├── .gitmodules ├── LICENSE ├── README.md ├── libigl-course-slides.pptx.zip ├── src ├── cube_twist.obj ├── main.cpp └── main_solution.cpp └── vector-field-design ├── CMakeLists.txt ├── README.md ├── bumpy.off ├── cmake ├── DownloadProject.CMakeLists.cmake.in ├── DownloadProject.cmake └── FindLIBIGL.cmake └── src ├── main.cpp ├── vector_field.cpp └── vector_field.h /.gitmodules: -------------------------------------------------------------------------------- 1 | [submodule "libigl"] 2 | path = libigl 3 | url = https://github.com/libigl/libigl/ 4 | [submodule "libigl-example-project"] 5 | path = libigl-example-project 6 | url = https://github.com/libigl/libigl-example-project 7 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | Mozilla Public License Version 2.0 2 | ================================== 3 | 4 | 1. Definitions 5 | -------------- 6 | 7 | 1.1. "Contributor" 8 | means each individual or legal entity that creates, contributes to 9 | the creation of, or owns Covered Software. 10 | 11 | 1.2. "Contributor Version" 12 | means the combination of the Contributions of others (if any) used 13 | by a Contributor and that particular Contributor's Contribution. 14 | 15 | 1.3. "Contribution" 16 | means Covered Software of a particular Contributor. 17 | 18 | 1.4. "Covered Software" 19 | means Source Code Form to which the initial Contributor has attached 20 | the notice in Exhibit A, the Executable Form of such Source Code 21 | Form, and Modifications of such Source Code Form, in each case 22 | including portions thereof. 23 | 24 | 1.5. "Incompatible With Secondary Licenses" 25 | means 26 | 27 | (a) that the initial Contributor has attached the notice described 28 | in Exhibit B to the Covered Software; or 29 | 30 | (b) that the Covered Software was made available under the terms of 31 | version 1.1 or earlier of the License, but not also under the 32 | terms of a Secondary License. 33 | 34 | 1.6. "Executable Form" 35 | means any form of the work other than Source Code Form. 36 | 37 | 1.7. "Larger Work" 38 | means a work that combines Covered Software with other material, in 39 | a separate file or files, that is not Covered Software. 40 | 41 | 1.8. "License" 42 | means this document. 43 | 44 | 1.9. "Licensable" 45 | means having the right to grant, to the maximum extent possible, 46 | whether at the time of the initial grant or subsequently, any and 47 | all of the rights conveyed by this License. 48 | 49 | 1.10. "Modifications" 50 | means any of the following: 51 | 52 | (a) any file in Source Code Form that results from an addition to, 53 | deletion from, or modification of the contents of Covered 54 | Software; or 55 | 56 | (b) any new file in Source Code Form that contains any Covered 57 | Software. 58 | 59 | 1.11. "Patent Claims" of a Contributor 60 | means any patent claim(s), including without limitation, method, 61 | process, and apparatus claims, in any patent Licensable by such 62 | Contributor that would be infringed, but for the grant of the 63 | License, by the making, using, selling, offering for sale, having 64 | made, import, or transfer of either its Contributions or its 65 | Contributor Version. 66 | 67 | 1.12. "Secondary License" 68 | means either the GNU General Public License, Version 2.0, the GNU 69 | Lesser General Public License, Version 2.1, the GNU Affero General 70 | Public License, Version 3.0, or any later versions of those 71 | licenses. 72 | 73 | 1.13. "Source Code Form" 74 | means the form of the work preferred for making modifications. 75 | 76 | 1.14. "You" (or "Your") 77 | means an individual or a legal entity exercising rights under this 78 | License. For legal entities, "You" includes any entity that 79 | controls, is controlled by, or is under common control with You. For 80 | purposes of this definition, "control" means (a) the power, direct 81 | or indirect, to cause the direction or management of such entity, 82 | whether by contract or otherwise, or (b) ownership of more than 83 | fifty percent (50%) of the outstanding shares or beneficial 84 | ownership of such entity. 85 | 86 | 2. License Grants and Conditions 87 | -------------------------------- 88 | 89 | 2.1. Grants 90 | 91 | Each Contributor hereby grants You a world-wide, royalty-free, 92 | non-exclusive license: 93 | 94 | (a) under intellectual property rights (other than patent or trademark) 95 | Licensable by such Contributor to use, reproduce, make available, 96 | modify, display, perform, distribute, and otherwise exploit its 97 | Contributions, either on an unmodified basis, with Modifications, or 98 | as part of a Larger Work; and 99 | 100 | (b) under Patent Claims of such Contributor to make, use, sell, offer 101 | for sale, have made, import, and otherwise transfer either its 102 | Contributions or its Contributor Version. 103 | 104 | 2.2. Effective Date 105 | 106 | The licenses granted in Section 2.1 with respect to any Contribution 107 | become effective for each Contribution on the date the Contributor first 108 | distributes such Contribution. 109 | 110 | 2.3. Limitations on Grant Scope 111 | 112 | The licenses granted in this Section 2 are the only rights granted under 113 | this License. No additional rights or licenses will be implied from the 114 | distribution or licensing of Covered Software under this License. 115 | Notwithstanding Section 2.1(b) above, no patent license is granted by a 116 | Contributor: 117 | 118 | (a) for any code that a Contributor has removed from Covered Software; 119 | or 120 | 121 | (b) for infringements caused by: (i) Your and any other third party's 122 | modifications of Covered Software, or (ii) the combination of its 123 | Contributions with other software (except as part of its Contributor 124 | Version); or 125 | 126 | (c) under Patent Claims infringed by Covered Software in the absence of 127 | its Contributions. 128 | 129 | This License does not grant any rights in the trademarks, service marks, 130 | or logos of any Contributor (except as may be necessary to comply with 131 | the notice requirements in Section 3.4). 132 | 133 | 2.4. Subsequent Licenses 134 | 135 | No Contributor makes additional grants as a result of Your choice to 136 | distribute the Covered Software under a subsequent version of this 137 | License (see Section 10.2) or under the terms of a Secondary License (if 138 | permitted under the terms of Section 3.3). 139 | 140 | 2.5. Representation 141 | 142 | Each Contributor represents that the Contributor believes its 143 | Contributions are its original creation(s) or it has sufficient rights 144 | to grant the rights to its Contributions conveyed by this License. 145 | 146 | 2.6. Fair Use 147 | 148 | This License is not intended to limit any rights You have under 149 | applicable copyright doctrines of fair use, fair dealing, or other 150 | equivalents. 151 | 152 | 2.7. Conditions 153 | 154 | Sections 3.1, 3.2, 3.3, and 3.4 are conditions of the licenses granted 155 | in Section 2.1. 