CGAL 6.1.2 - 3D Isosurfacing

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Isosurfacing_3/contouring_octree.cpp
#include <CGAL/Simple_cartesian.h>
#include <CGAL/Isosurfacing_3/dual_contouring_3.h>
#include <CGAL/Isosurfacing_3/Dual_contouring_domain_3.h>
#include <CGAL/Isosurfacing_3/marching_cubes_3.h>
#include <CGAL/Isosurfacing_3/Marching_cubes_domain_3.h>
#include <CGAL/Isosurfacing_3/Value_function_3.h>
#include <CGAL/Isosurfacing_3/Gradient_function_3.h>
#include <CGAL/Isosurfacing_3/Octree_partition.h>
#include <CGAL/Bbox_3.h>
#include <CGAL/IO/polygon_soup_io.h>
#include <cmath>
#include <iostream>
#include <vector>
using Kernel = CGAL::Simple_cartesian<double>;
using FT = typename Kernel::FT;
using Vector = typename Kernel::Vector_3;
using Point = typename Kernel::Point_3;
using Point_range = std::vector<Point>;
using Polygon_range = std::vector<std::vector<std::size_t> >;
using Octree = CGAL::Octree<Kernel, std::vector<Point> >;
using Values = CGAL::Isosurfacing::Value_function_3<Octree>;
using Gradients = CGAL::Isosurfacing::Gradient_function_3<Octree>;
using MC_Domain = CGAL::Isosurfacing::Marching_cubes_domain_3<Octree, Values>;
using Domain = CGAL::Isosurfacing::Dual_contouring_domain_3<Octree, Values, Gradients>;
namespace IS = CGAL::Isosurfacing;
auto sphere_function = [](const Point& p) -> FT
{
return std::sqrt(p.x()*p.x() + p.y()*p.y() + p.z()*p.z());
};
auto sphere_gradient = [](const Point& p) -> Vector
{
const Vector g = p - CGAL::ORIGIN;
return g / std::sqrt(g.squared_length());
};
auto blobby_function = [](const Point& p) -> FT
{
return std::exp(-1.5 * ((p.x() - 0.2) * (p.x() - 0.2) + (p.y() - 0.2) * (p.y() - 0.2) + (p.z() - 0.2) * (p.z() - 0.2))) +
std::exp(-1.5 * ((p.x() + 0.2) * (p.x() + 0.2) + (p.y() + 0.2) * (p.y() + 0.2) + (p.z() + 0.2) * (p.z() + 0.2))) +
std::exp(-1.5 * ((p.x() - 0.4) * (p.x() - 0.4) + (p.y() + 0.4) * (p.y() + 0.4) + (p.z() - 0.4) * (p.z() - 0.4))) +
std::exp(-6 * ((p.x() - 0.1) * (p.x() - 0.1) + (p.y() - 0.1) * (p.y() - 0.1))) +
std::exp(-6 * ((p.y() + 0.1) * (p.y() + 0.1) + (p.z() + 0.1) * (p.z() + 0.1))) +
std::exp(-6 * ((p.x() + 0.1) * (p.x() + 0.1) + (p.z() - 0.1) * (p.z() - 0.1))) -
0.3;
};
auto blobby_gradient = [](const Point& p) -> Vector
{
const FT g1 = -3 * std::exp(-1.5 * ((p.x() - 0.2) * (p.x() - 0.2) + (p.y() - 0.2) * (p.y() - 0.2) + (p.z() - 0.2) * (p.z() - 0.2)));
const FT g2 = -3 * std::exp(-1.5 * ((p.x() + 0.2) * (p.x() + 0.2) + (p.y() + 0.2) * (p.y() + 0.2) + (p.z() + 0.2) * (p.z() + 0.2)));
const FT g3 = -3 * std::exp(-1.5 * ((p.x() - 0.4) * (p.x() - 0.4) + (p.y() + 0.4) * (p.y() + 0.4) + (p.z() - 0.4) * (p.z() - 0.4)));
const FT g4 = -12 * std::exp(-6 * ((p.x() - 0.1) * (p.x() - 0.1) + (p.y() - 0.1) * (p.y() - 0.1)));
const FT g5 = -12 * std::exp(-6 * ((p.y() + 0.1) * (p.y() + 0.1) + (p.z() + 0.1) * (p.z() + 0.1)));
const FT g6 = -12 * std::exp(-6 * ((p.x() + 0.1) * (p.x() + 0.1) + (p.z() - 0.1) * (p.z() - 0.1)));
return Vector(g1 * (p.x() - 0.2) + g2 * (p.x() + 0.2) + g3 * (p.x() - 0.4) + g4 * (p.x() - 0.1) + g6 * (p.x() + 0.1),
g1 * (p.y() - 0.2) + g2 * (p.y() + 0.2) + g3 * (p.y() + 0.4) + g4 * (p.y() - 0.1) + g5 * (p.y() + 0.1),
g1 * (p.z() - 0.2) + g2 * (p.z() + 0.2) + g3 * (p.z() - 0.4) + g5 * (p.z() + 0.1) + g6 * (p.z() - 0.1));
};
// This is a naive refinement that is adapted to the isosurface:
// This refines:
// - at the minimum till minimum depth
// - at the maximum till maximum depth
// - we split if the the isovalue goes through the voxel, i.e. if not all vertices of the cell
// are on the same side of the isosurface defined by a function
// It's not a great refinement technique because the surface can enter and leave a cell
// without involving the cell's vertex. In practice, that means a hole if at nearby adjacent
// cells the voxels did get refined and registered the surface.
