CMakeLists.txt

@@ -6,10 +6,6 @@ find_package(Qt5 REQUIRED COMPONENTS Core Gui Widgets)
 add_subdirectory(external/OpenMesh)
 add_subdirectory(external/Eigen)
 
-add_subdirectory(external/MeshReconstruction)
-target_include_directories(MeshReconstruction INTERFACE
-  external/MeshReconstruction/lib)
-
 add_executable(${PROJECT_NAME})
 target_sources(${PROJECT_NAME} PRIVATE
   resources.qrc
@@ -32,14 +28,11 @@ target_sources(${PROJECT_NAME} PRIVATE
   src/quad_patch.cpp
   src/quad_patch.h
   src/quad_patch_tesselator.cpp
-  src/quad_patch_tesselator.h
+  src/quad_patch_tesselator.h)
-  src/hole_filling.h
-  src/hole_filling.cpp)
 target_link_libraries(${PROJECT_NAME} PRIVATE
   Qt5::Core Qt5::Gui Qt5::Widgets
   OpenMeshCore
-  eigen
+  eigen)
-  MeshReconstruction)
 target_compile_features(${PROJECT_NAME} PRIVATE cxx_std_17)
 set_target_properties(${PROJECT_NAME} PROPERTIES
   AUTOMOC ON

external/MeshReconstruction/.gitignore

@@ -1,3 +0,0 @@
-bin
-html/
-latex/

external/MeshReconstruction/CMakeLists.txt

@@ -1,16 +0,0 @@
-cmake_minimum_required (VERSION 3.0)
-project (MeshReconstruction)
-
-set(CMAKE_CXX_STANDARD 11)
-set(CMAKE_CXX_STANDARD_REQUIRED ON)
-
-# Parallel compilation.
-if(WIN32)
-	set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /MP")
-	set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /wd4250")
-endif()
-
-set(CMAKE_DEBUG_POSTFIX "d")
-
-add_subdirectory(lib)
-add_subdirectory(demo)

external/MeshReconstruction/Readme.md

@@ -1,13 +0,0 @@
-# MeshReconstruction
-
-This is a small library that can reconstruct a triangle mesh from a <a href="http://www.iquilezles.org/www/articles/distfunctions/distfunctions.htm">signed distance function</a> using the <a href="https://en.wikipedia.org/wiki/Marching_cubes">Marching Cubes algorithm</a> and export it to a file in the <a href="https://de.wikipedia.org/wiki/Wavefront_OBJ">obj format</a>.
-
-The library is self-contained and has no dependencies. The library is fast due to precomputed lookup tables and a narrow-band approach which excludes a lot of marching cubes that are far away from the surface.
-
-The library requires C++14 and has been tested under Visual Studio 2017 and Windows 10 but should port to other systems without major problems.
-
-The library can be used under the terms of the MIT License.
-
-<p align="center">
-  <img src="overview.png" width="400" alt="Overview">
-</p>

external/MeshReconstruction/demo/CMakeLists.txt

@@ -1,3 +0,0 @@
-include_directories("." ${PROJECT_SOURCE_DIR}/lib)
-add_executable(Demo main.cpp)
-target_link_libraries (Demo MeshReconstruction)

external/MeshReconstruction/demo/main.cpp

@@ -1,22 +0,0 @@
-#include <MeshReconstruction.h>
-#include <IO.h>
-
-using namespace MeshReconstruction;
-
-int main()
-{
-	auto sphereSdf = [](Vec3 const& pos)
-	{
-		auto const Radius = 1.0;
-		return pos.Norm() - Radius;
-	};
-
-	Rect3 domain;
-	domain.min = { -1.1, -1.1, -1.1 };
-	domain.size = {2.2, 2.2, 2.2};
-
-	Vec3 cubeSize{ 0.05, 0.05, 0.05 };
-
-	auto mesh = MarchCube(sphereSdf, domain, cubeSize);
-	WriteObjFile(mesh, "sphere.obj");
-}

external/MeshReconstruction/lib/CMakeLists.txt

@@ -1,12 +0,0 @@
-add_library(MeshReconstruction MeshReconstruction.h MeshReconstruction.cpp Cube.h Cube.cpp DataStructs.h IO.h IO.cpp Triangulation.h Triangulation.cpp)
-
-target_link_libraries(MeshReconstruction m)
-
-install(TARGETS MeshReconstruction
-        RUNTIME DESTINATION bin
-        LIBRARY DESTINATION lib
-        ARCHIVE DESTINATION lib)
-
-install(DIRECTORY .
-        DESTINATION .
-        FILES_MATCHING PATTERN "*.h")

