+v 42.7256 85.9956 98
	1927	+v 47.2457 89.4619 104
	1928	+v 50.3099 96.8022 109
	1929	+v 50.7873 103.761 114
	1930	+v 51.783 108.646 119
	1931	+v 51.3476 112.457 123
	1932	+v 46.9875 114.746 125
	1933	+v 293.956 169.117 117
	1934	+v 293.448 172.749 122
	1935	+v 292.714 179.238 127
	1936	+v 289.019 181.432 128
	1937	+v 280.559 183.853 130
	1938	+v 271.488 184.35 132
	1939	+v 265.8 184.505 133.822
	1940	+v 258 183.401 135.672
	1941	+v 252.599 180.135 134.477
	1942	+v 244.799 175.103 135.03
	1943	+v 239.999 168.18 132.079
	1944	+v 239.399 164.375 128.156
	1945	+v 238.199 160.64 126.847
	1946	+v 236.999 157.089 123.199
	1947	+v 235.199 153.936 120.545
	1948	+v 233.399 151.948 118.12
	1949	+v 264.6 204.084 142.76
	1950	+v 267 202.736 141.92
	1951	+v 270 204.066 142.025
	1952	+v 273 203.075 140.712
	1953	+v 276 202.796 139.549
	1954	+v 279 203.601 138.282
	1955	+v 282 200.913 137.02
	1956	+v 285 201.133 135.028
	1957	+v 288 200.615 133.567
	1958	+v 291 199.875 131.113
	1959	+v 294 197.37 125.747
	1960	+v 297 193.384 121.386
	1961	+v 300 190.033 117.815
	1962	+v 303 184.507 115.083
	1963	+v 306 182.768 113.492
	1964	+v 248.999 222.344 124.697
	1965	+v 251.999 223.181 125.181
	1966	+v 254.999 222.614 125.193
	1967	+v 258 225.178 124.012
	1968	+v 261 226.335 122.377
	1969	+v 264 227.177 122.948
	1970	+v 267 227.937 121.613
	1971	+v 270 229.88 119.603
	1972	+v 272.4 230.619 119.163
	1973	+v 274.8 230.682 118.492
	1974	+v 277.2 232.876 117.872
	1975	+v 279.6 236.082 119.889
	1976	+v 282.6 237.848 121.315
	1977	+v 285 240.357 123.081
	1978	+v 286.2 244.646 132.11
	1979	+v 288 250.298 135.246
	1980	+v 290.4 254.308 135.356
	1981	+v 285.6 199.131 208.212
	1982	+v 280.8 200.957 209.486
	1983	+v 277.2 200.441 206.509
	1984	+v 274.2 198.244 205.012
	1985	+v 270 199.849 206.114
	1986	+v 273.054 195.599 202.869
	1987	+v 274.852 192.599 202.831
	1988	+v 274.713 188.399 201.572
	1989	+v 274.787 184.199 201.162
	1990	+v 276.997 179.999 198.793
	1991	+v 277.888 175.199 199.725
	1992	+v 276.62 170.999 198.749
	1993	+v 280.8 167.372 197.929
	1994	+v 283.8 165.919 196.817
	1995	+v 288 163.925 193.593
	1996	+v 289.2 161.752 185.894
	1997	+v 290.4 159.669 177.289
	1998	+v 289.2 158.829 171.515
	1999	+v 291.6 156.101 165.746
	2000	+v 294 155.259 163.425
	2001	+v 297 152.613 157.863
	2002	+v 299.4 153.586 155.382
	2003	+v 301.2 152.56 154.996
	2004	+v 304.2 152.153 157.037
	2005	+v 306.6 150.332 159.468
	2006	+v 300 155.728 157.483
	2007	+v 301.8 159.278 157.773
	2008	+v 304.2 159.117 158.344
	2009	+v 306.6 159.698 157.441
	2010	+v 300.6 151.391 151.943
	2011	+v 303.6 149.302 149.301
	2012	+v 306 146.466 145.885
	2013	+v 306.6 140.92 145.07
	2014	+v 281.4 168.767 200.034
	2015	+v 283.8 170.614 201.122
	2016	+v 286.2 169.321 202.232
	2017	+v 288.6 169.23 200.73
	2018	+v 291 166.594 202.194
	2019	+v 293.4 164.662 201.531
	2020	+v 295.8 163.115 201.517
	2021	+v 298.2 161.893 202.699
	2022	+v 300 161.049 204.022
	2023	+v 301.8 159.791 205.271
	2024	+v 304.2 158.079 207.481
	2025	+v 306.6 156.756 210.298
	2026	+v 272.4 185.021 203.327
	2027	+v 270 185.594 205.031
	2028	+v 266.4 184.821 206.189
	2029	+v 262.8 183.513 207.867
	2030	+v 258 181.039 207.365
	2031	+v 254.399 177.882 212.261
	2032	+v 249.599 173.596 214.447
	2033	+v 248.399 172.614 221.356
	2034	+v 245.999 172.989 226.914
	2035	+v 243.599 171.001 233.234
	2036	+v 242.999 171.757 242.674
	2037	+v 245.399 175.758 249.567
	2038	+v 247.199 180.286 260.891
	2039	+v 249.599 182.754 267.289
	2040	+v 251.399 183.333 266.549
	2041	+v 253.799 185.12 267.999
	2042	+v 256.199 185.756 266.675
	2043	+v 258.6 185.068 266.317
	2044	+v 261.6 185.996 268.199
	2045	+v 265.8 187.451 270.774
	2046	+v 269.4 191.905 272.07
	2047	+v 274.2 193.585 275.396
	2048	+v 278.4 194.553 283.142
	2049	+v 282.6 194.858 287.749
	2050	+v 286.8 194.172 295.085
	2051	+v 248.999 171.611 211.439
	2052	+v 247.199 166.917 211.496
	2053	+v 244.199 164.519 211.633
	2054	+v 239.399 160.665 210.434
	2055	+v 235.199 154.879 206.825
	2056	+v 229.199 151.274 206.192
	2057	+v 223.799 144.166 205.741
	2058	+v 218.999 136.952 205.584
	2059	+v 214.199 134.804 208.202
	2060	+v 209.999 130.948 211.342
	2061	+v 206.399 126.608 216.406
	2062	+v 246.599 165.651 208.824
	2063	+v 248.399 165.207 206.53
	2064	+v 250.799 161.959 203.48
	2065	+v 252.599 161.55 203.256
	2066	+v 253.799 160.177 202.256
	2067	+v 256.799 157.491 201.563
	2068	+v 259.8 154.4 202.413
	2069	+v 262.8 153.658 203.779
	2070	+v 265.8 152.062 207.14
	2071	+v 268.2 151.812 210.202
	2072	+v 270 151.562 214.436
	2073	+v 272.4 152.258 219.362
	2074	+v 275.4 154.72 223.517
	2075	+v 277.8 156.213 226.421
	2076	+v 280.8 156.826 228.141
	2077	+v 285.6 157.547 231.524
	2078	+v 290.4 157.818 233.961
	2079	+v 295.2 156.82 235.486
	2080	+v 300 157.921 237.468
	2081	+v 303.6 158.096 237.631
	2082	+v 268.2 86.9667 76.6378
	2083	+v 270.6 85.3182 77.3077
	2084	+v 273 87.4782 75.6635
	2085	+v 275.4 88.3456 75.8503
	2086	+v 278.4 88.714 76.7204
	2087	+v 281.4 87.4129 76.2088
	2088	+v 284.4 87.79 77.1006
	2089	+v 286.8 88.0237 78.2113
	2090	+v 289.2 88.2574 79.3221
	2091	+v 291.6 88.8573 81.0148
	2092	+v 294 90.0653 81.8321
	2093	+v 296.4 91.9862 83.8035
	2094	+v 298.8 91.6789 85.2896
	2095	+v 301.2 94.1769 86.3903
	2096	+v 303.6 96.2954 86.9252
	2097	+v 306 97.6891 86.3396
	2098	+v 262.2 76.4817 73.9553
	2099	+v 264.6 74.3001 75.0297
	2100	+v 267 73.9859 73.862
	2101	+v 269.4 71.4869 71.1886
	2102	+v 271.8 70.8054 69.4557
	2103	+v 274.2 66.6119 68.5593
	2104	+v 276 65.6319 68.0986
	2105	+v 278.4 268.991 170.522
	2106	+v 280.2 264.895 169.797
	2107	+v 281.4 264.56 167.233
	2108	+v 271.8 104.795 164.526
	2109	+v 273.6 105.702 164.403
	2110	+v 275.4 106.042 164.616
	2111	+v 277.8 106.571 164.593
	2112	+v 280.2 106.302 167.842
	2113	+v 282.6 107.256 169.951
	2114	+v 285 104.054 171.725
	2115	+v 287.4 103.615 171.891
	2116	+v 289.8 102.97 171.018
	2117	+v 292.2 100.931 172.155
	2118	+v 294.6 100.417 172.793
	2119	+v 297 104.373 175.801
	2120	+v 299.4 111.64 179.836
	2121	+v 301.8 114.411 183.387
	2122	+v 304.2 116.556 183.901
	2123	+v 306.6 118.05 185.155
	2124	+v 291 97.0917 171.521
	2125	+v 288.6 91.2891 167.917
	2126	+v 286.2 87.3878 165.887
	2127	+v 283.2 84.968 163.595
	2128	+v 279 82.8963 161.894
	2129	+v 276 80.0948 159.307
	2130	+v 271.8 77.2644 155.36
	2131	+v 267.6 75.8257 151.364
	2132	+v 263.4 73.65 146.557
	2133	+v 259.2 71.1575 141.08
	2134	+v 257.4 69.7224 135.264
	2135	+v 255.763 66.3391 129
	2136	+v 255.696 62.5175 124
	2137	+v 256.174 59.8454 120
	2138	+v 255.977 57.6535 116
	2139	+v 257.105 52.8438 112
	2140	+v 258.6 49.4926 108.821
	2141	+v 261 46.6326 109.167
	2142	+v 263.4 43.0326 108.472
	2143	+v 266.4 42.5532 108.699
	2144	+v 268.8 41.0145 109.507
	2145	+v 271.2 38.1672 109.451
	2146	+v 269.4 32.5938 103.992
	2147	+v 266.4 31.5008 96.0399
	2148	+v 262.8 29.5445 89.4406
	2149	+v 260.4 28.827 82.3549
	2150	+v 258.6 24.1284 76.1159
	2151	+v 261.6 19.4328 70.5552
	2152	+v 264 14.7927 68.663
	2153	+v 266.4 12.6854 67.6084
	2154	+v 269.4 10.7503 66.4156
	2155	+v 272.4 11.4958 65.6128
	2156	+v 275.4 12.8193 64.6095
	2157	+v 277.8 14.1293 64.3975
	2158	+v 280.8 13.8768 66.3629
	2159	+v 283.2 16.9576 72.4747
	2160	+v 285.6 17.5615 73.5024
	2161	+v 288 20.5218 77.9207
	2162	+v 290.4 21.0948 78.9315
	2163	+v 292.8 22.2941 81.331
	2164	+v 295.2 22.7467 85.9124
	2165	+v 297.6 24.4845 88.0638
	2166	+v 300 25.2021 91.1979
	2167	+v 301.2 28.8964 97.8924
	2168	+v 302.4 29.4392 100.301
	2169	+v 303.6 29.5206 99.4083
	2170	+v 305.4 31.0971 105.689
	2171	+v 306.6 31.1637 111.307
	2172	+v 243.38 9.16297 103
	2173	+v 245.244 6.62384 107
	2174	+v 246.632 8.86877 111
	2175	+v 247.107 7.52203 115
	2176	+v 248.828 8.89141 119
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flow.h 0 → 100644

Wrap text Show/Hide comments View file @9191c39

	1	+++ a/flow.h
	1	+#ifndef FLOW3_H
	2	+#define FLOW3_H
	3	+
	4	+#include <algorithm>
	5	+
	6	+//STIM include
	7	+#include <stim/parser/arguments.h>
	8	+#include <stim/visualization/gl_network.h>
	9	+#include <stim/visualization/colormap.h>
	10	+#include <stim/math/matrix.h>
	11	+#include <stim/visualization/gl_aaboundingbox.h>
	12	+#include <stim/ui/progressbar.h>
	13	+#include <stim/grids/image_stack.h>
	14	+
	15	+#ifdef __CUDACC__
	16	+#include <cublas_v2.h>
	17	+#include <stim/cuda/cudatools/error.h>
	18	+#endif
	19	+
	20	+namespace stim {
	21	+ template <typename A, typename B, typename C>
	22	+ struct triple {
	23	+ A first;
	24	+ B second;
	25	+ C third;
	26	+ };
	27	+
	28	+ template <typename T>
	29	+ struct bridge {
	30	+ std::vector<unsigned> v; // vertices' indices
	31	+ std::vector<typename stim::vec3<T> > V; // vertices' coordinates
	32	+ T l; // length
	33	+ T r; // radii
	34	+ T deltaP; // pressure drop
	35	+ T Q; // volume flow rate
	36	+ };
	37	+
	38	+ template <typename T>
	39	+ struct sphere {
	40	+ stim::vec3<T> c; // center of sphere
	41	+ T r; // radii
	42	+ };
	43	+
	44	+ template <typename T>
	45	+ struct cone { // radii changes gradually
	46	+ stim::vec3<T> c1; // center of geometry start hat
	47	+ stim::vec3<T> c2; // center of geometry end hat
	48	+ T r1; // radii at start hat
	49	+ T r2; // radii at end hat
	50	+ };
	51	+
	52	+ template <typename T>
	53	+ struct cuboid {
	54	+ stim::vec3<T> c;
	55	+ T l; // length
	56	+ T w; // width
	57	+ T h; // height
	58	+ };
	59	+
	60	+ /// indicator function
	61	+#ifdef __CUDACC__
	62	+ // for sphere
	63	+ template <typename T>
	64	+ __global__ void inside_sphere(const stim::sphere<T> V, unsigned num, size_t R, T S, unsigned char ptr, unsigned x, unsigned y, unsigned z) {
	65	+
	66	+ unsigned ix = blockDim.x * blockIdx.x + threadIdx.x;
	67	+ unsigned iy = blockDim.y * blockIdx.y + threadIdx.y;
	68	+
	69	+ if (ix >= R[1] \|\| iy >= R[2]) return; // avoid seg-fault
	70	+
	71	+ // find world_pixel coordinates
	72	+ stim::vec3<T> world_pixel;
	73	+ world_pixel[0] = (T)ix * S[1] - x; // translate origin to center of the network
	74	+ world_pixel[1] = (T)iy * S[2] - y;
	75	+ world_pixel[2] = ((T)z - R[3] / 2) * S[3]; // ???center of box minus half width
	76	+
	77	+ float distance = FLT_MAX;
	78	+ float tmp_distance;
	79	+ unsigned idx;
	80	+
	81	+ for (unsigned i = 0; i < num; i++) {
	82	+ tmp_distance = (V[i].c - world_pixel).len();
	83	+ if (tmp_distance <= distance) {
	84	+ distance = tmp_distance;
	85	+ idx = i;
	86	+ }
	87	+ }
	88	+ if (distance <= V[idx].r)
	89	+ ptr[(R[2] - 1 - iy) * R[0] * R[1] + ix * R[0]] = 255;
	90	+ }
	91	+
	92	+ // for cone
	93	+ template <typename T>
	94	+ __global__ void inside_cone(const stim::cone<T> E, unsigned num, size_t R, T S, unsigned char ptr, unsigned x, unsigned y, unsigned z) {
	95	+
	96	+ unsigned ix = blockDim.x * blockIdx.x + threadIdx.x;
	97	+ unsigned iy = blockDim.y * blockIdx.y + threadIdx.y;
	98	+
	99	+ if (ix >= R[1] \|\| iy >= R[2]) return; // avoid segfault
	100	+
	101	+ stim::vec3<T> world_pixel;
	102	+ world_pixel[0] = (T)ix * S[1] - x;
	103	+ world_pixel[1] = (T)iy * S[2] - y;
	104	+ world_pixel[2] = ((T)z - R[3] / 2) * S[3];
	105	+
	106	+ float distance = FLT_MAX;