156 | 157 | 3. Responsibilities 158 | ------------------- 159 | 160 | 3.1. Distribution of Source Form 161 | 162 | All distribution of Covered Software in Source Code Form, including any 163 | Modifications that You create or to which You contribute, must be under 164 | the terms of this License. You must inform recipients that the Source 165 | Code Form of the Covered Software is governed by the terms of this 166 | License, and how they can obtain a copy of this License. You may not 167 | attempt to alter or restrict the recipients' rights in the Source Code 168 | Form. 169 | 170 | 3.2. Distribution of Executable Form 171 | 172 | If You distribute Covered Software in Executable Form then: 173 | 174 | (a) such Covered Software must also be made available in Source Code 175 | Form, as described in Section 3.1, and You must inform recipients of 176 | the Executable Form how they can obtain a copy of such Source Code 177 | Form by reasonable means in a timely manner, at a charge no more 178 | than the cost of distribution to the recipient; and 179 | 180 | (b) You may distribute such Executable Form under the terms of this 181 | License, or sublicense it under different terms, provided that the 182 | license for the Executable Form does not attempt to limit or alter 183 | the recipients' rights in the Source Code Form under this License. 184 | 185 | 3.3. Distribution of a Larger Work 186 | 187 | You may create and distribute a Larger Work under terms of Your choice, 188 | provided that You also comply with the requirements of this License for 189 | the Covered Software. If the Larger Work is a combination of Covered 190 | Software with a work governed by one or more Secondary Licenses, and the 191 | Covered Software is not Incompatible With Secondary Licenses, this 192 | License permits You to additionally distribute such Covered Software 193 | under the terms of such Secondary License(s), so that the recipient of 194 | the Larger Work may, at their option, further distribute the Covered 195 | Software under the terms of either this License or such Secondary 196 | License(s). 197 | 198 | 3.4. Notices 199 | 200 | You may not remove or alter the substance of any license notices 201 | (including copyright notices, patent notices, disclaimers of warranty, 202 | or limitations of liability) contained within the Source Code Form of 203 | the Covered Software, except that You may alter any license notices to 204 | the extent required to remedy known factual inaccuracies. 205 | 206 | 3.5. Application of Additional Terms 207 | 208 | You may choose to offer, and to charge a fee for, warranty, support, 209 | indemnity or liability obligations to one or more recipients of Covered 210 | Software. However, You may do so only on Your own behalf, and not on 211 | behalf of any Contributor. You must make it absolutely clear that any 212 | such warranty, support, indemnity, or liability obligation is offered by 213 | You alone, and You hereby agree to indemnify every Contributor for any 214 | liability incurred by such Contributor as a result of warranty, support, 215 | indemnity or liability terms You offer. You may include additional 216 | disclaimers of warranty and limitations of liability specific to any 217 | jurisdiction. 218 | 219 | 4. Inability to Comply Due to Statute or Regulation 220 | --------------------------------------------------- 221 | 222 | If it is impossible for You to comply with any of the terms of this 223 | License with respect to some or all of the Covered Software due to 224 | statute, judicial order, or regulation then You must: (a) comply with 225 | the terms of this License to the maximum extent possible; and (b) 226 | describe the limitations and the code they affect. Such description must 227 | be placed in a text file included with all distributions of the Covered 228 | Software under this License. Except to the extent prohibited by statute 229 | or regulation, such description must be sufficiently detailed for a 230 | recipient of ordinary skill to be able to understand it. 231 | 232 | 5. Termination 233 | -------------- 234 | 235 | 5.1. The rights granted under this License will terminate automatically 236 | if You fail to comply with any of its terms. However, if You become 237 | compliant, then the rights granted under this License from a particular 238 | Contributor are reinstated (a) provisionally, unless and until such 239 | Contributor explicitly and finally terminates Your grants, and (b) on an 240 | ongoing basis, if such Contributor fails to notify You of the 241 | non-compliance by some reasonable means prior to 60 days after You have 242 | come back into compliance. Moreover, Your grants from a particular 243 | Contributor are reinstated on an ongoing basis if such Contributor 244 | notifies You of the non-compliance by some reasonable means, this is the 245 | first time You have received notice of non-compliance with this License 246 | from such Contributor, and You become compliant prior to 30 days after 247 | Your receipt of the notice. 248 | 249 | 5.2. If You initiate litigation against any entity by asserting a patent 250 | infringement claim (excluding declaratory judgment actions, 251 | counter-claims, and cross-claims) alleging that a Contributor Version 252 | directly or indirectly infringes any patent, then the rights granted to 253 | You by any and all Contributors for the Covered Software under Section 254 | 2.1 of this License shall terminate. 255 | 256 | 5.3. In the event of termination under Sections 5.1 or 5.2 above, all 257 | end user license agreements (excluding distributors and resellers) which 258 | have been validly granted by You or Your distributors under this License 259 | prior to termination shall survive termination. 260 | 261 | ************************************************************************ 262 | * * 263 | * 6. Disclaimer of Warranty * 264 | * ------------------------- * 265 | * * 266 | * Covered Software is provided under this License on an "as is" * 267 | * basis, without warranty of any kind, either expressed, implied, or * 268 | * statutory, including, without limitation, warranties that the * 269 | * Covered Software is free of defects, merchantable, fit for a * 270 | * particular purpose or non-infringing. The entire risk as to the * 271 | * quality and performance of the Covered Software is with You. * 272 | * Should any Covered Software prove defective in any respect, You * 273 | * (not any Contributor) assume the cost of any necessary servicing, * 274 | * repair, or correction. This disclaimer of warranty constitutes an * 275 | * essential part of this License. No use of any Covered Software is * 276 | * authorized under this License except under this disclaimer. * 277 | * * 278 | ************************************************************************ 279 | 280 | ************************************************************************ 281 | * * 282 | * 7. Limitation of Liability * 283 | * -------------------------- * 284 | * * 285 | * Under no circumstances and under no legal theory, whether tort * 286 | * (including negligence), contract, or otherwise, shall any * 287 | * Contributor, or anyone who distributes Covered Software as * 288 | * permitted above, be liable to You for any direct, indirect, * 289 | * special, incidental, or consequential damages of any character * 290 | * including, without limitation, damages for lost profits, loss of * 291 | * goodwill, work stoppage, computer failure or malfunction, or any * 292 | * and all other commercial damages or losses, even if such party * 293 | * shall have been informed of the possibility of such damages. This * 294 | * limitation of liability shall not apply to liability for death or * 295 | * personal injury resulting from such party's negligence to the * 296 | * extent applicable law prohibits such limitation. Some * 297 | * jurisdictions do not allow the exclusion or limitation of * 298 | * incidental or consequential damages, so this exclusion and * 299 | * limitation may not apply to You. * 300 | * * 301 | ************************************************************************ 302 | 303 | 8. Litigation 304 | ------------- 305 | 306 | Any litigation relating to this License may be brought only in the 307 | courts of a jurisdiction where the defendant maintains its principal 308 | place of business and such litigation shall be governed by laws of that 309 | jurisdiction, without reference to its conflict-of-law provisions. 