Medusa  1.1
Coordinate Free Mehless Method implementation
test/domains/GeneralSurfaceFill_test.cpp
#include <medusa/bits/domains/GeneralSurfaceFill.hpp>
#include <medusa/bits/types/Vec.hpp>
#include <medusa/bits/types/Range_fwd.hpp>
#include <medusa/bits/domains/BoxShape.hpp>
#include <medusa/bits/domains/DomainDiscretization_fwd.hpp>
#include <medusa/bits/spatial_search/KDTree.hpp>
#include <string>
#include <fstream>
#include "gtest/gtest.h"
namespace mm {
TEST(DomainEngines, GeneralSurfaceFill2DConstantFill) {
// Define surface.
auto example_r = [](Vec1d t) {
t(0) = -t(0);
double r = pow(abs(cos(1.5 * t(0))), sin(3 * t(0)));
return Vec2d(r * cos(t(0)), r * sin(t(0)));
};
auto der_example_r = [](Vec1d t) {
t(0) = -t(0);
double r = pow(abs(cos(1.5 * t(0))), sin(3 * t(0)));
double der_r = (-1.5 * pow(abs(cos(1.5 * t(0))),
sin(3 * t(0))) * sin(3 * t(0)) * sin(1.5 * t(0)) +
3 * pow(abs(cos(1.5 * t(0))),
sin(3 * t(0))) * cos(3 * t(0)) * cos(1.5 * t(0))
* log(abs(cos(1.5 * t(0))))) / cos(1.5 * t(0));
Vec2d jm;
jm.col(0) << -(der_r * cos(t(0)) - r * sin(t(0))),
-(der_r * sin(t(0)) + r * cos(t(0)));
return jm;
};
double h = 0.02;
UnknownShape<Vec2d> shape;
DomainDiscretization<Vec2d> domain(shape);
// Fill domain.
GeneralSurfaceFill<Vec2d, Vec1d> gsf; gsf.seed(0); // deterministic
BoxShape<Vec1d> bs(Vec1d{0.0}, Vec1d{2 * PI});
domain.fill(gsf, bs, example_r, der_example_r, h);
// Calculate distances.
KDTree<Vec2d> tree(domain.positions());
Range<double> distances;
double avg_dist = 0;
for (const auto& pt : domain.positions()) {
distances.push_back(sqrt(tree.query(pt, 2).second[1]));
avg_dist += distances[distances.size() - 1];
}
avg_dist /= domain.positions().size();
auto err_avg = std::abs(avg_dist - h) / h;
EXPECT_LT(err_avg, 0.05);
auto err_min = std::abs(*std::min_element(distances.begin() + 1, distances.end() - 1) - h) / h;
EXPECT_LT(err_min, 0.35);
}
TEST(DomainEngines, GeneralSurfaceFill2DFunctionFill) {
// Define surface.
auto example_r = [](Vec1d t) {
t(0) = -t(0);
double r = pow(abs(cos(1.5 * t(0))), sin(3 * t(0)));
return Vec2d(r * cos(t(0)), r * sin(t(0)));
};
auto der_example_r = [](Vec1d t) {
t(0) = -t(0);
double r = pow(abs(cos(1.5 * t(0))), sin(3 * t(0)));
double der_r = (-1.5 * pow(abs(cos(1.5 * t(0))),
sin(3 * t(0))) * sin(3 * t(0)) * sin(1.5 * t(0)) +
3 * pow(abs(cos(1.5 * t(0))),
sin(3 * t(0))) * cos(3 * t(0)) * cos(1.5 * t(0))
* log(abs(cos(1.5 * t(0))))) / cos(1.5 * t(0));
Eigen::Matrix<double, 2, 1> jm;
jm.col(0) << -(der_r * cos(t(0)) - r * sin(t(0))), -(der_r * sin(t(0)) + r * cos(t(0)));
return jm;
};
auto gradient_h = [](Vec2d p){
double h_0 = 0.005;
double h_m = 0.03 - h_0;
return 0.5 * h_m * (p(0) + p(1) + 3.0) + h_0;
};
UnknownShape<Vec2d> shape;
DomainDiscretization<Vec2d> domain(shape);
// Fill domain.
GeneralSurfaceFill<Vec2d, Vec1d> gsf; gsf.seed(0); // deterministic
BoxShape<Vec1d> bs(Vec1d{0.0}, Vec1d{2 * PI});
DomainDiscretization<Vec1d> param_d(bs);
domain.fill(gsf, param_d, example_r, der_example_r, gradient_h);
// Calculate distances.