	107	+ float tmp_distance;
	108	+ float rr; // radii at the surface where projection meets
	109	+
	110	+ for (unsigned i = 0; i < num; i++) { // find the nearest cylinder
	111	+ tmp_distance = ((world_pixel - E[i].c1).cross(world_pixel - E[i].c2)).len() / (E[i].c2 - E[i].c1).len();
	112	+ if (tmp_distance <= distance) {
	113	+ // we only focus on point to line segment
	114	+ // check to see whether projection is lying outside the line segment
	115	+ float a = (world_pixel - E[i].c1).dot((E[i].c2 - E[i].c1).norm());
	116	+ float b = (world_pixel - E[i].c2).dot((E[i].c1 - E[i].c2).norm());
	117	+ float length = (E[i].c1 - E[i].c2).len();
	118	+ if (a <= length && b <= length) { // projection lying inside the line segment
	119	+ distance = tmp_distance;
	120	+ rr = E[i].r1 + (E[i].r2 - E[i].r1) * a / (length); // linear change
	121	+ }
	122	+ }
	123	+ }
	124	+ if (distance <= rr)
	125	+ ptr[(R[2] - 1 - iy) * R[0] * R[1] + ix * R[0]] = 255;
	126	+ }
	127	+
	128	+ // for source bus
	129	+ template <typename T>
	130	+ __global__ void inside_cuboid(const stim::cuboid<T> B, unsigned num, size_t R, T S, unsigned char ptr, unsigned x, unsigned y, unsigned z) {
	131	+
	132	+ unsigned ix = blockDim.x * blockIdx.x + threadIdx.x;
	133	+ unsigned iy = blockDim.y * blockIdx.y + threadIdx.y;
	134	+
	135	+ if (ix >= R[1] \|\| iy >= R[2]) return; // avoid segfault
	136	+
	137	+ stim::vec3<T> world_pixel;
	138	+ world_pixel[0] = (T)ix * S[1] - x;
	139	+ world_pixel[1] = (T)iy * S[2] - y;
	140	+ world_pixel[2] = ((T)z - R[3] / 2) * S[3];
	141	+
	142	+ for (unsigned i = 0; i < num; i++) {
	143	+ bool left_outside = false; // flag indicates point is outside the left bound
	144	+ bool right_outside = false;
	145	+
	146	+ stim::vec3<T> tmp = B[i].c;
	147	+ stim::vec3<T> L = stim::vec3<T>(tmp[0] - B[i].l / 2.0f, tmp[1] - B[i].h / 2.0f, tmp[2] - B[i].w / 2.0f);
	148	+ stim::vec3<T> U = stim::vec3<T>(tmp[0] + B[i].l / 2.0f, tmp[1] + B[i].h / 2.0f, tmp[2] + B[i].w / 2.0f);
	149	+
	150	+ for (unsigned d = 0; d < 3; d++) {
	151	+ if (world_pixel[d] < L[d]) // if the point is less than the minimum bound
	152	+ left_outside = true;
	153	+ if (world_pixel[d] > U[d]) // if the point is greater than the maximum bound
	154	+ right_outside = true;
	155	+ }
	156	+ if (!left_outside && !right_outside)
	157	+ ptr[(R[2] - 1 - iy) * R[0] * R[1] + ix * R[0]] = 255;
	158	+ }
	159	+ }
	160	+#endif
	161	+
	162	+ template <typename T>
	163	+ class flow : public stim::gl_network<T>{
	164	+
	165	+ private:
	166	+
	167	+ unsigned num_edge;
	168	+ unsigned num_vertex;
	169	+
	170	+ enum direction {UP, LEFT, DOWN, RIGHT};
	171	+
	172	+ // calculate the cofactor of elemen[row][col]
	173	+ void get_minor(T src, T dest, int row, int col, int order) {
	174	+
	175	+ // index of element to be copied
	176	+ int rowCount = 0;
	177	+ int colCount = 0;
	178	+
	179	+ for (int i = 0; i < order; i++) {
	180	+ if (i != row) {
	181	+ colCount = 0;
	182	+ for (int j = 0; j < order; j++) {
	183	+ // when j is not the element
	184	+ if (j != col) {
	185	+ dest[rowCount][colCount] = src[i][j];
	186	+ colCount++;
	187	+ }
	188	+ }
	189	+ rowCount++;
	190	+ }
	191	+ }
	192	+ }
	193	+
	194	+ // calculate the det()
	195	+ T determinant(T** mat, int order) {
	196	+
	197	+ // degenate case when n = 1
	198	+ if (order == 1)
	199	+ return mat[0][0];
	200	+
	201	+ T det = 0.0; // determinant value
	202	+
	203	+ // allocate the cofactor matrix
	204	+ T minor = (T)malloc((order - 1) * sizeof(T*));
	205	+ for (int i = 0; i < order - 1; i++)
	206	+ minor[i] = (T)malloc((order - 1) sizeof(T));
	207	+
	208	+
	209	+ for (int i = 0; i < order; i++) {
	210	+
	211	+ // get minor of element(0, i)
	212	+ get_minor(mat, minor, 0, i, order);
	213	+
	214	+ // recursion
	215	+ det += (i % 2 == 1 ? -1.0 : 1.0) * mat[0][i] * determinant(minor, order - 1);
	216	+ }
	217	+
	218	+ // release memory
	219	+ for (int i = 0; i < order - 1; i++)
	220	+ free(minor[i]);
	221	+ free(minor);
	222	+
	223	+ return det;
	224	+ }
	225	+
	226	+ protected:
	227	+
	228	+ using stim::network<T>::E;
	229	+ using stim::network<T>::V;
	230	+ using stim::network<T>::get_start_vertex;
	231	+ using stim::network<T>::get_end_vertex;
	232	+ using stim::network<T>::get_r;
	233	+ using stim::network<T>::get_average_r;
	234	+ using stim::network<T>::get_l;
	235	+
	236	+ T** C; // Conductance
	237	+ std::vector<typename stim::triple<unsigned, unsigned, float> > Q; // volume flow rate
	238	+ std::vector<T> QQ; // Q' vector
	239	+ std::vector<T> pressure; // final pressure
	240	+
	241	+ public:
	242	+
	243	+ std::vector<T> P; // initial pressure
	244	+ std::vector<T> v; // velocity
	245	+ std::vector<typename stim::vec3<T> > main_feeder; // inlet/outlet main feeder
	246	+ std::vector<unsigned> pendant_vertex;
	247	+ std::vector<typename stim::triple<unsigned, unsigned, T> > input; // first one store which vertex, second one stores which edge, third one stores in/out volume flow rate of that vertex
	248	+ std::vector<typename stim::triple<unsigned, unsigned, T> > output;
	249	+ std::vector<typename stim::bridge<T> > inlet; // input bridge
	250	+ std::vector<typename stim::bridge<T> > outlet; // output bridge
	251	+ std::vector<typename stim::sphere<T> > A; // sphere model for making image stack
	252	+ std::vector<typename stim::cone<T> > B; // cone(cylinder) model for making image stack
	253	+ std::vector<typename stim::cuboid<T> > CU; // cuboid model for making image stack
	254	+ stim::gl_aaboundingbox<T> bb; // bounding box
	255	+
	256	+ flow() {} // default constructor
	257	+ ~flow() {
	258	+ for (unsigned i = 0; i < num_vertex; i++)
	259	+ delete[] C[i];
	260	+ delete[] C;
	261	+ }
	262	+
	263	+ void init(unsigned n_e, unsigned n_v) {
	264	+
	265	+ num_edge = n_e;
	266	+ num_vertex = n_v;
	267	+
	268	+ C = new T*[n_v]();
	269	+ for (unsigned i = 0; i < n_v; i++) {
	270	+ C[i] = new T[n_v]();
	271	+ }
	272	+
	273	+ QQ.resize(n_v);
	274	+ P.resize(n_v);
	275	+ pressure.resize(n_v);
	276	+
	277	+ Q.resize(n_e);
	278	+ v.resize(n_e);
	279	+ }
	280	+
	281	+ void clear() {
	282	+
	283	+ for (unsigned i = 0; i < num_vertex; i++) {
	284	+ QQ[i] = 0;
	285	+ pressure[i] = 0;
	286	+ for (unsigned j = 0; j < num_vertex; j++) {
	287	+ C[i][j] = 0;
	288	+ }
	289	+ }
	290	+ main_feeder.clear();
	291	+ input.clear();
	292	+ output.clear();
	293	+ inlet.clear();
	294	+ outlet.clear();
	295	+ }
	296	+
	297	+ // copy radius from cylinder to flow
	298	+ void set_radius(unsigned i, T radius) {
	299	+
	300	+ for (unsigned j = 0; j < num_edge; j++) {
	301	+ if (E[j].v[0] == i)
	302	+ E[j].cylinder<T>::set_r(0, radius);
	303	+ else if (E[j].v[1] == i)
	304	+ E[j].cylinder<T>::set_r(E[j].size() - 1, radius);
	305	+ }
	306	+ }
	307	+
	308	+ // get the radii of vertex i
	309	+ T get_radius(unsigned i) {
	310	+
	311	+ unsigned tmp_e; // edge index
	312	+ unsigned tmp_v; // vertex index in that edge
	313	+ for (unsigned j = 0; j < num_edge; j++) {
	314	+ if (E[j].v[0] == i) {
	315	+ tmp_e = j;
	316	+ tmp_v = 0;
	317	+ }
	318	+ else if (E[j].v[1] == i) {
	319	+ tmp_e = j;
	320	+ tmp_v = E[j].size() - 1;
	321	+ }
	322	+ }
	323	+
	324	+ return E[tmp_e].r(tmp_v);
	325	+ }
	326	+
	327	+ // get the velocity of pendant vertex i
	328	+ T get_velocity(unsigned i) {
	329	+
	330	+ unsigned tmp_e; // edge index
	331	+ for (unsigned j = 0; j < num_edge; j++) {
	332	+ if (E[j].v[0] == i) {
	333	+ tmp_e = j;
	334	+ break;
	335	+ }
	336	+ else if (E[j].v[1] == i) {
	337	+ tmp_e = j;
	338	+ break;
	339	+ }
	340	+ }
	341	+
	342	+ return v[tmp_e];
	343	+ }
	344	+
	345	+ // set pressure at specifi vertex
	346	+ void set_pressure(unsigned i, T value) {
	347	+ P[i] = value;
	348	+ }
	349	+
	350	+ // solve the linear system to get stable flow state
	351	+ void solve_flow(T viscosity) {
	352	+
	353	+ // clear up last time simulation
	354	+ clear();
	355	+
	356	+ // get the pendant vertex indices
	357	+ pendant_vertex = get_boundary_vertex();
	358	+
	359	+ // get bounding box
	360	+ bb = (*this).boundingbox();
	361	+
	362	+ // set the conductance matrix of flow object
	363	+ unsigned start_vertex = 0;
	364	+ unsigned end_vertex = 0;
	365	+ for (unsigned i = 0; i < num_edge; i++) {
	366	+ start_vertex = get_start_vertex(i); // get the start vertex index of current edge
	367	+ end_vertex = get_end_vertex(i); // get the end vertex index of current edge
	368	+
	369	+ C[start_vertex][end_vertex] = -((float)stim::PI * std::pow(get_average_r(i), 4)) / (8 * u * get_l(i));
	370	+
	371	+ C[end_vertex][start_vertex] = C[start_vertex][end_vertex];
	372	+ }
	373	+ // set the diagonal to the negative sum of row element
	374	+ float sum = 0.0;
	375	+ for (unsigned i = 0; i < num_vertex; i++) {
	376	+ for (unsigned j = 0; j < num_vertex; j++) {
	377	+ sum += C[i][j];
	378	+ }
	379	+ C[i][i] = -sum;
	380	+ sum = 0.0;
	381	+ }
	382	+
	383	+ // get the Q' vector QQ
	384	+ // matrix manipulation to zero out the conductance matrix as defined by the boundary values that were enterd
	385	+ for (unsigned i = 0; i < num_vertex; i++) {
	386	+ if (P[i] != 0) { // for every dangle vertex
	387	+ for (unsigned j = 0; j < num_vertex; j++) {
	388	+ if (j == i) {
	389	+ QQ[i] = C[i][i] * P[i];
	390	+ }
	391	+ else {
	392	+ C[i][j] = 0;
	393	+ QQ[j] = QQ[j] - C[j][i] * P[i];
	394	+ C[j][i] = 0;
	395	+ }
	396	+ }
	397	+ }
	398	+ }
	399	+
	400	+ // get the inverse of conductance matrix
	401	+ stim::matrix<float> _C(num_vertex, num_vertex);
	402	+ inversion(C, num_vertex, _C.data());
	403	+
	404	+ // get the pressure in the network
	405	+ for (unsigned i = 0; i < num_vertex; i++) {
	406	+ for (unsigned j = 0; j < num_vertex; j++) {
	407	+ pressure[i] += _C(i, j) * QQ[j];
	408	+ }
	409	+ }
	410	+
	411	+ // get the flow state from known pressure
	412	+ float start_pressure = 0.0;
	413	+ float end_pressure = 0.0;
	414	+ float deltaP = 0.0;
	415	+ for (unsigned i = 0; i < num_edge; i++) {
	416	+ start_vertex = get_start_vertex(i);
	417	+ end_vertex = get_end_vertex(i);
	418	+ start_pressure = pressure[start_vertex]; // get the start vertex pressure of current edge
	419	+ end_pressure = pressure[end_vertex]; // get the end vertex pressure of current edge
	420	+ deltaP = start_pressure - end_pressure; // deltaP = Pa - Pb
	421	+
	422	+ Q[i].first = start_vertex;
	423	+ Q[i].second = end_vertex;
	424	+
	425	+ Q[i].third = ((float)stim::PI * std::pow(get_average_r(i), 4) * deltaP) / (8 * u * get_l(i));
	426	+ v[i] = Q[i].third / ((float)stim::PI * std::pow(get_average_r(i), 2));
	427	+ }
	428	+ }
	429	+
	430	+ // get the brewer color map based on velocity
	431	+ void get_color_map(T& max_v, T& min_v, std::vector<unsigned char>& color, std::vector<unsigned> pendant_vertex) {
	432	+
	433	+ unsigned num_edge = Q.size();
	434	+ unsigned num_vertex = QQ.size();
	435	+
	436	+ // find the absolute maximum velocity and minimum velocity
	437	+ std::vector<float> abs_V(num_edge);
	438	+ for (unsigned i = 0; i < num_edge; i++) {
	439	+ abs_V[i] = std::fabsf(v[i]);
	440	+ }
	441	+
	442	+ max_v = *std::max_element(abs_V.begin(), abs_V.end());