external/MeshReconstruction/lib/Cube.cpp

@@ -1,149 +0,0 @@
-#include "Cube.h"
-#include <cmath>
-
-using namespace MeshReconstruction;
-
-namespace
-{
-	// Cube has 8 vertices. Each vertex can have positive or negative sign.
-	// 2^8 = 256 possible configurations mapped to intersected edges in each case.
-	// The 12 edges are numbered as 1, 2, 4, ..., 2048 and are stored as a 12-bit bitstring for each configuration.
-	const int signConfigToIntersectedEdges[256] = {
-		0x0  , 0x109, 0x203, 0x30a, 0x406, 0x50f, 0x605, 0x70c,
-		0x80c, 0x905, 0xa0f, 0xb06, 0xc0a, 0xd03, 0xe09, 0xf00,
-		0x190, 0x99 , 0x393, 0x29a, 0x596, 0x49f, 0x795, 0x69c,
-		0x99c, 0x895, 0xb9f, 0xa96, 0xd9a, 0xc93, 0xf99, 0xe90,
-		0x230, 0x339, 0x33 , 0x13a, 0x636, 0x73f, 0x435, 0x53c,
-		0xa3c, 0xb35, 0x83f, 0x936, 0xe3a, 0xf33, 0xc39, 0xd30,
-		0x3a0, 0x2a9, 0x1a3, 0xaa , 0x7a6, 0x6af, 0x5a5, 0x4ac,
-		0xbac, 0xaa5, 0x9af, 0x8a6, 0xfaa, 0xea3, 0xda9, 0xca0,
-		0x460, 0x569, 0x663, 0x76a, 0x66 , 0x16f, 0x265, 0x36c,
-		0xc6c, 0xd65, 0xe6f, 0xf66, 0x86a, 0x963, 0xa69, 0xb60,
-		0x5f0, 0x4f9, 0x7f3, 0x6fa, 0x1f6, 0xff , 0x3f5, 0x2fc,
-		0xdfc, 0xcf5, 0xfff, 0xef6, 0x9fa, 0x8f3, 0xbf9, 0xaf0,
-		0x650, 0x759, 0x453, 0x55a, 0x256, 0x35f, 0x55 , 0x15c,
-		0xe5c, 0xf55, 0xc5f, 0xd56, 0xa5a, 0xb53, 0x859, 0x950,
-		0x7c0, 0x6c9, 0x5c3, 0x4ca, 0x3c6, 0x2cf, 0x1c5, 0xcc ,
-		0xfcc, 0xec5, 0xdcf, 0xcc6, 0xbca, 0xac3, 0x9c9, 0x8c0,
-		0x8c0, 0x9c9, 0xac3, 0xbca, 0xcc6, 0xdcf, 0xec5, 0xfcc,
-		0xcc , 0x1c5, 0x2cf, 0x3c6, 0x4ca, 0x5c3, 0x6c9, 0x7c0,
-		0x950, 0x859, 0xb53, 0xa5a, 0xd56, 0xc5f, 0xf55, 0xe5c,
-		0x15c, 0x55 , 0x35f, 0x256, 0x55a, 0x453, 0x759, 0x650,
-		0xaf0, 0xbf9, 0x8f3, 0x9fa, 0xef6, 0xfff, 0xcf5, 0xdfc,
-		0x2fc, 0x3f5, 0xff , 0x1f6, 0x6fa, 0x7f3, 0x4f9, 0x5f0,
-		0xb60, 0xa69, 0x963, 0x86a, 0xf66, 0xe6f, 0xd65, 0xc6c,
-		0x36c, 0x265, 0x16f, 0x66 , 0x76a, 0x663, 0x569, 0x460,
-		0xca0, 0xda9, 0xea3, 0xfaa, 0x8a6, 0x9af, 0xaa5, 0xbac,
-		0x4ac, 0x5a5, 0x6af, 0x7a6, 0xaa , 0x1a3, 0x2a9, 0x3a0,
-		0xd30, 0xc39, 0xf33, 0xe3a, 0x936, 0x83f, 0xb35, 0xa3c,
-		0x53c, 0x435, 0x73f, 0x636, 0x13a, 0x33 , 0x339, 0x230,
-		0xe90, 0xf99, 0xc93, 0xd9a, 0xa96, 0xb9f, 0x895, 0x99c,
-		0x69c, 0x795, 0x49f, 0x596, 0x29a, 0x393, 0x99 , 0x190,
-		0xf00, 0xe09, 0xd03, 0xc0a, 0xb06, 0xa0f, 0x905, 0x80c,
-		0x70c, 0x605, 0x50f, 0x406, 0x30a, 0x203, 0x109, 0x0 };
-
-	struct Edge
-	{
-		int edgeFlag : 12; // flag: 1, 2, 4, ... 2048
-		int vert0; // 0-7
-		int vert1; // 0-7
-	};
-
-	const Edge edges[12] =
-	{
-		{ 1, 0, 1 }, // edge 0
-		{ 2, 1, 2 }, // edge 1
-		{ 4, 2, 3 }, // ...
-		{ 8, 3, 0 },
-		{ 16, 4, 5 },
-		{ 32, 5, 6 },
-		{ 64, 6, 7 },
-		{ 128, 7, 4 },
-		{ 256, 0, 4 },
-		{ 512, 1, 5 },
-		{ 1024, 2, 6 },
-		{ 2048, 3, 7 } // edge 11
-	};
-}
-
-Vec3 Cube::LerpVertex(double isoLevel, int i1, int i2) const
-{
-	auto const Eps = 1e-5;
-	auto const v1 = sdf[i1];
-	auto const v2 = sdf[i2];
-	auto const& p1 = pos[i1];
-	auto const& p2 = pos[i2];
-
-	if (abs(isoLevel - v1) < Eps) return p1;
-	if (abs(isoLevel - v2) < Eps) return p2;
-	if (abs(v1 - v2) < Eps) return p1;
-
-	auto mu = (isoLevel - v1) / (v2 - v1);
-	return p1 + (p2 - p1)*mu;
-}
-
-Cube::Cube(Rect3 const& space, Fun3s const& sdf)
-{
-	auto mx = space.min.x;
-	auto my = space.min.y;
-	auto mz = space.min.z;
-
-	auto sx = space.size.x;
-	auto sy = space.size.y;
-	auto sz = space.size.z;
-
-	pos[0] = space.min;
-	pos[1] = { mx + sx, my, mz };
-	pos[2] = { mx + sx, my, mz + sz };
-	pos[3] = { mx, my, mz + sz };
-	pos[4] = { mx, my + sy, mz };
-	pos[5] = { mx + sx, my + sy, mz };
-	pos[6] = { mx + sx, my + sy, mz + sz };
-	pos[7] = { mx, my + sy, mz + sz };
-
-	for (auto i = 0; i < 8; ++i)
-	{
-		auto sd = sdf(pos[i]);
-		if (sd == 0) sd += 1e-6;
-		this->sdf[i] = sd;
-	}
-}
-
-int Cube::SignConfig(double isoLevel) const
-{
-	auto edgeIndex = 0;
-
-	for (auto i = 0; i < 8; ++i)
-	{
-		if (sdf[i] < isoLevel)
-		{
-			edgeIndex |= 1 << i;
-		}
-	}
-
-	return edgeIndex;
-}
-
-IntersectInfo Cube::Intersect(double iso) const
-{
-	// idea:
-	// from signs at 8 corners of cube a sign configuration (256 possible ones) is computed
-	// this configuration can be used to index into a table that tells which of the 12 edges are intersected
-	// find vertices adjacent to edges and interpolate cut vertex and store it in IntersectionInfo object
-
-	IntersectInfo intersect;
-	intersect.signConfig = SignConfig(iso);
-
-	for (auto e = 0; e<12; ++e)
-	{
-		if (signConfigToIntersectedEdges[intersect.signConfig] & edges[e].edgeFlag)
-		{
-			auto v0 = edges[e].vert0;
-			auto v1 = edges[e].vert1;
-			auto vert = LerpVertex(iso, v0, v1);
-			intersect.edgeVertIndices[e] = vert;
-		}
-	}
-
-	return intersect;
-}

external/MeshReconstruction/lib/Cube.h

@@ -1,30 +0,0 @@
-#pragma once
-#include "DataStructs.h"
-
-namespace MeshReconstruction
-{
-	struct IntersectInfo
-	{
-		// 0 - 255
-		int signConfig;
-
-		// If it exists, vertex on edge i is stored at position i.
-		// For edge numbering and location see numberings.png.
-		std::array<Vec3, 12> edgeVertIndices;
-	};
-
-	class Cube
-	{
-		Vec3 pos[8];
-		double sdf[8];
-
-		Vec3 LerpVertex(double isoLevel, int i1, int i2) const;
-		int SignConfig(double isoLevel) const;
-
-	public:
-		Cube(Rect3 const& space, Fun3s const& sdf);
-
-		// Find the vertices where the surface intersects the cube.
-		IntersectInfo Intersect(double isoLevel = 0) const;
-	};
-}

external/MeshReconstruction/lib/DataStructs.h

@@ -1,57 +0,0 @@
-#pragma once
-#include <vector>
-#include <array>
-#include <functional>
-#include <cmath>
-
-namespace MeshReconstruction
-{
-	struct Vec3
-	{
-		double x, y, z;
-
-		Vec3 operator+(Vec3 const& o) const
-		{
-			return { x + o.x, y + o.y, z + o.z };
-		}
-
-		Vec3 operator-(Vec3 const& o) const
-		{
-			return { x - o.x, y - o.y, z - o.z };
-		}
-
-		Vec3 operator*(double c) const
-		{
-			return { c*x, c*y, c*z };
-		}
-
-		double Norm() const
-		{
-			return sqrt(x*x + y*y + z*z);
-		}
-
-		Vec3 Normalized() const
-		{
-			auto n = Norm();
-			return { x / n, y / n, z / n };
-		}
-	};
-
-	struct Rect3
-	{
-		Vec3 min;
-		Vec3 size;
-	};
-
-	using Triangle = std::array<int, 3>;
-
-	struct Mesh
-	{
-		std::vector<Vec3> vertices;
-		std::vector<Triangle> triangles;
-		std::vector<Vec3> vertexNormals;
-	};
-
-	using Fun3s = std::function<double(Vec3 const&)>;
-	using Fun3v = std::function<Vec3(Vec3 const&)>;
-}