KDTree<Vec2d> tree(domain.positions());
auto positions = domain.positions();
for (int i = 1; i < positions.size() - 1 ; i++) {
auto pt = positions[i];
double dist = sqrt(tree.query(pt, 2).second[1]);
double h = gradient_h(pt);
double err = std::abs(dist - h) / h;
EXPECT_LT(err, 0.35);
}
}
TEST(DomainEngines, GeneralSurfaceFill3DConstantFill) {
auto torus_r = [](Vec2d t){
double a = 10.0, b = 25.0;
return Vec3d((a * cos(t(1)) + b) * cos(t(0)),
(a * cos(t(1)) + b) * sin(t(0)), a * sin(t(1)));
};
auto torus_jacobian_matrix = [](Vec2d t){
double a = 10.0, b = 25.0;
Eigen::Matrix<double, 3, 2> jm;
jm.col(0) << - (a * cos(t(1)) + b) * sin(t(0)), (a * cos(t(1)) + b) * cos(t(0)), 0;
jm.col(1) << - a * sin(t(1)) * cos(t(0)), - a * sin(t(1)) * sin(t(0)), a * cos(t(1));
return jm;
};
double h = 1.0;
UnknownShape<Vec3d> shape;
DomainDiscretization<Vec3d> domain(shape);
// Fill domain.
GeneralSurfaceFill<Vec3d, Vec2d> gsf; gsf.seed(0); // deterministic
BoxShape<Vec2d> bs(Vec2d{0.0, 0.0}, Vec2d{2 * PI, 2 * PI});
DomainDiscretization<Vec2d> param_d(bs);
domain.fill(gsf, param_d, torus_r, torus_jacobian_matrix, h);
// Calculate distances.
KDTree<Vec3d> tree(domain.positions());
Range<double> distances;
double avg_dist = 0;
for (const auto& pt : domain.positions()) {
auto d = tree.query(pt, 5).second;
double val = 0.0;
for (int i = 1; i < d.size(); i++) val += sqrt(d[i]);
val /= (d.size() - 1);
distances.push_back(val);
avg_dist += distances[distances.size() - 1];
}
avg_dist /= domain.positions().size();
auto err_avg = std::abs(avg_dist - h) / h;
EXPECT_LT(err_avg, 0.1);
auto err_min = std::abs(*std::min_element(distances.begin() + 1, distances.end() - 1) - h) / h;
EXPECT_LT(err_min, 0.2);
}
TEST(DomainEngines, GeneralSurfaceFill3DFunctionFill) {
// Define parametrization function.
auto torus_r = [](Vec2d t){
double a = 10.0, b = 25.0;
return Vec3d((a * cos(t(1)) + b) * cos(t(0)),
(a * cos(t(1)) + b) * sin(t(0)), a * sin(t(1)));
};
// Define Jacobian of parametrization function.
auto torus_jacobian = [](Vec2d t){
double a = 10.0, b = 25.0;
Eigen::Matrix<double, 3, 2> jm;
jm.col(0) << - (a * cos(t(1)) + b) * sin(t(0)), (a * cos(t(1)) + b) * cos(t(0)), 0;
jm.col(1) << - a * sin(t(1)) * cos(t(0)), - a * sin(t(1)) * sin(t(0)), a * cos(t(1));
return jm;
};
// Define density function.
auto gradient_h = [](Vec3d p){
double h_0 = 1.0;
return h_0 + (p[0] + p[1] + p[2]) / 500.0;
};
// Define domain.
UnknownShape<Vec3d> shape;
DomainDiscretization<Vec3d> domain(shape);
// Fill domain.
GeneralSurfaceFill<Vec3d, Vec2d> gsf; gsf.seed(0); // deterministic
BoxShape<Vec2d> param_domain_shape(Vec2d{0.0, 0.0}, Vec2d{2 * PI, 2 * PI});
DomainDiscretization<Vec2d> param_domain(param_domain_shape);
domain.fill(gsf, param_domain, torus_r, torus_jacobian, gradient_h);
// Calculate distances.
KDTree<Vec3d> tree(domain.positions());
auto positions = domain.positions();
for (int i = 1; i < positions.size() - 1 ; i++) {
auto pt = positions[i];
auto d = tree.query(pt, 7).second;
double val = 0.0;
for (int i = 1; i < d.size(); i++) val += sqrt(d[i]);
val /= (d.size() - 1);
double h = gradient_h(pt);
EXPECT_GE(val, 0.75 * h);
}
}
TEST(DomainEngines, GeneralSurfaceFill4DConstantFill) {
auto three_sphere_r = [](Vec3d t){
double R = 10.0;
return Vec<double, 4>(R * cos(t(0)), R * sin(t(0)) * cos(t(1)),
R * sin(t(0)) * sin(t(1)) * cos(t(2)),
R * sin(t(0)) * sin(t(1)) * sin(t(2)));
};
auto three_sphere_jacobian_matrix = [](Vec3d t){
double R = 10.0;
Eigen::Matrix<double, 4, 3> jm;
jm.col(0) << - R * sin(t(0)), R * cos(t(0)) * cos(t(1)),
R * cos(t(0)) * sin(t(1)) * cos(t(2)),
R * cos(t(0)) * sin(t(1)) * sin(t(2));
jm.col(1) << 0, - R * sin(t(0)) * sin(t(1)),
R * sin(t(0)) * cos(t(1)) * cos(t(2)),
R * sin(t(0)) * cos(t(1)) * sin(t(2));
jm.col(2) << 0, 0, - R * sin(t(0)) * sin(t(1)) * sin(t(2)),
R * sin(t(0)) * sin(t(1)) * cos(t(2));
return jm;
};
double h = 10.0;
// Define domain.