	443	+ min_v = *std::min_element(abs_V.begin(), abs_V.end());
	444	+
	445	+ // get the color map based on velocity range along the network
	446	+ color.clear();
	447	+ if (pendant_vertex.size() == 2 && num_edge - num_vertex + 1 <= 0) // only one inlet and one outlet
	448	+ color.resize(num_edge * 3, (unsigned char)255);
	449	+ else {
	450	+ color.resize(num_edge * 3);
	451	+ stim::cpu2cpu<float>(&abs_V[0], &color[0], num_edge, min_v, max_v, stim::cmBrewer);
	452	+ }
	453	+ }
	454	+
	455	+ // print flow
	456	+ void print_flow() {
	457	+
	458	+ // show the pressure information in console box
	459	+ std::cout << "PRESSURE(g/um/s^2):" << std::endl;
	460	+ for (unsigned i = 0; i < num_vertex; i++) {
	461	+ std::cout << "[" << i << "] " << pressure[i] << std::endl;
	462	+ }
	463	+ // show the flow rate information in console box
	464	+ std::cout << "VOLUME FLOW RATE(um^3/s):" << std::endl;
	465	+ for (unsigned i = 0; i < num_edge; i++) {
	466	+ std::cout << "(" << Q[i].first << "," << Q[i].second << ")" << Q[i].third << std::endl;
	467	+ }
	468	+ }
	469	+
	470	+ /// helper function
	471	+ // find hilbert curve order
	472	+ // @param: current direct length between two vertices
	473	+ // @param: desire length
	474	+ void find_hilbert_order(T l, T d, int &order) {
	475	+
	476	+ bool flag = false;
	477	+ int o = 1;
	478	+ T tmp; // temp of length
	479	+ while (!flag) {
	480	+ // convert from cartesian length to hilbert length
	481	+ // l -> l * (4 ^ order - 1)/(2 ^ order - 1)
	482	+ tmp = l * (std::pow(4, o) - 1) / (std::pow(2, o) - 1);
	483	+ if (tmp >= d)
	484	+ flag = true;
	485	+ else
	486	+ o++;
	487	+ }
	488	+ order = o;
	489	+ }
	490	+
	491	+ void move(unsigned i, T *c, direction dir, T dl, int feeder, bool invert) {
	492	+
	493	+ int cof = (invert) ? -1 : 1;
	494	+
	495	+ switch (dir) {
	496	+ case UP:
	497	+ c[1] += dl;
	498	+ break;
	499	+ case LEFT:
	500	+ c[0] -= cof * dl;
	501	+ break;
	502	+ case DOWN:
	503	+ c[1] -= dl;
	504	+ break;
	505	+ case RIGHT:
	506	+ c[0] += cof * dl;
	507	+ break;
	508	+ }
	509	+
	510	+ stim::vec3<T> tmp;
	511	+ for (unsigned i = 0; i < 3; i++)
	512	+ tmp[i] = c[i];
	513	+
	514	+ if (feeder == 1) // inlet main feeder
	515	+ inlet[i].V.push_back(tmp);
	516	+ else if (feeder == 0) // outlet main feeder
	517	+ outlet[i].V.push_back(tmp);
	518	+ }
	519	+
	520	+ void hilbert_curve(unsigned i, T *c, int order, T dl, int feeder, bool invert, direction dir = DOWN) {
	521	+
	522	+ if (order == 1) {
	523	+ switch (dir) {
	524	+ case UP:
	525	+ move(i, c, DOWN, dl, feeder, invert);
	526	+ move(i, c, RIGHT, dl, feeder, invert);
	527	+ move(i, c, UP, dl, feeder, invert);
	528	+ break;
	529	+ case LEFT:
	530	+ move(i, c, RIGHT, dl, feeder, invert);
	531	+ move(i, c, DOWN, dl, feeder, invert);
	532	+ move(i, c, LEFT, dl, feeder, invert);
	533	+ break;
	534	+ case DOWN:
	535	+ move(i, c, UP, dl, feeder, invert);
	536	+ move(i, c, LEFT, dl, feeder, invert);
	537	+ move(i, c, DOWN, dl, feeder, invert);
	538	+ break;
	539	+ case RIGHT:
	540	+ move(i, c, LEFT, dl, feeder, invert);
	541	+ move(i, c, UP, dl, feeder, invert);
	542	+ move(i, c, RIGHT, dl, feeder, invert);
	543	+ break;
	544	+ }
	545	+
	546	+ }
	547	+ else if (order > 1) {
	548	+ switch (dir) {
	549	+ case UP:
	550	+ hilbert_curve(i, c, order - 1, dl, feeder, invert, LEFT);
	551	+ move(i, c, DOWN, dl, feeder, invert);
	552	+ hilbert_curve(i, c, order - 1, dl, feeder, invert, UP);
	553	+ move(i, c, RIGHT, dl, feeder, invert);
	554	+ hilbert_curve(i, c, order - 1, dl, feeder, invert, UP);
	555	+ move(i, c, UP, dl, feeder, invert);
	556	+ hilbert_curve(i, c, order - 1, dl, feeder, invert, RIGHT);
	557	+ break;
	558	+ case LEFT:
	559	+ hilbert_curve(i, c, order - 1, dl, feeder, invert, UP);
	560	+ move(i, c, RIGHT, dl, feeder, invert);
	561	+ hilbert_curve(i, c, order - 1, dl, feeder, invert, LEFT);
	562	+ move(i, c, DOWN, dl, feeder, invert);
	563	+ hilbert_curve(i, c, order - 1, dl, feeder, invert, LEFT);
	564	+ move(i, c, LEFT, dl, feeder, invert);
	565	+ hilbert_curve(i, c, order - 1, dl, feeder, invert, DOWN);
	566	+ break;
	567	+ case DOWN:
	568	+ hilbert_curve(i, c, order - 1, dl, feeder, invert, RIGHT);
	569	+ move(i, c, UP, dl, feeder, invert);
	570	+ hilbert_curve(i, c, order - 1, dl, feeder, invert, DOWN);
	571	+ move(i, c, LEFT, dl, feeder, invert);
	572	+ hilbert_curve(i, c, order - 1, dl, feeder, invert, DOWN);
	573	+ move(i, c, DOWN, dl, feeder, invert);
	574	+ hilbert_curve(i, c, order - 1, dl, feeder, invert, LEFT);
	575	+ break;
	576	+ case RIGHT:
	577	+ hilbert_curve(i, c, order - 1, dl, feeder, invert, DOWN);
	578	+ move(i, c, LEFT, dl, feeder, invert);
	579	+ hilbert_curve(i, c, order - 1, dl, feeder, invert, RIGHT);
	580	+ move(i, c, UP, dl, feeder, invert);
	581	+ hilbert_curve(i, c, order - 1, dl, feeder, invert, RIGHT);
	582	+ move(i, c, RIGHT, dl, feeder, invert);
	583	+ hilbert_curve(i, c, order - 1, dl, feeder, invert, UP);
	584	+ break;
	585	+ }
	586	+ }
	587	+ }
	588	+
	589	+ void draw_hilbert_curve(unsigned i, T *c, int order, T l, T d, bool upper, int feeder, bool invert) {
	590	+
	591	+ T fragment = (d - l) / ((std::pow(4, order) - 1) / (std::pow(2, order) - 1) - 1); // the length of the opening of cup
	592	+ T dl = fragment / (std::pow(2, order) - 1); // unit cup length
	593	+
	594	+ if (upper)
	595	+ hilbert_curve(i, c, order, dl, feeder, invert, DOWN);
	596	+ else
	597	+ hilbert_curve(i, c, order, dl, feeder, invert, UP);
	598	+ }
	599	+
	600	+ /// render function
	601	+ // find two envelope caps for two spheres
	602	+ // @param cp1, cp2: list of points on the cap
	603	+ // @param center1, center2: center point of cap
	604	+ // @param r1, r2: radii of cap
	605	+ void find_envelope(std::vector<typename stim::vec3<float> > &cp1, std::vector<typename stim::vec3<float> > &cp2, stim::vec3<float> center1, stim::vec3<float> center2, float r1, float r2, GLint subdivision) {
	606	+
	607	+ stim::vec3<float> tmp_d;
	608	+ if (r1 == r2) { // two vertices have the same radius
	609	+ tmp_d = center2 - center1; // calculate the direction vector
	610	+ tmp_d = tmp_d.norm();
	611	+ stim::circle<float> tmp_c; // in order to get zero direction vector
	612	+ tmp_c.rotate(tmp_d);
	613	+
	614	+ stim::circle<float> c1(center1, r1, tmp_d, tmp_c.U);
	615	+ stim::circle<float> c2(center2, r2, tmp_d, tmp_c.U);
	616	+ cp1 = c1.glpoints(subdivision);
	617	+ cp2 = c2.glpoints(subdivision);
	618	+ }
	619	+ else {
	620	+ if (r1 < r2) { // switch index, we always want r1 to be larger than r2
	621	+ stim::vec3<float> tmp_c = center2;
	622	+ center2 = center1;
	623	+ center1 = tmp_c;
	624	+ float tmp_r = r2;
	625	+ r2 = r1;
	626	+ r1 = tmp_r;
	627	+ }
	628	+ tmp_d = center2 - center1; // bigger one points to smaller one
	629	+ tmp_d = tmp_d.norm();
	630	+
	631	+ float D = (center1 - center2).len();
	632	+ stim::vec3<float> exp;
	633	+ exp[0] = (center2[0] * r1 - center1[0] * r2) / (r1 - r2);
	634	+ exp[1] = (center2[1] * r1 - center1[1] * r2) / (r1 - r2);
	635	+
	636	+ stim::vec3<float> t1, t2, t3, t4;
	637	+ t1[2] = t2[2] = center1[2]; // decide the specific plane to work on
	638	+ t3[2] = t4[2] = center2[2];
	639	+
	640	+ // first two
	641	+ t1[0] = pow(r1, 2)*(exp[0] - center1[0]);
	642	+ t1[0] += r1(exp[1] - center1[1])sqrt(pow((exp[0] - center1[0]), 2) + pow((exp[1] - center1[1]), 2) - pow(r1, 2));
	643	+ t1[0] /= (pow((exp[0] - center1[0]), 2) + pow((exp[1] - center1[1]), 2));
	644	+ t1[0] += center1[0];
	645	+
	646	+ t2[0] = pow(r1, 2)*(exp[0] - center1[0]);
	647	+ t2[0] -= r1(exp[1] - center1[1])sqrt(pow((exp[0] - center1[0]), 2) + pow((exp[1] - center1[1]), 2) - pow(r1, 2));
	648	+ t2[0] /= (pow((exp[0] - center1[0]), 2) + pow((exp[1] - center1[1]), 2));
	649	+ t2[0] += center1[0];
	650	+
	651	+ t1[1] = pow(r1, 2)*(exp[1] - center1[1]);
	652	+ t1[1] -= r1(exp[0] - center1[0])sqrt(pow((exp[0] - center1[0]), 2) + pow((exp[1] - center1[1]), 2) - pow(r1, 2));
	653	+ t1[1] /= (pow((exp[0] - center1[0]), 2) + pow((exp[1] - center1[1]), 2));
	654	+ t1[1] += center1[1];
	655	+
	656	+ t2[1] = pow(r1, 2)*(exp[1] - center1[1]);
	657	+ t2[1] += r1(exp[0] - center1[0])sqrt(pow((exp[0] - center1[0]), 2) + pow((exp[1] - center1[1]), 2) - pow(r1, 2));
	658	+ t2[1] /= (pow((exp[0] - center1[0]), 2) + pow((exp[1] - center1[1]), 2));
	659	+ t2[1] += center1[1];
	660	+
	661	+ // check the correctness of the points
	662	+ //float s = (center1[1] - t1[1])(exp[1] - t1[1]) / ((t1[0] - center1[0])(t1[0] - exp[0]));
	663	+ //if (s != 1) { // swap t1[1] and t2[1]
	664	+ // float tmp_t = t2[1];
	665	+ // t2[1] = t1[1];
	666	+ // t1[1] = tmp_t;
	667	+ //}
	668	+
	669	+ // second two
	670	+ t3[0] = pow(r2, 2)*(exp[0] - center2[0]);
	671	+ t3[0] += r2(exp[1] - center2[1])sqrt(pow((exp[0] - center2[0]), 2) + pow((exp[1] - center2[1]), 2) - pow(r2, 2));
	672	+ t3[0] /= (pow((exp[0] - center2[0]), 2) + pow((exp[1] - center2[1]), 2));
	673	+ t3[0] += center2[0];
	674	+
	675	+ t4[0] = pow(r2, 2)*(exp[0] - center2[0]);
	676	+ t4[0] -= r2(exp[1] - center2[1])sqrt(pow((exp[0] - center2[0]), 2) + pow((exp[1] - center2[1]), 2) - pow(r2, 2));
	677	+ t4[0] /= (pow((exp[0] - center2[0]), 2) + pow((exp[1] - center2[1]), 2));
	678	+ t4[0] += center2[0];
	679	+
	680	+ t3[1] = pow(r2, 2)*(exp[1] - center2[1]);
	681	+ t3[1] -= r2(exp[0] - center2[0])sqrt(pow((exp[0] - center2[0]), 2) + pow((exp[1] - center2[1]), 2) - pow(r2, 2));
	682	+ t3[1] /= (pow((exp[0] - center2[0]), 2) + pow((exp[1] - center2[1]), 2));
	683	+ t3[1] += center2[1];
	684	+
	685	+ t4[1] = pow(r2, 2)*(exp[1] - center2[1]);
	686	+ t4[1] += r2(exp[0] - center2[0])sqrt(pow((exp[0] - center2[0]), 2) + pow((exp[1] - center2[1]), 2) - pow(r2, 2));
	687	+ t4[1] /= (pow((exp[0] - center2[0]), 2) + pow((exp[1] - center2[1]), 2));
	688	+ t4[1] += center2[1];
	689	+
	690	+ // check the correctness of the points
	691	+ //s = (center2[1] - t3[1])(exp[1] - t3[1]) / ((t3[0] - center2[0])(t3[0] - exp[0]));
	692	+ //if (s != 1) { // swap t1[1] and t2[1]
	693	+ // float tmp_t = t4[1];
	694	+ // t4[1] = t3[1];
	695	+ // t3[1] = tmp_t;
	696	+ //}
	697	+
	698	+ stim::vec3<float> d1;
	699	+ float dot;
	700	+ float a;
	701	+ float new_r;
	702	+ stim::vec3<float> new_u;
	703	+ stim::vec3<float> new_c;
	704	+
	705	+ // calculate the bigger circle
	706	+ d1 = t1 - center1;
	707	+ dot = d1.dot(tmp_d);
	708	+ a = dot / (r1 * 1) * r1; // a = cos(alpha) * radii
	709	+ new_c = center1 + a * tmp_d;
	710	+ new_r = sqrt(pow(r1, 2) - pow(a, 2));
	711	+ new_u = t1 - new_c;
	712	+
	713	+ stim::circle<float> c1(new_c, new_r, tmp_d, new_u);
	714	+ cp1 = c1.glpoints(subdivision);
	715	+
	716	+ // calculate the smaller circle
	717	+ d1 = t3 - center2;
	718	+ dot = d1.dot(tmp_d);
	719	+ a = dot / (r2 * 1) * r2;
	720	+ new_c = center2 + a * tmp_d;
	721	+ new_r = sqrt(pow(r2, 2) - pow(a, 2));
	722	+ new_u = t3 - new_c;
	723	+
	724	+ stim::circle<float> c2(new_c, new_r, tmp_d, new_u);
	725	+ cp2 = c2.glpoints(subdivision);
	726	+ }
	727	+ }
	728	+
	729	+ // draw solid sphere at every vertex
	730	+ void glSolidSphere(T max_pressure, GLint subdivision) {
	731	+
	732	+ // waste?
