├── .gitignore ├── .gitmodules ├── LICENSE.md ├── README.md ├── code ├── 3dviewer │ ├── CMakeLists.txt │ ├── cmake │ │ └── modules │ │ │ ├── FindEigen3.cmake │ │ │ └── FindQGLViewer.cmake │ ├── data │ │ ├── bevel_cube.off │ │ ├── bipyramid.off │ │ ├── circle_100.xyz │ │ ├── circle_16.xyz │ │ ├── cube.off │ │ ├── cube.xyz │ │ ├── cube2.xyz │ │ ├── ellipsoid.xyz │ │ ├── ellipsoid0-13.off │ │ ├── ellipsoid1-50.off │ │ ├── fandisk_simplified.xyz │ │ ├── fandisk_simplified2.xyz │ │ ├── fin90.xyz │ │ ├── hexagon.off │ │ ├── icosahedron.off │ │ ├── mannequin.off │ │ ├── sphere.off │ │ ├── sphere_100.off │ │ ├── sphere_1k.xyz │ │ ├── sphere_1k_noisy.xyz │ │ ├── sphere_200.xyz │ │ ├── sphere_20k.xyz │ │ ├── sphere_50.off │ │ ├── star.off │ │ ├── tetrahedron.off │ │ ├── torus_quad.off │ │ └── torus_tri.off │ ├── icons │ │ └── cgal_logo.xpm │ ├── polyhedron.qrc │ ├── polyhedron.ui │ └── src │ │ ├── AD.hpp │ │ ├── CGAL_AD.hpp │ │ ├── GradientUtils.hpp │ │ ├── add_noise.h │ │ ├── halfspace_intersection_with_constructions_3.h │ │ ├── halfspace_intersection_with_dual_3.h │ │ ├── inclusion_exclusion.hpp │ │ ├── interior_polyhedron_3.h │ │ ├── main.cpp │ │ ├── minkowski_sum_pointcloud_convex_polyhedron_3.h │ │ ├── minkowski_sum_pointcloud_convex_polyhedron_utils_3.h │ │ ├── misc.h │ │ ├── pointcloud.h │ │ ├── polyhedron.h │ │ ├── random_sphere_3.h │ │ ├── scene.cpp │ │ ├── scene.h │ │ ├── tag.h │ │ ├── types.h │ │ ├── vectorfield.h │ │ ├── viewer.cpp │ │ ├── viewer.h │ │ ├── window.cpp │ │ └── window.h ├── python │ ├── AD.hpp │ ├── CGAL_AD.hpp │ ├── CMakeLists.txt │ ├── cmake │ │ └── FindEigen3.cmake │ ├── examples │ │ ├── curvature.py │ │ ├── data │ │ │ ├── bird.xy │ │ │ ├── cartman.xy │ │ │ ├── kenny.xy │ │ │ ├── kyle.xy │ │ │ ├── shark.xy │ │ │ └── square.xy │ │ ├── descent.py │ │ ├── ellipse.py │ │ └── genpoints.py │ ├── union_balls_2.hpp │ ├── union_balls_2_utils.hpp │ └── unionballs.cpp └── viewer │ ├── CMakeLists.txt │ ├── CMakeLists.txt.Qt5 │ ├── cmake │ └── FindEigen3.cmake │ └── src │ ├── AD.hpp │ ├── CGAL_AD.hpp │ ├── CGAL_AD_typedefs.hpp │ ├── CGAL_typedefs.hpp │ ├── Consts.hpp │ ├── GradientUtils.hpp │ ├── Graphics.hpp │ ├── MainWindow.cpp │ ├── MainWindow.hpp │ ├── PointCloudUtils.hpp │ ├── QDelaunayTriangulationItem.hpp │ ├── QPointListItem.hpp │ ├── QSegmentListItem.hpp │ ├── QTriangulationItem.hpp │ ├── QVectorFieldItem.hpp │ ├── Scene.cpp │ ├── Scene.hpp │ ├── View.cpp │ ├── View.hpp │ ├── main.cpp │ ├── misc.hpp │ ├── ps.hpp │ ├── random_ellipse_2.hpp │ ├── random_square_2.hpp │ ├── union_balls_2.hpp │ ├── union_balls_2_utils.hpp │ └── volume_union_balls_2_debug.h ├── data └── pwsrec-data │ ├── MTSM10 │ ├── .svn │ │ ├── all-wcprops │ │ ├── entries │ │ ├── prop-base │ │ │ └── LICENSE.txt.svn-base │ │ └── text-base │ │ │ └── LICENSE.txt.svn-base │ ├── DATA_2D │ │ ├── .svn │ │ │ ├── all-wcprops │ │ │ ├── entries │ │ │ ├── prop-base │ │ │ │ └── README.txt.svn-base │ │ │ └── text-base │ │ │ │ └── README.txt.svn-base │ │ ├── Figure_3 │ │ │ ├── .svn │ │ │ │ ├── all-wcprops │ │ │ │ └── entries │ │ │ └── Dove │ │ │ │ ├── .svn │ │ │ │ ├── all-wcprops │ │ │ │ └── entries │ │ │ │ ├── 1.7percent_noise │ │ │ │ ├── .svn │ │ │ │ │ ├── all-wcprops │ │ │ │ │ ├── entries │ │ │ │ │ ├── prop-base │ │ │ │ │ │ └── Dove_1.7percent_noise.txt.svn-base │ │ │ │ │ └── text-base │ │ │ │ │ │ └── Dove_1.7percent_noise.txt.svn-base │ │ │ │ └── Dove_1.7percent_noise.txt │ │ │ │ ├── 1percent_noise │ │ │ │ ├── .svn │ │ │ │ │ ├── all-wcprops │ │ │ │ │ ├── entries │ │ │ │ │ ├── prop-base │ │ │ │ │ │ └── Dove_1percent_noise.txt.svn-base │ │ │ │ │ └── text-base │ │ │ │ │ │ └── Dove_1percent_noise.txt.svn-base │ │ │ │ └── Dove_1percent_noise.txt │ │ │ │ └── no_noise │ │ │ │ ├── .svn │ │ │ │ ├── all-wcprops │ │ │ │ ├── entries │ │ │ │ ├── prop-base │ │ │ │ │ └── Dove_no_noise.txt.svn-base │ │ │ │ └── text-base │ │ │ │ │ └── Dove_no_noise.txt.svn-base │ │ │ │ └── Dove_no_noise.txt │ │ ├── Figure_4 │ │ │ ├── .svn │ │ │ │ ├── all-wcprops │ │ │ │ └── entries │ │ │ └── Face │ │ │ │ ├── .svn │ │ │ │ ├── all-wcprops │ │ │ │ ├── entries │ │ │ │ ├── prop-base │ │ │ │ │ └── Face_guardzone.txt.svn-base │ │ │ │ └── text-base │ │ │ │ │ └── Face_guardzone.txt.svn-base │ │ │ │ └── Face_guardzone.txt │ │ ├── Figure_5 │ │ │ ├── .svn │ │ │ │ ├── all-wcprops │ │ │ │ ├── entries │ │ │ │ ├── prop-base │ │ │ │ │ └── Monkey.txt.svn-base │ │ │ │ └── text-base │ │ │ │ │ └── Monkey.txt.svn-base │ │ │ └── Monkey.txt │ │ ├── Figure_6 │ │ │ ├── .svn │ │ │ │ ├── all-wcprops │ │ │ │ └── entries │ │ │ ├── Apple │ │ │ │ ├── .svn │ │ │ │ │ ├── all-wcprops │ │ │ │ │ └── entries │ │ │ │ ├── 1percent_noise │ │ │ │ │ ├── .svn │ │ │ │ │ │ ├── all-wcprops │ │ │ │ │ │ ├── entries │ │ │ │ │ │ ├── prop-base │ │ │ │ │ │ │ └── apple_1percent_noise.txt.svn-base │ │ │ │ │ │ └── text-base │ │ │ │ │ │ │ └── apple_1percent_noise.txt.svn-base │ │ │ │ │ └── apple_1percent_noise.txt │ │ │ │ ├── 2percent_noise │ │ │ │ │ ├── .svn │ │ │ │ │ │ ├── all-wcprops │ │ │ │ │ │ ├── entries │ │ │ │ │ │ ├── prop-base │ │ │ │ │ │ │ └── apple_2percent_noise.txt.svn-base │ │ │ │ │ │ └── text-base │ │ │ │ │ │ │ └── apple_2percent_noise.txt.svn-base │ │ │ │ │ └── apple_2percent_noise.txt │ │ │ │ ├── 50percent_missing_samples │ │ │ │ │ ├── .svn │ │ │ │ │ │ ├── all-wcprops │ │ │ │ │ │ ├── entries │ │ │ │ │ │ ├── prop-base │ │ │ │ │ │ │ └── apple_50percent_missing.txt.svn-base │ │ │ │ │ │ └── text-base │ │ │ │ │ │ │ └── apple_50percent_missing.txt.svn-base │ │ │ │ │ └── apple_50percent_missing.txt │ │ │ │ ├── 75percent_missing_samples │ │ │ │ │ ├── .svn │ │ │ │ │ │ ├── all-wcprops │ │ │ │ │ │ ├── entries │ │ │ │ │ │ ├── prop-base │ │ │ │ │ │ │ └── apple_75percent_missing.txt.svn-base │ │ │ │ │ │ └── text-base │ │ │ │ │ │ │ └── apple_75percent_missing.txt.svn-base │ │ │ │ │ └── apple_75percent_missing.txt │ │ │ │ └── no_noise │ │ │ │ │ ├── .svn │ │ │ │ │ ├── all-wcprops │ │ │ │ │ ├── entries │ │ │ │ │ ├── prop-base │ │ │ │ │ │ └── apple_no_noise.txt.svn-base │ │ │ │ │ └── text-base │ │ │ │ │ │ └── apple_no_noise.txt.svn-base │ │ │ │ │ └── apple_no_noise.txt │ │ │ ├── Butterfly │ │ │ │ ├── .svn │ │ │ │ │ ├── all-wcprops │ │ │ │ │ └── entries │ │ │ │ ├── 1percent_noise │ │ │ │ │ ├── .svn │ │ │ │ │ │ ├── all-wcprops │ │ │ │ │ │ ├── entries │ │ │ │ │ │ ├── prop-base │ │ │ │ │ │ │ └── butterfly_1percent_noise.txt.svn-base │ │ │ │ │ │ └── text-base │ │ │ │ │ │ │ └── butterfly_1percent_noise.txt.svn-base │ │ │ │ │ └── butterfly_1percent_noise.txt │ │ │ │ ├── 