FastSweepingMethod.cpp

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#include "FastSweepingMethod.h"
 
namespace dyno
{
    IMPLEMENT_TCLASS(FastSweepingMethod, TDataType)
 
    template<typename TDataType>
    FastSweepingMethod<TDataType>::FastSweepingMethod()
        : ComputeModule()
    {
        this->varPadding()->setMin(2);
    }
 
    template<typename TDataType>
    FastSweepingMethod<TDataType>::~FastSweepingMethod()
    {
        faceList.clear();
        vertList.clear();
        phi.clear();
    }
 
    template<typename TDataType>
    void FastSweepingMethod<TDataType>::compute()
    {
        this->loadClosedSurface();
 
        if (this->outLevelSet()->isEmpty()) {
            this->outLevelSet()->allocate();
        }
        DistanceField3D<TDataType>& sdf = this->outLevelSet()->getDataPtr()->getSDF();
 
        Coord p0(origin.x, origin.y, origin.z);
        Coord p1(maxPoint.x, maxPoint.y, maxPoint.z);
 
        sdf.setSpace(p0, p1, this->varSpacing()->getValue());
        sdf.setDistance(phi);
    }
 
    template<typename TDataType>
    void FastSweepingMethod<TDataType>::loadClosedSurface()
    {
        Vec3f min_box(std::numeric_limits<float>::max(), std::numeric_limits<float>::max(), std::numeric_limits<float>::max());
        Vec3f max_box(-std::numeric_limits<float>::max(), -std::numeric_limits<float>::max(), -std::numeric_limits<float>::max());
 
        auto& mPoints = inTriangleSet()->getDataPtr()->getPoints();
        auto& mTriangles = inTriangleSet()->getDataPtr()->getTriangles();
        
        CArray<Coord> cPoints;
        cPoints.assign(mPoints);
 
        CArray<TopologyModule::Triangle> cTriangles;
        cTriangles.resize(mTriangles.size());
        cTriangles.assign(mTriangles);
 
        vertList.clear();
        faceList.clear();
 
        for (int i = 0; i < cPoints.size(); i++) {
            Coord point = cPoints[i];
            vertList.pushBack(point);
            min_box = min_box.minimum(point);
            max_box = max_box.maximum(point);
        }
    
        for (int i = 0; i < cTriangles.size(); i++) {
            faceList.pushBack(Vec3ui(cTriangles[i][0], cTriangles[i][1], cTriangles[i][2]));
        }
        
        Real dx = this->varSpacing()->getValue();
        uint padding = this->varPadding()->getValue();
        
        Vec3f unit(1, 1, 1);
        min_box -= padding * dx * unit;
        max_box += padding * dx * unit;
 
        ni = std::ceil((max_box[0] - min_box[0]) / dx);
        nj = std::ceil((max_box[1] - min_box[1]) / dx);
        nk = std::ceil((max_box[2] - min_box[2]) / dx);
        
        origin = min_box;
        maxPoint = max_box;
 
        makeLevelSet();
    
        cPoints.clear();
        cTriangles.clear();
        printf("Uniform grids: %f %f %f, %f %f %f, %f, %d %d %d, %d \n", origin[0], origin[1], origin[2], maxPoint[0], maxPoint[1], maxPoint[2], dx, ni, nj, nk, padding);
    }
 
    // find distance x0 is from segment x1-x2
    static float point_segment_distance(const Vec3f &x0, const Vec3f &x1, const Vec3f &x2)
    {
        Vec3f dx(x2 - x1);
        double m2 = dx.normSquared();
        // find parameter value of closest point on segment
        float s12 = (float)((x2 - x0).dot(dx) / m2);
        if (s12 < 0) {
            s12 = 0;
        }
        else if (s12 > 1) {
            s12 = 1;
        }
        // and find the distance
        return (x0 - (s12*x1 + (1 - s12)*x2)).norm();
    }
 