	733	+ for (unsigned i = 0; i < num_edge; i++) {
	734	+ for (unsigned j = 0; j < E[i].size(); j++) {
	735	+ if (j == 0) { // for start vertex
	736	+ if (P[E[i].v[0]] != 0) {
	737	+ stim::vec3<float> new_color;
	738	+ new_color[0] = (P[E[i].v[0]] / max_pressure) > 0.5f ? 1.0f : 2.0f * P[E[i].v[0]] / max_pressure; // red
	739	+ new_color[1] = 0.0f; // green
	740	+ new_color[2] = (P[E[i].v[0]] / max_pressure) > 0.5f ? 1.0f - 2.0f * (P[E[i].v[0]] / max_pressure - 0.5f) : 1.0f; // blue
	741	+ glColor3f(new_color[0], new_color[1], new_color[2]);
	742	+ }
	743	+ }
	744	+ else if (j == E[i].size() - 1) { // for end vertex
	745	+ if (P[E[i].v[1]] != 0) {
	746	+ stim::vec3<float> new_color;
	747	+ new_color[0] = (P[E[i].v[1]] / max_pressure) > 0.5f ? 1.0f : 2.0f * P[E[i].v[1]] / max_pressure; // red
	748	+ new_color[1] = 0.0f; // green
	749	+ new_color[2] = (P[E[i].v[1]] / max_pressure) > 0.5f ? 1.0f - 2.0f * (P[E[i].v[1]] / max_pressure - 0.5f) : 1.0f; // blue
	750	+ glColor3f(new_color[0], new_color[1], new_color[2]);
	751	+ }
	752	+ }
	753	+ else
	754	+ glColor3f(0.5f, 0.5f, 0.5f); // gray point
	755	+
	756	+ glPushMatrix();
	757	+ glTranslatef(E[i][j][0], E[i][j][1], E[i][j][2]);
	758	+ glutSolidSphere(get_r(i, j), subdivision, subdivision);
	759	+ glPopMatrix();
	760	+ }
	761	+ }
	762	+ }
	763	+
	764	+ // draw edges as series of cylinders
	765	+ void glSolidCylinder(GLint subdivision, std::vector<unsigned char> color) {
	766	+
	767	+ stim::vec3<float> tmp_d;
	768	+ stim::vec3<float> center1;
	769	+ stim::vec3<float> center2;
	770	+ float r1;
	771	+ float r2;
	772	+ std::vector<typename stim::vec3<float> > cp1(subdivision + 1);
	773	+ std::vector<typename stim::vec3<float> > cp2(subdivision + 1);
	774	+ for (unsigned i = 0; i < num_edge; i++) { // for every edge
	775	+ glEnable(GL_BLEND); // enable color blend
	776	+ glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA); // set blend function
	777	+ glDisable(GL_DEPTH_TEST);
	778	+ glColor4f((float)color[i * 3 + 0] / 255, (float)color[i * 3 + 1] / 255, (float)color[i * 3 + 2] / 255, 0.5f);
	779	+ for (unsigned j = 0; j < E[i].size() - 1; j++) { // for every point on the edge
	780	+ center1 = E[i][j];
	781	+ center2 = E[i][j + 1];
	782	+
	783	+ r1 = get_r(i, j);
	784	+ r2 = get_r(i, j + 1);
	785	+
	786	+ // calculate the envelope caps
	787	+ find_envelope(cp1, cp2, center1, center2, r1, r2, subdivision);
	788	+
	789	+ glBegin(GL_QUAD_STRIP);
	790	+ for (unsigned j = 0; j < cp1.size(); j++) {
	791	+ glVertex3f(cp1[j][0], cp1[j][1], cp1[j][2]);
	792	+ glVertex3f(cp2[j][0], cp2[j][1], cp2[j][2]);
	793	+ }
	794	+ glEnd();
	795	+ }
	796	+ }
	797	+ glFlush();
	798	+ glDisable(GL_BLEND);
	799	+ }
	800	+
	801	+ // draw the flow direction as cone
	802	+ void glSolidCone(GLint subdivision) {
	803	+
	804	+ stim::vec3<T> tmp_d; // direction
	805	+ stim::vec3<T> center; // cone hat center
	806	+ stim::vec3<T> head; // cone hat top
	807	+ stim::circle<T> tmp_c;
	808	+ std::vector<typename stim::vec3<T> > cp;
	809	+ T radius;
	810	+
	811	+ glColor3f(1.0f, 1.0f, 1.0f);
	812	+ for (unsigned i = 0; i < num_edge; i++) { // for every edge
	813	+ for (unsigned j = 0; j < E[i].size() - 1; j++) { // for every point on current edge
	814	+ tmp_d = E[i][j + 1] - E[i][j];
	815	+ tmp_d = tmp_d.norm();
	816	+ center = (E[i][j + 1] + E[i][j]) / 2;
	817	+ tmp_c.rotate(tmp_d);
	818	+ radius = (E[i].r(j + 1) + E[i].r(j)) / 2;
	819	+ if (v[i] > 0) // if flow flows from j to j+1
	820	+ head = center + tmp_d * sqrt(3) * radius;
	821	+ else
	822	+ head = center - tmp_d * sqrt(3) * radius;
	823	+
	824	+ stim::circle<float> c(center, radius, tmp_d, tmp_c.U);
	825	+ cp = c.glpoints(subdivision);
	826	+
	827	+ glBegin(GL_TRIANGLE_FAN);
	828	+ glVertex3f(head[0], head[1], head[2]);
	829	+ for (unsigned k = 0; k < cp.size(); k++)
	830	+ glVertex3f(cp[k][0], cp[k][1], cp[k][2]);
	831	+ glEnd();
	832	+ }
	833	+ }
	834	+ glFlush();
	835	+ }
	836	+
	837	+ // draw main feeder as solid cube
	838	+ void glSolidCuboid(T length = 210.0f, T height = 10.0f) {
	839	+
	840	+ T width;
	841	+ stim::vec3<T> L = bb.A; // get the bottom left corner
	842	+ stim::vec3<T> U = bb.B; // get the top right corner
	843	+ width = U[2] - L[2] + 10.0f;
	844	+
	845	+ glColor3f(1.0f, 1.0f, 1.0f);
	846	+ for (unsigned i = 0; i < main_feeder.size(); i++) {
	847	+ // front face
	848	+ glBegin(GL_QUADS);
	849	+ glVertex3f(main_feeder[i][0] - length / 2, main_feeder[i][1] - height / 2, main_feeder[i][2] - width / 2);
	850	+ glVertex3f(main_feeder[i][0] + length / 2, main_feeder[i][1] - height / 2, main_feeder[i][2] - width / 2);
	851	+ glVertex3f(main_feeder[i][0] + length / 2, main_feeder[i][1] + height / 2, main_feeder[i][2] - width / 2);
	852	+ glVertex3f(main_feeder[i][0] - length / 2, main_feeder[i][1] + height / 2, main_feeder[i][2] - width / 2);
	853	+ glEnd();
	854	+
	855	+ // back face
	856	+ glBegin(GL_QUADS);
	857	+ glVertex3f(main_feeder[i][0] - length / 2, main_feeder[i][1] - height / 2, main_feeder[i][2] + width / 2);
	858	+ glVertex3f(main_feeder[i][0] + length / 2, main_feeder[i][1] - height / 2, main_feeder[i][2] + width / 2);
	859	+ glVertex3f(main_feeder[i][0] + length / 2, main_feeder[i][1] + height / 2, main_feeder[i][2] + width / 2);
	860	+ glVertex3f(main_feeder[i][0] - length / 2, main_feeder[i][1] + height / 2, main_feeder[i][2] + width / 2);
	861	+ glEnd();
	862	+
	863	+ // top face
	864	+ glBegin(GL_QUADS);
	865	+ glVertex3f(main_feeder[i][0] - length / 2, main_feeder[i][1] + height / 2, main_feeder[i][2] - width / 2);
	866	+ glVertex3f(main_feeder[i][0] + length / 2, main_feeder[i][1] + height / 2, main_feeder[i][2] - width / 2);
	867	+ glVertex3f(main_feeder[i][0] + length / 2, main_feeder[i][1] + height / 2, main_feeder[i][2] + width / 2);
	868	+ glVertex3f(main_feeder[i][0] - length / 2, main_feeder[i][1] + height / 2, main_feeder[i][2] + width / 2);
	869	+ glEnd();
	870	+
	871	+ // bottom face
	872	+ glBegin(GL_QUADS);
	873	+ glVertex3f(main_feeder[i][0] - length / 2, main_feeder[i][1] - height / 2, main_feeder[i][2] - width / 2);
	874	+ glVertex3f(main_feeder[i][0] + length / 2, main_feeder[i][1] - height / 2, main_feeder[i][2] - width / 2);
	875	+ glVertex3f(main_feeder[i][0] + length / 2, main_feeder[i][1] - height / 2, main_feeder[i][2] + width / 2);
	876	+ glVertex3f(main_feeder[i][0] - length / 2, main_feeder[i][1] - height / 2, main_feeder[i][2] + width / 2);
	877	+ glEnd();
	878	+
	879	+ // left face
	880	+ glBegin(GL_QUADS);
	881	+ glVertex3f(main_feeder[i][0] - length / 2, main_feeder[i][1] - height / 2, main_feeder[i][2] - width / 2);
	882	+ glVertex3f(main_feeder[i][0] - length / 2, main_feeder[i][1] - height / 2, main_feeder[i][2] + width / 2);
	883	+ glVertex3f(main_feeder[i][0] - length / 2, main_feeder[i][1] + height / 2, main_feeder[i][2] + width / 2);
	884	+ glVertex3f(main_feeder[i][0] - length / 2, main_feeder[i][1] + height / 2, main_feeder[i][2] - width / 2);
	885	+ glEnd();
	886	+
	887	+ // right face
	888	+ glBegin(GL_QUADS);
	889	+ glVertex3f(main_feeder[i][0] + length / 2, main_feeder[i][1] - height / 2, main_feeder[i][2] - width / 2);
	890	+ glVertex3f(main_feeder[i][0] + length / 2, main_feeder[i][1] + height / 2, main_feeder[i][2] - width / 2);
	891	+ glVertex3f(main_feeder[i][0] + length / 2, main_feeder[i][1] + height / 2, main_feeder[i][2] + width / 2);
	892	+ glVertex3f(main_feeder[i][0] + length / 2, main_feeder[i][1] - height / 2, main_feeder[i][2] + width / 2);
	893	+ glEnd();
	894	+ }
	895	+ glFlush();
	896	+ }
	897	+
	898	+ // draw the bridge as lines
	899	+ void line_bridge() {
	900	+
	901	+ for (unsigned i = 0; i < inlet.size(); i++) {
	902	+ glBegin(GL_LINE_STRIP);
	903	+ for (unsigned j = 0; j < inlet[i].V.size(); j++)
	904	+ glVertex3f(inlet[i].V[j][0], inlet[i].V[j][1], inlet[i].V[j][2]);
	905	+ glEnd();
	906	+ }
	907	+ for (unsigned i = 0; i < outlet.size(); i++) {
	908	+ glBegin(GL_LINE_STRIP);
	909	+ for (unsigned j = 0; j < outlet[i].V.size(); j++)
	910	+ glVertex3f(outlet[i].V[j][0], outlet[i].V[j][1], outlet[i].V[j][2]);
	911	+ glEnd();
	912	+ }
	913	+ glFlush();
	914	+ }
	915	+
	916	+ // draw the bridge as tubes
	917	+ void tube_bridge(T subdivision, T radii = 5.0f) {
	918	+
	919	+ stim::vec3<T> dir; // direction vector
	920	+ stim::circle<T> unit_c; // unit circle for finding the rotation start direction
	921	+ std::vector<typename stim::vec3<T> > cp1;
	922	+ std::vector<typename stim::vec3<T> > cp2;
	923	+
	924	+ for (unsigned i = 0; i < inlet.size(); i++) {
	925	+ // render vertex as sphere
	926	+ for (unsigned j = 1; j < inlet[i].V.size() - 1; j++) {
	927	+ glPushMatrix();
	928	+ glTranslatef(inlet[i].V[j][0], inlet[i].V[j][1], inlet[i].V[j][2]);
	929	+ glutSolidSphere(radii, subdivision, subdivision);
	930	+ glPopMatrix();
	931	+ }
	932	+ // render edge as cylinder
	933	+ for (unsigned j = 0; j < inlet[i].V.size() - 1; j++) {
	934	+ dir = inlet[i].V[j] - inlet[i].V[j + 1];
	935	+ dir = dir.norm();
	936	+ unit_c.rotate(dir);
	937	+ stim::circle<T> c1(inlet[i].V[j], inlet[i].r, dir, unit_c.U);
	938	+ stim::circle<T> c2(inlet[i].V[j + 1], inlet[i].r, dir, unit_c.U);
	939	+ cp1 = c1.glpoints(subdivision);
	940	+ cp2 = c2.glpoints(subdivision);
	941	+
	942	+ glBegin(GL_QUAD_STRIP);
	943	+ for (unsigned k = 0; k < cp1.size(); k++) {
	944	+ glVertex3f(cp1[k][0], cp1[k][1], cp1[k][2]);
	945	+ glVertex3f(cp2[k][0], cp2[k][1], cp2[k][2]);
	946	+ }
	947	+ glEnd();
	948	+ }
	949	+ }
	950	+
	951	+ for (unsigned i = 0; i < outlet.size(); i++) {
	952	+ // render vertex as sphere
	953	+ for (unsigned j = 1; j < outlet[i].V.size() - 1; j++) {
	954	+ glPushMatrix();
	955	+ glTranslatef(outlet[i].V[j][0], outlet[i].V[j][1], outlet[i].V[j][2]);
	956	+ glutSolidSphere(radii, subdivision, subdivision);
	957	+ glPopMatrix();
	958	+ }
	959	+ // render edge as cylinder
	960	+ for (unsigned j = 0; j < outlet[i].V.size() - 1; j++) {
	961	+ dir = outlet[i].V[j] - outlet[i].V[j + 1];
	962	+ dir = dir.norm();
	963	+ unit_c.rotate(dir);
	964	+ stim::circle<T> c1(outlet[i].V[j], outlet[i].r, dir, unit_c.U);
	965	+ stim::circle<T> c2(outlet[i].V[j + 1], outlet[i].r, dir, unit_c.U);
	966	+ cp1 = c1.glpoints(subdivision);
	967	+ cp2 = c2.glpoints(subdivision);
	968	+
	969	+ glBegin(GL_QUAD_STRIP);
	970	+ for (unsigned k = 0; k < cp1.size(); k++) {
	971	+ glVertex3f(cp1[k][0], cp1[k][1], cp1[k][2]);
	972	+ glVertex3f(cp2[k][0], cp2[k][1], cp2[k][2]);
	973	+ }
	974	+ glEnd();
	975	+ }
	976	+ }
	977	+ }
	978	+
	979	+ // draw gradient color bounding box outside the object
	980	+ void bounding_box() {
	981	+
	982	+ stim::vec3<T> L = bb.A; // get the bottom left corner
	983	+ stim::vec3<T> U = bb.B; // get the top right corner
	984	+
	985	+ glLineWidth(1);
	986	+ // front face of the box (in L[2])
	987	+ glBegin(GL_LINE_LOOP);
	988	+ glColor3f(0.0f, 0.0f, 0.0f);
	989	+ glVertex3f(L[0], L[1], L[2]);
	990	+ glColor3f(0.0f, 1.0f, 0.0f);
	991	+ glVertex3f(L[0], U[1], L[2]);
	992	+ glColor3f(1.0f, 1.0f, 0.0f);
	993	+ glVertex3f(U[0], U[1], L[2]);
	994	+ glColor3f(1.0f, 0.0f, 0.0f);
	995	+ glVertex3f(U[0], L[1], L[2]);
	996	+ glEnd();
	997	+
	998	+ // back face of the box (in U[2])
