mesh_fair.cc

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/* SPDX-FileCopyrightText: 2023 Blender Authors
 *
 * SPDX-License-Identifier: GPL-2.0-or-later */

 
#include "BLI_map.hh"
#include "BLI_math_geom.h"
#include "BLI_math_vector.h"
#include "BLI_vector.hh"
 
#include "BKE_mesh.hh"
#include "BKE_mesh_fair.hh"
 
#include "eigen_capi.h"
 
using blender::Array;
using blender::float3;
using blender::Map;
using blender::MutableSpan;
using blender::Span;
using blender::Vector;
using std::array;
 
class VertexWeight {
 public:
  virtual float weight_at_index(const int index) const = 0;
  virtual ~VertexWeight() = default;
};
 
class LoopWeight {
 public:
  virtual float weight_at_index(const int index) const = 0;
  virtual ~LoopWeight() = default;
};
 
class FairingContext {
 public:
  /* Get coordinates of vertices which are adjacent to the loop with specified index. */
  virtual void adjacents_coords_from_loop(const int loop,
                                          float r_adj_next[3],
                                          float r_adj_prev[3]) = 0;
 
  /* Get the other vertex index for a loop. */
  virtual int other_vertex_index_from_loop(const int loop, const int v) = 0;
 
  int vertex_count_get()
  {
    return totvert_;
  }
 
  int loop_count_get()
  {
    return totvert_;
  }
 
  Span<int> vertex_loop_map_get(const int v)
  {
    return vlmap_[v];
  }
 
  float *vertex_deformation_co_get(const int v)
  {
    return co_[v];
  }
 
  virtual ~FairingContext() = default;
 
  void fair_verts(const bool affected_verts[],
                  const eMeshFairingDepth depth,
                  const VertexWeight &vertex_weight,
                  const LoopWeight &loop_weight)
  {
    fair_verts_ex(affected_verts, int(depth), vertex_weight, loop_weight);
  }
 
 protected:
  Vector<float *> co_;
 
  int totvert_;
  int totloop_;
 
  blender::GroupedSpan<int> vlmap_;
 
 private:
  void fair_setup_fairing(const int v,
                          const int i,
                          LinearSolver *solver,
                          float multiplier,
                          const int depth,
                          Map<int, int> &vert_col_map,
                          const VertexWeight &vertex_weight,
                          const LoopWeight &loop_weight)
  {
    if (depth == 0) {
      if (vert_col_map.contains(v)) {
        const int j = vert_col_map.lookup(v);
        EIG_linear_solver_matrix_add(solver, i, j, -multiplier);
        return;
      }
      for (int j = 0; j < 3; j++) {
        EIG_linear_solver_right_hand_side_add(solver, j, i, multiplier * co_[v][j]);
      }
      return;
    }
 
    float w_ij_sum = 0;
    const float w_i = vertex_weight.weight_at_index(v);
    const Span<int> vlmap_elem = vlmap_[v];
    for (const int l : vlmap_elem.index_range()) {
      const int l_index = vlmap_elem[l];
      const int other_vert = other_vertex_index_from_loop(l_index, v);
      const float w_ij = loop_weight.weight_at_index(l_index);
      w_ij_sum += w_ij;
      fair_setup_fairing(other_vert,
                         i,
                         solver,
                         w_i * w_ij * multiplier,
                         depth - 1,
                         vert_col_map,
                         vertex_weight,
                         loop_weight);
    }
    fair_setup_fairing(v,
                       i,
                       solver,
                       -1 * w_i * w_ij_sum * multiplier,
                       depth - 1,
                       vert_col_map,
                       vertex_weight,
                       loop_weight);
  }
 
  void fair_verts_ex(const bool affected_verts[],
                     const int order,
                     const VertexWeight &vertex_weight,
                     const LoopWeight &loop_weight)
  {
    Map<int, int> vert_col_map;
    int affected_verts_num = 0;
    for (int i = 0; i < totvert_; i++) {
      if (!affected_verts[i]) {
        continue;
      }
      vert_col_map.add(i, affected_verts_num);
      affected_verts_num++;
    }
 