UnknownShape<Vec<double, 4> > shape;
DomainDiscretization<Vec<double, 4> > domain(shape);
// Fill domain.
GeneralSurfaceFill<Vec<double, 4>, Vec3d> gsf; gsf.seed(0); // deterministic
BoxShape<Vec3d> bs(Vec3d{0.0, 0.0, 0.0}, Vec3d{PI, PI, 2 * PI});
DomainDiscretization<Vec3d> param_domain(bs);
domain.fill(gsf, param_domain, three_sphere_r, three_sphere_jacobian_matrix, h);
// Calculate distances.
KDTree<Vec<double, 4> > tree(domain.positions());
Range<double> distances;
double avg_dist = 0;
for (const auto& pt : domain.positions()) {
auto d = tree.query(pt, 10).second;
double val = 0.0;
for (int i = 1; i < d.size(); i++) val += sqrt(d[i]);
val /= (d.size() - 1);
distances.push_back(val);
avg_dist += distances[distances.size() - 1];
}
avg_dist /= domain.positions().size();
auto err_avg = std::abs(avg_dist - h) / h;
EXPECT_LT(err_avg, 0.2);
auto err_min = std::abs(*std::min_element(distances.begin() + 1, distances.end() - 1) - h) / h;
EXPECT_LT(err_min, 0.2);
}
TEST(DomainEngines, GeneralSurfaceFill4DFunctionFill) {
auto three_sphere_r = [](Vec3d t){
double R = 10.0;
return Vec<double, 4>(R * cos(t(0)), R * sin(t(0)) * cos(t(1)),
R * sin(t(0)) * sin(t(1)) * cos(t(2)),
R * sin(t(0)) * sin(t(1)) * sin(t(2)));
};
auto three_sphere_jacobian_matrix = [](Vec3d t){
double R = 10.0;
Eigen::Matrix<double, 4, 3> jm;
jm.col(0) << - R * sin(t(0)), R * cos(t(0)) * cos(t(1)),
R * cos(t(0)) * sin(t(1)) * cos(t(2)),
R * cos(t(0)) * sin(t(1)) * sin(t(2));
jm.col(1) << 0, - R * sin(t(0)) * sin(t(1)),
R * sin(t(0)) * cos(t(1)) * cos(t(2)),
R * sin(t(0)) * cos(t(1)) * sin(t(2));
jm.col(2) << 0, 0, - R * sin(t(0)) * sin(t(1)) * sin(t(2)),
R * sin(t(0)) * sin(t(1)) * cos(t(2));
return jm;
};
auto gradient_h = [](Vec<double, 4> p){
double h_0 = 10.0;
return h_0 + (p[0] + p[1] + p[2] + p[3]) / 80.0;
};
// Define domain.
UnknownShape<Vec<double, 4> > shape;
DomainDiscretization<Vec<double, 4> > domain(shape);
// Fill domain.
GeneralSurfaceFill<Vec<double, 4>, Vec3d> gsf; gsf.seed(0); // deterministic
BoxShape<Vec3d> bs(Vec3d{0.0, 0.0, 0.0}, Vec3d{PI, PI, 2 * PI});
DomainDiscretization<Vec3d> param_domain(bs);
domain.fill(gsf, param_domain, three_sphere_r, three_sphere_jacobian_matrix, gradient_h);
// Calculate distances.