310 | Nothing in this Section shall prevent a party's ability to bring 311 | cross-claims or counter-claims. 312 | 313 | 9. Miscellaneous 314 | ---------------- 315 | 316 | This License represents the complete agreement concerning the subject 317 | matter hereof. If any provision of this License is held to be 318 | unenforceable, such provision shall be reformed only to the extent 319 | necessary to make it enforceable. Any law or regulation which provides 320 | that the language of a contract shall be construed against the drafter 321 | shall not be used to construe this License against a Contributor. 322 | 323 | 10. Versions of the License 324 | --------------------------- 325 | 326 | 10.1. New Versions 327 | 328 | Mozilla Foundation is the license steward. Except as provided in Section 329 | 10.3, no one other than the license steward has the right to modify or 330 | publish new versions of this License. Each version will be given a 331 | distinguishing version number. 332 | 333 | 10.2. Effect of New Versions 334 | 335 | You may distribute the Covered Software under the terms of the version 336 | of the License under which You originally received the Covered Software, 337 | or under the terms of any subsequent version published by the license 338 | steward. 339 | 340 | 10.3. Modified Versions 341 | 342 | If you create software not governed by this License, and you want to 343 | create a new license for such software, you may create and use a 344 | modified version of this License if you rename the license and remove 345 | any references to the name of the license steward (except to note that 346 | such modified license differs from this License). 347 | 348 | 10.4. Distributing Source Code Form that is Incompatible With Secondary 349 | Licenses 350 | 351 | If You choose to distribute Source Code Form that is Incompatible With 352 | Secondary Licenses under the terms of this version of the License, the 353 | notice described in Exhibit B of this License must be attached. 354 | 355 | Exhibit A - Source Code Form License Notice 356 | ------------------------------------------- 357 | 358 | This Source Code Form is subject to the terms of the Mozilla Public 359 | License, v. 2.0. If a copy of the MPL was not distributed with this 360 | file, You can obtain one at http://mozilla.org/MPL/2.0/. 361 | 362 | If it is not possible or desirable to put the notice in a particular 363 | file, then You may include the notice in a location (such as a LICENSE 364 | file in a relevant directory) where a recipient would be likely to look 365 | for such a notice. 366 | 367 | You may add additional accurate notices of copyright ownership. 368 | 369 | Exhibit B - "Incompatible With Secondary Licenses" Notice 370 | --------------------------------------------------------- 371 | 372 | This Source Code Form is "Incompatible With Secondary Licenses", as 373 | defined by the Mozilla Public License, v. 2.0. 374 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # libigl-course 2 | Material for the short course on libigl. The course is composed of two parts. An overview of the coding style and purposed of the library (available in the [pptx slides](https://github.com/libigl/libigl-course/raw/master/libigl-course-slides.pptx.zip) in this repo), plus a live tutorial session. A longer version of the tutorial, which also contains an example of a vector field interpolation algorithm implemented in libigl is available in the [keynote slides](https://cs.nyu.edu/~panozzo/libigl/libigl-course-slides.key.zip). 3 | 4 | ## Part 1: libigl overview 5 | 6 | * 1.1 [How to clone the repository](https://libigl.github.io/tutorial/#chapter-1) 7 | 8 | * 1.2 [Structure of libigl](https://github.com/libigl/libigl) 9 | 10 | * 1.3 [Tutorial Compilation](https://libigl.github.io/tutorial/#chapter-1) 11 | 12 | * 1.4 [Structure of a simple libigl application (Tutorial 102)](https://libigl.github.io/tutorial/#visualizing-surfaces) 13 | * 1.5 [Overview of Discrete Geometric Quantities and Operators (202,203,204,205)](https://libigl.github.io/tutorial/#chapter-2-discrete-geometric-quantities-and-operators) 14 | * 1.6 [Overview of Shape Deformation (401,403,404,405)](https://libigl.github.io/tutorial/#chapter-4-shape-deformation) 15 | * 1.7 [Overview of Mesh Parametrization (501,502,503,505,710)](https://libigl.github.io/tutorial/#chapter-5-parametrization) 16 | 17 | ## Part 2: How to use libigl as a header-only library 18 | 19 | Libigl can be used as a header-only library, you can find an example of a simple application that computes mesh statistics in src/main_solution.cpp. 20 | 21 | ## Part 3: How to use libigl with libigl-example-project 22 | 23 | The recommended way to use libigl is by using the [libigl-example-project](https://github.com/libigl/libigl-example-project) repository. 24 | 25 | ## Part 4: Vector Field Design with libigl 26 | 27 | A complete example of how to code a simple field interpolation method using libigl. The source is available [here](https://github.com/libigl/libigl-course/tree/master/vector-field-design). 28 | 29 | ## Part 5: Advanced features 30 | 31 | * 4.1 [Serialization](https://libigl.github.io/tutorial/#state-serialization) 32 | * 4.2 [Booleans](https://libigl.github.io/tutorial/#boolean-operations-on-meshes) 33 | * 4.3 [Python](https://libigl.github.io/python-bindings/) 34 | 35 | ## Part 6: Coding Tips 36 | 37 | This is a short list of coding tips that will greatly reduce your pain and suffering before (and after) the SIGGRAPH deadline. 38 | 39 | * [Coding Tips](https://libigl.github.io/coding-guidelines/) 40 | 41 | 42 | Released under the MPL2 License, 43 | Copyright Alec Jacobson and Daniele Panozzo 44 | -------------------------------------------------------------------------------- /libigl-course-slides.pptx.zip: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/libigl/libigl-course/dd5a175e54f0afb787859db75295e3901e577bc2/libigl-course-slides.pptx.zip -------------------------------------------------------------------------------- /src/main.cpp: -------------------------------------------------------------------------------- 1 | // g++ -std=c++11 -I../libigl/include -I../libigl/external/eigen main.cpp 2 | 3 | #include 4 | 5 | int main(int argc, char *argv[]) 6 | { 7 | 8 | } 9 | -------------------------------------------------------------------------------- /src/main_solution.cpp: -------------------------------------------------------------------------------- 1 | // g++ -std=c++11 -I../libigl/include -I../libigl/external/eigen main_solution.cpp 2 | 3 | #include 4 | #include 5 | #include 6 | #include 7 | 8 | int main(int argc, char *argv[]) 9 | { 10 | using namespace Eigen; 11 | using namespace std; 12 | 13 | MatrixXd V; 14 | MatrixXi F; 15 | 16 | igl::readOBJ("cube_twist.obj",V,F); 17 | 18 | // Compute areas, min, max and standard deviation 19 | VectorXd area; 20 | igl::doublearea(V,F,area); 21 | area = area.array() / 2; 22 | 23 | double area_avg = area.mean(); 24 | double area_min = area.minCoeff() / area_avg; 25 | double area_max = area.maxCoeff() / area_avg; 26 | double area_sigma = sqrt(((area.array()-area_avg)/area_avg).square().mean()); 27 | 28 | printf("Areas (Min/Max)/Avg_Area Sigma: \n%.2f/%.2f (%.2f)\n", 29 | area_min,area_max,area_sigma); 30 | 31 | } 32 | -------------------------------------------------------------------------------- /vector-field-design/CMakeLists.txt: -------------------------------------------------------------------------------- 1 | cmake_minimum_required(VERSION 3.1) 2 | project(vector_field) 3 | 4 | set(CMAKE_MODULE_PATH ${CMAKE_MODULE_PATH} ${CMAKE_CURRENT_SOURCE_DIR}/cmake) 5 | 6 | include(DownloadProject) 7 | download_project( 8 | PROJ libigl 9 | SOURCE_DIR ${CMAKE_CURRENT_SOURCE_DIR}/external/libigl 10 | DOWNLOAD_DIR ${CMAKE_CURRENT_SOURCE_DIR}/external/.cache/libigl 11 | GIT_REPOSITORY https://github.com/libigl/libigl.git 12 | GIT_TAG e699d257fe860d4fd82709835e72438bd0cd1533 13 | ) 14 | # libigl 15 | option(LIBIGL_USE_STATIC_LIBRARY "Use libigl as static library" OFF) 16 | option(LIBIGL_WITH_ANTTWEAKBAR "Use AntTweakBar" OFF) 17 | option(LIBIGL_WITH_CGAL "Use CGAL" OFF) 18 | option(LIBIGL_WITH_COMISO "Use CoMiso" OFF) 19 | option(LIBIGL_WITH_CORK "Use Cork" OFF) 20 | option(LIBIGL_WITH_EMBREE "Use Embree" OFF) 21 | option(LIBIGL_WITH_LIM "Use LIM" OFF) 22 | option(LIBIGL_WITH_MATLAB "Use Matlab" OFF) 23 | option(LIBIGL_WITH_MOSEK "Use MOSEK" OFF) 24 | option(LIBIGL_WITH_OPENGL "Use OpenGL" ON) 25 | option(LIBIGL_WITH_OPENGL_GLFW "Use GLFW" ON) 26 | option(LIBIGL_WITH_OPENGL_GLFW_IMGUI "Use ImGui" ON) 27 | option(LIBIGL_WITH_PNG "Use PNG" OFF) 28 | option(LIBIGL_WITH_PYTHON "Use Python" OFF) 29 | option(LIBIGL_WITH_TETGEN "Use Tetgen" OFF) 30 | option(LIBIGL_WITH_TRIANGLE "Use Triangle" OFF) 31 | option(LIBIGL_WITH_VIEWER "Use OpenGL viewer" ON) 32 | option(LIBIGL_WITH_XML "Use XML" OFF) 33 | 34 | find_package(LIBIGL REQUIRED QUIET) 35 | 36 | # Add your project files 37 | file(GLOB SRCFILES src/main.cpp src/vector_field.cpp) 38 | add_executable(${PROJECT_NAME}_bin ${SRCFILES}) 39 | target_link_libraries(${PROJECT_NAME}_bin igl::core igl::opengl_glfw igl::opengl_glfw_imgui) 40 | -------------------------------------------------------------------------------- /vector-field-design/README.md: -------------------------------------------------------------------------------- 1 | [![Build Status](https://travis-ci.org/NYUGraphics/GM_Assignment_4.svg?branch=master)](https://travis-ci.org/NYUGraphics/GM_Assignment_4) 2 | # Assignment 4: Mesh Parameterization 3 | 4 | This repository contains the viewer/painting code and data files you'll need for 5 | assignment 4. General guideline will be the same as before. Link to [Handouts](https://cs.nyu.edu/~panozzo/gp18/Handout4.pdf) and [Slides](https://cs.nyu.edu/~panozzo/gp18/Assignment4.pdf) 6 | -------------------------------------------------------------------------------- /vector-field-design/bumpy.off: -------------------------------------------------------------------------------- 1 | OFF 2 | 1250 2496 0 3 | -2.09105 -2.09105 2.09105 4 | -0.833333 -2.23958 2.23958 5 | 0.833333 -2.23958 2.23958 6 | 2.09105 -2.09105 2.09105 7 | -2.23958 -0.833333 2.23958 8 | -0.833333 -0.833333 2.714 9 | 0.833333 -0.833333 2.714 10 | 2.23958 -0.833333 2.23958 11 | -2.23958 0.833333 2.23958 12 | -0.833333 0.833333 2.714 13 | 0.833333 0.833333 2.714 14 | 2.23958 0.833333 2.23958 15 | -2.09105 2.09105 2.09105 16 | -0.833333 2.23958 2.23958 17 | 0.833333 2.23958 2.23958 18 | 2.09105 2.09105 2.09105 19 | -2.23958 2.23958 0.833333 20 | -0.833333 2.714 0.833333 21 | 0.833333 2.714 0.833333 22 | 2.23958 2.23958 0.833333 23 | -2.23958 2.23958 -0.833333 24 | -0.833333 2.714 -0.833333 25 | 0.833333 2.714 -0.833333 26 | 2.23958 2.23958 -0.833333 27 | -2.09105 2.09105 -2.09105 28 | -0.833333 2.23958 -2.23958 29 | 0.833333 2.23958 -2.23958 30 | 2.09105 2.09105 -2.09105 31 | -2.23958 0.833333 -2.23958 32 | -0.833333 0.833333 -2.714 33 | 0.833333 0.833333 -2.714 34 | 2.23958 0.833333 -2.23958 35 | -2.23958 -0.833333 -2.23958 36 | -0.833333 -0.833333 -2.714 37 | 0.833333 -0.833333 -2.714 38 | 2.23958 -0.833333 -2.23958 39 | -2.09105 -2.09105 -2.09105 40 | -0.833333 -2.23958 -2.23958 41 | 0.833333 -2.23958 -2.23958 42 | 2.09105 -2.09105 -2.09105 43 | -2.23958 -2.23958 -0.833333 44 | -0.833333 -2.714 -0.833333 45 | 0.833333 -2.714 -0.833333 46 | 2.23958 -2.23958 -0.833333 47 | -2.23958 -2.23958 0.833333 48 | -0.833333 -2.714 0.833333 49 | 0.833333 -2.714 0.833333 50 | 2.23958 -2.23958 0.833333 51 | 2.714 -0.833333 -0.833333 52 | 2.714 -0.833333 0.833333 53 | 2.714 0.833333 -0.833333 54 | 2.714 0.833333 0.833333 55 | -2.714 -0.833333 -0.833333 56 | -2.714 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969 1508 | 3 969 125 404 1509 | 3 331 11 970 1510 | 3 970 11 408 1511 | 3 408 127 970 1512 | 3 970 127 659 1513 | 3 244 658 659 1514 | 3 659 658 970 1515 | 3 658 88 970 1516 | 3 970 88 331 1517 | 3 409 15 971 1518 | 3 971 15 337 1519 | 3 91 660 337 1520 | 3 337 660 971 1521 | 3 660 244 971 1522 | 3 971 244 659 1523 | 3 127 409 659 1524 | 3 659 409 971 1525 | 3 336 14 972 1526 | 3 972 14 407 1527 | 3 407 126 972 1528 | 3 972 126 661 1529 | 3 244 660 661 1530 | 3 661 660 972 1531 | 3 660 91 972 1532 | 3 972 91 336 1533 | 3 10 330 406 1534 | 3 406 330 973 1535 | 3 88 658 330 1536 | 3 330 658 973 1537 | 3 244 661 658 1538 | 3 658 661 973 1539 | 3 126 406 661 1540 | 3 661 406 973 1541 | 3 333 13 974 1542 | 3 974 13 412 1543 | 3 412 129 974 1544 | 3 974 129 663 1545 | 3 245 662 663 1546 | 3 663 662 974 1547 | 3 662 89 974 1548 | 3 974 89 333 1549 | 3 17 339 413 1550 | 3 413 339 975 1551 | 3 92 664 339 1552 | 3 339 664 975 1553 | 3 245 663 664 1554 | 3 664 663 975 1555 | 3 129 413 663 1556 | 3 663 413 975 1557 | 3 338 16 976 1558 | 3 976 16 411 1559 | 3 411 128 976 1560 | 3 976 128 665 1561 | 3 245 664 665 1562 | 3 665 664 976 1563 | 3 664 92 976 1564 | 3 976 92 338 1565 | 3 410 12 977 1566 | 3 977 12 332 1567 | 3 89 662 332 1568 | 3 332 662 977 1569 | 3 662 245 977 1570 | 3 977 245 665 1571 | 3 128 410 665 1572 | 3 665 410 977 1573 | 3 335 14 978 1574 | 3 978 14 414 1575 | 3 130 667 414 1576 | 3 414 667 978 1577 | 3 667 246 978 1578 | 3 978 246 666 1579 | 3 666 90 978 1580 | 3 978 90 335 1581 | 3 18 341 415 1582 | 3 415 341 979 1583 | 3 341 93 979 1584 | 3 979 93 668 1585 | 3 246 667 668 1586 | 3 668 667 979 1587 | 3 667 130 979 1588 | 3 979 130 415 1589 | 3 17 413 340 1590 | 3 340 413 980 1591 | 3 413 129 980 1592 | 3 980 129 669 1593 | 3 246 668 669 1594 | 3 669 668 980 1595 | 3 668 93 980 1596 | 3 980 93 340 1597 | 3 412 13 981 1598 | 3 981 13 334 1599 | 3 334 90 981 1600 | 3 981 90 666 1601 | 3 666 246 981 1602 | 3 981 246 669 1603 | 3 129 412 669 1604 | 3 669 412 981 1605 | 3 337 15 982 1606 | 3 982 15 416 1607 | 3 131 671 416 1608 | 3 416 671 982 1609 | 3 671 247 982 1610 | 3 982 247 670 1611 | 3 91 337 670 1612 | 3 670 337 982 1613 | 3 417 19 983 1614 | 3 983 19 343 1615 | 3 343 94 983 1616 | 3 983 94 672 1617 | 3 247 671 672 1618 | 3 672 671 983 1619 | 3 671 131 983 1620 | 3 983 131 417 1621 | 3 18 415 342 1622 | 3 342 415 984 1623 | 3 130 673 415 1624 | 3 415 673 984 1625 | 3 247 672 673 1626 | 3 673 672 984 1627 | 3 94 342 672 1628 | 3 672 342 984 1629 | 3 414 14 985 1630 | 3 985 14 336 1631 | 3 336 91 985 1632 | 3 985 91 670 1633 | 3 247 673 670 1634 | 3 670 673 985 1635 | 3 673 130 985 1636 | 3 985 130 414 1637 | 3 17 420 339 1638 | 3 339 420 986 1639 | 3 420 133 986 1640 | 3 986 133 675 1641 | 3 248 674 675 1642 | 3 675 674 986 1643 | 3 674 92 986 1644 | 3 986 92 339 1645 | 3 21 345 421 1646 | 3 421 345 987 1647 | 3 345 95 987 1648 | 3 987 95 676 1649 | 3 248 675 676 1650 | 3 676 675 987 1651 | 3 675 133 987 1652 | 3 987 133 421 1653 | 3 344 20 988 1654 | 3 988 20 419 1655 | 3 419 132 988 1656 | 3 988 132 677 1657 | 3 677 248 988 1658 | 3 988 248 676 1659 | 3 95 344 676 1660 | 3 676 344 988 1661 | 3 418 16 