    /* Early return, nothing to do. */
    if (ELEM(affected_verts_num, 0, totvert_)) {
      return;
    }
 
    /* Setup fairing matrices */
    LinearSolver *solver = EIG_linear_solver_new(affected_verts_num, affected_verts_num, 3);
    for (auto item : vert_col_map.items()) {
      const int v = item.key;
      const int col = item.value;
      fair_setup_fairing(v, col, solver, 1.0f, order, vert_col_map, vertex_weight, loop_weight);
    }
 
    /* Solve linear system */
    EIG_linear_solver_solve(solver);
 
    /* Copy the result back to the mesh */
    for (auto item : vert_col_map.items()) {
      const int v = item.key;
      const int col = item.value;
      for (int j = 0; j < 3; j++) {
        co_[v][j] = EIG_linear_solver_variable_get(solver, j, col);
      }
    }
 
    /* Free solver data */
    EIG_linear_solver_delete(solver);
  }
};
 
class MeshFairingContext : public FairingContext {
 public:
  MeshFairingContext(Mesh *mesh, MutableSpan<float3> deform_positions)
  {
    totvert_ = mesh->verts_num;
    totloop_ = mesh->corners_num;
 
    MutableSpan<float3> positions = mesh->vert_positions_for_write();
    edges_ = mesh->edges();
    faces = mesh->faces();
    corner_verts_ = mesh->corner_verts();
    corner_edges_ = mesh->corner_edges();
    vlmap_ = mesh->vert_to_corner_map();
 
    /* Deformation coords. */
    co_.resize(mesh->verts_num);
    if (!deform_positions.is_empty()) {
      for (int i = 0; i < mesh->verts_num; i++) {
        co_[i] = deform_positions[i];
      }
    }
    else {
      for (int i = 0; i < mesh->verts_num; i++) {
        co_[i] = positions[i];
      }
    }
 
    loop_to_face_map_ = mesh->corner_to_face_map();
  }
 
  void adjacents_coords_from_loop(const int loop,
                                  float r_adj_next[3],
                                  float r_adj_prev[3]) override
  {
    using namespace blender;
    const int vert = corner_verts_[loop];
    const blender::IndexRange face = faces[loop_to_face_map_[loop]];
    const int2 adjacent_verts = bke::mesh::face_find_adjacent_verts(face, corner_verts_, vert);
    copy_v3_v3(r_adj_next, co_[adjacent_verts[0]]);
    copy_v3_v3(r_adj_prev, co_[adjacent_verts[1]]);
  }
 
  int other_vertex_index_from_loop(const int loop, const int v) override
  {
    const blender::int2 &edge = edges_[corner_edges_[loop]];
    return blender::bke::mesh::edge_other_vert(edge, v);
  }
 
 protected:
  Mesh *mesh_;
  Span<int> corner_verts_;
  Span<int> corner_edges_;
  blender::OffsetIndices<int> faces;
  Span<blender::int2> edges_;
  Span<int> loop_to_face_map_;
};
 
class UniformVertexWeight : public VertexWeight {
 public:
  UniformVertexWeight(FairingContext &fairing_context)
  {
    const int totvert = fairing_context.vertex_count_get();
    vertex_weights_.resize(totvert);
    for (int i = 0; i < totvert; i++) {
      const int tot_loop = fairing_context.vertex_loop_map_get(i).size();
      if (tot_loop != 0) {
        vertex_weights_[i] = 1.0f / tot_loop;
      }
      else {
        vertex_weights_[i] = FLT_MAX;
      }
    }
  }
 
  float weight_at_index(const int index) const override
  {
    return vertex_weights_[index];
  }
 
 private:
  Vector<float> vertex_weights_;
};
 
