2017-09-12 2 views
0

opennlによって実装されたLeast square conformal mapアルゴリズムをそのまま使用しています。アルゴリズムのスペクトルモードでは、私はUVマッピングにおいて重なり合う三角形を得る。コーン三角オブジェクトの場合、それは私がコードや紙を経て次の出力は、出力は次のようなものでなければなりませんOpenNLによるLSCMの実装では、UVマッピングで重複する三角形が表示されます

enter image description here

enter image description here

を示しています。率直に言って私は実装の背後にある数学を理解していなかったし、なぜこれが起こっているのか分からなかった。コーンオブジェクトはhere

# This file uses centimeters as units for non-parametric coordinates. 

mtllib cone_triangulated.mtl 
g default 
v 5.440012 -1.000000 -0.309017 
v 5.297973 -1.000000 -0.587786 
v 5.076741 -1.000000 -0.809017 
v 4.797972 -1.000000 -0.951057 
v 4.488955 -1.000000 -1.000000 
v 4.179938 -1.000000 -0.951057 
v 3.901170 -1.000000 -0.809017 
v 3.679938 -1.000000 -0.587785 
v 3.537898 -1.000000 -0.309017 
v 3.488955 -1.000000 0.000000 
v 3.537898 -1.000000 0.309017 
v 3.679938 -1.000000 0.587785 
v 3.901170 -1.000000 0.809017 
v 4.179938 -1.000000 0.951057 
v 4.488955 -1.000000 1.000000 
v 4.797972 -1.000000 0.951057 
v 5.076741 -1.000000 0.809017 
v 5.297972 -1.000000 0.587785 
v 5.440012 -1.000000 0.309017 
v 5.488955 -1.000000 0.000000 
v 4.488955 1.000000 0.000000 
vt 0.710013 0.000454 
vt 0.773162 0.000454 
vt 0.640012 0.453512 
vt 0.823278 0.000454 
vt 0.640012 0.000454 
vt 0.570010 0.000454 
vt 0.506861 0.000454 
vt 0.456745 0.000454 
vt 0.413641 0.454510 
vt 0.476790 0.454510 
vt 0.546791 0.907569 
vt 0.546791 0.454510 
vt 0.363525 0.454510 
vt 0.616793 0.454510 
vt 0.679942 0.454510 
vt 0.730058 0.454510 
vt 0.442471 0.156982 
vt 0.453558 0.226983 
vt 0.442471 0.296985 
vt 0.410295 0.360134 
vt 0.360180 0.410249 
vt 0.297030 0.442425 
vt 0.227029 0.453512 
vt 0.157028 0.442425 
vt 0.093878 0.410249 
vt 0.043763 0.360134 
vt 0.011587 0.296985 
vt 0.000500 0.226983 
vt 0.011587 0.156982 
vt 0.043763 0.093832 
vt 0.093878 0.043717 
vt 0.157027 0.011541 
vt 0.227029 0.000454 
vt 0.297030 0.011541 
vt 0.360180 0.043717 
vt 0.410295 0.093832 
vt 0.999501 0.907569 
vt 0.936351 0.907569 
vt 0.866350 0.454510 
vt 0.866350 0.907569 
vt 0.796348 0.907569 
vt 0.733199 0.907569 
vt 0.094082 0.454510 
vt 0.157231 0.454510 
vt 0.227233 0.907569 
vt 0.227233 0.454510 
vt 0.297234 0.454510 
vt 0.360383 0.454510 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 -0.000000 
vn 0.000000 -1.000000 -0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.850651 0.447214 -0.276392 
vn 0.723607 0.447214 -0.525731 
vn 0.000000 1.000000 -0.000005 
vn 0.525731 0.447214 -0.723607 
vn 0.276393 0.447214 -0.850651 
vn -0.000000 0.447214 -0.894427 
vn -0.276393 0.447214 -0.850651 
vn -0.525731 0.447214 -0.723607 
vn -0.723607 0.447214 -0.525731 