struct Refine_around_isovalue
{
std::size_t min_depth_;
std::size_t max_depth_;
std::function<FT(const Point&)> function_;
FT isovalue_;
Refine_around_isovalue(std::size_t min_depth,
std::size_t max_depth,
std::function<FT(const Point&)> function,
FT isovalue)
: min_depth_(min_depth),
max_depth_(max_depth),
function_(function),
isovalue_(isovalue)
{}
bool operator()(const Octree::Node_index& ni, const Octree& octree) const
{
// Ensure minimum depth refinement
if (octree.depth(ni) < min_depth_)
return true;
// Stop refinement at maximum depth
if (octree.depth(ni) >= max_depth_)
return false;
// Get the bounding box of the node
auto bbox = octree.bbox(ni);
// Evaluate the function at the corners of the bounding box
std::array<FT, 8> corner_values;
int index = 0;
for (FT x : {bbox.xmin(), bbox.xmax()})
for (FT y : {bbox.ymin(), bbox.ymax()})
for (FT z : {bbox.zmin(), bbox.zmax()})
corner_values[index++] = function_(Point(x, y, z));
// Check if the function values cross the isovalue
bool has_positive = false, has_negative = false;
for (const auto& value : corner_values)
{
if (value > isovalue_)
has_positive = true;
if (value < isovalue_)
has_negative = true;
if (has_positive && has_negative)
return true; // Refine if the isosurface intersects the voxel
}
return false; // No refinement needed
}
};
// This is a refinement that is NOT adapted to the isosurface
struct Refine_one_eighth
{
std::size_t min_depth_;
std::size_t max_depth_;
std::size_t octree_dim_;
Refine_one_eighth(std::size_t min_depth,
std::size_t max_depth)
: min_depth_(min_depth),
max_depth_(max_depth)
{
octree_dim_ = std::size_t(1) << max_depth_;
}
Octree::Global_coordinates uniform_coordinates(const Octree::Node_index& node_index, const Octree& octree) const
{
auto coords = octree.global_coordinates(node_index);
const std::size_t depth_factor = std::size_t(1) << (max_depth_ - octree.depth(node_index));
for(int i=0; i < 3; ++i)
coords[i] *= uint32_t(depth_factor);
return coords;
}
bool operator()(const Octree::Node_index& ni, const Octree& octree) const
{
if(octree.depth(ni) < min_depth_)
return true;
if(octree.depth(ni) == max_depth_)
return false;
auto leaf_coords = uniform_coordinates(ni, octree);
if(leaf_coords[0] >= octree_dim_ / 2)
return false;
if(leaf_coords[1] >= octree_dim_ / 2)
return false;
if(leaf_coords[2] >= octree_dim_ / 2)
return false;
return true;
}
};
template <typename Splitter>
void run_DC_octree(const CGAL::Bbox_3 bbox,
const Splitter& split_predicate,
const std::function<FT(const Point&)> function,
const std::function<Vector(const Point&)> gradient,
const FT isovalue,
const std::string& name)
{
std::vector<Point> bbox_points { { bbox.xmin(), bbox.ymin(), bbox.zmin() },
{ bbox.xmax(), bbox.ymax(), bbox.zmax() } };
Octree octree(bbox_points);
octree.refine(split_predicate);
auto leaf_range = octree.traverse(CGAL::Orthtrees::Leaves_traversal<Octree>(octree));
std::size_t leaf_counter = std::distance(leaf_range.begin(), leaf_range.end());
std::cout << "octree has " << leaf_counter << " leaves" << std::endl;
// fill up values and gradients
Values values { function, octree };
Gradients gradients { gradient, octree };
Domain domain { octree, values, gradients };
// output containers
Point_range points;
Polygon_range triangles;
std::cout << "Running Dual Contouring with isovalue = " << isovalue << std::endl;
// run Dual Contouring
IS::dual_contouring<CGAL::Parallel_if_available_tag>(domain, isovalue, points, triangles,
CGAL::parameters::do_not_triangulate_faces(true)
.constrain_to_cell(false));
std::cout << "Output #vertices (DC): " << points.size() << std::endl;
std::cout << "Output #triangles (DC): " << triangles.size() << std::endl;
std::ofstream oo("octree_DC_" + name + ".polylines.txt");
oo.precision(17);