    // find distance x0 is from triangle x1-x2-x3
    static float point_triangle_distance(const Vec3f &x0, const Vec3f &x1, const Vec3f &x2, const Vec3f &x3)
    {
        // first find barycentric coordinates of closest point on infinite plane
        Vec3f x13(x1 - x3), x23(x2 - x3), x03(x0 - x3);
        float m13 = x13.normSquared(), m23 = x23.normSquared(), d = x13.dot(x23);
        float invdet = 1.f / std::max(m13*m23 - d * d, 1e-30f);
        float a = x13.dot(x03), b = x23.dot(x03);
        // the barycentric coordinates themselves
        float w23 = invdet * (m23*a - d * b);
        float w31 = invdet * (m13*b - d * a);
        float w12 = 1 - w23 - w31;
        if (w23 >= 0 && w31 >= 0 && w12 >= 0) { // if we're inside the triangle
            return (x0 - (w23*x1 + w31 * x2 + w12 * x3)).norm();
        }
        else { // we have to clamp to one of the edges
            if (w23 > 0) // this rules out edge 2-3 for us
                return std::min(point_segment_distance(x0, x1, x2), point_segment_distance(x0, x1, x3));
            else if (w31 > 0) // this rules out edge 1-3
                return std::min(point_segment_distance(x0, x1, x2), point_segment_distance(x0, x2, x3));
            else // w12 must be >0, ruling out edge 1-2
                return std::min(point_segment_distance(x0, x1, x3), point_segment_distance(x0, x2, x3));
        }
    }
 
    static void FSM_CheckNeighbour(const CArray<Vec3ui> &tri, const CArray<Vec3f> &vert,
        CArray3f &phi, CArray3i &closest_tri,
        const Vec3f &gx, int i0, int j0, int k0, int i1, int j1, int k1)
    {
        if (closest_tri(i1, j1, k1) >= 0) {
            unsigned int p, q, r; 
            Vec3ui trijk = tri[closest_tri(i1, j1, k1)];
            p = trijk[0];
            q = trijk[1];
            r = trijk[2];
            float d = point_triangle_distance(gx, vert[p], vert[q], vert[r]);
            if (d < phi(i0, j0, k0)) {
                phi(i0, j0, k0) = d;
                closest_tri(i0, j0, k0) = closest_tri(i1, j1, k1);
            }
        }
    }
 
    static void sweep(const CArray<Vec3ui> &tri, const CArray<Vec3f> &x,
        CArray3f &phi, CArray3i &closest_tri, const Vec3f &origin, float dx,
        int di, int dj, int dk)
    {
        int i0, i1;
        if (di > 0) { 
            i0 = 1; i1 = phi.nx(); 
        }
        else { 
            i0 = phi.nx() - 2; i1 = -1; 
        }
        int j0, j1;
        if (dj > 0) { 
            j0 = 1; j1 = phi.ny(); 
        }
        else { 
            j0 = phi.ny() - 2; j1 = -1; 
        }
        int k0, k1;
        if (dk > 0) { 
            k0 = 1; k1 = phi.nz(); 
        }
        else { 
            k0 = phi.nz() - 2; k1 = -1; 
        }
        for (int k = k0; k != k1; k += dk) for (int j = j0; j != j1; j += dj) for (int i = i0; i != i1; i += di) {
            Vec3f gx(i*dx + origin[0], j*dx + origin[1], k*dx + origin[2]);
            FSM_CheckNeighbour(tri, x, phi, closest_tri, gx, i, j, k, i - di, j, k);
            FSM_CheckNeighbour(tri, x, phi, closest_tri, gx, i, j, k, i, j - dj, k);
            FSM_CheckNeighbour(tri, x, phi, closest_tri, gx, i, j, k, i - di, j - dj, k);
            FSM_CheckNeighbour(tri, x, phi, closest_tri, gx, i, j, k, i, j, k - dk);
            FSM_CheckNeighbour(tri, x, phi, closest_tri, gx, i, j, k, i - di, j, k - dk);
            FSM_CheckNeighbour(tri, x, phi, closest_tri, gx, i, j, k, i, j - dj, k - dk);
            FSM_CheckNeighbour(tri, x, phi, closest_tri, gx, i, j, k, i - di, j - dj, k - dk);
        }
    }
 