external/MeshReconstruction/lib/IO.cpp

@@ -1,53 +0,0 @@
-#include "IO.h"
-#include <stdexcept>
-using namespace std;
-
-void MeshReconstruction::WriteObjFile(Mesh const& mesh, string const& fileName)
-{
-	// FILE faster than streams.
-
-	FILE* file;
-	//auto status = fopen_s(&file, fileName.c_str(), "w");
-	//if (status != 0)
-	//{
-	//	throw runtime_error("Could not write obj file.");
-	//}
-	file = fopen(fileName.c_str(), "w");
-	if (file == NULL)
-	{
-		throw runtime_error("Could not write obj file.");
-	}
-
-	// write stats
-	fprintf(file, "# %d vertices, %d triangles\n\n",
-		static_cast<int>(mesh.vertices.size()),
-		static_cast<int>(mesh.triangles.size()));
-
-	// vertices
-	for (auto vi = 0; vi < mesh.vertices.size(); ++vi)
-	{
-		auto const& v = mesh.vertices.at(vi);
-		fprintf(file, "v %f %f %f\n", v.x, v.y, v.z);
-	}
-
-	// vertex normals
-	fprintf(file, "\n");
-	for (auto ni = 0; ni < mesh.vertices.size(); ++ni)
-	{
-		auto const& vn = mesh.vertexNormals.at(ni);
-		fprintf(file, "vn %f %f %f\n", vn.x, vn.y, vn.z);
-	}
-
-	// triangles (1-based)
-	fprintf(file, "\n");
-	for (auto ti = 0; ti < mesh.triangles.size(); ++ti)
-	{
-		auto const& t = mesh.triangles.at(ti);
-		fprintf(file, "f %d//%d %d//%d %d//%d\n",
-			t[0] + 1, t[0] + 1,
-			t[1] + 1, t[1] + 1,
-			t[2] + 1, t[2] + 1);
-	}
-
-	fclose(file);
-}

external/MeshReconstruction/lib/IO.h

@@ -1,9 +0,0 @@
-#pragma once
-#include <string>
-#include "DataStructs.h"
-
-namespace MeshReconstruction
-{
-	/// Writes a mesh to a file in <a href="https://de.wikipedia.org/wiki/Wavefront_OBJ">obj format</a>.
-	void WriteObjFile(Mesh const& mesh, std::string const& file);
-}

external/MeshReconstruction/lib/MeshReconstruction.cpp

@@ -1,78 +0,0 @@
-#include "MeshReconstruction.h"
-#include "Cube.h"
-#include "Triangulation.h"
-
-using namespace MeshReconstruction;
-using namespace std;
-
-// Adapted from here: http://paulbourke.net/geometry/polygonise/
-
-namespace
-{
-	Vec3 NumGrad(Fun3s const& f, Vec3 const& p)
-	{
-		auto const Eps = 1e-6;
-		Vec3 epsX{ Eps, 0, 0 }, epsY{ 0, Eps, 0 }, epsZ{ 0, 0, Eps };
-		auto gx = (f(p + epsX) - f(p - epsX)) / 2;
-		auto gy = (f(p + epsY) - f(p - epsY)) / 2;
-		auto gz = (f(p + epsZ) - f(p - epsZ)) / 2;
-		return { gx, gy, gz };
-	}
-}
-
-Mesh MeshReconstruction::MarchCube(Fun3s const& sdf, Rect3 const& domain)
-{
-	auto const NumCubes = 50;
-	auto cubeSize = domain.size * (1.0 / NumCubes);
-
-	return MarchCube(sdf, domain, cubeSize);
-}
-
-Mesh MeshReconstruction::MarchCube(
-	Fun3s const& sdf,
-	Rect3 const& domain,
-	Vec3 const& cubeSize,
-	double isoLevel,
-	Fun3v sdfGrad)
-{
-	// Default value.
-	sdfGrad = sdfGrad == nullptr
-		? [&sdf](Vec3 const& p) { return NumGrad(sdf, p); }
-		: sdfGrad;
-
-	auto const NumX = static_cast<int>(ceil(domain.size.x / cubeSize.x));
-	auto const NumY = static_cast<int>(ceil(domain.size.y / cubeSize.y));
-	auto const NumZ = static_cast<int>(ceil(domain.size.z / cubeSize.z));
-
-	auto const HalfCubeDiag = cubeSize.Norm() / 2.0;
-	auto const HalfCubeSize = cubeSize * 0.5;
-
-	Mesh mesh;
-
-	for (auto ix = 0; ix < NumX; ++ix)
-	{
-		auto x = domain.min.x + ix * cubeSize.x;
-			
-		for (auto iy = 0; iy < NumY; ++iy)
-		{
-			auto y = domain.min.y + iy * cubeSize.y;
-			
-			for (auto iz = 0; iz < NumZ; ++iz)
-			{
-				auto z = domain.min.z + iz * cubeSize.z;
-				Vec3 min{ x, y, z };
-
-				// Process only if cube lies within narrow band around surface.
-				auto cubeCenter = min + HalfCubeSize;
-				auto dist = abs(sdf(cubeCenter) - isoLevel);
-				if (dist > HalfCubeDiag) continue;
-
-				Cube cube({ min, cubeSize }, sdf);
-				auto intersect = cube.Intersect(isoLevel);
-				Triangulate(intersect, sdfGrad, mesh);
-			}
-		}
-	}
-
-	return mesh;
-}

external/MeshReconstruction/lib/MeshReconstruction.h

@@ -1,27 +0,0 @@
-#pragma once
-#include "DataStructs.h"
-
-namespace MeshReconstruction
-{
-	/// Reconstructs a triangle mesh from a given signed distance function using <a href="https://en.wikipedia.org/wiki/Marching_cubes">Marching Cubes</a>.
-	/// @param sdf The <a href="http://www.iquilezles.org/www/articles/distfunctions/distfunctions.htm">Signed Distance Function</a>.
-	/// @param domain Domain of reconstruction.
-	/// @returns The reconstructed mesh.
-	Mesh MarchCube(
-		Fun3s const& sdf,
-		Rect3 const& domain);
-
-	/// Reconstructs a triangle mesh from a given signed distance function using <a href="https://en.wikipedia.org/wiki/Marching_cubes">Marching Cubes</a>.
-	/// @param sdf The <a href="http://www.iquilezles.org/www/articles/distfunctions/distfunctions.htm">Signed Distance Function</a>.
-	/// @param domain Domain of reconstruction.
-	/// @param cubeSize Size of marching cubes. Smaller cubes yields meshes of higher resolution.
-	/// @param isoLevel Level set of the SDF for which triangulation should be done. Changing this value moves the reconstructed surface.
-	/// @param sdfGrad Gradient of the SDF which yields the vertex normals of the reconstructed mesh. If none is provided a numerical approximation is used.
-	/// @returns The reconstructed mesh.
-	Mesh MarchCube(
-		Fun3s const& sdf,
-		Rect3 const& domain,
-		Vec3 const& cubeSize,
-		double isoLevel = 0,
-		Fun3v sdfGrad = nullptr);
-}

