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+// This file is part of libigl, a simple c++ geometry processing library.
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+//
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+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
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+//
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+// This Source Code Form is subject to the terms of the Mozilla Public License
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+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
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+// obtain one at http://mozilla.org/MPL/2.0/.
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+#include "reorient_facets_raycast.h"
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+#include "../per_face_normals.h"
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+#include "../doublearea.h"
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+#include "../random_dir.h"
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+#include "../boost/bfs_orient.h"
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+#include "orient_outward_ao.h"
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+#include "EmbreeIntersector.h"
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+#include <iostream>
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+#include <random>
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+#include <ctime>
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+#include <limits>
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+
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+ template <
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+ typename DerivedV,
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+ typename DerivedF,
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+ typename DerivedI>
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+ IGL_INLINE void igl::reorient_facets_raycast(
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+ const Eigen::PlainObjectBase<DerivedV> & V,
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+ const Eigen::PlainObjectBase<DerivedF> & F,
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+ int rays_total,
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+ int rays_minimum,
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+ bool face_wise,
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+ bool use_parity,
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+ bool is_verbose,
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+ Eigen::PlainObjectBase<DerivedI> & I)
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+{
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+ using namespace Eigen;
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+ using namespace std;
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+ assert(F.cols() == 3);
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+ assert(V.cols() == 3);
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+
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+ // number of faces
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+ const int m = F.rows();
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+
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+ VectorXi C;
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+ MatrixXi FF = F;
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+ if (face_wise) {
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+ C.resize(m);
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+ for (int i = 0; i < m; ++i) C(i) = i;
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+
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+ } else {
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+ if (is_verbose) cout << "extracting patches... ";
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+ bfs_orient(F,FF,C);
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+ }
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+ if (is_verbose) cout << (C.maxCoeff() + 1) << " components. ";
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+
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+ // number of patches
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+ const int num_cc = C.maxCoeff()+1;
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+
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+ // Init Embree
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+ EmbreeIntersector ei;
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+ ei.init(V.template cast<float>(),FF);
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+
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+ // face normal
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+ MatrixXd N;
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+ per_face_normals(V,FF,N);
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+
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+ // face area
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+ Matrix<typename DerivedV::Scalar,Dynamic,1> A;
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+ doublearea(V,FF,A);
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+ double area_min = numeric_limits<double>::max();
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+ for (int f = 0; f < m; ++f)
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+ {
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+ area_min = A(f) != 0 && A(f) < area_min ? A(f) : area_min;
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+ }
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+ double area_total = A.sum();
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+
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+ // determine number of rays per component according to its area
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+ VectorXd area_per_component;
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+ area_per_component.setZero(num_cc);
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+ for (int f = 0; f < m; ++f)
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+ {
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+ area_per_component(C(f)) += A(f);
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+ }
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+ VectorXi num_rays_per_component(num_cc);
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+ for (int c = 0; c < num_cc; ++c)
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+ {
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+ num_rays_per_component(c) = max<int>(static_cast<int>(rays_total * area_per_component(c) / area_total), rays_minimum);
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+ }
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+ rays_total = num_rays_per_component.sum();
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+
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+ // generate all the rays
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+ if (is_verbose) cout << "generating rays... ";
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+ uniform_real_distribution<float> rdist;
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+ mt19937 prng;
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+ prng.seed(time(nullptr));
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+ vector<int > ray_face;
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+ vector<Vector3f> ray_ori;
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+ vector<Vector3f> ray_dir;
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+ ray_face.reserve(rays_total);
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+ ray_ori .reserve(rays_total);
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+ ray_dir .reserve(rays_total);
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+ for (int c = 0; c < num_cc; ++c)
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+ {
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+ if (area_per_component[c] == 0)
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+ {
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+ continue;
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+ }
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+ vector<int> CF; // set of faces per component
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+ vector<unsigned long long> CF_area;
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+ for (int f = 0; f < m; ++f)
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+ {
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+ if (C(f)==c)
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+ {
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+ CF.push_back(f);
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+ CF_area.push_back(static_cast<unsigned long long>(100 * A(f) / area_min));
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+ }
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+ }
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+ // discrete distribution for random selection of faces with probability proportional to their areas
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+ auto ddist_func = [&] (double i) { return CF_area[static_cast<int>(i)]; };
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+ discrete_distribution<int> ddist(CF.size(), 0, CF.size(), ddist_func); // simple ctor of (Iter, Iter) not provided by the stupid VC11 impl...