    // calculate twice signed area of triangle (0,0)-(x1,y1)-(x2,y2)
    // return an SOS-determined sign (-1, +1, or 0 only if it's a truly degenerate triangle)
    static int orientation(double x1, double y1, double x2, double y2, double &twice_signed_area)
    {
        twice_signed_area = y1 * x2 - x1 * y2;
        if (twice_signed_area > 0) return 1;
        else if (twice_signed_area < 0) return -1;
        else if (y2 > y1) return 1;
        else if (y2 < y1) return -1;
        else if (x1 > x2) return 1;
        else if (x1 < x2) return -1;
        else return 0; // only true when x1==x2 and y1==y2
    }
 
    // robust test of (x0,y0) in the triangle (x1,y1)-(x2,y2)-(x3,y3)
    // if true is returned, the barycentric coordinates are set in a,b,c.
    static bool point_in_triangle_2d(double x0, double y0,
        double x1, double y1, double x2, double y2, double x3, double y3,
        double& a, double& b, double& c)
    {
        x1 -= x0; x2 -= x0; x3 -= x0;
        y1 -= y0; y2 -= y0; y3 -= y0;
        int signa = orientation(x2, y2, x3, y3, a);
        if (signa == 0) return false;
        int signb = orientation(x3, y3, x1, y1, b);
        if (signb != signa) return false;
        int signc = orientation(x1, y1, x2, y2, c);
        if (signc != signa) return false;
        double sum = a + b + c;
        assert(sum != 0); // if the SOS signs match and are nonkero, there's no way all of a, b, and c are zero.
        a /= sum;
        b /= sum;
        c /= sum;
        return true;
    }
 
#define TRI_MIN(x, y, z) std::min(x, std::min(y, z))
#define TRI_MAX(x, y, z) std::max(x, std::max(y, z))
 
    template<typename TDataType>
    void FastSweepingMethod<TDataType>::makeLevelSet()
    {
        const int exact_band = 1;
        Real dx = this->varSpacing()->getValue();
 
