SIM_mass_spring.cc

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/* SPDX-FileCopyrightText: 2004-2023 Blender Authors
 *
 * SPDX-License-Identifier: GPL-2.0-or-later */

 
#include "MEM_guardedalloc.h"
 
#include "DNA_cloth_types.h"
#include "DNA_modifier_types.h"
#include "DNA_object_force_types.h"
#include "DNA_object_types.h"
#include "DNA_scene_types.h"
 
#include "BLI_linklist.h"
#include "BLI_math_geom.h"
#include "BLI_math_vector.h"
#include "BLI_math_vector.hh"
#include "BLI_utildefines.h"
 
#include "BKE_cloth.hh"
#include "BKE_collision.h"
#include "BKE_effect.h"
 
#include "SIM_mass_spring.h"
#include "implicit.h"
 
#include "DEG_depsgraph.hh"
#include "DEG_depsgraph_query.hh"
 
static float I3[3][3] = {{1.0, 0.0, 0.0}, {0.0, 1.0, 0.0}, {0.0, 0.0, 1.0}};
 
/* Number of off-diagonal non-zero matrix blocks.
 * Basically there is one of these for each vertex-vertex interaction.
 */
static int cloth_count_nondiag_blocks(Cloth *cloth)
{
  LinkNode *link;
  int nondiag = 0;
 
  for (link = cloth->springs; link; link = link->next) {
    ClothSpring *spring = (ClothSpring *)link->link;
    switch (spring->type) {
      case CLOTH_SPRING_TYPE_BENDING_HAIR:
        /* angular bending combines 3 vertices */
        nondiag += 3;
        break;
 
      default:
        /* all other springs depend on 2 vertices only */
        nondiag += 1;
        break;
    }
  }
 
  return nondiag;
}
 
static bool cloth_get_pressure_weights(ClothModifierData *clmd,
                                       const blender::int3 &vert_tri,
                                       float *r_weights)
{
  /* We have custom vertex weights for pressure. */
  if (clmd->sim_parms->vgroup_pressure > 0) {
    Cloth *cloth = clmd->clothObject;
    ClothVertex *verts = cloth->verts;
 
    for (uint j = 0; j < 3; j++) {
      r_weights[j] = verts[vert_tri[j]].pressure_factor;
 
      /* Skip the entire triangle if it has a zero weight. */
      if (r_weights[j] == 0.0f) {
        return false;
      }
    }
  }
 
  return true;
}
 
static void cloth_calc_pressure_gradient(ClothModifierData *clmd,
                                         const float gradient_vector[3],
                                         float *r_vertex_pressure)
{
  Cloth *cloth = clmd->clothObject;
  Implicit_Data *data = cloth->implicit;
  uint mvert_num = cloth->mvert_num;
  float pt[3];
 
  for (uint i = 0; i < mvert_num; i++) {
    SIM_mass_spring_get_position(data, i, pt);
    r_vertex_pressure[i] = dot_v3v3(pt, gradient_vector);
  }
}
 
static float cloth_calc_volume(ClothModifierData *clmd)
{
  /* Calculate the (closed) cloth volume. */
  Cloth *cloth = clmd->clothObject;
  const blender::int3 *vert_tris = cloth->vert_tris;
  Implicit_Data *data = cloth->implicit;
  float weights[3] = {1.0f, 1.0f, 1.0f};
  float vol = 0;
 
  /* Early exit for hair, as it never has volume. */
  if (clmd->hairdata) {
    return 0.0f;
  }
 
  for (uint i = 0; i < cloth->primitive_num; i++) {
    const blender::int3 tri = vert_tris[i];
 
    if (cloth_get_pressure_weights(clmd, tri, weights)) {
      vol += SIM_tri_tetra_volume_signed_6x(data, tri[0], tri[1], tri[2]);
    }
  }
 
  /* We need to divide by 6 to get the actual volume. */
  vol = vol / 6.0f;
 
  return vol;
}
 
static float cloth_calc_rest_volume(ClothModifierData *clmd)
{
  /* Calculate the (closed) cloth volume. */
  Cloth *cloth = clmd->clothObject;
  const blender::int3 *vert_tris = cloth->vert_tris;
  const ClothVertex *v = cloth->verts;
  float weights[3] = {1.0f, 1.0f, 1.0f};
  float vol = 0;
 