external/MeshReconstruction/lib/Triangulation.cpp

@@ -1,301 +0,0 @@
-#include "Triangulation.h"
-
-namespace
-{
-	// Indices into vertex buffer (0 - 11).
-	// Three successive entries make up one triangle.
-	// -1 means unused.
-	const int signConfigToTriangles[256][16] =
-		{ { -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 1, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 8, 3, 9, 8, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 8, 3, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 9, 2, 10, 0, 2, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 2, 8, 3, 2, 10, 8, 10, 9, 8, -1, -1, -1, -1, -1, -1, -1 },
-		{ 3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 11, 2, 8, 11, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 9, 0, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 11, 2, 1, 9, 11, 9, 8, 11, -1, -1, -1, -1, -1, -1, -1 },
-		{ 3, 10, 1, 11, 10, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 10, 1, 0, 8, 10, 8, 11, 10, -1, -1, -1, -1, -1, -1, -1 },
-		{ 3, 9, 0, 3, 11, 9, 11, 10, 9, -1, -1, -1, -1, -1, -1, -1 },
-		{ 9, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 4, 3, 0, 7, 3, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 1, 9, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 4, 1, 9, 4, 7, 1, 7, 3, 1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 2, 10, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 3, 4, 7, 3, 0, 4, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1 },
-		{ 9, 2, 10, 9, 0, 2, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1 },
-		{ 2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4, -1, -1, -1, -1 },
-		{ 8, 4, 7, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 11, 4, 7, 11, 2, 4, 2, 0, 4, -1, -1, -1, -1, -1, -1, -1 },
-		{ 9, 0, 1, 8, 4, 7, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1 },
-		{ 4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1, -1, -1, -1, -1 },
-		{ 3, 10, 1, 3, 11, 10, 7, 8, 4, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4, -1, -1, -1, -1 },
-		{ 4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3, -1, -1, -1, -1 },
-		{ 4, 7, 11, 4, 11, 9, 9, 11, 10, -1, -1, -1, -1, -1, -1, -1 },
-		{ 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 9, 5, 4, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 5, 4, 1, 5, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 8, 5, 4, 8, 3, 5, 3, 1, 5, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 2, 10, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 3, 0, 8, 1, 2, 10, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1 },
-		{ 5, 2, 10, 5, 4, 2, 4, 0, 2, -1, -1, -1, -1, -1, -1, -1 },
-		{ 2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8, -1, -1, -1, -1 },
-		{ 9, 5, 4, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 11, 2, 0, 8, 11, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 5, 4, 0, 1, 5, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1 },
-		{ 2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5, -1, -1, -1, -1 },
-		{ 10, 3, 11, 10, 1, 3, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1 },
-		{ 4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10, -1, -1, -1, -1 },
-		{ 5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3, -1, -1, -1, -1 },
-		{ 5, 4, 8, 5, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1 },
-		{ 9, 7, 8, 5, 7, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 9, 3, 0, 9, 5, 3, 5, 7, 3, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 7, 8, 0, 1, 7, 1, 5, 7, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 9, 7, 8, 9, 5, 7, 10, 1, 2, -1, -1, -1, -1, -1, -1, -1 },
-		{ 10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3, -1, -1, -1, -1 },
-		{ 8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2, -1, -1, -1, -1 },
-		{ 2, 10, 5, 2, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1 },
-		{ 7, 9, 5, 7, 8, 9, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1 },
-		{ 9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11, -1, -1, -1, -1 },
-		{ 2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7, -1, -1, -1, -1 },
-		{ 11, 2, 1, 11, 1, 7, 7, 1, 5, -1, -1, -1, -1, -1, -1, -1 },
-		{ 9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11, -1, -1, -1, -1 },
-		{ 5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0, -1 },
-		{ 11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0, -1 },
-		{ 11, 10, 5, 7, 11, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 8, 3, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 9, 0, 1, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 8, 3, 1, 9, 8, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 6, 5, 2, 6, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 6, 5, 1, 2, 6, 3, 0, 8, -1, -1, -1, -1, -1, -1, -1 },
-		{ 9, 6, 5, 9, 0, 6, 0, 2, 6, -1, -1, -1, -1, -1, -1, -1 },
-		{ 5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8, -1, -1, -1, -1 },
-		{ 2, 3, 11, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 11, 0, 8, 11, 2, 0, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 1, 9, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1 },
-		{ 5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11, -1, -1, -1, -1 },
-		{ 6, 3, 11, 6, 5, 3, 5, 1, 3, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6, -1, -1, -1, -1 },
-		{ 3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9, -1, -1, -1, -1 },
-		{ 6, 5, 9, 6, 9, 11, 11, 9, 8, -1, -1, -1, -1, -1, -1, -1 },
-		{ 5, 10, 6, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 4, 3, 0, 4, 7, 3, 6, 5, 10, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 9, 0, 5, 10, 6, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1 },
-		{ 10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4, -1, -1, -1, -1 },
-		{ 6, 1, 2, 6, 5, 1, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7, -1, -1, -1, -1 },
-		{ 8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6, -1, -1, -1, -1 },
-		{ 7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9, -1 },
-		{ 3, 11, 2, 7, 8, 4, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1 },
-		{ 5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11, -1, -1, -1, -1 },
-		{ 0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1 },
-		{ 9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6, -1 },
-		{ 8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6, -1, -1, -1, -1 },
-		{ 5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11, -1 },
-		{ 0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7, -1 },
-		{ 6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9, -1, -1, -1, -1 },
-		{ 10, 4, 9, 6, 4, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 4, 10, 6, 4, 9, 10, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1 },
-		{ 10, 0, 1, 10, 6, 0, 6, 4, 0, -1, -1, -1, -1, -1, -1, -1 },
-		{ 8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10, -1, -1, -1, -1 },
-		{ 1, 4, 9, 1, 2, 4, 2, 6, 4, -1, -1, -1, -1, -1, -1, -1 },
-		{ 3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4, -1, -1, -1, -1 },
-		{ 0, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 8, 3, 2, 8, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1 },
-		{ 10, 4, 9, 10, 6, 4, 11, 2, 3, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6, -1, -1, -1, -1 },
-		{ 3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10, -1, -1, -1, -1 },
-		{ 6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1, -1 },
-		{ 9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3, -1, -1, -1, -1 },
-		{ 8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1, -1 },
-		{ 3, 11, 6, 3, 6, 0, 0, 6, 4, -1, -1, -1, -1, -1, -1, -1 },
-		{ 6, 4, 8, 11, 6, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 7, 10, 6, 7, 8, 10, 8, 9, 10, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10, -1, -1, -1, -1 },
-		{ 10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0, -1, -1, -1, -1 },
-		{ 10, 6, 7, 10, 7, 1, 1, 7, 3, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7, -1, -1, -1, -1 },
-		{ 2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9, -1 },
-		{ 7, 8, 0, 7, 0, 6, 6, 0, 2, -1, -1, -1, -1, -1, -1, -1 },
-		{ 7, 3, 2, 6, 7, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7, -1, -1, -1, -1 },
-		{ 2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7, -1 },
-		{ 1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11, -1 },
-		{ 11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1, -1, -1, -1, -1 },
-		{ 8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6, -1 },
-		{ 0, 9, 1, 11, 6, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0, -1, -1, -1, -1 },
-		{ 7, 11, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 3, 0, 8, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 1, 9, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 8, 1, 9, 8, 3, 1, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1 },
-		{ 10, 1, 2, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 2, 10, 3, 0, 8, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1 },
-		{ 2, 9, 0, 2, 10, 9, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1 },