        phi.resize(ni, nj, nk);
        phi.assign((ni + nj + nk)*dx);
        //TODO: phi.assign((ni + nj + nk)*dx); // upper bound on distance
        CArray3i closest_tri(ni, nj, nk);//CArray3i closest_tri(ni, nj, nk, -1);
        closest_tri.assign(-1);
        CArray3i intersection_count(ni, nj, nk); //CArray3i intersection_count(ni, nj, nk, 0); // intersection_count(i,j,k) is # of tri intersections in (i-1,i]x{j}x{k}
        intersection_count.assign(0);
        // we begin by initializing distances near the mesh, and figuring out intersection counts
        for (uint t = 0; t < faceList.size(); ++t) {
            uint p, q, r;
            p = faceList[t][0];
            q = faceList[t][1];
            r = faceList[t][2];
            // coordinates in grid to high precision
            double fip = ((double)vertList[p][0] - origin[0]) / dx;
            double fjp = ((double)vertList[p][1] - origin[1]) / dx;
            double fkp = ((double)vertList[p][2] - origin[2]) / dx;
            double fiq = ((double)vertList[q][0] - origin[0]) / dx; 
            double fjq = ((double)vertList[q][1] - origin[1]) / dx; 
            double fkq = ((double)vertList[q][2] - origin[2]) / dx;
            double fir = ((double)vertList[r][0] - origin[0]) / dx; 
            double fjr = ((double)vertList[r][1] - origin[1]) / dx; 
            double fkr = ((double)vertList[r][2] - origin[2]) / dx;
            // do distances nearby
            int i0 = clamp(int(TRI_MIN(fip, fiq, fir)) - exact_band, 0, ni - 1);
            int i1 = clamp(int(TRI_MAX(fip, fiq, fir)) + exact_band + 1, 0, ni - 1);
            int j0 = clamp(int(TRI_MIN(fjp, fjq, fjr)) - exact_band, 0, nj - 1);
            int j1 = clamp(int(TRI_MAX(fjp, fjq, fjr)) + exact_band + 1, 0, nj - 1);
            int k0 = clamp(int(TRI_MIN(fkp, fkq, fkr)) - exact_band, 0, nk - 1);
            int k1 = clamp(int(TRI_MAX(fkp, fkq, fkr)) + exact_band + 1, 0, nk - 1);
            for (int k = k0; k <= k1; ++k) for (int j = j0; j <= j1; ++j) for (int i = i0; i <= i1; ++i) {
                Vec3f gx(i*dx + origin[0], j*dx + origin[1], k*dx + origin[2]);
                float d = point_triangle_distance(gx, vertList[p], vertList[q], vertList[r]);
                if (d < phi(i, j, k)) {
                    phi(i, j, k) = d;
                    closest_tri(i, j, k) = t;
                }
            }
            // and do intersection counts
            j0 = clamp((int)std::ceil(TRI_MIN(fjp, fjq, fjr)), 0, nj - 1);
            j1 = clamp((int)std::floor(TRI_MAX(fjp, fjq, fjr)), 0, nj - 1);
            k0 = clamp((int)std::ceil(TRI_MIN(fkp, fkq, fkr)), 0, nk - 1);
            k1 = clamp((int)std::floor(TRI_MAX(fkp, fkq, fkr)), 0, nk - 1);
            for (int k = k0; k <= k1; ++k) for (int j = j0; j <= j1; ++j) {
                double a, b, c;
                if (point_in_triangle_2d(j, k, fjp, fkp, fjq, fkq, fjr, fkr, a, b, c)) {
                    double fi = a * fip + b * fiq + c * fir; // intersection i coordinate
                    int i_interval = int(std::ceil(fi)); // intersection is in (i_interval-1,i_interval]
                    if (i_interval < 0) ++intersection_count(0, j, k); // we enlarge the first interval to include everything to the -x direction
                    else if (i_interval < ni) ++intersection_count(i_interval, j, k);
                    // we ignore intersections that are beyond the +x side of the grid
                }
            }
        }
        // and now we fill in the rest of the distances with fast sweeping
        for (unsigned int pass = 0; pass < 2; ++pass) {
            sweep(faceList, vertList, phi, closest_tri, origin, dx, +1, +1, +1);
            sweep(faceList, vertList, phi, closest_tri, origin, dx, -1, -1, -1);
            sweep(faceList, vertList, phi, closest_tri, origin, dx, +1, +1, -1);
            sweep(faceList, vertList, phi, closest_tri, origin, dx, -1, -1, +1);
            sweep(faceList, vertList, phi, closest_tri, origin, dx, +1, -1, +1);
            sweep(faceList, vertList, phi, closest_tri, origin, dx, -1, +1, -1);
            sweep(faceList, vertList, phi, closest_tri, origin, dx, +1, -1, -1);
            sweep(faceList, vertList, phi, closest_tri, origin, dx, -1, +1, +1);
        }
        // then figure out signs (inside/outside) from intersection counts
        for (int k = 0; k < nk; ++k) for (int j = 0; j < nj; ++j) {
            int total_count = 0;
            for (int i = 0; i < ni; ++i) {
                total_count += intersection_count(i, j, k);
                if (total_count % 2 == 1) { // if parity of intersections so far is odd,
                    phi(i, j, k) = -phi(i, j, k); // we are inside the mesh
                }
            }
        }
    }
 
    DEFINE_CLASS(FastSweepingMethod);
}