vn -0.850651 0.447214 -0.276393 
vn -0.894427 0.447214 0.000000 
vn -0.850651 0.447214 0.276393 
vn -0.723607 0.447214 0.525731 
vn -0.525731 0.447214 0.723607 
vn -0.276393 0.447214 0.850651 
vn 0.000000 0.447214 0.894427 
vn 0.276393 0.447214 0.850651 
vn 0.525731 0.447214 0.723607 
vn 0.723607 0.447214 0.525731 
vn 0.850651 0.447214 0.276393 
vn 0.894427 0.447214 0.000001 
s 1 
g pasted__pCone1 group1 
usemtl initialShadingGroup 
f 1/17/1 20/18/2 2/36/3 
f 20/18/2 19/19/4 2/36/3 
f 19/19/4 18/20/5 2/36/3 
f 18/20/5 17/21/6 2/36/3 
f 17/21/6 16/22/7 2/36/3 
f 16/22/7 15/23/8 2/36/3 
f 15/23/8 14/24/9 2/36/3 
f 14/24/9 13/25/10 2/36/3 
f 13/25/10 12/26/11 2/36/3 
f 12/26/11 11/27/12 2/36/3 
f 11/27/12 10/28/13 2/36/3 
f 10/28/13 9/29/14 2/36/3 
f 9/29/14 8/30/15 2/36/3 
f 8/30/15 7/31/16 2/36/3 
f 7/31/16 6/32/17 2/36/3 
f 6/32/17 5/33/18 2/36/3 
f 5/33/18 4/34/19 2/36/3 
f 4/34/19 3/35/20 2/36/3 
s 2 
f 1/1/21 2/2/22 21/3/23 
f 2/2/22 3/4/24 21/3/23 
f 3/37/24 4/38/25 21/39/23 
f 4/38/25 5/40/26 21/39/23 
f 5/40/26 6/41/27 21/39/23 
f 6/41/27 7/42/28 21/39/23 
f 7/13/28 8/9/29 21/11/23 
f 8/9/29 9/10/30 21/11/23 
f 9/10/30 10/12/31 21/11/23 
f 10/12/31 11/14/32 21/11/23 
f 11/14/32 12/15/33 21/11/23 
f 12/15/33 13/16/34 21/11/23 
f 13/43/34 14/44/35 21/45/23 
f 14/44/35 15/46/36 21/45/23 
f 15/46/36 16/47/37 21/45/23 
f 16/47/37 17/48/38 21/45/23 
f 17/8/38 18/7/39 21/3/23 
f 18/7/39 19/6/40 21/3/23 
f 19/6/40 20/5/41 21/3/23 
f 20/5/41 1/1/21 21/3/23 
g default 
v 5.440012 -1.000000 -0.309017 
v 5.297973 -1.000000 -0.587786 
v 5.076741 -1.000000 -0.809017 
v 4.797972 -1.000000 -0.951057 
v 4.488955 -1.000000 -1.000000 
v 4.179938 -1.000000 -0.951057 
v 3.901170 -1.000000 -0.809017 
v 3.679938 -1.000000 -0.587785 
v 3.537898 -1.000000 -0.309017 
v 3.488955 -1.000000 0.000000 
v 3.537898 -1.000000 0.309017 
v 3.679938 -1.000000 0.587785 
v 3.901170 -1.000000 0.809017 
v 4.179938 -1.000000 0.951057 
v 4.488955 -1.000000 1.000000 
v 4.797972 -1.000000 0.951057 
v 5.076741 -1.000000 0.809017 
v 5.297972 -1.000000 0.587785 
v 5.440012 -1.000000 0.309017 
v 5.488955 -1.000000 0.000000 
v 4.488955 1.000000 0.000000 
vt 0.710013 0.000454 
vt 0.773162 0.000454 
vt 0.640012 0.453512 
vt 0.823278 0.000454 
vt 0.640012 0.000454 
vt 0.570010 0.000454 
vt 0.506861 0.000454 
vt 0.456745 0.000454 
vt 0.413641 0.454510 
vt 0.476790 0.454510 
vt 0.546791 0.907569 
vt 0.546791 0.454510 
vt 0.363525 0.454510 
vt 0.616793 0.454510 
vt 0.679942 0.454510 
vt 0.730058 0.454510 
vt 0.442471 0.156982 
vt 0.453558 0.226983 
vt 0.442471 0.296985 
vt 0.410295 0.360134 
vt 0.360180 0.410249 
