107 lines
3.4 KiB
C++
107 lines
3.4 KiB
C++
#pragma once
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#include "DataStructs.h"
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#include "Cube.h"
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#include "Triangulation.h"
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namespace MeshReconstruction
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{
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/// Reconstructs a triangle mesh from a given signed distance function using <a href="https://en.wikipedia.org/wiki/Marching_cubes">Marching Cubes</a>.
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/// @param sdf The <a href="http://www.iquilezles.org/www/articles/distfunctions/distfunctions.htm">Signed Distance Function</a>.
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/// @param domain Domain of reconstruction.
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/// @returns The reconstructed mesh.
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Mesh MarchCube(
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Fun3s const &sdf,
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Rect3 const &domain);
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/// Reconstructs a triangle mesh from a given signed distance function using <a href="https://en.wikipedia.org/wiki/Marching_cubes">Marching Cubes</a>.
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/// @param sdf The <a href="http://www.iquilezles.org/www/articles/distfunctions/distfunctions.htm">Signed Distance Function</a>.
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/// @param domain Domain of reconstruction.
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/// @param cubeSize Size of marching cubes. Smaller cubes yields meshes of higher resolution.
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/// @param isoLevel Level set of the SDF for which triangulation should be done. Changing this value moves the reconstructed surface.
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/// @param sdfGrad Gradient of the SDF which yields the vertex normals of the reconstructed mesh. If none is provided a numerical approximation is used.
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/// @returns The reconstructed mesh.
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Mesh MarchCube(
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Fun3s const &sdf,
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Rect3 const &domain,
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Vec3 const &cubeSize,
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double isoLevel = 0,
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Fun3v sdfGrad = nullptr);
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}
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using namespace MeshReconstruction;
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using namespace std;
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// Adapted from here: http://paulbourke.net/geometry/polygonise/
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namespace
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{
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Vec3 NumGrad(Fun3s const &f, Vec3 const &p)
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{
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auto const Eps = 1e-6;
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Vec3 epsX{Eps, 0, 0}, epsY{0, Eps, 0}, epsZ{0, 0, Eps};
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auto gx = (f(p + epsX) - f(p - epsX)) / 2;
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auto gy = (f(p + epsY) - f(p - epsY)) / 2;
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auto gz = (f(p + epsZ) - f(p - epsZ)) / 2;
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return {gx, gy, gz};
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}
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}
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Mesh MeshReconstruction::MarchCube(Fun3s const &sdf, Rect3 const &domain)
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{
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auto const NumCubes = 50;
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auto cubeSize = domain.size * (1.0 / NumCubes);
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return MarchCube(sdf, domain, cubeSize);
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}
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Mesh MeshReconstruction::MarchCube(
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Fun3s const &sdf,
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Rect3 const &domain,
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Vec3 const &cubeSize,
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double isoLevel,
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Fun3v sdfGrad)
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{
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// Default value.
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sdfGrad = sdfGrad == nullptr
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? [&sdf](Vec3 const &p)
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{ return NumGrad(sdf, p); }
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: sdfGrad;
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auto const NumX = static_cast<int>(ceil(domain.size.x / cubeSize.x));
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auto const NumY = static_cast<int>(ceil(domain.size.y / cubeSize.y));
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auto const NumZ = static_cast<int>(ceil(domain.size.z / cubeSize.z));
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auto const HalfCubeDiag = cubeSize.Norm() / 2.0;
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auto const HalfCubeSize = cubeSize * 0.5;
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Mesh mesh;
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for (auto ix = 0; ix < NumX; ++ix)
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{
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auto x = domain.min.x + ix * cubeSize.x;
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for (auto iy = 0; iy < NumY; ++iy)
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{
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auto y = domain.min.y + iy * cubeSize.y;
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for (auto iz = 0; iz < NumZ; ++iz)
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{
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auto z = domain.min.z + iz * cubeSize.z;
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Vec3 min{x, y, z};
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// Process only if cube lies within narrow band around surface.
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auto cubeCenter = min + HalfCubeSize;
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auto dist = abs(sdf(cubeCenter) - isoLevel);
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if (dist > HalfCubeDiag)
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continue;
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Cube cube({min, cubeSize}, sdf);
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auto intersect = cube.Intersect(isoLevel);
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Triangulate(intersect, sdfGrad, mesh);
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}
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}
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}
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return mesh;
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}
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