-		{ 6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8, -1, -1, -1, -1 },
-		{ 7, 2, 3, 6, 2, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 7, 0, 8, 7, 6, 0, 6, 2, 0, -1, -1, -1, -1, -1, -1, -1 },
-		{ 2, 7, 6, 2, 3, 7, 0, 1, 9, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6, -1, -1, -1, -1 },
-		{ 10, 7, 6, 10, 1, 7, 1, 3, 7, -1, -1, -1, -1, -1, -1, -1 },
-		{ 10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8, -1, -1, -1, -1 },
-		{ 0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7, -1, -1, -1, -1 },
-		{ 7, 6, 10, 7, 10, 8, 8, 10, 9, -1, -1, -1, -1, -1, -1, -1 },
-		{ 6, 8, 4, 11, 8, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 3, 6, 11, 3, 0, 6, 0, 4, 6, -1, -1, -1, -1, -1, -1, -1 },
-		{ 8, 6, 11, 8, 4, 6, 9, 0, 1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6, -1, -1, -1, -1 },
-		{ 6, 8, 4, 6, 11, 8, 2, 10, 1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6, -1, -1, -1, -1 },
-		{ 4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9, -1, -1, -1, -1 },
-		{ 10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3, -1 },
-		{ 8, 2, 3, 8, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8, -1, -1, -1, -1 },
-		{ 1, 9, 4, 1, 4, 2, 2, 4, 6, -1, -1, -1, -1, -1, -1, -1 },
-		{ 8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1, -1, -1, -1, -1 },
-		{ 10, 1, 0, 10, 0, 6, 6, 0, 4, -1, -1, -1, -1, -1, -1, -1 },
-		{ 4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3, -1 },
-		{ 10, 9, 4, 6, 10, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 4, 9, 5, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 8, 3, 4, 9, 5, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1 },
-		{ 5, 0, 1, 5, 4, 0, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1 },
-		{ 11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5, -1, -1, -1, -1 },
-		{ 9, 5, 4, 10, 1, 2, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1 },
-		{ 6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5, -1, -1, -1, -1 },
-		{ 7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2, -1, -1, -1, -1 },
-		{ 3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6, -1 },
-		{ 7, 2, 3, 7, 6, 2, 5, 4, 9, -1, -1, -1, -1, -1, -1, -1 },
-		{ 9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7, -1, -1, -1, -1 },
-		{ 3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0, -1, -1, -1, -1 },
-		{ 6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8, -1 },
-		{ 9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7, -1, -1, -1, -1 },
-		{ 1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4, -1 },
-		{ 4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10, -1 },
-		{ 7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10, -1, -1, -1, -1 },
-		{ 6, 9, 5, 6, 11, 9, 11, 8, 9, -1, -1, -1, -1, -1, -1, -1 },
-		{ 3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5, -1, -1, -1, -1 },
-		{ 0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11, -1, -1, -1, -1 },
-		{ 6, 11, 3, 6, 3, 5, 5, 3, 1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6, -1, -1, -1, -1 },
-		{ 0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10, -1 },
-		{ 11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5, -1 },
-		{ 6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3, -1, -1, -1, -1 },
-		{ 5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2, -1, -1, -1, -1 },
-		{ 9, 5, 6, 9, 6, 0, 0, 6, 2, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8, -1 },
-		{ 1, 5, 6, 2, 1, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6, -1 },
-		{ 10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0, -1, -1, -1, -1 },
-		{ 0, 3, 8, 5, 6, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 10, 5, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 11, 5, 10, 7, 5, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 11, 5, 10, 11, 7, 5, 8, 3, 0, -1, -1, -1, -1, -1, -1, -1 },
-		{ 5, 11, 7, 5, 10, 11, 1, 9, 0, -1, -1, -1, -1, -1, -1, -1 },
-		{ 10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1, -1, -1, -1, -1 },
-		{ 11, 1, 2, 11, 7, 1, 7, 5, 1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11, -1, -1, -1, -1 },
-		{ 9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7, -1, -1, -1, -1 },
-		{ 7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2, -1 },
-		{ 2, 5, 10, 2, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1 },
-		{ 8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5, -1, -1, -1, -1 },
-		{ 9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2, -1, -1, -1, -1 },
-		{ 9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2, -1 },
-		{ 1, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 8, 7, 0, 7, 1, 1, 7, 5, -1, -1, -1, -1, -1, -1, -1 },
-		{ 9, 0, 3, 9, 3, 5, 5, 3, 7, -1, -1, -1, -1, -1, -1, -1 },
-		{ 9, 8, 7, 5, 9, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 5, 8, 4, 5, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1 },
-		{ 5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0, -1, -1, -1, -1 },
-		{ 0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5, -1, -1, -1, -1 },
-		{ 10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4, -1 },
-		{ 2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8, -1, -1, -1, -1 },
-		{ 0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11, -1 },
-		{ 0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5, -1 },
-		{ 9, 4, 5, 2, 11, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4, -1, -1, -1, -1 },
-		{ 5, 10, 2, 5, 2, 4, 4, 2, 0, -1, -1, -1, -1, -1, -1, -1 },
-		{ 3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9, -1 },
-		{ 5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2, -1, -1, -1, -1 },
-		{ 8, 4, 5, 8, 5, 3, 3, 5, 1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 4, 5, 1, 0, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5, -1, -1, -1, -1 },
-		{ 9, 4, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 4, 11, 7, 4, 9, 11, 9, 10, 11, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11, -1, -1, -1, -1 },
-		{ 1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11, -1, -1, -1, -1 },
-		{ 3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4, -1 },
-		{ 4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2, -1, -1, -1, -1 },
-		{ 9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3, -1 },
-		{ 11, 7, 4, 11, 4, 2, 2, 4, 0, -1, -1, -1, -1, -1, -1, -1 },
-		{ 11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4, -1, -1, -1, -1 },
-		{ 2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9, -1, -1, -1, -1 },
-		{ 9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7, -1 },
-		{ 3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10, -1 },
-		{ 1, 10, 2, 8, 7, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 4, 9, 1, 4, 1, 7, 7, 1, 3, -1, -1, -1, -1, -1, -1, -1 },
-		{ 4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1, -1, -1, -1, -1 },
-		{ 4, 0, 3, 7, 4, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 4, 8, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 9, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 3, 0, 9, 3, 9, 11, 11, 9, 10, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 1, 10, 0, 10, 8, 8, 10, 11, -1, -1, -1, -1, -1, -1, -1 },
-		{ 3, 1, 10, 11, 3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 2, 11, 1, 11, 9, 9, 11, 8, -1, -1, -1, -1, -1, -1, -1 },
-		{ 3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9, -1, -1, -1, -1 },
-		{ 0, 2, 11, 8, 0, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 3, 2, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 2, 3, 8, 2, 8, 10, 10, 8, 9, -1, -1, -1, -1, -1, -1, -1 },
-		{ 9, 10, 2, 0, 9, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8, -1, -1, -1, -1 },
-		{ 1, 10, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 1, 3, 8, 9, 1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 9, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ 0, 3, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
-		{ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 } };
-}
-
-/// Given a grid cube and an isolevel the triangles (5 max)
-/// required to represent the isosurface in the cube are computed.
-void MeshReconstruction::Triangulate(
-	IntersectInfo const& intersect,
-	Fun3v const& grad,
-	Mesh& mesh)
-{
-	// Cube is entirely in/out of the surface. Generate no triangles.
-	if (intersect.signConfig == 0 || intersect.signConfig == 255) return;
-
-	auto const& tri = signConfigToTriangles[intersect.signConfig];
-
-	for (auto i = 0; tri[i] != -1; i += 3)
-	{
-		auto const& v0 = intersect.edgeVertIndices[tri[i]];
-		auto const& v1 = intersect.edgeVertIndices[tri[i + 1]];
-		auto const& v2 = intersect.edgeVertIndices[tri[i + 2]];
-
-		mesh.vertices.push_back(v0);
-		mesh.vertices.push_back(v1);
-		mesh.vertices.push_back(v2);
-
-		auto normal0 = grad(v0).Normalized();
-		auto normal1 = grad(v1).Normalized();
-		auto normal2 = grad(v2).Normalized();
-
-		mesh.vertexNormals.push_back(normal0);
-		mesh.vertexNormals.push_back(normal1);
-		mesh.vertexNormals.push_back(normal2);
-
-		auto last = static_cast<int>(mesh.vertices.size() - 1);
-
-		mesh.triangles.push_back({ last - 2, last - 1, last });
-	}
-}