vt 0.297030 0.442425 
vt 0.227029 0.453512 
vt 0.157028 0.442425 
vt 0.093878 0.410249 
vt 0.043763 0.360134 
vt 0.011587 0.296985 
vt 0.000500 0.226983 
vt 0.011587 0.156982 
vt 0.043763 0.093832 
vt 0.093878 0.043717 
vt 0.157027 0.011541 
vt 0.227029 0.000454 
vt 0.297030 0.011541 
vt 0.360180 0.043717 
vt 0.410295 0.093832 
vt 0.999501 0.907569 
vt 0.936351 0.907569 
vt 0.866350 0.454510 
vt 0.866350 0.907569 
vt 0.796348 0.907569 
vt 0.733199 0.907569 
vt 0.094082 0.454510 
vt 0.157231 0.454510 
vt 0.227233 0.907569 
vt 0.227233 0.454510 
vt 0.297234 0.454510 
vt 0.360383 0.454510 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 -0.000000 
vn 0.000000 -1.000000 -0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.000000 -1.000000 0.000000 
vn 0.850651 0.447214 -0.276392 
vn 0.723607 0.447214 -0.525731 
vn 0.000000 1.000000 -0.000005 
vn 0.525731 0.447214 -0.723607 
vn 0.276393 0.447214 -0.850651 
vn -0.000000 0.447214 -0.894427 
vn -0.276393 0.447214 -0.850651 
vn -0.525731 0.447214 -0.723607 
vn -0.723607 0.447214 -0.525731 
vn -0.850651 0.447214 -0.276393 
vn -0.894427 0.447214 0.000000 
vn -0.850651 0.447214 0.276393 
vn -0.723607 0.447214 0.525731 
vn -0.525731 0.447214 0.723607 
vn -0.276393 0.447214 0.850651 
vn 0.000000 0.447214 0.894427 
vn 0.276393 0.447214 0.850651 
vn 0.525731 0.447214 0.723607 
vn 0.723607 0.447214 0.525731 
vn 0.850651 0.447214 0.276393 
vn 0.894427 0.447214 0.000001 
s 1 
g pasted__pCone1 group1 
f 22/65/42 41/66/43 23/84/44 
f 41/66/43 40/67/45 23/84/44 
f 40/67/45 39/68/46 23/84/44 
f 39/68/46 38/69/47 23/84/44 
f 38/69/47 37/70/48 23/84/44 
f 37/70/48 36/71/49 23/84/44 
f 36/71/49 35/72/50 23/84/44 
f 35/72/50 34/73/51 23/84/44 
f 34/73/51 33/74/52 23/84/44 
f 33/74/52 32/75/53 23/84/44 
f 32/75/53 31/76/54 23/84/44 
f 31/76/54 30/77/55 23/84/44 
f 30/77/55 29/78/56 23/84/44 
f 29/78/56 28/79/57 23/84/44 
f 28/79/57 27/80/58 23/84/44 
f 27/80/58 26/81/59 23/84/44 
f 26/81/59 25/82/60 23/84/44 
f 25/82/60 24/83/61 23/84/44 
s 2 
f 22/49/62 23/50/63 42/51/64 
f 23/50/63 24/52/65 42/51/64 
f 24/85/65 25/86/66 42/87/64 
f 25/86/66 26/88/67 42/87/64 
f 26/88/67 27/89/68 42/87/64 
f 27/89/68 28/90/69 42/87/64 
f 28/61/69 29/57/70 42/59/64 
f 29/57/70 30/58/71 42/59/64 
f 30/58/71 31/60/72 42/59/64 
f 31/60/72 32/62/73 42/59/64 
f 32/62/73 33/63/74 42/59/64 
f 33/63/74 34/64/75 42/59/64 
f 34/91/75 35/92/76 42/93/64 
f 35/92/76 36/94/77 42/93/64 
f 36/94/77 37/95/78 42/93/64 
f 37/95/78 38/96/79 42/93/64 
f 38/56/79 39/55/80 42/51/64 
f 39/55/80 40/54/81 42/51/64 
f 40/54/81 41/53/82 42/51/64 
f 41/53/82 22/49/62 42/51/64 