989 1662 | 3 989 16 338 1663 | 3 92 674 338 1664 | 3 338 674 989 1665 | 3 674 248 989 1666 | 3 989 248 677 1667 | 3 677 132 989 1668 | 3 989 132 418 1669 | 3 535 57 990 1670 | 3 990 57 538 1671 | 3 192 679 538 1672 | 3 538 679 990 1673 | 3 679 249 990 1674 | 3 990 249 678 1675 | 3 190 535 678 1676 | 3 678 535 990 1677 | 3 539 58 991 1678 | 3 991 58 543 1679 | 3 194 680 543 1680 | 3 543 680 991 1681 | 3 680 249 991 1682 | 3 991 249 679 1683 | 3 192 539 679 1684 | 3 679 539 991 1685 | 3 542 59 992 1686 | 3 992 59 545 1687 | 3 195 681 545 1688 | 3 545 681 992 1689 | 3 681 249 992 1690 | 3 992 249 680 1691 | 3 194 542 680 1692 | 3 680 542 992 1693 | 3 544 56 993 1694 | 3 993 56 534 1695 | 3 190 678 534 1696 | 3 534 678 993 1697 | 3 678 249 993 1698 | 3 993 249 681 1699 | 3 195 544 681 1700 | 3 681 544 993 1701 | 3 343 19 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| 3 1000 24 427 1751 | 3 136 689 427 1752 | 3 427 689 1000 1753 | 3 689 251 1000 1754 | 3 1000 251 688 1755 | 3 98 350 688 1756 | 3 688 350 1000 1757 | 3 426 20 1001 1758 | 3 1001 20 344 1759 | 3 344 95 1001 1760 | 3 1001 95 686 1761 | 3 251 689 686 1762 | 3 686 689 1001 1763 | 3 689 136 1001 1764 | 3 1001 136 426 1765 | 3 22 430 347 1766 | 3 347 430 1002 1767 | 3 430 138 1002 1768 | 3 1002 138 691 1769 | 3 252 690 691 1770 | 3 691 690 1002 1771 | 3 690 96 1002 1772 | 3 1002 96 347 1773 | 3 431 26 1003 1774 | 3 1003 26 353 1775 | 3 353 99 1003 1776 | 3 1003 99 692 1777 | 3 692 252 1003 1778 | 3 1003 252 691 1779 | 3 138 431 691 1780 | 3 691 431 1003 1781 | 3 352 25 1004 1782 | 3 1004 25 429 1783 | 3 137 693 429 1784 | 3 429 693 1004 1785 | 3 693 252 1004 1786 | 3 1004 252 692 1787 | 3 692 99 1004 1788 | 3 1004 99 352 1789 | 3 21 346 428 1790 | 3 428 346 1005 1791 | 3 346 96 1005 1792 | 3 1005 96 690 1793 | 3 252 693 690 1794 | 3 690 693 1005 1795 | 3 693 137 1005 1796 | 3 1005 137 428 1797 | 3 349 23 1006 1798 | 3 1006 23 432 1799 | 3 432 139 1006 1800 | 3 1006 139 695 1801 | 3 253 694 695 1802 | 3 695 694 1006 1803 | 3 694 97 1006 1804 | 3 1006 97 349 1805 | 3 433 27 1007 1806 | 3 1007 27 355 1807 | 3 100 696 355 1808 | 3 355 696 1007 1809 | 3 696 253 1007 1810 | 3 1007 253 695 1811 | 3 139 433 695 1812 | 3 695 433 1007 1813 | 3 354 26 1008 1814 | 3 1008 26 431 1815 | 3 431 138 1008 1816 | 3 1008 138 697 1817 | 3 253 696 697 1818 | 3 697 696 1008 1819 | 3 696 100 1008 1820 | 3 1008 100 354 1821 | 3 22 348 430 1822 | 3 430 348 1009 1823 | 3 97 694 348 1824 | 3 348 694 1009 1825 | 3 253 697 694 1826 | 3 694 697 1009 1827 | 3 138 430 697 1828 | 3 697 430 1009 1829 | 3 351 25 1010 1830 | 3 1010 25 436 1831 | 3 436 141 1010 1832 | 3 1010 141 699 1833 | 3 254 698 699 1834 | 3 699 698 1010 1835 | 3 698 98 1010 1836 | 3 1010 98 351 1837 | 3 29 357 437 1838 | 3 437 357 1011 1839 | 3 101 700 357 1840 | 3 357 700 1011 1841 | 3 254 699 700 1842 | 3 700 699 1011 1843 | 3 141 437 699 1844 | 3 699 437 1011 1845 | 3 356 28 1012 1846 | 3 1012 28 435 1847 | 3 435 140 1012 1848 | 3 1012 140 701 1849 | 3 254 700 701 1850 | 3 701 700 1012 1851 | 3 700 101 1012 1852 | 3 1012 101 356 1853 | 3 434 24 1013 1854 | 3 1013 24 350 1855 | 3 98 698 350 1856 | 3 350 698 1013 1857 | 3 698 254 1013 1858 | 3 1013 254 701 1859 | 3 140 434 701 1860 | 3 701 434 1013 1861 | 3 353 26 1014 1862 | 3 1014 26 438 1863 | 3 142 703 438 1864 | 3 438 703 1014 1865 | 3 703 255 1014 1866 | 3 1014 255 702 1867 | 3 702 99 1014 1868 | 3 1014 99 353 1869 | 3 30 359 439 1870 | 3 439 359 1015 1871 | 3 359 102 1015 1872 | 3 1015 102 704 1873 | 3 255 703 704 1874 | 3 704 703 1015 1875 | 3 703 142 1015 1876 | 3 1015 142 439 1877 | 3 29 437 358 1878 | 3 358 437 1016 1879 | 3 437 141 1016 1880 | 3 1016 141 705 1881 | 3 255 704 705 1882 | 3 705 704 1016 1883 | 3 704 102 1016 1884 | 3 1016 102 358 1885 | 3 436 25 1017 1886 | 3 1017 25 352 1887 | 3 352 99 1017 1888 | 3 1017 99 702 1889 | 3 702 255 1017 1890 | 3 1017 255 705 1891 | 3 141 436 705 1892 | 3 705 436 1017 1893 | 3 355 27 1018 1894 | 3 1018 27 440 1895 | 3 143 707 440 1896 | 3 440 707 1018 1897 | 3 707 256 1018 1898 | 3 1018 256 706 1899 | 3 100 355 706 1900 | 3 706 355 1018 1901 | 3 441 31 1019 1902 | 3 1019 31 361 1903 | 3 361 103 1019 1904 | 3 1019 103 708 1905 | 3 256 707 708 1906 | 3 708 707 1019 1907 | 3 707 143 1019 1908 | 3 1019 143 441 1909 | 3 30 439 360 1910 | 3 360 439 1020 1911 | 3 142 709 439 1912 | 3 439 709 1020 1913 | 3 256 708 709 1914 | 3 709 708 1020 1915 | 3 103 360 708 1916 | 3 708 360 1020 1917 | 3 438 26 1021 1918 | 3 1021 26 354 1919 | 3 354 100 1021 1920 | 3 1021 100 706 1921 | 3 256 709 706 1922 | 3 706 709 1021 1923 | 3 709 142 1021 1924 | 3 1021 142 438 1925 | 3 29 444 357 1926 | 3 357 444 1022 1927 | 3 444 145 1022 1928 | 3 1022 145 711 1929 | 3 257 710 711 1930 | 3 711 710 1022 1931 | 3 710 101 1022 1932 | 3 1022 101 357 1933 | 3 33 363 445 1934 | 3 445 363 1023 1935 | 3 363 104 1023 1936 | 3 1023 104 712 1937 | 3 257 711 712 1938 | 3 712 711 1023 1939 | 3 711 145 1023 1940 | 3 1023 145 445 1941 | 3 362 32 1024 1942 | 3 1024 32 443 1943 | 3 443 144 1024 1944 | 3 1024 144 713 1945 | 3 713 257 1024 1946 | 3 1024 257 712 1947 | 3 104 362 712 1948 | 3 712 362 1024 1949 | 3 442 28 1025 1950 | 3 1025 28 356 1951 | 3 101 710 356 1952 | 3 356 710 1025 1953 | 3 710 257 1025 1954 | 3 1025 257 713 1955 | 3 713 144 1025 1956 | 3 1025 144 442 1957 | 3 583 69 1026 1958 | 3 1026 69 586 1959 | 3 216 715 586 1960 | 3 586 715 1026 1961 | 3 715 258 1026 1962 | 3 1026 258 714 1963 | 3 214 583 714 1964 | 3 714 583 1026 1965 | 3 587 70 1027 1966 | 3 1027 70 591 1967 | 3 218 716 591 1968 | 3 591 716 1027 1969 | 3 716 258 1027 1970 | 3 1027 258 715 1971 | 3 216 587 715 1972 | 3 715 587 1027 1973 | 3 590 71 1028 1974 | 3 1028 71 593 1975 | 3 219 717 593 1976 | 3 593 717 1028 1977 | 3 717 258 1028 1978 | 3 1028 258 716 1979 | 3 218 590 716 1980 | 3 716 590 1028 1981 | 3 592 68 1029 1982 | 3 1029 68 582 1983 | 3 214 714 582 1984 | 3 582 714 1029 1985 | 3 714 258 1029 1986 | 3 1029 258 717 1987 | 3 219 592 717 1988 | 3 717 592 1029 1989 | 3 361 31 1030 1990 | 3 1030 31 448 1991 | 3 448 147 1030 1992 | 3 1030 147 719 1993 | 3 719 259 1030 1994 | 3 1030 259 718 1995 | 3 103 361 718 1996 | 3 718 361 1030 1997 | 3 449 35 1031 1998 | 3 1031 35 367 1999 | 3 106 720 367 2000 | 3 367 720 1031 2001 | 3 720 259 1031 2002 | 3 1031 259 719 2003 | 3 719 147 1031 2004 | 3 1031 147 449 2005 | 3 34 447 366 2006 | 3 366 447 1032 2007 | 3 447 146 1032 2008 | 3 1032 146 721 2009 | 3 259 720 721 2010 | 3 721 720 1032 2011 | 3 720 106 1032 2012 | 3 1032 106 366 2013 | 3 30 360 446 2014 | 3 446 360 1033 2015 | 3 360 103 1033 2016 | 3 1033 103 718 2017 | 3 259 721 718 2018 | 3 718 721 1033 2019 | 3 721 146 1033 2020 | 3 1033 146 446 2021 | 3 33 452 363 2022 | 3 363 452 1034 2023 | 3 149 723 452 2024 | 3 452 723 1034 2025 | 3 260 722 723 2026 | 3 723 722 1034 2027 | 3 104 363 722 2028 | 3 722 363 1034 2029 | 3 453 37 1035 2030 | 3 1035 37 369 2031 | 3 369 107 1035 2032 | 3 1035 107 724 2033 | 3 260 723 724 2034 | 3 724 723 1035 2035 | 3 723 149 1035 2036 | 3 1035 149 453 2037 | 3 368 36 1036 2038 | 3 1036 36 451 2039 | 3 148 725 451 2040 | 3 451 725 1036 2041 | 3 725 260 1036 2042 | 3 1036 260 724 2043 | 3 107 368 724 2044 | 3 724 368 1036 2045 | 3 450 32 1037 2046 | 3 1037 32 362 2047 | 3 362 104 1037 2048 | 3 1037 104 722 2049 | 3 260 725 722 2050 | 3 722 725 1037 2051 | 3 725 148 1037 2052 | 3 1037 148 450 2053 | 3 34 454 365 2054 | 3 365 454 1038 2055 | 3 454 150 1038 2056 | 3 1038 150 727 2057 | 3 261 726 727 2058 | 3 727 726 1038 2059 | 3 726 105 1038 2060 | 3 1038 105 365 2061 | 3 455 38 1039 2062 | 3 1039 38 371 