	999	+ glBegin(GL_LINE_LOOP);
	1000	+ glColor3f(1.0f, 1.0f, 1.0f);
	1001	+ glVertex3f(U[0], U[1], U[2]);
	1002	+ glColor3f(0.0f, 1.0f, 1.0f);
	1003	+ glVertex3f(L[0], U[1], U[2]);
	1004	+ glColor3f(0.0f, 0.0f, 1.0f);
	1005	+ glVertex3f(L[0], L[1], U[2]);
	1006	+ glColor3f(1.0f, 0.0f, 1.0f);
	1007	+ glVertex3f(U[0], L[1], U[2]);
	1008	+ glEnd();
	1009	+
	1010	+ // fill out the rest of the lines to connect the two faces
	1011	+ glBegin(GL_LINES);
	1012	+ glColor3f(0.0f, 1.0f, 0.0f);
	1013	+ glVertex3f(L[0], U[1], L[2]);
	1014	+ glColor3f(0.0f, 1.0f, 1.0f);
	1015	+ glVertex3f(L[0], U[1], U[2]);
	1016	+ glColor3f(1.0f, 1.0f, 1.0f);
	1017	+ glVertex3f(U[0], U[1], U[2]);
	1018	+ glColor3f(1.0f, 1.0f, 0.0f);
	1019	+ glVertex3f(U[0], U[1], L[2]);
	1020	+ glColor3f(1.0f, 0.0f, 0.0f);
	1021	+ glVertex3f(U[0], L[1], L[2]);
	1022	+ glColor3f(1.0f, 0.0f, 1.0f);
	1023	+ glVertex3f(U[0], L[1], U[2]);
	1024	+ glColor3f(0.0f, 0.0f, 1.0f);
	1025	+ glVertex3f(L[0], L[1], U[2]);
	1026	+ glColor3f(0.0f, 0.0f, 0.0f);
	1027	+ glVertex3f(L[0], L[1], L[2]);
	1028	+ glEnd();
	1029	+ }
	1030	+
	1031	+ // mark the vertex
	1032	+ void mark_vertex() {
	1033	+
	1034	+ glColor3f(1.0f, 1.0f, 1.0f);
	1035	+ for (unsigned i = 0; i < num_vertex; i++) {
	1036	+ glRasterPos3f(V[i][0], V[i][1] + get_radius(i), V[i][2]);
	1037	+ std::stringstream ss;
	1038	+ ss << i;
	1039	+ glutBitmapString(GLUT_BITMAP_HELVETICA_18, (const unsigned char*)(ss.str().c_str()));
	1040	+ }
	1041	+ }
	1042	+
	1043	+ // find the nearest vertex of current click position
	1044	+ // return true and a value if found
	1045	+ inline bool epsilon_vertex(T x, T y, T z, T eps, unsigned& v) {
	1046	+
	1047	+ float d = FLT_MAX; // minimum distance between 2 vertices
	1048	+ float tmp_d = 0.0f; // temporary stores distance for loop
	1049	+ unsigned tmp_i = 0; // temporary stores connection index for loop
	1050	+ stim::vec3<float> tmp_v; // temporary stores current loop point
	1051	+ d = FLT_MAX; // set to max of float number
	1052	+
	1053	+ for (unsigned i = 0; i < V.size(); i++) {
	1054	+ tmp_v = stim::vec3<float>(x, y, z);
	1055	+
	1056	+ tmp_v = tmp_v - V[i]; // calculate a vector between two vertices
	1057	+ tmp_d = tmp_v.len(); // calculate length of that vector
	1058	+ if (tmp_d < d) {
	1059	+ d = tmp_d; // if found a nearer vertex
	1060	+ tmp_i = i; // get the index of that vertex
	1061	+ }
	1062	+ }
	1063	+ eps += get_radius(tmp_i); // increase epsilon accordingly
	1064	+ if (d < eps) { // if current click is close to any vertex
	1065	+ v = tmp_i; // copy the extant vertex's index to v
	1066	+ return true;
	1067	+ }
	1068	+
	1069	+ return false;
	1070	+ }
	1071	+
	1072	+ /// build main feeder connection
	1073	+ // set up main feeder and main port of both input and output
	1074	+ void set_main_feeder(T border = 200.0f) {
	1075	+
	1076	+ // 0 means outgoing while 1 means incoming
	1077	+ stim::vec3<T> inlet_main_feeder;
	1078	+ stim::vec3<T> outlet_main_feeder;
	1079	+
	1080	+ inlet_main_feeder = stim::vec3<T>(bb.A[0] - border, bb.center()[1], bb.center()[2]);
	1081	+ outlet_main_feeder = stim::vec3<T>(bb.B[0] + border, bb.center()[1], bb.center()[2]);
	1082	+
	1083	+ main_feeder.push_back(inlet_main_feeder);
	1084	+ main_feeder.push_back(outlet_main_feeder);
	1085	+
	1086	+ // find both input and output vertex
	1087	+ stim::triple<unsigned, unsigned, float> tmp;
	1088	+ unsigned N = pendant_vertex.size(); // get the number of dangle vertex
	1089	+ unsigned idx = 0;
	1090	+ for (unsigned i = 0; i < N; i++) { // for every boundary vertex
	1091	+ idx = pendant_vertex[i];
	1092	+ for (unsigned j = 0; j < num_edge; j++) { // for every edge
	1093	+ if (Q[j].first == idx) { // starting vertex
	1094	+ if (Q[j].third > 0) { // flow comes in
	1095	+ tmp.first = idx;
	1096	+ tmp.second = j;
	1097	+ tmp.third = Q[j].third;
	1098	+ input.push_back(tmp);
	1099	+ break;
	1100	+ }
	1101	+ // their might be a degenerate case that it equals to 0?
	1102	+ else if (Q[j].third < 0) { // flow comes out
	1103	+ tmp.first = idx;
	1104	+ tmp.second = j;
	1105	+ tmp.third = -Q[j].third;
	1106	+ output.push_back(tmp);
	1107	+ break;
	1108	+ }
	1109	+ }
	1110	+ else if (Q[j].second == idx) { // ending vertex
	1111	+ if (Q[j].third > 0) { // flow comes in
	1112	+ tmp.first = idx;
	1113	+ tmp.second = j;
	1114	+ tmp.third = Q[j].third;
	1115	+ output.push_back(tmp);
	1116	+ break;
	1117	+ }
	1118	+ // their might be a degenerate case that it equals to 0?
	1119	+ else if (Q[j].third < 0) { // flow comes out
	1120	+ tmp.first = idx;
	1121	+ tmp.second = j;
	1122	+ tmp.third = -Q[j].third;
	1123	+ input.push_back(tmp);
	1124	+ break;
	1125	+ }
	1126	+ }
	1127	+ }
	1128	+ }
	1129	+ }
	1130	+
	1131	+ // build connection between all inlets and outlets
	1132	+ // connection will trail along one axis around the bounding box
	1133	+ void build_synthetic_connection(T viscosity, T radii = 5.0f) {
	1134	+
	1135	+ stim::vec3<T> L = bb.A; // get the bottom left corner
	1136	+ stim::vec3<T> U = bb.B; // get the top right corner
	1137	+ T box_length = U[0] - L[0];
	1138	+ T x0, dx;
	1139	+
	1140	+ stim::vec3<T> tmp_v; // start vertex
	1141	+ stim::vec3<T> mid_v; // middle point of the bridge
	1142	+ stim::vec3<T> bus_v; // point on the bus
	1143	+ x0 = main_feeder[0][0] + 100.0f; // assume bus length is 210.0f
	1144	+ for (unsigned i = 0; i < input.size(); i++) {
	1145	+
	1146	+ tmp_v = V[input[i].first];
	1147	+ dx = 200.0f * ((tmp_v[0] - L[0]) / box_length); // the socket position depends on proximity
	1148	+ bus_v = stim::vec3<T>(x0 - dx, main_feeder[0][1], tmp_v[2]);
	1149	+ mid_v = stim::vec3<T>(x0 - dx, tmp_v[1], tmp_v[2]);
	1150	+
	1151	+ stim::bridge<T> tmp_b;
	1152	+ tmp_b.V.push_back(bus_v);
	1153	+ tmp_b.V.push_back(mid_v);
	1154	+ tmp_b.V.push_back(tmp_v);
	1155	+ tmp_b.v.push_back(input[i].first);
	1156	+ tmp_b.Q = input[i].third;
	1157	+ tmp_b.l = (bus_v - mid_v).len() + (mid_v - tmp_v).len();
	1158	+ tmp_b.r = radii;
	1159	+
	1160	+ inlet.push_back(tmp_b);
	1161	+ }
	1162	+
	1163	+ x0 = main_feeder[1][0] - 100.0f;
	1164	+ for (unsigned i = 0; i < output.size(); i++) {
	1165	+
	1166	+ tmp_v = V[output[i].first];
	1167	+ dx = 200.0f * ((U[0] - tmp_v[0]) / box_length); // the socket position depends on proximity
	1168	+ bus_v = stim::vec3<T>(x0 + dx, main_feeder[1][1], tmp_v[2]);
	1169	+ mid_v = stim::vec3<T>(x0 + dx, tmp_v[1], tmp_v[2]);
	1170	+
	1171	+ stim::bridge<T> tmp_b;
	1172	+ tmp_b.V.push_back(bus_v);
	1173	+ tmp_b.V.push_back(mid_v);
	1174	+ tmp_b.V.push_back(tmp_v);
	1175	+ tmp_b.v.push_back(output[i].first);
	1176	+ tmp_b.Q = output[i].third;
	1177	+ tmp_b.l = (bus_v - mid_v).len() + (mid_v - tmp_v).len();
	1178	+ tmp_b.r = radii;
	1179	+
	1180	+ outlet.push_back(tmp_b);
	1181	+ }
	1182	+ }
	1183	+
	1184	+ // automatically modify bridge to make it feasible
	1185	+ void modify_synthetic_connection(T viscosity, T rou, T radii = 5.0f) {
	1186	+
	1187	+ // because of radii change at the port vertex, there will be a pressure drop at that port
	1188	+ // it follows the bernoulli equation
	1189	+ // p1 + 1/2rouv1^2 + rough1 = p2 + 1/2rouv2^2 + rough2
	1190	+ // Q1 = Q2 -> v1r1^2 = v2r2^2
	1191	+ std::vector<T> new_pressure = pressure;
	1192	+ unsigned idx;
	1193	+ for (unsigned i = 0; i < pendant_vertex.size(); i++) {
	1194	+ idx = pendant_vertex[i];
	1195	+ T tmp_v = get_velocity(idx); // velocity at that pendant vertex
	1196	+ T ar = get_radius(idx) / radii;
	1197	+ new_pressure[idx] = pressure[idx] + 1.0f / 2.0f * rou * std::pow(tmp_v, 2) * (1.0f - std::pow(ar, 4));
	1198	+ }
	1199	+
	1200	+ // increase r -> increase Q -> decrease l
	1201	+ // find maximum pressure inlet port
	1202	+ T source_pressure = FLT_MIN; // source pressure
	1203	+ unsigned inlet_index;
	1204	+ T tmp_p;
	1205	+ for (unsigned i = 0; i < inlet.size(); i++) {
	1206	+ tmp_p = new_pressure[inlet[i].v[0]] + ((8 * viscosity * inlet[i].l * inlet[i].Q) / ((float)stim::PI * std::pow(radii, 4)));
	1207	+ if (tmp_p > source_pressure) {
	1208	+ source_pressure = tmp_p;
	1209	+ inlet_index = i;
	1210	+ }
	1211	+ }
	1212	+
	1213	+ // automatically modify inlet bridge to make it feasible
	1214	+ bool upper = false; // flag indicates the whether the port is upper than main feeder
	1215	+ bool invert = false; // there are two version of hilbert curve depends on starting position with respect to the cup
	1216	+ T new_l;
	1217	+ stim::vec3<T> bus_v; // the port point on the bus
	1218	+ stim::vec3<T> mid_v; // the original corner point
	1219	+ stim::vec3<T> tmp_v; // the pendant point
	1220	+ int order = 0; // order of hilbert curve (iteration)
	1221	+ for (unsigned i = 0; i < inlet.size(); i++) {
	1222	+ if (i != inlet_index) {
	1223	+ new_l = (source_pressure - new_pressure[inlet[i].v[0]]) * ((float)stim::PI * std::pow(radii, 4)) / (8 * viscosity * inlet[i].Q);
	1224	+
	1225	+ if (inlet[i].V[2][1] > main_feeder[0][1]) { // check out upper side of lower side
	1226	+ upper = true;
	1227	+ invert = false;
	1228	+ }
	1229	+ else {
	1230	+ upper = false;
	1231	+ invert = true;
	1232	+ }
	1233	+
	1234	+ T origin_l = (inlet[i].V[1] - inlet[i].V[2]).len();
	1235	+ T desire_l = new_l - (inlet[i].V[0] - inlet[i].V[1]).len();
	1236	+ find_hilbert_order(origin_l, desire_l, order);
	1237	+
	1238	+ bus_v = inlet[i].V[0];
	1239	+ mid_v = inlet[i].V[1];
	1240	+ tmp_v = inlet[i].V[2];
	1241	+ inlet[i].V.clear();
	1242	+ inlet[i].V.push_back(tmp_v);
	1243	+ inlet[i].l = new_l;
	1244	+
	1245	+ draw_hilbert_curve(i, &tmp_v[0], order, origin_l, desire_l, upper, 1, invert);
	1246	+ if (tmp_v[0] != mid_v[0])
	1247	+ inlet[i].V.push_back(mid_v);
	1248	+ inlet[i].V.push_back(bus_v);
	1249	+ std::reverse(inlet[i].V.begin(), inlet[i].V.end());
	1250	+ }
	1251	+ }
	1252	+
	1253	+ // find minimum pressure outlet port
	1254	+ source_pressure = FLT_MAX;
	1255	+ unsigned outlet_index;
	1256	+ for (unsigned i = 0; i < outlet.size(); i++) {
	1257	+ tmp_p = new_pressure[outlet[i].v[0]] - ((8 * viscosity * outlet[i].l * outlet[i].Q) / ((float)stim::PI * std::pow(radii, 4)));
	1258	+ if (tmp_p < source_pressure) {
	1259	+ source_pressure = tmp_p;
	1260	+ outlet_index = i;
	1261	+ }
	1262	+ }
	1263	+
	1264	+ // automatically modify outlet bridge to make it feasible
	1265	+ for (unsigned i = 0; i < outlet.size(); i++) {
	1266	+ if (i != outlet_index) {
	1267	+ new_l = (new_pressure[outlet[i].v[0]] - source_pressure) * ((float)stim::PI * std::pow(radii, 4)) / (8 * viscosity * outlet[i].Q);
	1268	+
	1269	+ if (outlet[i].V[2][1] > main_feeder[1][1]) {
	1270	+ upper = true;
	1271	+ invert = true;
	1272	+ }
	1273	+ else {
	1274	+ upper = false;
	1275	+ invert = false;
	1276	+ }
	1277	+
	1278	+ T origin_l = (outlet[i].V[1] - outlet[i].V[2]).len();
	1279	+ T desire_l = new_l - (outlet[i].V[0] - outlet[i].V[1]).len();
	1280	+ find_hilbert_order(origin_l, desire_l, order);
	1281	+
	1282	+ bus_v = outlet[i].V[0];
	1283	+ mid_v = outlet[i].V[1];
	1284	+ tmp_v = outlet[i].V[2];
	1285	+ outlet[i].V.clear();
	1286	+ outlet[i].V.push_back(tmp_v);
	1287	+ outlet[i].l = new_l;
	1288	+
	1289	+ draw_hilbert_curve(i, &tmp_v[0], order, origin_l, desire_l, upper, 0, invert);
