239 lines
9.8 KiB
C++
239 lines
9.8 KiB
C++
/*
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Copyright 2012 SINTEF ICT, Applied Mathematics.
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This file is part of the Open Porous Media project (OPM).
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OPM is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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OPM is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with OPM. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include "config.h"
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#include <opm/core/utility/WachspressCoord.hpp>
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#include <opm/core/grid.h>
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#include <cmath>
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#include <map>
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#include <set>
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namespace Opm
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{
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// -------- Helper methods for class WachspressCoord --------
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namespace
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{
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/// Calculates the determinant of a 2 x 2 matrix, represented as
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/// two two-dimensional arrays.
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double determinantOf(const double* a0,
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const double* a1)
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{
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return
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a0[0] * a1[1] - a0[1] * a1[0];
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}
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/// Calculates the determinant of a 3 x 3 matrix, represented as
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/// three three-dimensional arrays.
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double determinantOf(const double* a0,
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const double* a1,
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const double* a2)
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{
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return
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a0[0] * (a1[1] * a2[2] - a2[1] * a1[2]) -
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a0[1] * (a1[0] * a2[2] - a2[0] * a1[2]) +
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a0[2] * (a1[0] * a2[1] - a2[0] * a1[1]);
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}
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/// Calculates the volume of the parallelepiped given by
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/// the vectors n[i] for i = 0..(dim-1), each n[i] is of size dim.
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double cornerVolume(double** n, const int dim)
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{
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assert(dim == 2 || dim == 3);
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double det = (dim == 2) ? determinantOf(n[0], n[1]) : determinantOf(n[0], n[1], n[2]);
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return std::fabs(det);
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}
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} // anonymous namespace
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// -------- Methods of class WachspressCoord --------
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// The formula used is a modification of the formula given in:
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// M. Meyer, A. Barr, H. Lee, and M. Desbrun.
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// Generalized barycentric coordinates on irregular poly-
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// gons. Journal of Graphics Tools, 7(1):13–22, 2002.
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//
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// The formula given there is, for a corner i,
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// b_i = w_i / sum_{k} w_k
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// w_i = V_i / (prod_{j \in adjacent faces} n_j * (x_i - x) )
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// ^^^ ^^^ ^^^
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// corner "volume" normal corner coordinates
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// V_i = |Det({n_j}_{j \in adjacent faces})|
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// The corner coordinate x_i above can be replaced with any point on face j
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// without changing the value of w_i, and we replace it with c_j, the face
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// centroid.
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// However, this formula has the problem that the denominator of w_i becomes zero
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// close to the boundary. Our solution is to multiply all w_i by
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/// prod_{all j} n_j * (c_j - x), resulting in the formula:
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// w_i = V_i * (prod_{j \in nonadjacent faces} n_j * (c_j - x) ).
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// Another implementation note is that the above formulas assumes that
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// the normals have length 1 (are unit normals). It is easy to see that this
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// can be relaxed, since each normal occurs once in the formula for w_i, and
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// all w_i will be scaled by the same number. In our implementation we therefore
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// use the area-scaled normals directly as provided by the UnstructuredGrid.
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/// Constructor.
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/// \param[in] grid A grid.
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WachspressCoord::WachspressCoord(const UnstructuredGrid& grid)
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: grid_(grid)
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{
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enum { Maxdim = 3 };
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const int dim = grid.dimensions;
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if (dim > Maxdim) {
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OPM_THROW(std::runtime_error, "Grid has more than " << Maxdim << " dimensions.");
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}
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// Compute static data for each corner.