class VoronoiVertexWeight : public VertexWeight {
 
 public:
  VoronoiVertexWeight(FairingContext &fairing_context)
  {
 
    const int totvert = fairing_context.vertex_count_get();
    vertex_weights_.resize(totvert);
    for (int i = 0; i < totvert; i++) {
 
      float area = 0.0f;
      float a[3];
      copy_v3_v3(a, fairing_context.vertex_deformation_co_get(i));
      const float acute_threshold = M_PI_2;
 
      const Span<int> vlmap_elem = fairing_context.vertex_loop_map_get(i);
      for (const int l : vlmap_elem.index_range()) {
        const int l_index = vlmap_elem[l];
 
        float b[3], c[3], d[3];
        fairing_context.adjacents_coords_from_loop(l_index, b, c);
 
        if (angle_v3v3v3(c, fairing_context.vertex_deformation_co_get(i), b) < acute_threshold) {
          calc_circumcenter(d, a, b, c);
        }
        else {
          add_v3_v3v3(d, b, c);
          mul_v3_fl(d, 0.5f);
        }
 
        float t[3];
        add_v3_v3v3(t, a, b);
        mul_v3_fl(t, 0.5f);
        area += area_tri_v3(a, t, d);
 
        add_v3_v3v3(t, a, c);
        mul_v3_fl(t, 0.5f);
        area += area_tri_v3(a, d, t);
      }
 
      vertex_weights_[i] = area != 0.0f ? 1.0f / area : 1e12;
    }
  }
 
  float weight_at_index(const int index) const override
  {
    return vertex_weights_[index];
  }
 
 private:
  Vector<float> vertex_weights_;
 
  void calc_circumcenter(float r[3], const float a[3], const float b[3], const float c[3])
  {
    float ab[3];
    sub_v3_v3v3(ab, b, a);
 
    float ac[3];
    sub_v3_v3v3(ac, c, a);
 
    float ab_cross_ac[3];
    cross_v3_v3v3(ab_cross_ac, ab, ac);
 
    if (len_squared_v3(ab_cross_ac) > 0.0f) {
      float d[3];
      cross_v3_v3v3(d, ab_cross_ac, ab);
      mul_v3_fl(d, len_squared_v3(ac));
 
      float t[3];
      cross_v3_v3v3(t, ac, ab_cross_ac);
      mul_v3_fl(t, len_squared_v3(ab));
 
      add_v3_v3(d, t);
 
      mul_v3_fl(d, 1.0f / (2.0f * len_squared_v3(ab_cross_ac)));
 
      add_v3_v3v3(r, a, d);
      return;
    }
    copy_v3_v3(r, a);
  }
};
 
class UniformLoopWeight : public LoopWeight {
 public:
  float weight_at_index(const int /*index*/) const override
  {
    return 1.0f;
  }
};
 
static void prefair_and_fair_verts(FairingContext &fairing_context,
                                   const bool affected_verts[],
                                   const eMeshFairingDepth depth)
{
  /* Pre-fair. */
  UniformVertexWeight uniform_vertex_weights(fairing_context);
  UniformLoopWeight uniform_loop_weights;
  fairing_context.fair_verts(affected_verts, depth, uniform_vertex_weights, uniform_loop_weights);
 
  /* Fair. */
  VoronoiVertexWeight voronoi_vertex_weights(fairing_context);
  /* TODO: Implement cotangent loop weights. */
  fairing_context.fair_verts(affected_verts, depth, voronoi_vertex_weights, uniform_loop_weights);
}
 
void BKE_mesh_prefair_and_fair_verts(Mesh *mesh,
                                     blender::MutableSpan<float3> deform_vert_positions,
                                     const bool affected_verts[],
                                     const eMeshFairingDepth depth)
{
  MutableSpan<float3> deform_positions_span;
  if (!deform_vert_positions.is_empty()) {
    deform_positions_span = deform_vert_positions;
  }
  MeshFairingContext fairing_context(mesh, deform_positions_span);
  prefair_and_fair_verts(fairing_context, affected_verts, depth);
}