external/MeshReconstruction/lib/Triangulation.h

@@ -1,11 +0,0 @@
-#pragma once
-#include "Cube.h"
-#include "DataStructs.h"
-
-namespace MeshReconstruction
-{
-	void Triangulate(
-		IntersectInfo const& intersect,
-		Fun3v const& grad,
-		Mesh& mesh);
-}

notes_réparation_bac.txt

@@ -1,5 +0,0 @@
-Notes du TP de réparation de maillage par surface implicite de Mme Bac
-
-Fonction implicite f(x) = Σ(1,n)[αi φ(||X-Xi||) + …]
-
-φ(r) = r²ln(r) : fonction radiale, une par point, =0 au point

src/curvature.cpp

@@ -54,9 +54,7 @@ QuadPatch Courbures::fit_quad(MyMesh::VertexHandle vh) {
     static std::vector<MyMesh::VertexHandle> neigh;
 	neigh.clear();
 	get_two_neighborhood(neigh, vh);
-    if (neigh.size() < 5) {
+    if (neigh.size() < 5) throw "Quad fitting: not enough neighbors";
-		throw std::runtime_error("Quad fitting: not enough neighbors");
-	}
 
     // Calcul de la matrice de changement de base
 	Eigen::Vector3d Oz(0,0,1);

src/curvature.h

@@ -14,10 +14,7 @@ public:
     OpenMesh::VPropHandleT<double> vprop_H;
 	OpenMesh::VPropHandleT<QuadPatch> vprop_quad;
 
-	Courbures(MyMesh &mesh) : _mesh(mesh) {
+	Courbures(MyMesh &mesh) : _mesh(mesh) {}
-		_mesh.request_vertex_normals();
-		_mesh.update_normals();
-	}
 
     void set_fixed_colors();
     void normales_locales();

src/hole_filling.cpp

@@ -1,58 +0,0 @@
-#include "hole_filling.h"
-#include "util.h"
-#include <MeshReconstruction.h>
-
-
-static std::vector<std::vector<HalfedgeHandle>> findHoles(MyMesh &mesh) {
-	std::vector<std::vector<HalfedgeHandle>> holes;
-	std::set<HalfedgeHandle> ignore;
-	for (HalfedgeHandle it : mesh.halfedges()) {
-		if (mesh.is_boundary(it)
-			&& ignore.find(it) == ignore.end()) {
-			holes.emplace_back();
-			holes.back().push_back(it);
-			ignore.insert(it);
-			for (HalfedgeHandle it2 : HalfedgeLoopRange<MyMesh>(mesh, it)) {
-				holes.back().push_back(it2);
-				ignore.insert(it2);
-			}
-		}
-	}
-	return holes;
-}
-
-
-void fillHoleDumb(MyMesh &mesh, std::vector<HalfedgeHandle> &hole) {
-	mesh.request_vertex_status();
-	mesh.request_edge_status();
-	mesh.request_face_status();
-
-	Point center(0, 0, 0);
-	size_t length = 0;
-	for (HalfedgeHandle it : hole) {
-		VertexHandle vert = mesh.to_vertex_handle(it);
-		center += mesh.point(vert);
-		length++;
-	}
-	center /= length;
-	VertexHandle center_handle = mesh.new_vertex_dirty(center);
-	mesh.set_color(center_handle, mesh.default_color);
-
-	for (HalfedgeHandle it : hole) {
-		mesh.add_face(mesh.from_vertex_handle(it),
-					  mesh.to_vertex_handle(it),
-					  center_handle);
-	}
-}
-
-
-void fillHolesDumb(MyMesh &mesh) {
-	mesh.holes = findHoles(mesh);
-	for (auto hole : mesh.holes) {
-		fillHoleDumb(mesh, hole);
-	}
-}
-
-
-void fillHolesImplicit(MyMesh &mesh) {
-}

src/hole_filling.h

@@ -1,13 +0,0 @@
-#ifndef HOLE_FILLING_H
-#define HOLE_FILLING_H
-
-#include "my_mesh.h"
-#include <vector>
-
-
-void fillHoleDumb(MyMesh &mesh, std::vector<HalfedgeHandle> &hole);
-void fillHolesDumb(MyMesh &mesh);
-void fillHolesImplicit(MyMesh &mesh);
-
-
-#endif

src/main.cpp

@@ -5,27 +5,11 @@
 #include <QApplication>
 
 
-static MeshProcessor *create_mesh_processor(const QString &path,
-											MainWindow &main_window) {
-	MeshViewer &mesh_viewer = main_window.mesh_viewer;
-	MeshProcessor *mesh_processor = new MeshProcessor(path, mesh_viewer);
-	QObject::connect(&main_window, &MainWindow::fillHolesDumbClicked,
-					 mesh_processor, &MeshProcessor::fillHolesDumb);
-	QObject::connect(&main_window, &MainWindow::fillHolesImplicitClicked,
-					 mesh_processor, &MeshProcessor::fillHolesImplicit);
-	QObject::connect(&main_window, &MainWindow::smoothClicked,
-					 mesh_processor, &MeshProcessor::smooth);
-	QObject::connect(&main_window, &MainWindow::patchViewToggled,
-					 mesh_processor, &MeshProcessor::setPatchView);
-	return mesh_processor;
-}
-
-
 int main(int argc, char *argv[]) {
 	using namespace std;
 	QSurfaceFormat format;
 	format.setRenderableType(QSurfaceFormat::OpenGL);
-#ifdef QT_DEBUG
+#ifndef QT_DEBUG
 	qDebug("Debug build");
 	format.setOption(QSurfaceFormat::DebugContext);
 #endif
@@ -33,17 +17,32 @@ int main(int argc, char *argv[]) {
 	QApplication app(argc, argv);
 	MeshProcessor *mesh_processor = nullptr;
 	MainWindow main_window;
+	MeshViewer *mesh_viewer = &main_window.mesh_viewer;
+	QObject::connect(mesh_viewer, &MeshViewer::initialized,
+					 [&]() {
+						 if (mesh_processor) {
+							 mesh_viewer->addMesh(mesh_processor->mesh);
+						 }
+					 });
+
 	if (argc > 2) {
 		qWarning("Utilisation : %s [MAILLAGE]", argv[0]);
 		return 1;
 	} else if (argc == 2) {
-		mesh_processor = create_mesh_processor(argv[1], main_window);
+		mesh_processor = new MeshProcessor(argv[1], *mesh_viewer);
+		QObject::connect(mesh_viewer, &MeshViewer::clicked,
+						 mesh_processor, &MeshProcessor::click);
 	}
 	QObject::connect(&main_window, &MainWindow::open,
 					 [&](const QString &path) {
-						 if (mesh_processor) delete mesh_processor;
+						 if (mesh_processor) {
-						 mesh_processor = create_mesh_processor
+							 mesh_viewer->removeMesh(mesh_processor->mesh);
-							 (path, main_window);
+							 delete mesh_processor;
+						 }
+						 mesh_processor = new MeshProcessor(path, *mesh_viewer);
+						 mesh_viewer->addMesh(mesh_processor->mesh);
+						 QObject::connect(mesh_viewer, &MeshViewer::clicked,
+										  mesh_processor, &MeshProcessor::click);
 					 });
 	main_window.show();
 	return app.exec();

src/main_window.cpp

@@ -3,21 +3,20 @@
 
 #include <QApplication>
 #include <QFileDialog>
-#include <QMenuBar>
-#include <QGroupBox>
-#include <QPushButton>
 