KDTree<Vec<double, 4> > tree(domain.positions());
auto positions = domain.positions();
for (int i = 1; i < positions.size() - 1 ; i++) {
auto pt = positions[i];
auto d = tree.query(pt, 9).second;
double val = 0.0;
for (int i = 1; i < d.size(); i++) val += sqrt(d[i]);
val /= (d.size() - 1);
double h = gradient_h(pt);
EXPECT_GE(val, 0.75 * h);
}
}
TEST(DomainEngines, GeneralSurfaceFillMaxPoints) {
// Define surface.
auto example_r = [](Vec1d t) {
t(0) = -t(0);
double r = pow(abs(cos(1.5 * t(0))), sin(3 * t(0)));
return Vec2d(r * cos(t(0)), r * sin(t(0)));
};
auto der_example_r = [](Vec1d t) {
t(0) = -t(0);
double r = pow(abs(cos(1.5 * t(0))), sin(3 * t(0)));
double der_r = (-1.5 * pow(abs(cos(1.5 * t(0))),
sin(3 * t(0))) * sin(3 * t(0)) * sin(1.5 * t(0)) +
3 * pow(abs(cos(1.5 * t(0))),
sin(3 * t(0))) * cos(3 * t(0)) * cos(1.5 * t(0))
* log(abs(cos(1.5 * t(0))))) / cos(1.5 * t(0));
Eigen::Matrix<double, 2, 1> jm;
jm.col(0) << -(der_r * cos(t(0)) - r * sin(t(0))),
-(der_r * sin(t(0)) + r * cos(t(0)));
return jm;
};
double h = 0.02;
UnknownShape<Vec2d> shape;
DomainDiscretization<Vec2d> domain(shape);
int max_points = 400, num_samples = 2;
// Fill domain.
GeneralSurfaceFill<Vec2d, Vec1d> gsf; gsf.seed(0); // deterministic
gsf.maxPoints(max_points).numSamples(num_samples);
BoxShape<Vec1d> bs(Vec1d{0.0}, Vec1d{2 * PI});
DomainDiscretization<Vec1d> param_d(bs);
domain.fill(gsf, param_d, example_r, der_example_r, h);
EXPECT_LE(domain.positions().size(), max_points + num_samples);
EXPECT_GE(domain.positions().size(), max_points - num_samples);
}
TEST(DomainEngines, DISABLED_EarthModel) {
std::ifstream fin("../testdata/topo.txt");
double map[180][360];
std::string is, s;
double mx = -10000000, mn = 10000000;
for (int i = 0; !fin.eof() && i < 180; i++) {
fin >> is;
std::istringstream ss(is);
for (int j = 0; std::getline(ss, s, ',') && j < 360; j++) {
map[i][j] = std::stoi(s);
mx = std::max(mx, map[i][j]);
mn = std::min(mn, map[i][j]);
}
}
for (int i = 0; i < 180; i++) {
for (int j = 0; j < 360; j++) {
map[i][j] = (map[i][j] - mn) / (mx - mn);
}
}
auto sphere_r = [](Vec2d t) {
double R = 1.001;
return Vec3d(R * cos(t(0)) * sin(t(1)),
R * sin(t(0)) * sin(t(1)), R * cos(t(1)));
};
auto sphere_jacobian_matrix = [](Vec2d t) {
double R = 1.001;
Eigen::Matrix<double, 3, 2> jm;
jm.col(0) << - R * sin(t(0)) * sin(t(1)),
R * cos(t(0)) * sin(t(1)), 0;
jm.col(1) << R * cos(t(0)) * cos(t(1)),
R * sin(t(0)) * cos(t(1)), - R * sin(t(1));
return jm;
};
auto earth_h = [&map](Vec3d p) {
double R = p.norm();
double theta = (90.0 - acos(p(2) / R) * 180.0 / 3.14);
double phi = atan2(-p(0), p(1)) * 180.0 / 3.14;
double h_0 = 0.005;
return h_0 / (1 * map[static_cast<int>(theta - 0.5) + 90]
[static_cast<int>(phi - 0.5) + 180]);
};
UnknownShape<Vec3d> shape;
DomainDiscretization<Vec3d> domain(shape);
GeneralSurfaceFill<Vec3d, Vec2d> gsf; gsf.seed(0); // deterministic
BoxShape<Vec2d> bs({0.0, 0.0}, {2 * PI, PI});
DomainDiscretization<Vec2d> param_domain(bs);
domain.fill(gsf, param_domain, sphere_r, sphere_jacobian_matrix, earth_h);
}
} // namespace mm
mm
Root namespace for the whole library.
Definition: Gaussian.hpp:14
GeneralSurfaceFill.hpp
Range_fwd.hpp
mm::Vec1d
Vec< double, 1 > Vec1d
Convenience typedef for 1d vector of doubles.
Definition: Vec_fwd.hpp:33
KDTree.hpp
mm::Vec3d
Vec< double, 3 > Vec3d
Convenience typedef for 3d vector of doubles.
Definition: Vec_fwd.hpp:35
DomainDiscretization_fwd.hpp
Vec.hpp
mm::PI
static const double PI
Mathematical constant pi in double precision.
Definition: Config.hpp:44
BoxShape.hpp
mm::Vec2d
Vec< double, 2 > Vec2d
Convenience typedef for 2d vector of doubles.
Definition: Vec_fwd.hpp:34