	1290	+ if (tmp_v[0] != mid_v[0])
	1291	+ outlet[i].V.push_back(mid_v);
	1292	+ outlet[i].V.push_back(bus_v);
	1293	+ std::reverse(outlet[i].V.begin(), outlet[i].V.end());
	1294	+ }
	1295	+ }
	1296	+ }
	1297	+
	1298	+ // check current bridge to see feasibility
	1299	+ void check_synthetic_connection(T viscosity, T radii = 5.0f) {
	1300	+
	1301	+ T eps = 0.01f;
	1302	+ T source_pressure = pressure[inlet[0].v[0]] + (8 * viscosity * inlet[0].l * inlet[0].Q) / ((float)stim::PI * std::pow(radii, 4));
	1303	+ T tmp_p;
	1304	+ for (unsigned i = 1; i < inlet.size(); i++) {
	1305	+ tmp_p = pressure[inlet[i].v[0]] + (8 * viscosity * inlet[i].l * inlet[i].Q) / ((float)stim::PI * std::pow(radii, 4));
	1306	+ T delta = fabs(tmp_p - source_pressure);
	1307	+ if (delta > eps) {
	1308	+ std::cout << "Nonfeasible connection!" << std::endl;
	1309	+ break;
	1310	+ }
	1311	+ }
	1312	+ source_pressure = pressure[outlet[0].v[0]] - (8 * viscosity * outlet[0].l * outlet[0].Q) / ((float)stim::PI * std::pow(radii, 4));
	1313	+ for (unsigned i = 1; i < outlet.size(); i++) {
	1314	+ tmp_p = pressure[outlet[i].v[0]] - (8 * viscosity * outlet[i].l * outlet[i].Q) / ((float)stim::PI * std::pow(radii, 4));
	1315	+ T delta = fabs(tmp_p - source_pressure);
	1316	+ if (delta > eps) {
	1317	+ std::cout << "Nonfeasible connection!" << std::endl;
	1318	+ break;
	1319	+ }
	1320	+ }
	1321	+ }
	1322	+
	1323	+ /// make binary image stack
	1324	+ // prepare for image stack
	1325	+ void preparation(T &Xl, T &Xr, T &Yt, T &Yb, T &Z, T length = 210.0f, T height = 10.0f) {
	1326	+
	1327	+ T max_radii = 0.0f;
	1328	+ T top = FLT_MIN;
	1329	+ T bottom = FLT_MAX;
	1330	+
	1331	+ // clear up last time result
	1332	+ A.clear();
	1333	+ B.clear();
	1334	+ CU.clear();
	1335	+
	1336	+ // firstly push back the original network
	1337	+ stim::sphere<T> new_sphere;
	1338	+ stim::cone<T> new_cone;
	1339	+ stim::cuboid<T> new_cuboid;
	1340	+
	1341	+ // take every source bus as cuboid
	1342	+ new_cuboid.c = main_feeder[0];
	1343	+ new_cuboid.l = length;
	1344	+ new_cuboid.w = bb.B[2] - bb.A[2] + 10.0f;
	1345	+ new_cuboid.h = height;
	1346	+ CU.push_back(new_cuboid);
	1347	+ new_cuboid.c = main_feeder[1];
	1348	+ CU.push_back(new_cuboid);
	1349	+
	1350	+ // take every point as sphere, every line as cone
	1351	+ for (unsigned i = 0; i < num_edge; i++) {
	1352	+ for (unsigned j = 0; j < E[i].size(); j++) {
	1353	+ new_sphere.c = E[i][j];
	1354	+ new_sphere.r = E[i].r(j);
	1355	+ A.push_back(new_sphere);
	1356	+ if (j != E[i].size() - 1) {
	1357	+ new_cone.c1 = E[i][j];
	1358	+ new_cone.c2 = E[i][j + 1];
	1359	+ new_cone.r1 = E[i].r(j);
	1360	+ new_cone.r2 = E[i].r(j + 1);
	1361	+ B.push_back(new_cone);
	1362	+ }
	1363	+ }
	1364	+ }
	1365	+
	1366	+ // secondly push back outside connection
	1367	+ for (unsigned i = 0; i < inlet.size(); i++) {
	1368	+ if (inlet[i].V.size() == 3) {
	1369	+ new_sphere.c = inlet[i].V[1];
	1370	+ new_sphere.r = inlet[i].r;
	1371	+ A.push_back(new_sphere);
	1372	+ }
	1373	+ else {
	1374	+ new_sphere.c = inlet[i].V[1];
	1375	+ new_sphere.r = inlet[i].r;
	1376	+ A.push_back(new_sphere);
	1377	+ new_sphere.c = inlet[i].V[2];
	1378	+ A.push_back(new_sphere);
	1379	+ }
	1380	+ }
	1381	+ for (unsigned i = 0; i < outlet.size(); i++) {
	1382	+ if (outlet[i].V.size() == 3) {
	1383	+ new_sphere.c = outlet[i].V[1];
	1384	+ new_sphere.r = outlet[i].r;
	1385	+ A.push_back(new_sphere);
	1386	+ }
	1387	+ else {
	1388	+ new_sphere.c = outlet[i].V[1];
	1389	+ new_sphere.r = outlet[i].r;
	1390	+ A.push_back(new_sphere);
	1391	+ new_sphere.c = outlet[i].V[2];
	1392	+ A.push_back(new_sphere);
	1393	+ }
	1394	+ }
	1395	+
	1396	+ for (unsigned i = 0; i < inlet.size(); i++) {
	1397	+ for (unsigned j = 0; j < inlet[i].V.size() - 1; j++) {
	1398	+ new_cone.c1 = inlet[i].V[j];
	1399	+ new_cone.c2 = inlet[i].V[j + 1];
	1400	+ new_cone.r1 = inlet[i].r;
	1401	+ new_cone.r2 = inlet[i].r;
	1402	+ B.push_back(new_cone);
	1403	+ }
	1404	+ }
	1405	+ for (unsigned i = 0; i < outlet.size(); i++) {
	1406	+ for (unsigned j = 0; j < outlet[i].V.size() - 1; j++) {
	1407	+ new_cone.c1 = outlet[i].V[j];
	1408	+ new_cone.c2 = outlet[i].V[j + 1];
	1409	+ new_cone.r1 = outlet[i].r;
	1410	+ new_cone.r2 = outlet[i].r;
	1411	+ B.push_back(new_cone);
	1412	+ }
	1413	+ }
	1414	+
	1415	+ // find out the image stack size
	1416	+ Xl = main_feeder[0][0] - length / 2; // left bound x coordinate
	1417	+ Xr = main_feeder[1][0] + length / 2; // right bound x coordinate
	1418	+
	1419	+ for (unsigned i = 0; i < A.size(); i++) {
	1420	+ if (A[i].c[1] > top)
	1421	+ top = A[i].c[1];
	1422	+ if (A[i].c[1] < bottom)
	1423	+ bottom = A[i].c[1];
	1424	+ if (A[i].r > max_radii)
	1425	+ max_radii = A[i].r;
	1426	+ }
	1427	+
	1428	+ Yt = top; // top bound y coordinate
	1429	+ Yb = bottom; // bottom bound y coordinate
	1430	+ Z = (bb.B[2] - bb.A[2] + 2 * max_radii); // bounding box width(along z-axis)
	1431	+ }
	1432	+
	1433	+ /// making image stack main function
	1434	+ void make_image_stack(T dx, T dy, T dz, std::string stackdir, T radii = 5.0f) {
	1435	+
	1436	+ /// preparation for making image stack
	1437	+ T X, Xl, Xr, Y, Yt, Yb, Z;
	1438	+ preparation(Xl, Xr, Yt, Yb, Z);
	1439	+ X = Xr - Xl; // bounding box length(along x-axis)
	1440	+ Y = Yt - Yb; // bounding box height(along y-axis)
	1441	+
	1442	+ /// make
	1443	+ stim::image_stack<unsigned char, T> I;
	1444	+ T size_x, size_y, size_z;
	1445	+
	1446	+ stim::vec3<T> center = bb.center(); // get the center of bounding box
	1447	+
	1448	+ size_x = X / dx + 1; // set the size of image
	1449	+ size_y = Y / dy + 1;
	1450	+ size_z = Z / dz + 1;
	1451	+
	1452	+ /// initialize image stack object
	1453	+ I.init(1, size_x, size_y, size_z);
	1454	+ I.set_dim(dx, dy, dz);
	1455	+
	1456	+ // because of lack of memory, we have to computer one slice of stack per time
	1457	+ // allocate vertex, edge and bus
	1458	+ stim::sphere<T> *d_V;
	1459	+ stim::cone<T> *d_E;
	1460	+ stim::cuboid<T> *d_B;
	1461	+
	1462	+ HANDLE_ERROR(cudaMalloc((void*)&d_V, A.size() sizeof(stim::sphere<T>)));
	1463	+ HANDLE_ERROR(cudaMalloc((void*)&d_E, B.size() sizeof(stim::cone<T>)));
	1464	+ HANDLE_ERROR(cudaMalloc((void*)&d_B, CU.size() sizeof(stim::cuboid<T>)));
	1465	+ HANDLE_ERROR(cudaMemcpy(d_V, &A[0], A.size() * sizeof(stim::sphere<T>), cudaMemcpyHostToDevice));
	1466	+ HANDLE_ERROR(cudaMemcpy(d_E, &B[0], B.size() * sizeof(stim::cone<T>), cudaMemcpyHostToDevice));
	1467	+ HANDLE_ERROR(cudaMemcpy(d_B, &CU[0], CU.size() * sizeof(stim::cuboid<T>), cudaMemcpyHostToDevice));
	1468	+
	1469	+ // allocate image stack information memory
	1470	+ size_t* d_R;
	1471	+ T *d_S;
	1472	+
	1473	+ size_t* R = (size_t)malloc(4 sizeof(size_t)); // size in 4 dimension
	1474	+ R[0] = 1;
	1475	+ R[1] = (size_t)size_x;
	1476	+ R[2] = (size_t)size_y;
	1477	+ R[3] = (size_t)size_z;
	1478	+ T S = (T)malloc(4 * sizeof(T)); // spacing in 4 dimension
	1479	+ S[0] = 1.0f;
	1480	+ S[1] = dx;
	1481	+ S[2] = dy;
	1482	+ S[3] = dz;
	1483	+ size_t num = size_x * size_y;
	1484	+
	1485	+ HANDLE_ERROR(cudaMalloc((void*)&d_R, 4 sizeof(size_t)));
	1486	+ HANDLE_ERROR(cudaMalloc((void*)&d_S, 4 sizeof(T)));
	1487	+ HANDLE_ERROR(cudaMemcpy(d_R, R, 4 * sizeof(size_t), cudaMemcpyHostToDevice));
	1488	+ HANDLE_ERROR(cudaMemcpy(d_S, S, 4 * sizeof(T), cudaMemcpyHostToDevice));
	1489	+
	1490	+ // for every slice of image
	1491	+ unsigned p = 0; // percentage of progress
	1492	+ for (unsigned i = 0; i < size_z; i++) {
	1493	+
	1494	+ unsigned x = 0 - (unsigned)Xl; // translate whole network(including inlet/outlet) to origin
	1495	+ unsigned y = 0 - (unsigned)Yb;
	1496	+ unsigned z = i + (unsigned)center[2]; // box symmetric along z-axis
	1497	+ // allocate image slice memory
	1498	+ unsigned char* d_ptr;
	1499	+ unsigned char* ptr = (unsigned char)malloc(num sizeof(unsigned char));
	1500	+ memset(ptr, 0, num * sizeof(unsigned char));
	1501	+
	1502	+ HANDLE_ERROR(cudaMalloc((void*)&d_ptr, num sizeof(unsigned char)));
	1503	+
	1504	+ cudaDeviceProp prop;
	1505	+ cudaGetDeviceProperties(&prop, 0); // get cuda device properties structure
	1506	+ size_t max_thread = sqrt(prop.maxThreadsPerBlock); // get the maximum number of thread per block
	1507	+
	1508	+ dim3 block(size_x / max_thread + 1, size_y / max_thread + 1);
	1509	+ dim3 thread(max_thread, max_thread);
	1510	+ inside_sphere << <block, thread >> > (d_V, A.size(), d_R, d_S, d_ptr, x, y, z);
	1511	+ cudaDeviceSynchronize();
	1512	+ inside_cone << <block, thread >> > (d_E, B.size(), d_R, d_S, d_ptr, x, y, z);
	1513	+ cudaDeviceSynchronize();
	1514	+ inside_cuboid << <block, thread >> > (d_B, CU.size(), d_R, d_S, d_ptr, x, y, z);
	1515	+
	1516	+ HANDLE_ERROR(cudaMemcpy(ptr, d_ptr, num * sizeof(unsigned char), cudaMemcpyDeviceToHost));
	1517	+
	1518	+ I.set(ptr, i);
	1519	+
	1520	+ free(ptr);
	1521	+ HANDLE_ERROR(cudaFree(d_ptr));
	1522	+
	1523	+ // print progress bar
	1524	+ p = (float)(i + 1) / (float)size_z * 100;
	1525	+ rtsProgressBar(p);
	1526	+ }
	1527	+
	1528	+ // clear up
	1529	+ free(R);
	1530	+ free(S);
	1531	+ HANDLE_ERROR(cudaFree(d_R));
	1532	+ HANDLE_ERROR(cudaFree(d_S));
	1533	+ HANDLE_ERROR(cudaFree(d_V));
	1534	+ HANDLE_ERROR(cudaFree(d_E));
	1535	+ HANDLE_ERROR(cudaFree(d_B));
	1536	+
	1537	+ if (stackdir == "")
	1538	+ I.save_images("image????.bmp");
	1539	+ else
	1540	+ I.save_images(stackdir + "/image????.bmp");
	1541	+ }
	1542	+
	1543	+ /// Calculate the inverse of A and store the result in C
	1544	+ void inversion(T** A, int order, T* C) {
	1545	+
	1546	+#ifdef __CUDACC__
	1547	+
	1548	+ // convert from double pointer to single pointer, make it flat
	1549	+ T* Aflat = (T)malloc(order order * sizeof(T));
	1550	+ for (unsigned i = 0; i < order; i++)
	1551	+ for (unsigned j = 0; j < order; j++)
	1552	+ Aflat[i * order + j] = A[i][j];
	1553	+
	1554	+ // create device pointer
	1555	+ T* d_Aflat; // flat original matrix
	1556	+ T* d_Cflat; // flat inverse matrix
	1557	+ T** d_A; // put the flat original matrix into another array of pointer
	1558	+ T** d_C;
	1559	+ int *d_P;
	1560	+ int *d_INFO;
	1561	+
	1562	+ // allocate memory on device
	1563	+ HANDLE_ERROR(cudaMalloc((void*)&d_Aflat, order order * sizeof(T)));
	1564	+ HANDLE_ERROR(cudaMalloc((void*)&d_Cflat, order order * sizeof(T)));
	1565	+ HANDLE_ERROR(cudaMalloc((void*)&d_A, sizeof(T)));
	1566	+ HANDLE_ERROR(cudaMalloc((void*)&d_C, sizeof(T)));
	1567	+ HANDLE_ERROR(cudaMalloc((void*)&d_P, order 1 * sizeof(int)));
	1568	+ HANDLE_ERROR(cudaMalloc((void*)&d_INFO, 1 sizeof(int)));
	1569	+
	1570	+ // copy matrix from host to device
	1571	+ HANDLE_ERROR(cudaMemcpy(d_Aflat, Aflat, order * order * sizeof(T), cudaMemcpyHostToDevice));
	1572	+
	1573	+ // copy matrix from device to device
	1574	+ HANDLE_ERROR(cudaMemcpy(d_A, &d_Aflat, sizeof(T*), cudaMemcpyHostToDevice));
	1575	+ HANDLE_ERROR(cudaMemcpy(d_C, &d_Cflat, sizeof(T*), cudaMemcpyHostToDevice));
	1576	+
	1577	+ // calculate the inverse of matrix based on cuBLAS
	1578	+ cublasHandle_t handle;
	1579	+ CUBLAS_HANDLE_ERROR(cublasCreate_v2(&handle)); // create cuBLAS handle object
	1580	+
	1581	+ CUBLAS_HANDLE_ERROR(cublasSgetrfBatched(handle, order, d_A, order, d_P, d_INFO, 1));