 
 MainWindow::MainWindow(QWidget *parent)
 	:QMainWindow(parent),
 	 toolbar(this),
 	 mesh_viewer() {
+	connect(&mesh_viewer, &MeshViewer::initialized, [&]() {
+		open_action->setEnabled(true);
+	});
 	setCentralWidget(&mesh_viewer);
-	// addToolBar(Qt::RightToolBarArea, &toolbar);
+	addToolBar(Qt::RightToolBarArea, &toolbar);
-
+	open_action = toolbar.addAction("Ouvrir…", [&](){
-	// open_action = toolbar.addAction("Ouvrir…", [&](){
+		emit open(QFileDialog::getOpenFileName(this, "Ouvrir un maillage"));
-	// 	emit open(QFileDialog::getOpenFileName(this, "Ouvrir un maillage"));
+	});
-	// });
 	// toolbar_actions.append(toolbar.addAction("Fractionner", [&](){
 	// 	QVector<QPair<MyMesh::Point, MyMesh>> fragments = shatter(mesh);
 	// 	mesh_viewer.removeOpenGLMesh(glm);
@@ -29,62 +28,8 @@ MainWindow::MainWindow(QWidget *parent)
 	// 		mesh_viewer.addOpenGLMeshFromOpenMesh(&fragment, mat);
 	// 	}
 	// }));
-
+	open_action->setEnabled(false);
-	QMenuBar *menu_bar = new QMenuBar();
+	for (QAction *a : toolbar_actions) {
-	setMenuBar(menu_bar);
+		a->setEnabled(false);
-
-	// File menu
-	QMenu *file_menu = new QMenu("Fichier");
-	open_action = file_menu->addAction("Ouvrir…", [&](){
-		emit open(QFileDialog::getOpenFileName(this, "Ouvrir un maillage"));
-	});
-	save_action = file_menu->addAction("Enregistrer sous…", [&]() {
-		emit save(QFileDialog::getSaveFileName(this,
-											   "Enregistrer un maillage"));
-	});
-	menu_bar->addMenu(file_menu);
-	if (!mesh_viewer.isInitialized()) {
-		open_action->setEnabled(false);
-		connect(&mesh_viewer, &MeshViewer::initialized, [&]() {
-			open_action->setEnabled(true);
-		});
 	}
-
-	addToolBar(Qt::RightToolBarArea, &toolbar);
-
-	// Hole filling tools
-	QGroupBox *hole_box = new QGroupBox("Remplissage de trous");
-	QLayout *hole_vbox = new QVBoxLayout();
-	hole_box->setLayout(hole_vbox);
-	QPushButton *fill_holes_dumb = new QPushButton("Remplir bêtement");
-	connect(fill_holes_dumb, &QPushButton::clicked,
-			this, &MainWindow::fillHolesDumbClicked);
-	hole_vbox->addWidget(fill_holes_dumb);
-	QPushButton *fill_holes_implicit = new QPushButton("Remplir bêtement");
-	connect(fill_holes_implicit, &QPushButton::clicked,
-			this, &MainWindow::fillHolesImplicitClicked);
-	hole_vbox->addWidget(fill_holes_implicit);
-	toolbar.addWidget(hole_box);
-
-	// Smoothing tools
-	QGroupBox *smooth_box = new QGroupBox("Adoucissement");
-	QLayout *smooth_vbox = new QVBoxLayout();
-	smooth_box->setLayout(smooth_vbox);
-	QPushButton *smooth = new QPushButton("Adoucir");
-	connect(smooth, &QPushButton::clicked,
-			this, &MainWindow::smoothClicked);
-	smooth_vbox->addWidget(smooth);
-	toolbar.addWidget(smooth_box);
-
-	// Curvature tools
-	QGroupBox *curvature_box = new QGroupBox("Analyse de courbure");
-	QLayout *curvature_vbox = new QVBoxLayout();
-	curvature_box->setLayout(curvature_vbox);
-	QPushButton *patch_mode = new QPushButton(
-		"Afficher le patch de la sélection");
-	patch_mode->setCheckable(true);
-	connect(patch_mode, &QPushButton::toggled,
-			this, &MainWindow::patchViewToggled);
-	curvature_vbox->addWidget(patch_mode);
-	toolbar.addWidget(curvature_box);
 }

src/main_window.h

@@ -3,7 +3,6 @@
 
 #include <QMainWindow>
 #include <QToolBar>
-#include <QVBoxLayout>
 
 #include "mesh_viewer.h"
 #include "my_mesh.h"
@@ -14,15 +13,10 @@ class MainWindow : public QMainWindow {
 
 	QToolBar toolbar;
 	QAction *open_action;
-	QAction *save_action;
+	QList<QAction *> toolbar_actions;
 
 signals:
 	void open(const QString &path);
-	void save(const QString &path);
-	void fillHolesDumbClicked();
-	void fillHolesImplicitClicked();
-	void smoothClicked();
-	void patchViewToggled(bool checked);
 
 public:
 	MeshViewer mesh_viewer;

src/mesh_processor.cpp

@@ -1,13 +1,31 @@
 #include "quad_patch_tesselator.h"
 #include "mesh_processor.h"
 #include "util.h"
-#include "hole_filling.h"
 #include "smoothing.h"
 #include "curvature.h"
 #include <QGenericMatrix>
 #include <unordered_set>
 
 
+static std::vector<std::vector<HalfedgeHandle>> findHoles(MyMesh &mesh) {
+	std::vector<std::vector<HalfedgeHandle>> holes;
+	std::set<HalfedgeHandle> ignore;
+	for (HalfedgeHandle it : mesh.halfedges()) {
+		if (mesh.is_boundary(it)
+			&& ignore.find(it) == ignore.end()) {
+			holes.emplace_back();
+			holes.back().push_back(it);
+			ignore.insert(it);
+			for (HalfedgeHandle it2 : HalfedgeLoopRange<MyMesh>(mesh, it)) {
+				holes.back().push_back(it2);
+				ignore.insert(it2);
+			}
+		}
+	}
+	return holes;
+}
+
+
 MeshProcessor::MeshProcessor(const QString &path, MeshViewer &mesh_viewer)
 	:mesh_viewer(mesh_viewer) {
 	OpenMesh::IO::Options options;
@@ -16,68 +34,52 @@ MeshProcessor::MeshProcessor(const QString &path, MeshViewer &mesh_viewer)
 		qWarning() << "Failed to read" << path;
 		return;
 	}
-	for (VertexHandle vh : mesh.vertices()) {
+	mesh.update_normals();
-		mesh.set_color(vh, MyMesh::Color(.5, .5, .5));
-	}
 	courbure = new Courbures(mesh);
-	try {
+	courbure->compute_KH();
-		courbure->compute_KH();
+    courbure->set_K_colors();
-		courbure->set_K_colors();
+	// mesh.holes = findHoles(mesh);
-	} catch (std::runtime_error &e) {
+	// fillHoles();
-		qWarning() << "Curvature computation failed";
+	// smooth(mesh);
-	}
-	connect(&mesh_viewer, &MeshViewer::clicked, this, &MeshProcessor::click);
-	updateView();
 }
 
 
 MeshProcessor::~MeshProcessor() {
-	if (mesh_viewer.isInitialized()) {
-		mesh_viewer.removeMesh(mesh);
-	}
 	if (courbure) delete courbure;
 }
 
 
-void MeshProcessor::updateView() const {
+void fillHoleDumb(MyMesh &mesh, std::vector<HalfedgeHandle> &hole) {
-	if (mesh_viewer.isInitialized()) {
+	mesh.request_vertex_status();
-		mesh_viewer.removeMesh(mesh);
+	mesh.request_edge_status();
-		mesh_viewer.addMesh(mesh);
+	mesh.request_face_status();
-		mesh_viewer.updateForReal();
+
-	} else {
+	Point center(0, 0, 0);
-		connect(&mesh_viewer, &MeshViewer::initialized, [&]() {
+	size_t length = 0;
-			mesh_viewer.addMesh(mesh);
+	for (HalfedgeHandle it : hole) {
-			mesh_viewer.updateForReal();
+		VertexHandle vert = mesh.to_vertex_handle(it);
-		});
+		center += mesh.point(vert);
+		length++;
+	}
+	center /= length;
+	VertexHandle center_handle = mesh.new_vertex_dirty(center);
+
+	for (HalfedgeHandle it : hole) {
+		mesh.add_face(mesh.from_vertex_handle(it),
+					  mesh.to_vertex_handle(it),
+					  center_handle);
 	}
 }
 