octree.dump_to_polylines(oo);
CGAL::IO::write_polygon_soup("DC_" + name + ".off", points, triangles);
}
template <typename Splitter>
void run_MC_octree(const CGAL::Bbox_3 bbox,
const Splitter& split_predicate,
const std::function<FT(const Point&)> function,
const FT isovalue,
const std::string& name)
{
std::vector<Point> bbox_points { { bbox.xmin(), bbox.ymin(), bbox.zmin() },
{ bbox.xmax(), bbox.ymax(), bbox.zmax() } };
Octree octree(bbox_points);
octree.refine(split_predicate);
Values values { function, octree };
Point_range points;
Polygon_range triangles;
MC_Domain mcdomain { octree, values };
std::cout << "Running MC" << std::endl;
CGAL::Isosurfacing::marching_cubes<CGAL::Parallel_if_available_tag>(mcdomain, isovalue, points, triangles);
std::cout << "Output #vertices (MC): " << points.size() << std::endl;
std::cout << "Output #triangles (MC): " << triangles.size() << std::endl;
std::ofstream oo("octree_MC_" + name + ".polylines.txt");
oo.precision(17);
octree.dump_to_polylines(oo);
CGAL::IO::write_polygon_soup("MC_" + name + ".off", points, triangles);
}
// Whether you are using MC, TMC, or DC, there is no guarantee for an octree:
// it should behave well if your nodes are split with a uniform size around the surface,
// but it is sure to produce cracks if you have varying depths around the isosurface.
int main(int argc, char** argv)
{
const FT isovalue = (argc > 1) ? std::stod(argv[1]) : 0.3;
const CGAL::Bbox_3 bbox { -1., -1., -1., 1., 1., 1. };
Refine_one_eighth one_eight_splitter(3, 5);
run_DC_octree(bbox, one_eight_splitter, sphere_function, sphere_gradient, isovalue, "one_eight");
// This is
Refine_around_isovalue isovalue_splitter(3, 5, sphere_function, isovalue);
run_DC_octree(bbox, isovalue_splitter, sphere_function, sphere_gradient, isovalue, "sphere_adapted");
Refine_around_isovalue isvalue_splitter_2(3, 5, blobby_function, isovalue);
run_DC_octree(bbox, isvalue_splitter_2, blobby_function, blobby_gradient, isovalue, "blobby_adapted");
// to illustrate cracks
run_MC_octree(bbox, isovalue_splitter, sphere_function, isovalue, "adapted");
run_MC_octree(bbox, one_eight_splitter, sphere_function, isovalue, "one_eight");
std::cout << "Done" << std::endl;
return EXIT_SUCCESS;
}
CGAL::Bbox_3
CGAL::Bbox_3::ymin
double ymin() const
CGAL::Bbox_3::xmax
double xmax() const
CGAL::Bbox_3::zmin
double zmin() const
CGAL::Bbox_3::zmax
double zmax() const
CGAL::Bbox_3::ymax
double ymax() const
CGAL::Bbox_3::xmin
double xmin() const
CGAL::Isosurfacing::Dual_contouring_domain_3
A domain that can be used as input in the Dual Contouring algorithm.
Definition: Dual_contouring_domain_3.h:52
CGAL::Isosurfacing::Gradient_function_3
The class Gradient_function_3 represents a field of vectors computed using a user-provided unary func...
Definition: Gradient_function_3.h:39
CGAL::Isosurfacing::Marching_cubes_domain_3
A domain that can be used with the Marching Cubes algorithm.
Definition: Marching_cubes_domain_3.h:50
CGAL::Isosurfacing::Value_function_3
The class Value_function_3 represents a field of scalars computed using a user-provided unary functio...
Definition: Value_function_3.h:40
CGAL::Orthtree
Kernel::Point_3
Kernel::Vector_3
CGAL::IO::write_polygon_soup
bool write_polygon_soup(const std::string &fname, const PointRange &points, const PolygonRange &polygons, const NamedParameters &np=parameters::default_values())
CGAL::Octree
Orthtree< Orthtree_traits_point< GeomTraits, PointRange, PointMap, cubic_nodes, 3 > > Octree
CGAL::Polygon_mesh_processing::bbox
CGAL::Bbox_3 bbox(const PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
CGAL::ORIGIN
const CGAL::Origin ORIGIN
CGAL::Isosurfacing
Definition: partition_traits.h:2
Kernel
CGAL::Orthtrees::Leaves_traversal
CGAL::Simple_cartesian