	1582	+
	1583	+ int INFO = 0;
	1584	+ HANDLE_ERROR(cudaMemcpy(&INFO, d_INFO, sizeof(int), cudaMemcpyDeviceToHost));
	1585	+ if (INFO == order)
	1586	+ {
	1587	+ std::cout << "Factorization Failed : Matrix is singular." << std::endl;
	1588	+ cudaDeviceReset();
	1589	+ exit(1);
	1590	+ }
	1591	+
	1592	+ CUBLAS_HANDLE_ERROR(cublasSgetriBatched(handle, order, (const T **)d_A, order, d_P, d_C, order, d_INFO, 1));
	1593	+
	1594	+ CUBLAS_HANDLE_ERROR(cublasDestroy_v2(handle));
	1595	+
	1596	+ // copy inverse matrix from device to device
	1597	+ HANDLE_ERROR(cudaMemcpy(&d_Cflat, d_C, sizeof(T*), cudaMemcpyDeviceToHost));
	1598	+
	1599	+ // copy inverse matrix from device to host
	1600	+ HANDLE_ERROR(cudaMemcpy(C, d_Cflat, order * order * sizeof(T), cudaMemcpyDeviceToHost));
	1601	+
	1602	+ // clear up
	1603	+ free(Aflat);
	1604	+ HANDLE_ERROR(cudaFree(d_Aflat));
	1605	+ HANDLE_ERROR(cudaFree(d_Cflat));
	1606	+ HANDLE_ERROR(cudaFree(d_A));
	1607	+ HANDLE_ERROR(cudaFree(d_C));
	1608	+ HANDLE_ERROR(cudaFree(d_P));
	1609	+ HANDLE_ERROR(cudaFree(d_INFO));
	1610	+
	1611	+#else
	1612	+ // get the determinant of a
	1613	+ double det = 1.0 / determinant(A, order);
	1614	+
	1615	+ // memory allocation
	1616	+ T* tmp = (T)malloc((order - 1)(order - 1) * sizeof(T));
	1617	+ T minor = (T)malloc((order - 1) * sizeof(T*));
	1618	+ for (int i = 0; i < order - 1; i++)
	1619	+ minor[i] = tmp + (i * (order - 1));
	1620	+
	1621	+ for (int j = 0; j < order; j++) {
	1622	+ for (int i = 0; i < order; i++) {
	1623	+ // get the co-factor (matrix) of A(j,i)
	1624	+ get_minor(A, minor, j, i, order);
	1625	+ C[i][j] = det * determinant(minor, order - 1);
	1626	+ if ((i + j) % 2 == 1)
	1627	+ C[i][j] = -C[i][j];
	1628	+ }
	1629	+ }
	1630	+
	1631	+ // release memory
	1632	+ free(tmp);
	1633	+ free(minor);
	1634	+#endif
	1635	+ }
	1636	+ };
	1637	+}
	1638	+
	1639	+#endif
0	1640	\ No newline at end of file
...	...

main.cu 0 → 100644

Wrap text Show/Hide comments View file @9191c39

	1	+++ a/main.cu
	1	+#include <stdlib.h>
	2	+#include <string>
	3	+#include <fstream>
	4	+#include <algorithm>
	5	+
	6	+// CUDA include
	7	+#ifdef __CUDACC__
	8	+#include "device_launch_parameters.h"
	9	+#include <cuda.h>
	10	+#include <cuda_runtime_api.h>
	11	+#include "cuda_runtime.h"
	12	+#endif
	13	+
	14	+// OPENGL include
	15	+#include <GL/glut.h>
	16	+#include <GL/freeglut.h>
	17	+
	18	+#include "flow.h"
	19	+
	20	+// STIM include
	21	+#include <stim/visualization/gl_aaboundingbox.h>
	22	+#include <stim/parser/arguments.h>
	23	+#include <stim/visualization/camera.h>
	24	+#include <stim/visualization/colormap.h>
	25	+#include <stim/cuda/cudatools/error.h>
	26	+
	27	+
	28	+//******************parameter setting******************
	29	+// overall parameters
	30	+int vX, vY;
	31	+float dx, dy, dz; // x, y and z image scaling(units/pixel)
	32	+std::string stackdir = ""; // directory where image stacks will be stored
	33	+stim::arglist args; // create an instance of arglist
	34	+stim::gl_aaboundingbox<float> bb; // axis-aligned bounding box object
	35	+stim::camera cam; // camera object
	36	+unsigned num_edge; // number of edges in the network
	37	+unsigned num_vertex; // number of vertex in the network
	38	+std::vector<unsigned> pendant_vertex; // list of pendant vertex index in GT
	39	+std::vector<std::string> menu_option = { "simulation", "build inlet/outlet", "manufacture" };
	40	+stim::flow<float> flow; // flow object
	41	+float move_pace; // camera moving parameter
	42	+float u; // viscosity
	43	+float rou; // density
	44	+float max_v;
	45	+float min_v;
	46	+int mods; // special keyboard input
	47	+std::vector<unsigned char> color; // velocity color map
	48	+std::vector<int> velocity_bar; // velocity bar
	49	+
	50	+// hard-coded parameters
	51	+float camera_factor = 1.2f; // start point of the camera as a function of X and Y size
	52	+float orbit_factor = 0.01f; // degrees per pixel used to orbit the camera
	53	+float zoom_factor = 10.0f; // zooming factor
	54	+float border_factor = 20.0f; // border
	55	+float radii_factor = 1.0f; // radii changing factor
	56	+GLint subdivision = 20; // slices and stacks
	57	+float default_radii = 5.0f; // default radii of network vertex
	58	+float delta = 0.01f; // small discrepancy
	59	+float eps = 20.0f; // epsilon threshold
	60	+float max_pressure = 0.0f; // maximum pressure that the channel can bear
	61	+
	62	+// glut event parameters
	63	+int mouse_x; // window x-coordinate
	64	+int mouse_y; // window y-coordinate
	65	+bool LTbutton = false; // true means down while false means up
	66	+
	67	+// simulation parameters
	68	+bool simulation = false; // flag indicates simulation mode
	69	+bool color_bound = false; // flag indicates velocity color map bound
	70	+bool to_select_pressure = false; // flag indicates having selected a vertex to modify pressure
	71	+unsigned pressure_index; // the index of vertex that is clicked
	72	+
	73	+// build inlet/outlet parameters
	74	+bool build_inlet_outlet = false; // flag indicates building inlets and outlets
	75	+bool modified_bridge = false; // flag indicates having modified inlet/outlet connection
	76	+
	77	+// manufacture parameters
	78	+bool manufacture = false; // flag indicates manufacture mode
	79	+
	80	+
	81	+//******************helper function*******************
	82	+// get the network basic information
	83	+inline void get_background() {
	84	+
	85	+ pendant_vertex = flow.get_boundary_vertex();
	86	+ num_edge = flow.edges();
	87	+ num_vertex = flow.vertices();
	88	+
	89	+ // set the initial radii
	90	+ flow.init(num_edge, num_vertex); // initialize flow object
	91	+ for (unsigned i = 0; i < num_edge; i++)
	92	+ flow.set_r(i, default_radii);
	93	+}
	94	+
	95	+// convert from window coordinates to world coordinates
	96	+inline void window_to_world(GLdouble &x, GLdouble &y, GLdouble &z) {
	97	+
	98	+ GLint viewport[4];
	99	+ GLdouble modelview[16];
	100	+ GLdouble projection[16];
	101	+ GLdouble winX, winY;
	102	+ GLfloat winZ;
	103	+
	104	+ glGetIntegerv(GL_VIEWPORT, viewport);
	105	+ glGetDoublev(GL_MODELVIEW_MATRIX, modelview);
	106	+ glGetDoublev(GL_PROJECTION_MATRIX, projection);
	107	+
	108	+ winX = (GLdouble)mouse_x;
	109	+ winY = viewport[3] - (GLdouble)mouse_y;
	110	+ glReadPixels((GLint)winX, (GLint)winY, (GLsizei)1, (GLsizei)1, GL_DEPTH_COMPONENT, GL_FLOAT, &winZ);
	111	+ gluUnProject(winX, winY, winZ, modelview, projection, viewport, &x, &y, &z);
	112	+}
	113	+
	114	+
	115	+//******************simulation function********************
	116	+// initialize flow object
	117	+void flow_initialize() {
	118	+
	119	+ stim::vec3<float> center = bb.center();
	120	+
	121	+ for (unsigned i = 0; i < pendant_vertex.size(); i++) {
	122	+ if (flow.get_vertex(pendant_vertex[i])[0] <= center[0])
	123	+ flow.P[pendant_vertex[i]] = max_pressure - i * delta; // should set minor discrepancy
	124	+ else
	125	+ flow.P[pendant_vertex[i]] = (i + 1) * delta; // algorithm treat 0 as no initial pressure
	126	+ }
	127	+}
	128	+
	129	+// find the stable flow state
	130	+void flow_stable_state() {
	131	+
	132	+ flow.solve_flow(u);
	133	+ flow.get_color_map(max_v, min_v, color, pendant_vertex);
	134	+ color_bound = true;
	135	+
	136	+ velocity_bar.resize(num_edge);
	137	+ for (unsigned i = 0; i < num_edge; i++)
	138	+ velocity_bar[i] = i;
	139	+ std::sort(velocity_bar.begin(), velocity_bar.end(), [&](int x, int y) {return abs(flow.v[x]) < abs(flow.v[y]); });
	140	+}
	141	+
	142	+
	143	+//******************glut function******************
	144	+// dynamically set menu
	145	+// @param num: number of current menu options
	146	+// @param range: range of option to be set from menu_option list
	147	+void glut_set_menu(int num, int range) {
	148	+
	149	+ // remove last time menu options
	150	+ for (int i = 1; i < num + 1; i++)
	151	+ glutRemoveMenuItem(1);
	152	+
	153	+ // set new menu options
	154	+ std::string menu_name;
	155	+ for (int i = 1; i < range + 1; i++) {
	156	+ menu_name = menu_option[i - 1];
	157	+ glutAddMenuEntry(menu_name.c_str(), i);
	158	+ }
	159	+}
	160	+
	161	+// set up the squash transform to whole screen
	162	+void glut_projection() {
	163	+
	164	+ glMatrixMode(GL_PROJECTION); // load the projection matrix for editing
	165	+ glLoadIdentity(); // start with the identity matrix
	166	+ vX = glutGet(GLUT_WINDOW_WIDTH); // use the whole screen for rendering
	167	+ vY = glutGet(GLUT_WINDOW_HEIGHT);
	168	+ glViewport(0, 0, vX, vY); // specify a viewport for the entire window
	169	+ float aspect = (float)vX / (float)vY; // calculate the aspect ratio
	170	+ gluPerspective(60, aspect, 0.1, 1000000); // set up a perspective projection
	171	+}
	172	+
	173	+// translate camera to origin
	174	+void glut_modelview() {
	175	+
	176	+ glMatrixMode(GL_MODELVIEW); // load the modelview matrix for editing
	177	+ glLoadIdentity(); // start with the identity matrix
	178	+ stim::vec3<float> eye = cam.getPosition(); // get the camera position (eye point)
	179	+ stim::vec3<float> focus = cam.getLookAt(); // get the camera focal point
	180	+ stim::vec3<float> up = cam.getUp(); // get the camera "up" orientation
	181	+
	182	+ gluLookAt(eye[0], eye[1], eye[2], focus[0], focus[1], focus[2], up[0], up[1], up[2]); // set up the OpenGL camera
	183	+}
	184	+
	185	+// glut render function
	186	+void glut_render() {
	187	+
	188	+ glEnable(GL_DEPTH_TEST);
	189	+ glClear(GL_COLOR_BUFFER_BIT \| GL_DEPTH_BUFFER_BIT);
	190	+ glut_projection();
	191	+ glut_modelview();
	192	+
	193	+ if (!simulation && !build_inlet_outlet \|\| manufacture) {
	194	+ flow.glCylinder0();
	195	+ }
	196	+ else {
	197	+ flow.bounding_box();
	198	+ flow.glSolidSphere(max_pressure, subdivision);
	199	+ flow.mark_vertex();
	200	+ flow.glSolidCone(subdivision);
	201	+ flow.glSolidCylinder(subdivision, color);
	202	+ flow.glSolidCuboid();
	203	+ }
	204	+
	205	+ if (build_inlet_outlet) {
	206	+ flow.line_bridge();
	207	+ }
	208	+
	209	+ if (manufacture) {
	210	+ flow.glSolidCuboid();
	211	+ flow.tube_bridge(subdivision);
	212	+ }
	213	+
	214	+
	215	+ // render bars
	216	+ // bring up a pressure bar on left
	217	+ if (to_select_pressure) {
	218	+
	219	+ glMatrixMode(GL_PROJECTION); // set up the 2d viewport for mode text printing
	220	+ glPushMatrix();
	221	+ glLoadIdentity();
	222	+ vX = glutGet(GLUT_WINDOW_WIDTH); // get the current window width
	223	+ vY = glutGet(GLUT_WINDOW_HEIGHT); // get the current window height
	224	+ glViewport(0, 0, vX, vY); // locate to left bottom corner
	225	+ gluOrtho2D(0, vX, 0, vY); // define othogonal aspect
	226	+
	227	+ glMatrixMode(GL_MODELVIEW);
	228	+ glPushMatrix();
	229	+ glLoadIdentity();
	230	+
	231	+ glLineWidth(border_factor);
	232	+ glBegin(GL_LINES);
	233	+ glColor3f(0.0, 0.0, 1.0); // blue to red
	234	+ glVertex2f(border_factor, border_factor);
	235	+ glColor3f(1.0, 0.0, 0.0);
	236	+ glVertex2f(border_factor, (vY - 2.0f * border_factor));
	237	+ glEnd();
	238	+ glFlush();
	239	+
	240	+ // pressure bar text
	241	+ glColor3f(1.0f, 1.0f, 1.0f);
	242	+ glRasterPos2f(0.0f, vY - border_factor);
	243	+ std::stringstream ss_p;
	244	+ ss_p << "Pressure Bar";