2063 | 3 371 108 1039 2064 | 3 1039 108 728 2065 | 3 728 261 1039 2066 | 3 1039 261 727 2067 | 3 150 455 727 2068 | 3 727 455 1039 2069 | 3 370 37 1040 2070 | 3 1040 37 453 2071 | 3 149 729 453 2072 | 3 453 729 1040 2073 | 3 729 261 1040 2074 | 3 1040 261 728 2075 | 3 728 108 1040 2076 | 3 1040 108 370 2077 | 3 33 364 452 2078 | 3 452 364 1041 2079 | 3 364 105 1041 2080 | 3 1041 105 726 2081 | 3 261 729 726 2082 | 3 726 729 1041 2083 | 3 729 149 1041 2084 | 3 1041 149 452 2085 | 3 367 35 1042 2086 | 3 1042 35 456 2087 | 3 456 151 1042 2088 | 3 1042 151 731 2089 | 3 262 730 731 2090 | 3 731 730 1042 2091 | 3 730 106 1042 2092 | 3 1042 106 367 2093 | 3 457 39 1043 2094 | 3 1043 39 373 2095 | 3 109 732 373 2096 | 3 373 732 1043 2097 | 3 732 262 1043 2098 | 3 1043 262 731 2099 | 3 151 457 731 2100 | 3 731 457 1043 2101 | 3 372 38 1044 2102 | 3 1044 38 455 2103 | 3 455 150 1044 2104 | 3 1044 150 733 2105 | 3 262 732 733 2106 | 3 733 732 1044 2107 | 3 732 109 1044 2108 | 3 1044 109 372 2109 | 3 34 366 454 2110 | 3 454 366 1045 2111 | 3 106 730 366 2112 | 3 366 730 1045 2113 | 3 262 733 730 2114 | 3 730 733 1045 2115 | 3 150 454 733 2116 | 3 733 454 1045 2117 | 3 369 37 1046 2118 | 3 1046 37 460 2119 | 3 460 153 1046 2120 | 3 1046 153 735 2121 | 3 263 734 735 2122 | 3 735 734 1046 2123 | 3 734 107 1046 2124 | 3 1046 107 369 2125 | 3 41 375 461 2126 | 3 461 375 1047 2127 | 3 110 736 375 2128 | 3 375 736 1047 2129 | 3 263 735 736 2130 | 3 736 735 1047 2131 | 3 153 461 735 2132 | 3 735 461 1047 2133 | 3 374 40 1048 2134 | 3 1048 40 459 2135 | 3 459 152 1048 2136 | 3 1048 152 737 2137 | 3 263 736 737 2138 | 3 737 736 1048 2139 | 3 736 110 1048 2140 | 3 1048 110 374 2141 | 3 458 36 1049 2142 | 3 1049 36 368 2143 | 3 107 734 368 2144 | 3 368 734 1049 2145 | 3 734 263 1049 2146 | 3 1049 263 737 2147 | 3 152 458 737 2148 | 3 737 458 1049 2149 | 3 371 38 1050 2150 | 3 1050 38 462 2151 | 3 154 739 462 2152 | 3 462 739 1050 2153 | 3 739 264 1050 2154 | 3 1050 264 738 2155 | 3 738 108 1050 2156 | 3 1050 108 371 2157 | 3 42 377 463 2158 | 3 463 377 1051 2159 | 3 377 111 1051 2160 | 3 1051 111 740 2161 | 3 264 739 740 2162 | 3 740 739 1051 2163 | 3 739 154 1051 2164 | 3 1051 154 463 2165 | 3 41 461 376 2166 | 3 376 461 1052 2167 | 3 461 153 1052 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375 468 1058 2215 | 3 468 157 1058 2216 | 3 1058 157 747 2217 | 3 266 746 747 2218 | 3 747 746 1058 2219 | 3 746 110 1058 2220 | 3 1058 110 375 2221 | 3 45 381 469 2222 | 3 469 381 1059 2223 | 3 381 113 1059 2224 | 3 1059 113 748 2225 | 3 266 747 748 2226 | 3 748 747 1059 2227 | 3 747 157 1059 2228 | 3 1059 157 469 2229 | 3 380 44 1060 2230 | 3 1060 44 467 2231 | 3 467 156 1060 2232 | 3 1060 156 749 2233 | 3 749 266 1060 2234 | 3 1060 266 748 2235 | 3 113 380 748 2236 | 3 748 380 1060 2237 | 3 466 40 1061 2238 | 3 1061 40 374 2239 | 3 110 746 374 2240 | 3 374 746 1061 2241 | 3 746 266 1061 2242 | 3 1061 266 749 2243 | 3 749 156 1061 2244 | 3 1061 156 466 2245 | 3 615 77 1062 2246 | 3 1062 77 618 2247 | 3 232 751 618 2248 | 3 618 751 1062 2249 | 3 751 267 1062 2250 | 3 1062 267 750 2251 | 3 230 615 750 2252 | 3 750 615 1062 2253 | 3 619 78 1063 2254 | 3 1063 78 623 2255 | 3 234 752 623 2256 | 3 623 752 1063 2257 | 3 752 267 1063 2258 | 3 1063 267 751 2259 | 3 232 619 751 2260 | 3 751 619 1063 2261 | 3 622 79 1064 2262 | 3 1064 79 625 2263 | 3 235 753 625 2264 | 3 625 753 1064 2265 | 3 753 267 1064 2266 | 3 1064 267 752 2267 | 3 234 622 752 2268 | 3 752 622 1064 2269 | 3 624 76 1065 2270 | 3 1065 76 614 2271 | 3 230 750 614 2272 | 3 614 750 1065 2273 | 3 750 267 1065 2274 | 3 1065 267 753 2275 | 3 235 624 753 2276 | 3 753 624 1065 2277 | 3 379 43 1066 2278 | 3 1066 43 472 2279 | 3 472 159 1066 2280 | 3 1066 159 755 2281 | 3 755 268 1066 2282 | 3 1066 268 754 2283 | 3 112 379 754 2284 | 3 754 379 1066 2285 | 3 473 47 1067 2286 | 3 1067 47 385 2287 | 3 115 756 385 2288 | 3 385 756 1067 2289 | 3 756 268 1067 2290 | 3 1067 268 755 2291 | 3 755 159 1067 2292 | 3 1067 159 473 2293 | 3 46 471 384 2294 | 3 384 471 1068 2295 | 3 471 158 1068 2296 | 3 1068 158 757 2297 | 3 268 756 757 2298 | 3 757 756 1068 2299 | 3 756 115 1068 2300 | 3 1068 115 384 2301 | 3 42 378 470 2302 | 3 470 378 1069 2303 | 3 378 112 1069 2304 | 3 1069 112 754 2305 | 3 268 757 754 2306 | 3 754 757 1069 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3700 | 3 931 621 1243 3701 | 3 623 78 1244 3702 | 3 1244 78 617 3703 | 3 231 933 617 3704 | 3 617 933 1244 3705 | 3 933 312 1244 3706 | 3 1244 312 932 3707 | 3 234 623 932 3708 | 3 932 623 1244 3709 | 3 46 383 616 3710 | 3 616 383 1245 3711 | 3 383 114 1245 3712 | 3 1245 114 930 3713 | 3 312 933 930 3714 | 3 930 933 1245 3715 | 3 933 231 1245 3716 | 3 1245 231 616 3717 | 3 41 610 468 3718 | 3 468 610 1246 3719 | 3 610 228 1246 3720 | 3 1246 228 935 3721 | 3 313 934 935 3722 | 3 935 934 1246 3723 | 3 934 157 1246 3724 | 3 1246 157 468 3725 | 3 611 76 1247 3726 | 3 1247 76 624 3727 | 3 235 936 624 3728 | 3 624 936 1247 3729 | 3 936 313 1247 3730 | 3 1247 313 935 3731 | 3 228 611 935 3732 | 3 935 611 1247 3733 | 3 625 79 1248 3734 | 3 1248 79 621 3735 | 3 233 937 621 3736 | 3 621 937 1248 3737 | 3 937 313 1248 3738 | 3 1248 313 936 3739 | 3 235 625 936 3740 | 3 936 625 1248 3741 | 3 45 469 620 3742 | 3 620 469 1249 3743 | 3 469 157 1249 3744 | 3 1249 157 934 3745 | 3 313 937 934 3746 | 3 934 937 1249 3747 | 3 937 233 1249 3748 | 3 1249 233 620 3749 | -------------------------------------------------------------------------------- /vector-field-design/cmake/DownloadProject.CMakeLists.cmake.in: -------------------------------------------------------------------------------- 1 | # Distributed under the OSI-approved MIT License. See accompanying 2 | # file LICENSE or https://github.com/Crascit/DownloadProject for details. 3 | 4 | cmake_minimum_required(VERSION 2.8.2) 5 | 6 | project(${DL_ARGS_PROJ}-download NONE) 7 | 8 | include(ExternalProject) 9 | ExternalProject_Add(${DL_ARGS_PROJ}-download 10 | ${DL_ARGS_UNPARSED_ARGUMENTS} 11 | SOURCE_DIR "${DL_ARGS_SOURCE_DIR}" 12 | BINARY_DIR "${DL_ARGS_BINARY_DIR}" 13 | CONFIGURE_COMMAND "" 14 | BUILD_COMMAND "" 15 | INSTALL_COMMAND "" 16 | TEST_COMMAND "" 17 | ) 18 | -------------------------------------------------------------------------------- /vector-field-design/cmake/DownloadProject.cmake: -------------------------------------------------------------------------------- 1 | # Distributed under the OSI-approved MIT License. See accompanying 2 | # file LICENSE or https://github.com/Crascit/DownloadProject for details. 3 | # 4 | # MODULE: DownloadProject 5 | # 6 | # PROVIDES: 7 | # download_project( PROJ projectName 8 | # [PREFIX prefixDir] 9 | # [DOWNLOAD_DIR downloadDir] 10 | # [SOURCE_DIR srcDir] 11 | # [BINARY_DIR binDir] 12 | # [QUIET] 13 | # ... 14 | # ) 15 | # 16 | # Provides the ability to download and unpack a tarball, zip file, git repository, 17 | # etc. at configure time (i.e. when the cmake command is run). How the downloaded 18 | # and unpacked contents are used is up to the caller, but the motivating case is 19 | # to download source code which can then be included directly in the build with 20 | # add_subdirectory() after the call to download_project(). Source and build 21 | # directories are set up with this in mind. 22 | # 23 | # The PROJ argument is required. The projectName value will be used to construct 24 | # the following variables upon exit (obviously replace projectName with its actual 25 | # value): 26 | # 27 | # projectName_SOURCE_DIR 28 | # projectName_BINARY_DIR 29 | # 30 | # The SOURCE_DIR and BINARY_DIR arguments are optional and would not typically 31 | # need to be provided. They can be specified if you want the downloaded source 32 | # and build directories to be located in a specific place. The contents of 33 | # projectName_SOURCE_DIR and projectName_BINARY_DIR will be populated with the 34 | # locations used whether you provide SOURCE_DIR/BINARY_DIR or not. 35 | # 36 | # The DOWNLOAD_DIR argument does not normally need to be set. It controls the 37 | # location of the temporary CMake build used to perform the download. 