 
-void MeshProcessor::fillHolesDumb() {
+void MeshProcessor::fillHoles() {
-	::fillHolesDumb(mesh);
+	for (auto hole : mesh.holes) {
-	updateView();
+		fillHoleDumb(mesh, hole);
-}
+	}
-
-
-void MeshProcessor::fillHolesImplicit() {
-	::fillHolesImplicit(mesh);
-	updateView();
-}
-
-
-void MeshProcessor::smooth() {
-	::smooth(mesh);
-	updateView();
-}
-
-
-void MeshProcessor::setPatchView(bool on) {
-	view_patches = on;
 }
 
 
 void MeshProcessor::click(QVector3D position) {
-	if (!view_patches) return;
 	Eigen::Vector3d pos {position.x(), position.y(), position.z()};
 	MyMesh::VertexIter it = mesh.vertices_begin();
 	VertexHandle min_vert = *it;

src/mesh_processor.h

@@ -3,6 +3,7 @@
 
 #include "my_mesh.h"
 #include "curvature.h"
+#include "mesh_processor_painter.h"
 #include "mesh_viewer.h"
 #include <vector>
 #include <QObject>
@@ -13,9 +14,6 @@ class MeshProcessor : public QObject {
 
 	Courbures *courbure = nullptr;
 	MeshViewer &mesh_viewer;
-	bool view_patches = false;
-
-	void updateView() const;
 
 public:
 	MyMesh mesh;
@@ -25,10 +23,7 @@ public:
 	~MeshProcessor();
 
 public slots:
-	void fillHolesDumb();
+	void fillHoles();
-	void fillHolesImplicit();
-	void smooth();
-	void setPatchView(bool on);
 	void click(QVector3D position);
 };
 

src/mesh_processor_painter.cpp

@@ -0,0 +1,6 @@
+#include "mesh_processor_painter.h"
+
+
+void MeshProcessorPainter::paint() {
+	
+}

src/mesh_processor_painter.h

@@ -0,0 +1,15 @@
+#ifndef MESH_PAINTER_H
+#define MESH_PAINTER_H
+
+#include <QObject>
+
+
+class MeshProcessorPainter {
+	Q_OBJECT
+
+public slots:
+	void paint();
+};
+
+
+#endif

src/mesh_viewer.cpp

@@ -64,7 +64,6 @@ void MeshViewer::initializeGL() {
 	glf->glEnable(GL_MULTISAMPLE);
 
 	qDebug("MeshViewer: initialization complete");
-	is_initialized = true;
 	emit initialized();
 }
 

src/mesh_viewer.h

@@ -35,7 +35,6 @@ class MeshViewer : public QOpenGLWidget {
 	QMatrix4x4 view = trans * rot;
 	QPoint mouse_pos;
 	void updateViewMatrix();
-	bool is_initialized = false;
 
 public:
     MeshViewer(QWidget *parent=nullptr);
@@ -43,7 +42,6 @@ public:
     void initializeGL() override;
     void resizeGL(int w, int h) override;
     void paintGL() override;
-	constexpr bool isInitialized() { return is_initialized; }
 
 public slots:
 	void addMesh(const MyMesh &mesh);

src/my_mesh.h

@@ -17,14 +17,14 @@ struct MyTraits : public OpenMesh::DefaultTraits {
     VertexAttributes(OpenMesh::Attributes::Normal | OpenMesh::Attributes::Color);
     HalfedgeAttributes(OpenMesh::Attributes::PrevHalfedge);
     FaceAttributes(OpenMesh::Attributes::Normal);
-    // EdgeAttributes(OpenMesh::Attributes::Color);
+    EdgeAttributes(OpenMesh::Attributes::Color);
 };
 
 class MyMesh : public OpenMesh::TriMesh_ArrayKernelT<MyTraits> {
 public:
-	Color default_color {.5, .5, .5};
 	QMatrix4x4 transform;
 	std::vector<std::vector<HalfedgeHandle>> holes;
+	// QColor color = {127, 127, 127};
 };
 
 typedef MyMesh::FaceHandle FaceHandle;

src/smoothing.cpp

@@ -42,9 +42,8 @@ Point laplace_beltrami(const MyMesh &mesh, VertexHandle vert) {
 		area += triangle_area(p, pi, pb);
 		count++;
 	}
-	// area /= 3.;
+	area /= 3.;
-	// return sum / (2.*area);
+	return sum / (2.*count);
-	return sum / count;
 }
 
 
@@ -74,48 +73,46 @@ Eigen::SparseMatrix<qreal> laplacian_matrix(const MyMesh &mesh) {
 			area += triangle_area(p, pi, pb);
 			count++;
 		}
-		// area /= 3.;
+		area /= 3.;
 		cotangent.insert(vert.idx(), vert.idx()) = -sum;
-		mass.insert(vert.idx(), vert.idx()) = 1. / (4. * area);
+		mass.insert(vert.idx(), vert.idx()) = 1. / area;
-		// mass.insert(vert.idx(), vert.idx()) = 1. / count;
 	}
 	return mass * cotangent;
 }
 
 
 void smooth(MyMesh &mesh) {
-	auto new_pos = OpenMesh::makeTemporaryProperty<VertexHandle, Point>(mesh);
+	// auto new_pos = OpenMesh::makeTemporaryProperty<VertexHandle, Point>(mesh);
-	for (VertexHandle v : mesh.vertices()) {
+	// for (VertexHandle v : mesh.vertices()) {
-		if (!mesh.is_boundary(v)) {
+	// 	if (!mesh.is_boundary(v)) {
-			new_pos[v] = mesh.point(v) - laplace_beltrami(mesh, v);
+	// 		new_pos[v] = mesh.point(v) - laplace_beltrami(mesh, v);
-		}
+	// 	}
-	}
+	// }
-	for (VertexHandle v : mesh.vertices()) {
+	// for (VertexHandle v : mesh.vertices()) {
-		if (!mesh.is_boundary(v)) {
+	// 	if (!mesh.is_boundary(v)) {
-			mesh.set_point(v, new_pos[v]);
+	// 		mesh.set_point(v, new_pos[v]);
-		}
+	// 	}
-	}
+	// }
 
-	// // Approche matricielle
+	// Approche matricielle
-	// Eigen::SparseMatrix<qreal> laplacian = laplacian_matrix(mesh);
+	Eigen::SparseMatrix<qreal> laplacian = laplacian_matrix(mesh);
-	// // laplacian = laplacian * laplacian;
+	size_t n_verts = mesh.n_vertices();
-	// size_t n_verts = mesh.n_vertices();
+	Eigen::VectorX<qreal> X(n_verts), Y(n_verts), Z(n_verts);
-	// Eigen::VectorX<qreal> X(n_verts), Y(n_verts), Z(n_verts);
+	for (VertexHandle vert : mesh.vertices()) {
-	// for (VertexHandle vert : mesh.vertices()) {
+		if (mesh.is_boundary(vert)) continue;
-	// 	if (mesh.is_boundary(vert)) continue;
+		size_t id = vert.idx();
-	// 	size_t id = vert.idx();
+		Point p = mesh.point(vert);
-	// 	Point p = mesh.point(vert);
+		X(id) = p[0];
-	// 	X(id) = p[0];
+		Y(id) = p[1];
-	// 	Y(id) = p[1];
+		Z(id) = p[2];
-	// 	Z(id) = p[2];
+	}
-	// }
+	X = laplacian * X;
-	// X = laplacian * X;
+	Y = laplacian * Y;
-	// Y = laplacian * Y;
+	Z = laplacian * Z;
-	// Z = laplacian * Z;
+	for (VertexHandle vert : mesh.vertices()) {
-	// for (VertexHandle vert : mesh.vertices()) {
+		if (mesh.is_boundary(vert)) continue;
-	// 	if (mesh.is_boundary(vert)) continue;
+		size_t id = vert.idx();
-	// 	size_t id = vert.idx();
+		Point offset {X(id), Y(id), Z(id)};
-	// 	Point offset {X(id), Y(id), Z(id)};
+		mesh.set_point(vert, mesh.point(vert) - offset);
-	// 	mesh.set_point(vert, mesh.point(vert) - offset);
+	}
-	// }
 }