	245	+ glutBitmapString(GLUT_BITMAP_HELVETICA_18, (const unsigned char*)(ss_p.str().c_str()));
	246	+
	247	+ // pressure range text
	248	+ float step = vY - 3.0f * border_factor;
	249	+ step /= 10;
	250	+ for (unsigned i = 0; i < 11; i++) {
	251	+ glRasterPos2f((border_factor * 1.5f), (border_factor + i * step));
	252	+ std::stringstream ss_n;
	253	+ ss_n << (float)i * max_pressure / 10;
	254	+ glutBitmapString(GLUT_BITMAP_TIMES_ROMAN_10, (const unsigned char*)(ss_n.str().c_str()));
	255	+ }
	256	+ glPopMatrix();
	257	+ glMatrixMode(GL_PROJECTION);
	258	+ glPopMatrix();
	259	+ }
	260	+
	261	+ // bring up a velocity bar on left
	262	+ if (simulation && !to_select_pressure) {
	263	+
	264	+ glMatrixMode(GL_PROJECTION); // set up the 2d viewport for mode text printing
	265	+ glPushMatrix();
	266	+ glLoadIdentity();
	267	+ vX = glutGet(GLUT_WINDOW_WIDTH); // get the current window width
	268	+ vY = glutGet(GLUT_WINDOW_HEIGHT); // get the current window height
	269	+ glViewport(0, 0, vX, vY); // locate to left bottom corner
	270	+ gluOrtho2D(0, vX, 0, vY); // define othogonal aspect
	271	+
	272	+ glMatrixMode(GL_MODELVIEW);
	273	+ glPushMatrix();
	274	+ glLoadIdentity();
	275	+
	276	+ float step = (vY - 3 * border_factor);
	277	+ step /= num_edge;
	278	+ for (unsigned i = 0; i < num_edge; i++) {
	279	+ glLineWidth(border_factor);
	280	+ glBegin(GL_LINES);
	281	+ glColor3f((float)color[velocity_bar[i] * 3 + 0] / 255, (float)color[velocity_bar[i] * 3 + 1] / 255, (float)color[velocity_bar[i] * 3 + 2] / 255);
	282	+ glVertex2f(border_factor, border_factor + i * step);
	283	+ glVertex2f(border_factor, border_factor + (i + 1) * step);
	284	+ glEnd();
	285	+ }
	286	+ glFlush();
	287	+
	288	+ // pressure bar text
	289	+ glColor3f(1.0f, 1.0f, 1.0f);
	290	+ glRasterPos2f(0.0f, vY - border_factor);
	291	+ std::stringstream ss_p;
	292	+ ss_p << "Velocity range";
	293	+ glutBitmapString(GLUT_BITMAP_HELVETICA_18, (const unsigned char*)(ss_p.str().c_str()));
	294	+
	295	+ // pressure range text
	296	+ step = vY - 3 * border_factor;
	297	+ step /= 10;
	298	+ for (unsigned i = 0; i < 11; i++) {
	299	+ glRasterPos2f(border_factor * 1.5f, border_factor + i * step);
	300	+ std::stringstream ss_n;
	301	+ ss_n << min_v + i * (max_v - min_v) / 10;
	302	+ glutBitmapString(GLUT_BITMAP_TIMES_ROMAN_10, (const unsigned char*)(ss_n.str().c_str()));
	303	+ }
	304	+ glPopMatrix();
	305	+ glMatrixMode(GL_PROJECTION);
	306	+ glPopMatrix();
	307	+ }
	308	+
	309	+ glutSwapBuffers();
	310	+}
	311	+
	312	+// register glut menu options
	313	+void glut_menu(int value) {
	314	+
	315	+ int num = glutGet(GLUT_MENU_NUM_ITEMS);
	316	+ if (value == 1) {
	317	+ simulation = true;
	318	+ build_inlet_outlet = false;
	319	+ manufacture = false;
	320	+ modified_bridge = false;
	321	+ flow_initialize();
	322	+ flow_stable_state(); // main function of solving the linear system
	323	+ flow.print_flow();
	324	+
	325	+ glut_set_menu(num, 2);
	326	+ }
	327	+
	328	+ if (value == 2) {
	329	+ simulation = false;
	330	+ build_inlet_outlet = true;
	331	+ manufacture = false;
	332	+ if (!modified_bridge) {
	333	+ flow.set_main_feeder();
	334	+ flow.build_synthetic_connection(u);
	335	+ }
	336	+
	337	+ glut_set_menu(num, 3);
	338	+ }
	339	+
	340	+ if (value == 3) {
	341	+ simulation = false;
	342	+ build_inlet_outlet = false;
	343	+ manufacture = true;
	344	+ flow.check_synthetic_connection(u);
	345	+ }
	346	+
	347	+ glutPostRedisplay();
	348	+}
	349	+
	350	+// defines camera motion based on mouse dragging
	351	+void glut_motion(int x, int y) {
	352	+
	353	+ mods = glutGetModifiers();
	354	+ if (LTbutton && mods == 0) {
	355	+
	356	+ float theta = orbit_factor * (mouse_x - x); // determine the number of degrees along the x-axis to rotate
	357	+ float phi = orbit_factor * (y - mouse_y); // number of degrees along the y-axis to rotate
	358	+
	359	+ cam.OrbitFocus(theta, phi); // rotate the camera around the focal point
	360	+ }
	361	+ mouse_x = x; // update the mouse position
	362	+ mouse_y = y;
	363	+
	364	+ glutPostRedisplay(); // re-draw the visualization
	365	+}
	366	+
	367	+// get click window coordinates
	368	+void glut_mouse(int button, int state, int x, int y) {
	369	+
	370	+ mouse_x = x;
	371	+ mouse_y = y;
	372	+ if (button == GLUT_LEFT_BUTTON && state == GLUT_DOWN)
	373	+ LTbutton = true;
	374	+ else if (button == GLUT_LEFT_BUTTON && state == GLUT_UP)
	375	+ LTbutton = false;
	376	+
	377	+ if (button == GLUT_LEFT_BUTTON && state == GLUT_DOWN && simulation && !to_select_pressure) {
	378	+
	379	+ GLdouble posX, posY, posZ;
	380	+ window_to_world(posX, posY, posZ); // get the world coordinates
	381	+
	382	+ bool flag = flow.epsilon_vertex((float)posX, (float)posY, (float)posZ, eps, pressure_index);
	383	+ if (flag) {
	384	+ std::vector<unsigned>::iterator it = std::find(pendant_vertex.begin(), pendant_vertex.end(), pressure_index);
	385	+ if (it != pendant_vertex.end()) // if it is dangle vertex
	386	+ to_select_pressure = true;
	387	+ }
	388	+ }
	389	+ else if (button == GLUT_LEFT_BUTTON && state == GLUT_DOWN && simulation && to_select_pressure) {
	390	+ if (y > 2 * border_factor \|\| y < vY - border_factor) { // within the pressure bar range
	391	+ to_select_pressure = false;
	392	+ float tmp_pressure = (float)(vY - y - border_factor) / ((float)vY - border_factor) * max_pressure;
	393	+ flow.set_pressure(pressure_index, tmp_pressure);
	394	+
	395	+ flow_stable_state(); // main function of solving the linear system
	396	+ flow.print_flow();
	397	+ }
	398	+ }
	399	+}
	400	+
	401	+// define camera move based on mouse wheel move
	402	+void glut_wheel(int wheel, int direction, int x, int y) {
	403	+
	404	+ mouse_x = x;
	405	+ mouse_y = y;
	406	+
	407	+ GLdouble posX, posY, posZ;
	408	+ window_to_world(posX, posY, posZ); // get the world coordinates
	409	+
	410	+ if (!to_select_pressure) {
	411	+ bool flag = flow.epsilon_vertex((float)posX, (float)posY, (float)posZ, eps, pressure_index);
	412	+ if (flag && simulation) {
	413	+ float tmp_r;
	414	+ if (direction > 0) { // increase radii
	415	+ tmp_r = flow.get_radius(pressure_index);
	416	+ tmp_r += radii_factor;
	417	+ }
	418	+ else {
	419	+ tmp_r = flow.get_radius(pressure_index);
	420	+ tmp_r -= radii_factor;
	421	+ if (tmp_r <= 0)
	422	+ tmp_r = default_radii;
	423	+ }
	424	+ flow.set_radius(pressure_index, tmp_r);
	425	+ flow_stable_state();
	426	+ flow.print_flow();
	427	+ }
	428	+ else {
	429	+ if (direction > 0) // if it is button 3(up), move closer
	430	+ move_pace = zoom_factor;
	431	+ else // if it is button 4(down), leave farther
	432	+ move_pace = -zoom_factor;
	433	+
	434	+ cam.Push(move_pace);
	435	+ }
	436	+ }
	437	+
	438	+ glutPostRedisplay();
	439	+}
	440	+
	441	+// define keyboard inputs
	442	+void glut_keyboard(unsigned char key, int x, int y) {
	443	+
	444	+ // register different keyboard operation
	445	+ switch (key) {
	446	+
	447	+ // zooming
	448	+ case 'w': // if keyboard 'w' is pressed, then move closer
	449	+ move_pace = zoom_factor;
	450	+ cam.Push(move_pace);
	451	+ break;
	452	+ case 's': // if keyboard 's' is pressed, then leave farther
	453	+ move_pace = -zoom_factor;
	454	+ cam.Push(move_pace);
	455	+ break;
	456	+
	457	+ // output image stack
	458	+ case 'm':
	459	+ if (manufacture) {
	460	+#ifdef __CUDACC__
	461	+ flow.make_image_stack(dx, dy, dz, stackdir);
	462	+#else
	463	+ std::cout << "You need to have a gpu to make image stack, sorry." << std::endl;
	464	+#endif
	465	+ }
	466	+ else if (build_inlet_outlet && !modified_bridge) {
	467	+ flow.modify_synthetic_connection(u, rou);
	468	+ modified_bridge = true;
	469	+ }
	470	+ break;
	471	+ }
	472	+
	473	+ glutPostRedisplay();
	474	+}
	475	+
	476	+// glut initialization
	477	+void glut_initialize() {
	478	+
	479	+ int myargc = 1;
	480	+ char* myargv[1];
	481	+ myargv[0] = strdup("generate_network_network");
	482	+
	483	+ glutInit(&myargc, myargv);
	484	+ glutInitDisplayMode(GLUT_DEPTH \| GLUT_DOUBLE \| GLUT_RGBA);
	485	+ glutInitWindowPosition(100, 100); // set the initial window position
	486	+ glutInitWindowSize(1000, 1000);
	487	+ glutCreateWindow("3D flow simulation");
	488	+
	489	+ glutDisplayFunc(glut_render);
	490	+ glutMouseFunc(glut_mouse);
	491	+ glutMotionFunc(glut_motion);
	492	+ glutMouseWheelFunc(glut_wheel);
	493	+ glutKeyboardFunc(glut_keyboard);
	494	+
	495	+ glutCreateMenu(glut_menu); // create a menu object
	496	+ glut_set_menu(0, 1);
	497	+ glutAttachMenu(GLUT_RIGHT_BUTTON); // register right mouse to open menu option
	498	+
	499	+ stim::vec3<float> c = bb.center(); // get the center of the network bounding box
	500	+ // place the camera along the z-axis at a distance determined by the network size along x and y
	501	+ cam.setPosition(c + stim::vec<float>(0, 0, camera_factor * std::max(bb.size()[0], bb.size()[1])));
	502	+ cam.LookAt(c[0], c[1], c[2]);
	503	+}
	504	+
	505	+int main(int argc, char* argv[]) {
	506	+
	507	+ // add arguments
	508	+ args.add("help", "prints the help");
	509	+ args.add("network", "load network from .obj or .swc file");
	510	+ args.add("maxpress", "maximum allowed pressure in g / units / s^2, default 2 is for blood when units = um", "2", "real value > 0");
	511	+ args.add("viscosity", "set the viscosity of the fluid (in g / units / s), default .00001 is for blood when units = um", ".00001", "real value > 0");
	512	+ args.add("rou", "set the desity of the fluid (in g / units^3), default 1.06*10^-12 is for blood when units = um", ".00000000000106", "real value > 0");
	513	+ args.add("stackres", "spacing between pixel samples in each dimension(in units/pixel)", "1 1 1", "real value > 0");
	514	+ args.add("stackdir", "set the directory of the output image stack", "", "any existing directory (ex. /home/name/network)");
	515	+
	516	+ args.parse(argc, argv); // parse the command line
	517	+
	518	+ // load network
	519	+ if (args["network"].is_set()) { // load network from user
	520	+ std::vector<std::string> tmp = stim::parser::split(args["network"].as_string(), '.');
	521	+ if ("obj" == tmp[1])
	522	+ flow.load_obj(args["network"].as_string());
	523	+ else if ("swc" == tmp[1])
	524	+ flow.load_swc(args["network"].as_string());
	525	+ else {
	526	+ std::cout << "Invalid file type" << std::endl;
	527	+ std::exit(1);
	528	+ }
	529	+ }
	530	+ get_background();
	531	+
	532	+ // blood pressure in capillaries range from 15 - 35 torr
	533	+ // 1 torr = 133.3 Pa
	534	+ max_pressure = args["maxpress"].as_float();
	535	+
	536	+ // normal blood viscosity range from 4 - 15 mPa·s(cP)
	537	+ // 1 Pa·s = 1 g / mm / s
	538	+ u = args["viscosity"].as_float(); // g / units / s
	539	+
	540	+ // normally the blood density in capillaries: 1060 kg/m^3 = 1.06*10^-12 g/um^3
	541	+ rou = args["rou"].as_float();
	542	+
	543	+ // get the vexel and image stack size
	544	+ dx = args["stackres"].as_float(0);
	545	+ dy = args["stackres"].as_float(1);
	546	+ dz = args["stackres"].as_float(2);
	547	+
	548	+ // get the save directory of image stack
	549	+ if (args["stackdir"].is_set())
	550	+ stackdir = args["stackdir"].as_string();
	551	+
	552	+ // glut main loop
	553	+ bb = flow.boundingbox();
	554	+ glut_initialize();
	555	+ glutMainLoop();
	556	+}
...	...