38 | # 39 | # The PREFIX argument can be provided to change the base location of the default 40 | # values of DOWNLOAD_DIR, SOURCE_DIR and BINARY_DIR. If all of those three arguments 41 | # are provided, then PREFIX will have no effect. The default value for PREFIX is 42 | # CMAKE_BINARY_DIR. 43 | # 44 | # The QUIET option can be given if you do not want to show the output associated 45 | # with downloading the specified project. 46 | # 47 | # In addition to the above, any other options are passed through unmodified to 48 | # ExternalProject_Add() to perform the actual download, patch and update steps. 49 | # The following ExternalProject_Add() options are explicitly prohibited (they 50 | # are reserved for use by the download_project() command): 51 | # 52 | # CONFIGURE_COMMAND 53 | # BUILD_COMMAND 54 | # INSTALL_COMMAND 55 | # TEST_COMMAND 56 | # 57 | # Only those ExternalProject_Add() arguments which relate to downloading, patching 58 | # and updating of the project sources are intended to be used. Also note that at 59 | # least one set of download-related arguments are required. 60 | # 61 | # If using CMake 3.2 or later, the UPDATE_DISCONNECTED option can be used to 62 | # prevent a check at the remote end for changes every time CMake is run 63 | # after the first successful download. See the documentation of the ExternalProject 64 | # module for more information. It is likely you will want to use this option if it 65 | # is available to you. Note, however, that the ExternalProject implementation contains 66 | # bugs which result in incorrect handling of the UPDATE_DISCONNECTED option when 67 | # using the URL download method or when specifying a SOURCE_DIR with no download 68 | # method. Fixes for these have been created, the last of which is scheduled for 69 | # inclusion in CMake 3.8.0. Details can be found here: 70 | # 71 | # https://gitlab.kitware.com/cmake/cmake/commit/bdca68388bd57f8302d3c1d83d691034b7ffa70c 72 | # https://gitlab.kitware.com/cmake/cmake/issues/16428 73 | # 74 | # If you experience build errors related to the update step, consider avoiding 75 | # the use of UPDATE_DISCONNECTED. 76 | # 77 | # EXAMPLE USAGE: 78 | # 79 | # include(DownloadProject) 80 | # download_project(PROJ googletest 81 | # GIT_REPOSITORY https://github.com/google/googletest.git 82 | # GIT_TAG master 83 | # UPDATE_DISCONNECTED 1 84 | # QUIET 85 | # ) 86 | # 87 | # add_subdirectory(${googletest_SOURCE_DIR} ${googletest_BINARY_DIR}) 88 | # 89 | #======================================================================================== 90 | 91 | 92 | set(_DownloadProjectDir "${CMAKE_CURRENT_LIST_DIR}") 93 | 94 | include(CMakeParseArguments) 95 | 96 | function(download_project) 97 | 98 | set(options QUIET) 99 | set(oneValueArgs 100 | PROJ 101 | PREFIX 102 | DOWNLOAD_DIR 103 | SOURCE_DIR 104 | BINARY_DIR 105 | # Prevent the following from being passed through 106 | CONFIGURE_COMMAND 107 | BUILD_COMMAND 108 | INSTALL_COMMAND 109 | TEST_COMMAND 110 | ) 111 | set(multiValueArgs "") 112 | 113 | cmake_parse_arguments(DL_ARGS "${options}" "${oneValueArgs}" "${multiValueArgs}" ${ARGN}) 114 | 115 | # Hide output if requested 116 | if (DL_ARGS_QUIET) 117 | set(OUTPUT_QUIET "OUTPUT_QUIET") 118 | else() 119 | unset(OUTPUT_QUIET) 120 | message(STATUS "Downloading/updating ${DL_ARGS_PROJ}") 121 | endif() 122 | 123 | # Set up where we will put our temporary CMakeLists.txt file and also 124 | # the base point below which the default source and binary dirs will be. 125 | # The prefix must always be an absolute path. 126 | if (NOT DL_ARGS_PREFIX) 127 | set(DL_ARGS_PREFIX "${CMAKE_BINARY_DIR}") 128 | else() 129 | get_filename_component(DL_ARGS_PREFIX "${DL_ARGS_PREFIX}" ABSOLUTE 130 | BASE_DIR "${CMAKE_CURRENT_BINARY_DIR}") 131 | endif() 132 | if (NOT DL_ARGS_DOWNLOAD_DIR) 133 | set(DL_ARGS_DOWNLOAD_DIR "${DL_ARGS_PREFIX}/${DL_ARGS_PROJ}-download") 134 | endif() 135 | 136 | # Ensure the caller can know where to find the source and build directories 137 | if (NOT DL_ARGS_SOURCE_DIR) 138 | set(DL_ARGS_SOURCE_DIR "${DL_ARGS_PREFIX}/${DL_ARGS_PROJ}-src") 139 | endif() 140 | if (NOT DL_ARGS_BINARY_DIR) 141 | set(DL_ARGS_BINARY_DIR "${DL_ARGS_PREFIX}/${DL_ARGS_PROJ}-build") 142 | endif() 143 | set(${DL_ARGS_PROJ}_SOURCE_DIR "${DL_ARGS_SOURCE_DIR}" PARENT_SCOPE) 144 | set(${DL_ARGS_PROJ}_BINARY_DIR "${DL_ARGS_BINARY_DIR}" PARENT_SCOPE) 145 | 146 | # The way that CLion manages multiple configurations, it causes a copy of 147 | # the CMakeCache.txt to be copied across due to it not expecting there to 148 | # be a project within a project. This causes the hard-coded paths in the 149 | # cache to be copied and builds to fail. To mitigate this, we simply 150 | # remove the cache if it exists before we configure the new project. It 151 | # is safe to do so because it will be re-generated. Since this is only 152 | # executed at the configure step, it should not cause additional builds or 153 | # downloads. 154 | file(REMOVE "${DL_ARGS_DOWNLOAD_DIR}/CMakeCache.txt") 155 | 156 | # Create and build a separate CMake project to carry out the download. 157 | # If we've already previously done these steps, they will not cause 158 | # anything to be updated, so extra rebuilds of the project won't occur. 159 | # Make sure to pass through CMAKE_MAKE_PROGRAM in case the main project 160 | # has this set to something not findable on the PATH. 161 | configure_file("${_DownloadProjectDir}/DownloadProject.CMakeLists.cmake.in" 162 | "${DL_ARGS_DOWNLOAD_DIR}/CMakeLists.txt") 163 | execute_process(COMMAND ${CMAKE_COMMAND} -G "${CMAKE_GENERATOR}" 164 | -D "CMAKE_MAKE_PROGRAM:FILE=${CMAKE_MAKE_PROGRAM}" 165 | . 166 | RESULT_VARIABLE result 167 | ${OUTPUT_QUIET} 168 | WORKING_DIRECTORY "${DL_ARGS_DOWNLOAD_DIR}" 169 | ) 170 | if(result) 171 | message(FATAL_ERROR "CMake step for ${DL_ARGS_PROJ} failed: ${result}") 172 | endif() 173 | execute_process(COMMAND ${CMAKE_COMMAND} --build . 174 | RESULT_VARIABLE result 175 | ${OUTPUT_QUIET} 176 | WORKING_DIRECTORY "${DL_ARGS_DOWNLOAD_DIR}" 177 | ) 178 | if(result) 179 | message(FATAL_ERROR "Build step for ${DL_ARGS_PROJ} failed: ${result}") 180 | endif() 181 | 182 | endfunction() 183 | -------------------------------------------------------------------------------- /vector-field-design/cmake/FindLIBIGL.cmake: -------------------------------------------------------------------------------- 1 | # - Try to find the LIBIGL library 2 | # Once done this will define 3 | # 4 | # LIBIGL_FOUND - system has LIBIGL 5 | # LIBIGL_INCLUDE_DIR - **the** LIBIGL include directory 6 | if(LIBIGL_FOUND) 7 | return() 8 | endif() 9 | 10 | find_path(LIBIGL_INCLUDE_DIR igl/readOBJ.h 11 | HINTS 12 | # ENV LIBIGL 13 | # ENV LIBIGLROOT 14 | # ENV LIBIGL_ROOT 15 | # ENV LIBIGL_DIR 16 | PATHS 17 | ${CMAKE_SOURCE_DIR}/external/libigl 18 | # ${CMAKE_SOURCE_DIR}/../.. 19 | # ${CMAKE_SOURCE_DIR}/.. 