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const int num_cells = grid.number_of_cells;
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int corner_id_count = 0;
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for (int cell = 0; cell < num_cells; ++cell) {
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std::set<int> cell_vertices;
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std::vector<int> cell_faces;
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std::multimap<int, int> vertex_adj_faces;
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for (int hface = grid.cell_facepos[cell]; hface < grid.cell_facepos[cell + 1]; ++hface) {
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const int face = grid.cell_faces[hface];
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cell_faces.push_back(face);
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const int fn0 = grid.face_nodepos[face];
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const int fn1 = grid.face_nodepos[face + 1];
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cell_vertices.insert(grid.face_nodes + fn0, grid.face_nodes + fn1);
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for (int fn = fn0; fn < fn1; ++fn) {
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const int vertex = grid.face_nodes[fn];
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vertex_adj_faces.insert(std::make_pair(vertex, face));
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}
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}
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std::sort(cell_faces.begin(), cell_faces.end()); // set_difference requires sorted ranges
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std::vector<CornerInfo> cell_corner_info;
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std::set<int>::const_iterator it = cell_vertices.begin();
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for (; it != cell_vertices.end(); ++it) {
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CornerInfo ci;
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ci.corner_id = corner_id_count++;;
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ci.vertex = *it;
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double* fnorm[Maxdim] = { 0 };
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typedef std::multimap<int, int>::const_iterator MMIt;
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std::pair<MMIt, MMIt> frange = vertex_adj_faces.equal_range(ci.vertex);
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int fi = 0;
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std::vector<int> vert_adj_faces(dim);
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for (MMIt face_it = frange.first; face_it != frange.second; ++face_it, ++fi) {
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if (fi >= dim) {
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OPM_THROW(std::runtime_error, "In cell " << cell << ", vertex " << ci.vertex << " has "
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<< " more than " << dim << " adjacent faces.");
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}
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fnorm[fi] = grid_.face_normals + dim*(face_it->second);
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vert_adj_faces[fi] = face_it->second;
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}
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assert(fi == dim);
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adj_faces_.insert(adj_faces_.end(), vert_adj_faces.begin(), vert_adj_faces.end());
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const double corner_vol = cornerVolume(fnorm, dim);
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ci.volume = corner_vol;
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cell_corner_info.push_back(ci);
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std::sort(vert_adj_faces.begin(), vert_adj_faces.end());
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std::vector<int> vert_nonadj_faces(cell_faces.size() - vert_adj_faces.size());
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std::set_difference(cell_faces.begin(), cell_faces.end(),
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vert_adj_faces.begin(), vert_adj_faces.end(),
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vert_nonadj_faces.begin());
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nonadj_faces_.appendRow(vert_nonadj_faces.begin(), vert_nonadj_faces.end());
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}
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corner_info_.appendRow(cell_corner_info.begin(), cell_corner_info.end());
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}
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assert(corner_id_count == corner_info_.dataSize());
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}
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/// Count of vertices adjacent to a call.
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/// \param[in] cell A cell index.
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/// \return Number of corners of cell.
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int WachspressCoord::numCorners(const int cell) const
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{
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return corner_info_[cell].size();
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}
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/// The class stores some info for each corner.
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/// \return The corner info container.
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const SparseTable<WachspressCoord::CornerInfo>& WachspressCoord::cornerInfo() const
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{
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return corner_info_;
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}
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/// The class stores some info for each corner.
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/// \return The corner info container.
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const std::vector<int>& WachspressCoord::adjacentFaces() const
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{
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return adj_faces_;
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}
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/// Compute generalized barycentric coordinates for some point x
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/// with respect to the vertices of a grid cell.
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/// \param[in] cell Cell in which to compute coordinates.
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/// \param[in] x Coordinates of point in cartesian coordinates.
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/// Must be array of length grid.dimensions.
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/// \param[out] xb Coordinates of point in barycentric coordinates.
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/// Must be array of length numCorners(cell).
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void WachspressCoord::cartToBary(const int cell,
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const double* x,
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double* xb) const
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{
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// Note:
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// A possible optimization is: compute all n_j * (c_j - x) factors
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// once, instead of repeating computation for all corners (for
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// which j is a nonadjacent face).
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const int n = numCorners(cell);
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const int dim = grid_.dimensions;
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double totw = 0.0;
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for (int i = 0; i < n; ++i) {
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const CornerInfo& ci = corner_info_[cell][i];
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// Weight (unnormalized) is equal to:
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// V_i * (prod_{j \in nonadjacent faces} n_j * (c_j - x) )
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// ^^^ ^^^ ^^^
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// corner "volume" normal centroid
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xb[i] = ci.volume;
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const int num_nonadj_faces = nonadj_faces_[ci.corner_id].size();
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for (int j = 0; j < num_nonadj_faces; ++j) {
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const int face = nonadj_faces_[ci.corner_id][j];
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double factor = 0.0;
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for (int dd = 0; dd < dim; ++dd) {
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factor += grid_.face_normals[dim*face + dd]*(grid_.face_centroids[dim*face + dd] - x[dd]);
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}
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// Assumes outward-pointing normals, so negate factor if necessary.
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if (grid_.face_cells[2*face] != cell) {
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assert(grid_.face_cells[2*face + 1] == cell);
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factor = -factor;
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}
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xb[i] *= factor;
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}
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totw += xb[i];
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}
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for (int i = 0; i < n; ++i) {
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xb[i] /= totw;
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}
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}
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} // namespace Opm
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