で、出力オブジェクトは、セグメンテーションと梱包せずにこのアルゴリズムの実装は、それが唯一のLSCMソルバーだと思わhere

v 5.44001 -1 -0.309017 
v 5.29797 -1 -0.587786 
v 5.07674 -1 -0.809017 
v 4.79797 -1 -0.951057 
v 4.48895 -1 -1 
v 4.17994 -1 -0.951057 
v 3.90117 -1 -0.809017 
v 3.67994 -1 -0.587785 
v 3.5379 -1 -0.309017 
v 3.48895 -1 0 
v 3.5379 -1 0.309017 
v 3.67994 -1 0.587785 
v 3.90117 -1 0.809017 
v 4.17994 -1 0.951057 
v 4.48895 -1 1 
v 4.79797 -1 0.951057 
v 5.07674 -1 0.809017 
v 5.29797 -1 0.587785 
v 5.44001 -1 0.309017 
v 5.48895 -1 0 
v 4.48895 1 0 
v 5.44001 -1 -0.309017 
v 5.29797 -1 -0.587786 
v 5.07674 -1 -0.809017 
v 4.79797 -1 -0.951057 
v 4.48895 -1 -1 
v 4.17994 -1 -0.951057 
v 3.90117 -1 -0.809017 
v 3.67994 -1 -0.587785 
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v 3.48895 -1 0 
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v 3.67994 -1 0.587785 
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v 4.48895 -1 1 
v 4.79797 -1 0.951057 
v 5.07674 -1 0.809017 
v 5.29797 -1 0.587785 
v 5.44001 -1 0.309017 
v 5.48895 -1 0 
v 4.48895 1 0 
vt 0.800609 0.153437 
vt 0.853187 0.342951 
vt 0.97054 0.500774 
vt 0.982749 0.680535 
vt 0.904224 0.836086 
vt 0.768956 0.942029 
vt 0.610931 0.994182 
vt 0.454482 1 
vt 0.313817 0.969889 
vt 0.196085 0.912795 
vt 0.104498 0.83501 
vt 0.0405186 0.740541 
vt 0.00520155 0.63205 
vt 0 0.512002 
vt 0.027181 0.384009 
vt 0.0897402 0.254473 
vt 0.190352 0.134527 
vt 0.328514 0.0417729 
vt 0.495176 0 
vt 0.666179 0.0334716 
vt 0.440147 0.545027 
vt 0.662707 0.392667 
vt 0.667107 0.492235 
vt 0.707101 0.583524 
vt 0.692675 0.673683 
vt 0.636199 0.741562 
vt 0.557346 0.778488 
vt 0.473376 0.786261 
vt 0.395457 0.771332 
vt 0.32942 0.740458 
vt 0.277778 0.698867 
vt 0.241401 0.650034 
vt 0.220556 0.596104 
vt 0.215461 0.53851 
vt 0.226552 0.478636 
vt 0.254538 0.418524 
vt 0.30017 0.361675 
vt 0.363502 0.313891 
vt 0.442283 0.283808 
vt 0.529337 0.282144 
vt 0.609973 0.31813 
vt 0.440147 0.545027 
f 1/1 20/20 2/2 
f 20/20 19/19 2/2 
f 19/19 18/18 2/2 
f 18/18 17/17 2/2 
f 17/17 16/16 2/2 
f 16/16 15/15 2/2 
f 15/15 14/14 2/2 
f 14/14 13/13 2/2 
f 13/13 12/12 2/2 
f 12/12 11/11 2/2 
f 11/11 10/10 2/2 
f 10/10 9/9 2/2 
f 9/9 8/8 2/2 
f 8/8 7/7 2/2 
f 7/7 6/6 2/2 
f 6/6 5/5 2/2 
f 5/5 4/4 2/2 
f 4/4 3/3 2/2 
f 1/1 2/2 21/21 
f 2/2 3/3 21/21 
f 3/3 4/4 21/21 
f 4/4 5/5 21/21 
f 5/5 6/6 21/21 
f 6/6 7/7 21/21 
f 7/7 8/8 21/21 
f 8/8 9/9 21/21 
f 9/9 10/10 21/21 
f 10/10 11/11 21/21 
f 11/11 12/12 21/21 
f 12/12 13/13 21/21 
f 13/13 14/14 21/21 
f 14/14 15/15 21/21 
f 15/15 16/16 21/21 
f 16/16 17/17 21/21 
f 17/17 18/18 21/21 
f 18/18 19/19 21/21 
f 19/19 20/20 21/21 
f 20/20 1/1 21/21 
f 22/22 41/41 23/23 
f 41/41 40/40 23/23 
f 40/40 39/39 23/23 
f 39/39 38/38 23/23 
f 38/38 37/37 23/23 
f 37/37 36/36 23/23 
f 36/36 35/35 23/23 
f 35/35 34/34 23/23 
f 34/34 33/33 23/23 
f 33/33 32/32 23/23 
f 32/32 31/31 23/23 
f 31/31 30/30 23/23 
f 30/30 29/29 23/23 
f 29/29 28/28 23/23 
f 28/28 27/27 23/23 
f 27/27 26/26 23/23 
f 26/26 25/25 23/23 
f 25/25 24/24 23/23 
f 22/22 23/23 42/42 
f 23/23 24/24 42/42 
f 24/24 25/25 42/42 
f 25/25 26/26 42/42 
f 26/26 27/27 42/42 
f 27/27 28/28 42/42 
f 28/28 29/29 42/42 
f 29/29 30/30 42/42 
f 30/30 31/31 42/42 
f 31/31 32/32 42/42 
f 32/32 33/33 42/42 
f 33/33 34/34 42/42 
f 34/34 35/35 42/42 
f 35/35 36/36 42/42 
f 36/36 37/37 42/42 
f 37/37 38/38 42/42 
f 38/38 39/39 42/42 
f 39/39 40/40 42/42 
f 40/40 41/41 42/42 
f 41/41 22/22 42/42 

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