20 | # ${CMAKE_SOURCE_DIR} 21 | # ${CMAKE_SOURCE_DIR}/libigl 22 | # ${CMAKE_SOURCE_DIR}/../libigl 23 | # ${CMAKE_SOURCE_DIR}/../../libigl 24 | # /usr 25 | # /usr/local 26 | # /usr/local/igl/libigl 27 | PATH_SUFFIXES include 28 | ) 29 | 30 | include(FindPackageHandleStandardArgs) 31 | find_package_handle_standard_args(LIBIGL 32 | "\nlibigl not found --- You can download it using:\n\tgit clone --recursive https://github.com/libigl/libigl.git ${CMAKE_SOURCE_DIR}/../libigl" 33 | LIBIGL_INCLUDE_DIR) 34 | mark_as_advanced(LIBIGL_INCLUDE_DIR) 35 | 36 | list(APPEND CMAKE_MODULE_PATH "${LIBIGL_INCLUDE_DIR}/../cmake") 37 | include(libigl) 38 | -------------------------------------------------------------------------------- /vector-field-design/src/main.cpp: -------------------------------------------------------------------------------- 1 | // Copyright (C) 2019 Daniele Panozzo 2 | // 3 | // This Source Code Form is subject to the terms of the Mozilla Public License 4 | // v. 2.0. If a copy of the MPL was not distributed with this file, You can 5 | // obtain one at http://mozilla.org/MPL/2.0/. 6 | #include 7 | #include 8 | #include 9 | #include 10 | #include 11 | #include 12 | #include 13 | #include 14 | 15 | #include "vector_field.h" 16 | 17 | // Mesh 18 | Eigen::MatrixXd V; 19 | Eigen::MatrixXi F; 20 | 21 | // Triangle-triangle adjacency 22 | Eigen::MatrixXi TT; 23 | Eigen::MatrixXi TTi; 24 | 25 | // Constrained faces id 26 | Eigen::VectorXi b; 27 | 28 | // Cosntrained faces representative vector 29 | Eigen::MatrixXd bc; 30 | 31 | // Currently selected face 32 | int selected; 33 | 34 | // Local basis 35 | Eigen::MatrixXd B1, B2, B3; 36 | 37 | // Plots the mesh with a vector field 38 | // The constrained faces (b) are colored in red. 39 | void plot_vector_field( 40 | igl::opengl::glfw::Viewer& viewer, 41 | Eigen::MatrixXd& V, 42 | Eigen::MatrixXi& F, 43 | Eigen::MatrixXd& Y, 44 | Eigen::VectorXi& b) 45 | { 46 | using namespace Eigen; 47 | using namespace std; 48 | 49 | // Clear the mesh 50 | viewer.data().clear(); 51 | viewer.data().set_mesh(V,F); 52 | 53 | // Compute average edge lengh for scaling 54 | double avg = igl::avg_edge_length(V, F); 55 | 56 | // Compute face barycenters 57 | MatrixXd B; 58 | igl::barycenter(V,F,B); 59 | 60 | // Show the vector field as lines 61 | viewer.data().add_edges(B,B+Y*(avg/2),RowVector3d(0,0,1)); 62 | 63 | // Highlight in red the constrained faces 64 | MatrixXd C = MatrixXd::Constant(F.rows(),3,1); 65 | for (unsigned i=0; i= '1') 77 | { 78 | MatrixXd R = vector_field(V,F,TT,b,bc); 79 | plot_vector_field(viewer,V,F,R,b); 80 | } 81 | 82 | // Rotate the field 83 | if (key == '[' || key == ']') 84 | { 85 | if (selected >= b.size() || selected < 0) 86 | return false; 87 | 88 | int i = b(selected); 89 | Vector3d v = bc.row(selected); 90 | 91 | double x = B1.row(i) * v; 92 | double y = B2.row(i) * v; 93 | double norm = sqrt(x*x+y*y); 94 | double angle = atan2(y,x); 95 | 96 | angle += key == '[' ? -M_PI/16 : M_PI/16; 97 | 98 | double xj = cos(angle)*norm; 99 | double yj = sin(angle)*norm; 100 | 101 | bc.row(selected) = xj * B1.row(i) + yj * B2.row(i); 102 | MatrixXd R = vector_field(V,F,TT,b,bc); 103 | plot_vector_field(viewer,V,F,R,b); 104 | } 105 | 106 | // Scale the field 107 | if (key == 'Q' || key == 'W') 108 | { 109 | if (selected >= b.size() || selected < 0) 110 | return false; 111 | 112 | bc.row(selected) = bc.row(selected) * (key == 'Q' ? 3./2. : 2./3.); 113 | 114 | MatrixXd R = vector_field(V,F,TT,b,bc); 115 | plot_vector_field(viewer,V,F,R,b); 116 | } 117 | 118 | // Erase the currently selected constraint 119 | if (key == 'E') 120 | { 121 | if (selected >= b.size() || selected < 0) 122 | return false; 123 | 124 | b(selected) = b(b.rows()-1); 125 | b.conservativeResize(b.size()-1); 126 | bc.row(selected) = bc.row(bc.rows()-1); 127 | bc.conservativeResize(b.size(),bc.cols()); 128 | MatrixXd R = vector_field(V,F,TT,b,bc); 129 | plot_vector_field(viewer,V,F,R,b); 130 | } 131 | 132 | return false; 133 | } 134 | 135 | bool mouse_down(igl::opengl::glfw::Viewer& viewer, int, int) 136 | { 137 | int fid_ray; 138 | Eigen::Vector3f bary; 139 | // Cast a ray in the view direction starting from the mouse position 140 | double x = viewer.current_mouse_x; 141 | double y = viewer.core.viewport(3) - viewer.current_mouse_y; 142 | if(igl::unproject_onto_mesh(Eigen::Vector2f(x,y), viewer.core.view, 143 | viewer.core.proj, viewer.core.viewport, V, F, fid_ray, bary)) 144 | { 145 | // If it is a constraint, just make it current 146 | bool found = false; 147 | for (int i=0;i 2 | // 3 | // This Source Code Form is subject to the terms of the Mozilla Public License 4 | // v. 2.0. If a copy of the MPL was not distributed with this file, You can 5 | // obtain one at http://mozilla.org/MPL/2.0/. 6 | #include "vector_field.h" 7 | #include 8 | #include 9 | #include 10 | #include 11 | #include 12 | 13 | using namespace std; 14 | using namespace Eigen; 15 | 16 | MatrixXd vector_field 17 | ( 18 | const MatrixXd& V, // Vertices of the mesh 19 | const MatrixXi& F, // Faces 20 | const MatrixXi& TT, // Adjacency triangle-triangle 21 | const VectorXi& soft_id, // Soft constraints face ids 22 | const MatrixXd& soft_value // Soft constraints 3d vectors 23 | ) 24 | { 25 | assert(soft_id.size() > 0); // One constraint is necessary to make the solution unique 26 | 27 | Matrix T1(F.rows(),3), T2(F.rows(),3); 28 | 29 | // Compute the local reference systems for each face 30 | for (unsigned i=0;i > > t; 40 | std::vector< Triplet > > tb; 41 | 42 | unsigned count = 0; 43 | for (unsigned f=0;f g) continue; 53 | // Compute the complex representation of the common edge 54 | Vector3d e = (V.row(F(f,(ei+1)%3)) - V.row(F(f,ei))); 55 | Vector2d vef = Vector2d(e.dot(T1.row(f)),e.dot(T2.row(f))).normalized(); 56 | std::complex ef(vef(0),vef(1)); 57 | Vector2d veg = Vector2d(e.dot(T1.row(g)),e.dot(T2.row(g))).normalized(); 58 | std::complex eg(veg(0),veg(1)); 59 | // Add the term conj(f)^n*ui - conj(g)^n*uj to the energy matrix 60 | t.push_back(Triplet >(count,f, std::conj(ef))); 61 | t.push_back(Triplet >(count,g,-1.*std::conj(eg))); 62 | ++count; 63 | } 64 | } 65 | 66 | // Convert the constraints into the complex polynomial coefficients and add them as soft constraints 67 | double lambda = 10e6; 68 | for (unsigned r=0; r c(v.dot(T1.row(f)),v.dot(T2.row(f))); 73 | t.push_back(Triplet >(count,f, sqrt(lambda))); 74 | tb.push_back(Triplet >(count,0, c * std::complex(sqrt(lambda),0))); 75 | ++count; 76 | } 77 | 78 | // Solve the linear system 79 | typedef SparseMatrix> SparseMatrixXcd; 80 | SparseMatrixXcd A(count,F.rows()); 81 | A.setFromTriplets(t.begin(), t.end()); 82 | SparseMatrixXcd b(count,1); 83 | b.setFromTriplets(tb.begin(), tb.end()); 84 | SimplicialLDLT< SparseMatrixXcd > solver; 85 | solver.compute(A.adjoint()*A); 86 | assert(solver.info()==Success); 87 | MatrixXcd u = solver.solve(A.adjoint()*MatrixXcd(b)); 88 | assert(solver.info()==Success); 89 | 90 | // Convert the interpolated polyvector into Euclidean vectors 91 | MatrixXd R(F.rows(),3); 92 | for (int f=0; f 2 | // 3 | // This Source Code Form is subject to the terms of the Mozilla Public License 4 | // v. 2.0. If a copy of the MPL was not distributed with this file, You can 5 | // obtain one at http://mozilla.org/MPL/2.0/. 6 | #ifndef VECTOR_FIELD 7 | #define VECTOR_FIELD 8 | 9 | #include 10 | 11 | Eigen::MatrixXd vector_field 12 | ( 13 | const Eigen::MatrixXd& V, // Vertices of the mesh 14 | const Eigen::MatrixXi& F, // Faces 15 | const Eigen::MatrixXi& TT, // Adjacency triangle-triangle 16 | const Eigen::VectorXi& soft_id, // Soft constraints face ids 17 | const Eigen::MatrixXd& soft_value // Soft constraints 3d vectors 18 | ); 19 | 20 | #endif 21 | --------------------------------------------------------------------------------