2percent_noise │ │ │ │ │ ├── .svn │ │ │ │ │ │ ├── all-wcprops │ │ │ │ │ │ ├── entries │ │ │ │ │ │ ├── prop-base │ │ │ │ │ │ │ └── butterfly_2percent_noise.txt.svn-base │ │ │ │ │ │ └── text-base │ │ │ │ │ │ │ └── butterfly_2percent_noise.txt.svn-base │ │ │ │ │ └── butterfly_2percent_noise.txt │ │ │ │ ├── 50percent_missing_samples │ │ │ │ │ ├── .svn │ │ │ │ │ │ ├── all-wcprops │ │ │ │ │ │ ├── entries │ │ │ │ │ │ ├── prop-base │ │ │ │ │ │ │ └── butterfly_50percent_missing.txt.svn-base │ │ │ │ │ │ └── text-base │ │ │ │ │ │ │ └── butterfly_50percent_missing.txt.svn-base │ │ │ │ │ └── butterfly_50percent_missing.txt │ │ │ │ ├── 75percent_missing_samples │ │ │ │ │ ├── .svn │ │ │ │ │ │ ├── all-wcprops │ │ │ │ │ │ ├── entries │ │ │ │ │ │ ├── prop-base │ │ │ │ │ │ │ └── butterfly_75percent_missing.txt.svn-base │ │ │ │ │ │ └── text-base │ │ │ │ │ │ │ └── butterfly_75percent_missing.txt.svn-base │ │ │ │ │ └── butterfly_75percent_missing.txt │ │ │ │ └── no_noise │ │ │ │ │ ├── .svn │ │ │ │ │ ├── all-wcprops │ │ │ │ │ ├── entries │ │ │ │ │ ├── prop-base │ │ │ │ │ │ └── butterfly_no_noise.txt.svn-base │ │ │ │ │ └── text-base │ │ │ │ │ │ └── butterfly_no_noise.txt.svn-base │ │ │ │ │ └── butterfly_no_noise.txt │ │ │ ├── Crab │ │ │ │ ├── .svn │ │ │ │ │ ├── all-wcprops │ │ │ │ │ └── entries │ │ │ │ ├── 1percent_noise │ │ │ │ │ ├── .svn │ │ │ │ │ │ ├── all-wcprops │ │ │ │ │ │ ├── entries │ │ │ │ │ │ ├── prop-base │ │ │ │ │ │ │ └── crab_1percent_noise.txt.svn-base │ │ │ │ │ │ └── text-base │ │ │ │ │ │ │ └── crab_1percent_noise.txt.svn-base │ │ │ │ │ └── crab_1percent_noise.txt │ │ │ │ ├── 2percent_noise │ │ │ │ │ ├── .svn │ │ │ │ │ │ ├── all-wcprops │ │ │ │ │ │ ├── entries │ │ │ │ │ │ ├── prop-base │ │ │ │ │ │ │ └── crab_2percent_noise.txt.svn-base │ │ │ │ │ │ └── text-base │ │ │ │ │ │ │ └── crab_2percent_noise.txt.svn-base │ │ │ │ │ └── crab_2percent_noise.txt │ │ │ │ ├── 50percent_missing_samples │ │ │ │ │ ├── .svn │ │ │ │ │ │ ├── all-wcprops │ │ │ │ │ │ ├── entries │ │ │ │ │ │ ├── prop-base │ │ │ │ │ │ │ └── crab_50percent_missing.txt.svn-base │ │ │ │ │ │ └── text-base │ │ │ │ │ │ │ └── crab_50percent_missing.txt.svn-base │ │ │ │ │ └── crab_50percent_missing.txt │ │ │ │ ├── 75percent_missing_samples │ │ │ │ │ ├── .svn │ │ │ │ │ │ ├── all-wcprops │ │ │ │ │ │ ├── entries │ │ │ │ │ │ ├── prop-base │ │ │ │ │ │ │ └── crab_75percent_missing.txt.svn-base │ │ │ │ │ │ └── text-base │ │ │ │ │ │ │ └── crab_75percent_missing.txt.svn-base │ │ │ │ │ └── crab_75percent_missing.txt │ │ │ │ └── no_noise │ │ │ │ │ ├── .svn │ │ │ │ │ ├── all-wcprops │ │ │ │ │ ├── entries │ │ │ │ │ ├── prop-base │ │ │ │ │ │ └── crab_no_noise.txt.svn-base │ │ │ │ │ └── text-base │ │ │ │ │ │ └── crab_no_noise.txt.svn-base │ │ │ │ │ └── crab_no_noise.txt │ │ │ └── Dolphin │ │ │ │ ├── .svn │ │ │ │ ├── all-wcprops │ │ │ │ └── entries │ │ │ │ ├── 1percent_noise │ │ │ │ ├── .svn │ │ │ │ │ ├── all-wcprops │ │ │ │ │ ├── entries │ │ │ │ │ ├── prop-base │ │ │ │ │ │ └── dolphin_1percent_noise.txt.svn-base │ │ │ │ │ └── text-base │ │ │ │ │ │ └── dolphin_1percent_noise.txt.svn-base │ │ │ │ └── dolphin_1percent_noise.txt │ │ │ │ ├── 2percent_noise │ │ │ │ ├── .svn │ │ │ │ │ ├── all-wcprops │ │ │ │ │ ├── entries │ │ │ │ │ ├── prop-base │ │ │ │ │ │ └── dolphin_2percent_noise.txt.svn-base │ │ │ │ │ └── text-base │ │ │ │ │ │ └── dolphin_2percent_noise.txt.svn-base │ │ │ │ └── dolphin_2percent_noise.txt │ │ │ │ ├── 50percent_missing_samples │ │ │ │ ├── .svn │ │ │ │ │ ├── all-wcprops │ │ │ │ │ ├── entries │ │ │ │ │ ├── prop-base │ │ │ │ │ │ └── dolphin_50percent_missing.txt.svn-base │ │ │ │ │ └── text-base │ │ │ │ │ │ └── dolphin_50percent_missing.txt.svn-base │ │ │ │ └── dolphin_50percent_missing.txt │ │ │ │ ├── 75percent_missing_samples │ │ │ │ ├── .svn │ │ │ │ │ ├── all-wcprops │ │ │ │ │ ├── entries │ │ │ │ │ ├── prop-base │ │ │ │ │ │ └── dolphin_75percent_missing.txt.svn-base │ │ │ │ │ └── text-base │ │ │ │ │ │ └── dolphin_75percent_missing.txt.svn-base │ │ │ │ └── dolphin_75percent_missing.txt │ │ │ │ └── no_noise │ │ │ │ ├── .svn │ │ │ │ ├── all-wcprops │ │ │ │ ├── entries │ │ │ │ ├── prop-base │ │ │ │ │ └── dolphin_no_noise.txt.svn-base │ │ │ │ └── text-base │ │ │ │ │ └── dolphin_no_noise.txt.svn-base │ │ │ │ └── dolphin_no_noise.txt │ │ └── README.txt │ └── LICENSE.txt │ ├── abstr09-shapes │ ├── .svn │ │ ├── all-wcprops │ │ ├── entries │ │ ├── prop-base │ │ │ └── README.txt.svn-base │ │ └── text-base │ │ │ └── README.txt.svn-base │ ├── README.txt │ ├── fig1.australia │ │ ├── .svn │ │ │ ├── all-wcprops │ │ │ ├── entries │ │ │ ├── prop-base │ │ │ │ ├── Australia-abs0.dat.svn-base │ │ │ │ ├── Australia-abs1.dat.svn-base │ │ │ │ ├── Australia-cf0.dat.svn-base │ │ │ │ ├── Australia-dp0.dat.svn-base │ │ │ │ ├── Australia-dp0.xy.dat.svn-base │ │ │ │ ├── Australia-orig.dat.svn-base │ │ │ │ ├── Australia-pm0.dat.svn-base │ │ │ │ └── Australia-pm0.xy.dat.svn-base │ │ │ └── text-base │ │ │ │ ├── Australia-abs0.dat.svn-base │ │ │ │ ├── Australia-abs1.dat.svn-base │ │ │ │ ├── Australia-cf0.dat.svn-base │ │ │ │ ├── Australia-dp0.dat.svn-base │ │ │ │ ├── Australia-dp0.xy.dat.svn-base │ │ │ │ ├── Australia-orig.dat.svn-base │ │ │ │ ├── Australia-pm0.dat.svn-base │ │ │ │ └── Australia-pm0.xy.dat.svn-base │ │ ├── Australia-abs0.dat │ │ ├── Australia-abs1.dat │ │ ├── Australia-cf0.dat │ │ ├── Australia-dp0.dat │ │ ├── Australia-dp0.xy.dat │ │ ├── Australia-orig.dat │ │ ├── Australia-pm0.dat │ │ └── Australia-pm0.xy.dat │ ├── fig15.nonmaps │ │ ├── .svn │ │ │ ├── all-wcprops │ │ │ └── entries │ │ ├── crab │ │ │ ├── .svn │ │ │ │ ├── all-wcprops │ │ │ │ ├── entries │ │ │ │ ├── prop-base │ │ │ │ │ ├── crab-abs0.dat.svn-base │ │ │ │ │ ├── crab-cf0.dat.svn-base │ │ │ │ │ ├── crab-dp0.dat.svn-base │ │ │ │ │ ├── crab-orig.dat.svn-base │ │ │ │ │ └── crab-pm0.dat.svn-base │ │ │ │ └── text-base │ │ │ │ │ ├── crab-abs0.dat.svn-base │ │ │ │ │ ├── crab-cf0.dat.svn-base │ │ │ │ │ ├── crab-dp0.dat.svn-base │ │ │ │ │ ├── crab-orig.dat.svn-base │ │ │ │ │ └── crab-pm0.dat.svn-base │ │ │ ├── crab-abs0.dat │ │ │ ├── crab-cf0.dat │ │ │ ├── crab-dp0.dat │ │ │ ├── crab-orig.dat │ │ │ └── crab-pm0.dat │ │ ├── lighthouse │ │ │ ├── .svn │ │ │ │ ├── all-wcprops │ │ │ │ ├── entries │ │ │ │ ├── prop-base │ │ │ │ │ ├── lighthouse-abs0.dat.svn-base │ │ │ │ │ ├── lighthouse-cf0.dat.svn-base │ │ │ │ │ ├── lighthouse-dp0.dat.svn-base │ │ │ │ │ ├── lighthouse-orig.dat.svn-base │ │ │ │ │ └── lighthouse-pm0.dat.svn-base │ │ │ │ └── text-base │ │ │ │ │ ├── lighthouse-abs0.dat.svn-base │ │ │ │ │ ├── lighthouse-cf0.dat.svn-base │ │ │ │ │ ├── lighthouse-dp0.dat.svn-base │ │ │ │ │ ├── lighthouse-orig.dat.svn-base │ │ │ │ │ └── lighthouse-pm0.dat.svn-base │ │ │ ├── lighthouse-abs0.dat │ │ │ ├── lighthouse-cf0.dat │ │ │ ├── lighthouse-dp0.dat │ │ │ ├── lighthouse-orig.dat │ │ │ └── lighthouse-pm0.dat │ │ ├── maple-leaf │ │ │ ├── .svn │ │ │ │ ├── all-wcprops │ │ │ │ ├── entries │ │ │ │ ├── prop-base │ │ │ │ │ ├── maple-leaf-abs0.dat.svn-base │ │ │ │ │ ├── maple-leaf-cf0.dat.svn-base │ │ │ │ │ ├── maple-leaf-dp0.dat.svn-base │ │ │ │ │ ├── maple-leaf-orig.dat.svn-base │ │ │ │ │ └── maple-leaf-pm0.dat.svn-base │ │ │ │ └── text-base │ │ │ │ │ ├── maple-leaf-abs0.dat.svn-base │ │ │ │ │ ├── maple-leaf-cf0.dat.svn-base │ │ │ │ │ ├── maple-leaf-dp0.dat.svn-base │ │ │ │ │ ├── maple-leaf-orig.dat.svn-base │ │ │ │ │ └── maple-leaf-pm0.dat.svn-base │ │ │ ├── maple-leaf-abs0.dat │ │ │ ├── maple-leaf-cf0.dat │ │ │ ├── maple-leaf-dp0.dat │ │ │ ├── maple-leaf-orig.dat │ │ │ └── maple-leaf-pm0.dat │ │ ├── pine │ │ │ ├── .svn │ │ │ │ ├── all-wcprops │ │ │ │ ├── entries │ │ │ │ ├── prop-base │ │ │ │ │ ├── pine-abs0.dat.svn-base │ │ │ │ │ ├── pine-cf0.dat.svn-base │ │ │ │ │ ├── pine-dp0.dat.svn-base │ │ │ │ │ ├── pine-orig.dat.svn-base │ │ │ │ │ └── pine-pm0.dat.svn-base │ │ │ │ └── text-base │ │ │ │ │ ├── pine-abs0.dat.svn-base │ │ │ │ │ ├── pine-cf0.dat.svn-base │ │ │ │ │ ├── pine-dp0.dat.svn-base │ │ │ │ │ ├── pine-orig.dat.svn-base │ │ │ │ │ └── pine-pm0.dat.svn-base │ │ │ ├── pine-abs0.dat │ │ │ ├── pine-cf0.dat │ │ │ ├── pine-dp0.dat │ │ │ ├── pine-orig.dat │ │ │ └── pine-pm0.dat │ │ └── shark2 │ │ │ ├── .svn │ │ │ ├── all-wcprops │ │ │ ├── entries │ │ │ ├── prop-base │ │ │ │ ├── shark2-abs0.dat.svn-base │ │ │ │ ├── shark2-cf0.dat.svn-base │ │ │ │ ├── shark2-dp0.dat.svn-base │ │ │ │ ├── shark2-orig.dat.svn-base │ │ │ │ └── shark2-pm0.dat.svn-base │ │ │ └── text-base │ │ │ │ ├── shark2-abs0.dat.svn-base │ │ │ │ ├── shark2-cf0.dat.svn-base │ │ │ │ ├── shark2-dp0.dat.svn-base │ │ │ │ ├── shark2-orig.dat.svn-base │ │ │ │ └── shark2-pm0.dat.svn-base │ │ │ ├── shark2-abs0.dat │ │ │ ├── shark2-cf0.dat │ │ │ ├── shark2-dp0.dat │ │ │ ├── shark2-orig.dat │ │ │ └── shark2-pm0.dat │ ├── fig16.ukir │ │ ├── .svn │ │ │ ├── all-wcprops │ │ │ ├── entries │ │ │ ├── prop-base │ │ │ │ ├── ukir-abs0.dat.svn-base │ │ │ │ ├── ukir-abs1.dat.svn-base │ │ │ │ ├── ukir-cf0.dat.svn-base │ │ │ │ ├── ukir-cf1.dat.svn-base │ │ │ │ ├── ukir-dp0.dat.svn-base │ │ │ │ ├── ukir-dp1.dat.svn-base │ │ │ │ ├── ukir-orig.dat.svn-base │ │ │ │ ├── ukir-pm0.dat.svn-base │ │ │ │ └── ukir-pm1.dat.svn-base │ │ │ └── text-base │ │ │ │ ├── ukir-abs0.dat.svn-base │ │ │ │ ├── ukir-abs1.dat.svn-base │ │ │ │ ├── ukir-cf0.dat.svn-base │ │ │ │ ├── ukir-cf1.dat.svn-base │ │ │ │ ├── ukir-dp0.dat.svn-base │ │ │ │ ├── ukir-dp1.dat.svn-base │ │ │ │ ├── ukir-orig.dat.svn-base │ │ │ │ ├── ukir-pm0.dat.svn-base │ │ │ │ └── ukir-pm1.dat.svn-base │ │ ├── ukir-abs0.dat │ │ ├── ukir-abs1.dat │ │ ├── ukir-cf0.dat │ │ ├── ukir-cf1.dat │ │ ├── ukir-dp0.dat │ │ ├── ukir-dp1.dat │ │ ├── ukir-orig.dat │ │ ├── ukir-pm0.dat │ │ └── ukir-pm1.dat │ └── fig18.maps-misc │ │ ├── .svn │ │ ├── all-wcprops │ │ ├── entries │ │ ├── prop-base │ │ │ ├── BaffinIsland-abs0.dat.svn-base │ │ │ ├── BaffinIsland-abs1.dat.svn-base │ │ │ ├── BaffinIsland-cf0.dat.svn-base │ │ │ ├── BaffinIsland-orig.dat.svn-base │ │ │ ├── China-abs0.dat.svn-base │ │ │ ├── China-abs1.dat.svn-base │ │ │ ├── China-cf0.dat.svn-base │ │ │ ├── China-orig.dat.svn-base │ │ │ ├── Iceland-abs0.dat.svn-base │ │ │ ├── Iceland-abs1.dat.svn-base │ │ │ ├── Iceland-cf0.dat.svn-base │ │ │ ├── Iceland-orig.dat.svn-base │ │ │ ├── NewGuinea-abs0.dat.svn-base │ │ │ ├── NewGuinea-abs1.dat.svn-base │ │ │ ├── NewGuinea-cf0.dat.svn-base │ │ │ ├── NewGuinea-orig.dat.svn-base │ │ │ ├── Newfoundland-abs0.dat.svn-base │ │ │ ├── Newfoundland-abs1.dat.svn-base │ │ │ ├── Newfoundland-cf0.dat.svn-base │ │ │ ├── Newfoundland-orig.dat.svn-base │ │ │ ├── Philippines-abs0.dat.svn-base │ │ │ ├── Philippines-abs1.dat.svn-base │ │ │ ├── Philippines-cf0.dat.svn-base │ │ │ └── Philippines-orig.dat.svn-base │ │ └── text-base │ │ │ ├── BaffinIsland-abs0.dat.svn-base │ │ │ ├── BaffinIsland-abs1.dat.svn-base │ │ │ ├── BaffinIsland-cf0.dat.svn-base │ │ │ ├── BaffinIsland-orig.dat.svn-base │ │ │ ├── China-abs0.dat.svn-base │ │ │ ├── China-abs1.dat.svn-base │ │ │ ├── China-cf0.dat.svn-base │ │ │ ├── China-orig.dat.svn-base │ │ │ ├── Iceland-abs0.dat.svn-base │ │ │ ├── Iceland-abs1.dat.svn-base │ │ │ ├── Iceland-cf0.dat.svn-base │ │ │ ├── Iceland-orig.dat.svn-base │ │ │ ├── NewGuinea-abs0.dat.svn-base │ │ │ ├── NewGuinea-abs1.dat.svn-base │ │ │ ├── NewGuinea-cf0.dat.svn-base │ │ │ ├── NewGuinea-orig.dat.svn-base │ │ │ ├── Newfoundland-abs0.dat.svn-base │ │ │ ├── Newfoundland-abs1.dat.svn-base │ │ │ ├── Newfoundland-cf0.dat.svn-base │ │ │ ├── Newfoundland-orig.dat.svn-base │ │ │ ├── Philippines-abs0.dat.svn-base │ │ │ ├── Philippines-abs1.dat.svn-base │ │ │ ├── Philippines-cf0.dat.svn-base │ │ │ └── Philippines-orig.dat.svn-base │ │ ├── BaffinIsland-abs0.dat │ │ ├── BaffinIsland-abs1.dat │ │ ├── BaffinIsland-cf0.dat │ │ ├── BaffinIsland-orig.dat │ │ ├── China-abs0.dat │ │ ├── China-abs1.dat │ │ ├── China-cf0.dat │ │ ├── China-orig.dat │ │ ├── Iceland-abs0.dat │ │ ├── Iceland-abs1.dat │ │ ├── Iceland-cf0.dat │ │ ├── Iceland-orig.dat │ │ ├── NewGuinea-abs0.dat │ │ ├── NewGuinea-abs1.dat │ │ ├── NewGuinea-cf0.dat │ │ ├── NewGuinea-orig.dat │ │ ├── Newfoundland-abs0.dat │ │ ├── Newfoundland-abs1.dat │ │ ├── Newfoundland-cf0.dat │ │ ├── Newfoundland-orig.dat │ │ ├── Philippines-abs0.dat │ │ ├── Philippines-abs1.dat │ │ ├── Philippines-cf0.dat │ │ └── Philippines-orig.dat │ ├── australia.dat │ ├── blob00.xy │ ├── c-shape00.xy │ ├── c-shape01.xy │ ├── cartman.xy │ ├── circle00.xy │ ├── circle01.xy │ ├── circle02.xy │ ├── circle03.xy │ ├── flower00.xy │ ├── kenny.xy │ ├── kyle.xy │ ├── nested_circles00.xy │ ├── nested_circles01.xy │ ├── round_rect00.xy │ ├── skyline_noisy00.xy │ ├── stair-noise00.xy │ ├── stan.xy │ ├── test.xy │ ├── test0.xy │ ├── test1.xy │ └── test2.xy ├── pres ├── agpig │ ├── img │ │ ├── circle-cube-inter.png │ │ ├── curvature-ellipse-200-15-area.png │ │ ├── curvature-ellipse-200-15-perimeter.png │ │ ├── elephant-mesh.png │ │ ├── elephant-point-cloud.png │ │ ├── ellipse-200-noised-var-1-area.png │ │ ├── ellipse-200-noised-var-1-perimeter.png │ │ ├── ellipse-balls-15.png │ │ ├── ellipse-noised-area-5-01.png │ │ ├── ellipse-noised-perimeter-7-2.png │ │ ├── ellipse-outliers-area.png │ │ ├── ellipse-outliers-perimeter.png │ │ ├── ellipse-outliers.png │ │ ├── mean-curvature-flow-cube.png │ │ ├── mean-curvature-flow-rabbit.png │ │ ├── noise-2d.png │ │ ├── osculating-circle.png │ │ ├── sphere-1000.png │ │ ├── sphere-bipyramid-10.png │ │ ├── sphere-bipyramid-bipyramid.png │ │ ├── sphere-cube-0.png │ │ ├── sphere-cube-10.png │ │ ├── sphere-cube-cube.png │ │ ├── sphere-polyhedron-200.png │ │ ├── sphere-sphere-1000-05.png │ │ ├── voronoi-curve-2d.eps │ │ ├── voronoi-diagram-2d.eps │ │ └── voronoi-offset-2d.eps │ ├── ipe │ │ └── voronoi-curve-2d.ipe │ └── pres.tex └── defense │ ├── img │ ├── 3d_perimeter_squares.eps │ ├── 3d_perimeter_squares_truth.eps │ ├── area-dense.png │ ├── area-sparse.png │ ├── ball-15.png │ ├── bipyramid.png │ ├── catenoid.jpg │ ├── circle-cube-inter.png │ ├── costa-minimal.png │ ├── cube-cube-15-ie.png │ ├── cube-cube-15-naive.png │ ├── cube.png │ ├── curvature-ellipse-200-15-area.png │ ├── curvature-ellipse-200-15-perimeter.png │ ├── curvatures-3d.png │ ├── curve-2d-offset.eps │ ├── curve-2d.eps │ ├── elephant-mesh.png │ ├── elephant-point-cloud.png │ ├── ellipse-area-dense-0.png │ ├── ellipse-area-dense-10.png │ ├── ellipse-area-dense-50.png │ ├── ellipse-area-sparse-0.png │ ├── ellipse-area-sparse-10.png │ ├── ellipse-area-sparse-50.png │ ├── ellipse-balls-15.png │ ├── ellipse-outliers-area.png │ ├── ellipse-outliers-perimeter.png │ ├── ellipse-outliers.png │ ├── ellipse-perimeter-dense-0.png │ ├── ellipse-perimeter-dense-10.png │ ├── ellipse-perimeter-dense-50.png │ ├── ellipse-perimeter-sparse-0.png │ ├── ellipse-perimeter-sparse-10.png │ ├── ellipse-perimeter-sparse-50.png │ ├── fandisk-normals.png │ ├── icosahedron.png │ ├── image-pixels.png │ ├── lena-denoising.png │ ├── lena-ft.jpg │ ├── lena.png │ ├── mean-curvature-flow-cube.png │ ├── mean-curvature-flow-rabbit.png │ ├── noise-2d.png │ ├── osculating-circle.png │ ├── perimeter-dense.png │ ├── perimeter-sparse.png │ ├── sphere-025-05-0.png │ ├── sphere-025-05-15.png │ ├── sphere-025-05-2.png │ ├── sphere-1000.png │ ├── sphere-bipyramid-10.png │ ├── sphere-bipyramid-bipyramid.png │ ├── sphere-cube-0.png │ ├── sphere-cube-10.png │ ├── sphere-cube-cube.png │ ├── sphere-cube-inter.png │ ├── sphere-polyhedron-200.png │ ├── sphere-sphere-1000-05.png │ ├── square-noisy-3-15-01-3.png │ ├── square-noisy-3-15-01-6.png │ ├── square-noisy-3-15-01.png │ ├── voronoi-curve-2d.eps │ ├── voronoi-diagram-2d.eps │ └── voronoi-offset-2d.eps │ ├── ipe │ ├── voronoi-curve-2d-no-noise.ipe │ └── voronoi-curve-2d.ipe │ └── pres.tex └── report ├── A-intro.tex ├── B-2d.tex ├── C-3d.tex ├── D-theory.tex ├── E-conclusion.tex ├── abstract.tex ├── appendix-A-AD.tex ├── appendix-B-code-intersection.tex ├── appendix-C-voronoi-polyhedral-norm.tex ├── bibfile.bib ├── code ├── halfspace_intersection_with_dual_3.h └── sqrt_AD.h ├── img ├── 2d │ ├── 2d_proof_gradient_area.eps │ ├── area │ │ ├── circle-100-01-15-gradients.png │ │ ├── circle-100-01-15.png │ │ ├── curvature-ellipse-200-15.png │ │ ├── curvature-error-ellipse-200-05.png │ │ ├── ellipse-100-01-15-100.png │ │ ├── ellipse-100-01-15-gradients.png │ │ ├── ellipse-100-01-15-outliers-40.png │ │ ├── ellipse-100-01-15-outliers.png │ │ ├── ellipse-100-01-15.png │ │ ├── ellipse-noise-5-75.png │ │ ├── ellipse-osc-25-15-25.png │ │ ├── ellipse-osc2-20-15-25.png │ │ ├── ellipse-weighted-15-10.png │ │ ├── line-01-15-0.png │ │ ├── line-01-15-50.png │ │ ├── square-40-001-100-gradients.png │ │ ├── square-40-001-100.png │ │ └── square-area-4-15-01.png │ ├── ellipse-balls-15.png │ ├── ellipse-noise-5-0.png │ ├── ellipse-osc-25-15-0.png │ ├── ellipse-osc2-20.png │ ├── inter_voronoi_ball_2d.eps │ ├── inter_voronoi_ball_2d_2_inter.eps │ ├── inter_voronoi_ball_2d_no_inter.eps │ ├── perimeter │ │ ├── bird-0.png │ │ ├── bird-24.png │ │ ├── bird-49.png │ │ ├── circle-100-01-15-gradients.png │ │ ├── circle-100-01-15.png │ │ ├── curvature-ellipse-200-15.png │ │ ├── curvature-error-ellipse-200-05.png │ │ ├── ellipse-100-01-15-100.png │ │ ├── ellipse-100-01-15-gradients.png │ │ ├── ellipse-100-01-15.png │ │ ├── ellipse-100-1-15-outliers-100.png │ │ ├── ellipse-100-1-15-outliers.png │ │ ├── ellipse-noise-5-75.png │ │ ├── ellipse-osc-25-15-50.png │ │ ├── ellipse-osc2-20-100-15-05-0&55.png │ │ ├── ellipse-osc2-20-15-55.png │ │ ├── line-05-15-0.png │ │ ├── line-05-15-50.png │ │ ├── shark-0.png │ │ ├── shark-24.png │ │ ├── shark-49.png │ │ ├── square-40-001-100-gradients.png │ │ ├── square-40-001-100.png │ │ └── square-perimeter-10-15-05.png │ ├── square-0-balls-15.png │ ├── square-0.png │ ├── values-ellipse-perimeter.jpg │ └── values-square-area.jpg ├── 3d │ ├── 3d_perimeter_squares.eps │ ├── 3d_perimeter_squares_truth.eps │ ├── circle-gradients.png │ ├── circle-inter-cube.png │ ├── cube-cube-15-ie.png │ ├── cube-cube-15-naive.png │ ├── fandisk-normals.png │ ├── fin90-normals.png │ ├── fin90.png │ ├── inclusion-exclusion-counter-l2.eps │ ├── inclusion-exclusion-counter-linfty.eps │ ├── sphere-1000.png │ ├── sphere-bipyramid-10.png │ ├── sphere-bipyramid-bipyramid.png │ ├── sphere-cube-0.png │ ├── sphere-cube-10.png │ ├── sphere-cube-cube.png │ ├── sphere-icosahedron-0.png │ ├── sphere-icosahedron-10.png │ ├── sphere-icosahedron-icosahedron.png │ ├── sphere-polyhedron-200.png │ ├── sphere-sphere-1000-05.png │ ├── voronoi-cube-aligned.eps │ └── voronoi-cube-non-aligned.eps ├── logoINP.png ├── logoUJF.jpg ├── mean-curvature-flow-rabbit.png ├── offset-parametrization.eps ├── reach-union-2-spheres.eps ├── voronoi-curve-2d.eps ├── voronoi-cylinder.eps └── voronoi-offset-2d.eps ├── ipe ├── 2d_proof_gradient_area.ipe ├── 3d_perimeter_squares.ipe ├── inclusion-exclusion.ipe ├── inter_voronoi_ball_2d.ipe ├── inter_voronoi_ball_2d_2_inter.ipe ├── inter_voronoi_ball_2d_no_inter.ipe ├── offset-parametrization.ipe ├── reach-union-2-spheres.ipe ├── voronoi-cube-aligned.ipe ├── voronoi-cube-non-aligned.ipe ├── voronoi-curve-2d.ipe ├── voronoi-cylinder.ipe └── voronoi-diagram-2d.ipe ├── report.pdf ├── report.tex └── res ├── 2d ├── area-dense.txt ├── area-sparse.txt ├── ellipse-area-100.xy ├── ellipse-area-outliers-40.xy ├── ellipse-noise-5-75-area.xy ├── ellipse-noise-5-75-perimeter.xy ├── ellipse-noise-5.xy ├── ellipse-noisy-dense.xy ├── ellipse-noisy-sparse.xy ├── ellipse-osc2.xy ├── ellipse-outliers.xy ├── ellipse-perimeter-100.xy 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