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+ for (int i = 0; i < num_rays_per_component[c]; ++i)
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+ {
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+ int f = CF[ddist(prng)]; // select face with probability proportional to face area
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+ float s = rdist(prng); // random barycentric coordinate (reference: Generating Random Points in Triangles [Turk, Graphics Gems I 1990])
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+ float t = rdist(prng);
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+ float sqrt_t = sqrtf(t);
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+ float a = 1 - sqrt_t;
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+ float b = (1 - s) * sqrt_t;
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+ float c = s * sqrt_t;
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+ Vector3f p = a * V.row(FF(f,0)).template cast<float>().eval() // be careful with the index!!!
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+ + b * V.row(FF(f,1)).template cast<float>().eval()
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+ + c * V.row(FF(f,2)).template cast<float>().eval();
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+ Vector3f n = N.row(f).cast<float>();
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+ if (n.isZero()) continue;
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+ // random direction in hemisphere around n (avoid too grazing angle)
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+ Vector3f d;
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+ while (true) {
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+ d = random_dir().cast<float>();
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+ float ndotd = n.dot(d);
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+ if (fabsf(ndotd) < 0.1f)
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+ {
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+ continue;
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+ }
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+ if (ndotd < 0)
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+ {
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+ d *= -1.0f;
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+ }
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+ break;
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+ }
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+ ray_face.push_back(f);
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+ ray_ori .push_back(p);
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+ ray_dir .push_back(d);
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+
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+ if (is_verbose && ray_face.size() % (rays_total / 10) == 0) cout << ".";
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+ }
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+ }
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+ if (is_verbose) cout << ray_face.size() << " rays. ";
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+
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+ // per component voting: first=front, second=back
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+ vector<pair<float, float>> C_vote_distance(num_cc, make_pair(0, 0)); // sum of distance between ray origin and intersection
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+ vector<pair<int , int >> C_vote_infinity(num_cc, make_pair(0, 0)); // number of rays reaching infinity
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+ vector<pair<int , int >> C_vote_parity(num_cc, make_pair(0, 0)); // sum of parity count for each ray
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+
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+ if (is_verbose) cout << "shooting rays... ";
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+#pragma omp parallel for
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+ for (int i = 0; i < (int)ray_face.size(); ++i)
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+ {
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+ int f = ray_face[i];
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+ Vector3f o = ray_ori [i];
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+ Vector3f d = ray_dir [i];
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+ int c = C(f);
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+
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+ // shoot ray toward front & back
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+ vector<Hit> hits_front;
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+ vector<Hit> hits_back;
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+ int num_rays_front;
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+ int num_rays_back;
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+ ei.intersectRay(o, d, hits_front, num_rays_front);
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+ ei.intersectRay(o, -d, hits_back , num_rays_back );
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+ if (!hits_front.empty() && hits_front[0].id == f) hits_front.erase(hits_front.begin());
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+ if (!hits_back .empty() && hits_back [0].id == f) hits_back .erase(hits_back .begin());
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+
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+ if (use_parity) {
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+#pragma omp atomic
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+ C_vote_parity[c].first += hits_front.size() % 2;
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+#pragma omp atomic
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+ C_vote_parity[c].second += hits_back .size() % 2;
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+
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+ } else {
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+ if (hits_front.empty())
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+ {
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+#pragma omp atomic
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+ C_vote_infinity[c].first++;
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+ } else {
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+#pragma omp atomic
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+ C_vote_distance[c].first += hits_front[0].t;
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+ }
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+
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+ if (hits_back.empty())
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+ {
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+#pragma omp atomic
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+ C_vote_infinity[c].second++;
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+ } else {
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+#pragma omp atomic
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+ C_vote_distance[c].second += hits_back[0].t;
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+ }
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+ }
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+ }
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+
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+ I.resize(m);
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+ for(int f = 0; f < m; ++f)
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+ {
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+ int c = C(f);
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+ if (use_parity) {
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+ I(f) = C_vote_parity[c].first > C_vote_parity[c].second ? 1 : 0; // Ideally, parity for the front/back side should be 1/0 (i.e., parity sum for all rays should be smaller on the front side)
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+
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+ } else {
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+ I(f) = (C_vote_infinity[c].first == C_vote_infinity[c].second && C_vote_distance[c].first < C_vote_distance[c].second) ||
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+ C_vote_infinity[c].first < C_vote_infinity[c].second
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+ ? 1 : 0;
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+ }
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+ }
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+ if (is_verbose) cout << "done!" << endl;
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+}
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+
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+#ifndef IGL_HEADER_ONLY
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+// Explicit template specialization
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+#endif
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Alec Jacobson (jalec