  /* Early exit for hair, as it never has volume. */
  if (clmd->hairdata) {
    return 0.0f;
  }
 
  for (uint i = 0; i < cloth->primitive_num; i++) {
    const blender::int3 tri = vert_tris[i];
 
    if (cloth_get_pressure_weights(clmd, tri, weights)) {
      vol += volume_tri_tetrahedron_signed_v3_6x(
          v[tri[0]].xrest, v[tri[1]].xrest, v[tri[2]].xrest);
    }
  }
 
  /* We need to divide by 6 to get the actual volume. */
  vol = vol / 6.0f;
 
  return vol;
}
 
static float cloth_calc_average_pressure(ClothModifierData *clmd, const float *vertex_pressure)
{
  Cloth *cloth = clmd->clothObject;
  const blender::int3 *vert_tris = cloth->vert_tris;
  Implicit_Data *data = cloth->implicit;
  float weights[3] = {1.0f, 1.0f, 1.0f};
  float total_force = 0;
  float total_area = 0;
 
  for (uint i = 0; i < cloth->primitive_num; i++) {
    const blender::int3 tri = vert_tris[i];
 
    if (cloth_get_pressure_weights(clmd, tri, weights)) {
      float area = SIM_tri_area(data, tri[0], tri[1], tri[2]);
 
      total_force += (vertex_pressure[tri[0]] + vertex_pressure[tri[1]] +
                      vertex_pressure[tri[2]]) *
                     area / 3.0f;
      total_area += area;
    }
  }
 
  return total_force / total_area;
}
 
int SIM_cloth_solver_init(Object * /*ob*/, ClothModifierData *clmd)
{
  Cloth *cloth = clmd->clothObject;
  ClothVertex *verts = cloth->verts;
  const float ZERO[3] = {0.0f, 0.0f, 0.0f};
  Implicit_Data *id;
  uint i, nondiag;
 
  nondiag = cloth_count_nondiag_blocks(cloth);
  cloth->implicit = id = SIM_mass_spring_solver_create(cloth->mvert_num, nondiag);
 
  for (i = 0; i < cloth->mvert_num; i++) {
    SIM_mass_spring_set_implicit_vertex_mass(id, i, verts[i].mass);
  }
 
  for (i = 0; i < cloth->mvert_num; i++) {
    SIM_mass_spring_set_motion_state(id, i, verts[i].x, ZERO);
  }
 
  return 1;
}
 
void SIM_mass_spring_set_implicit_vertex_mass(Implicit_Data *data, int index, float mass)
{
  SIM_mass_spring_set_vertex_mass(data, index, mass);
}
 
void SIM_cloth_solver_free(ClothModifierData *clmd)
{
  Cloth *cloth = clmd->clothObject;
 
  if (cloth->implicit) {
    SIM_mass_spring_solver_free(cloth->implicit);
    cloth->implicit = nullptr;
  }
}
 
void SIM_cloth_solver_set_positions(ClothModifierData *clmd)
{
  Cloth *cloth = clmd->clothObject;
  ClothVertex *verts = cloth->verts;
  uint mvert_num = cloth->mvert_num, i;
  ClothHairData *cloth_hairdata = clmd->hairdata;
  Implicit_Data *id = cloth->implicit;
 
  for (i = 0; i < mvert_num; i++) {
    if (cloth_hairdata) {
      ClothHairData *root = &cloth_hairdata[i];
      SIM_mass_spring_set_rest_transform(id, i, root->rot);
    }
    else {
      SIM_mass_spring_set_rest_transform(id, i, I3);
    }
 
    SIM_mass_spring_set_motion_state(id, i, verts[i].x, verts[i].v);
  }
}
 
void SIM_cloth_solver_set_volume(ClothModifierData *clmd)
{
  Cloth *cloth = clmd->clothObject;
 
  cloth->initial_mesh_volume = cloth_calc_rest_volume(clmd);
}
 
/* Init constraint matrix
 * This is part of the modified CG method suggested by Baraff/Witkin in
 * "Large Steps in Cloth Simulation" (SIGGRAPH 1998)
 */
static void cloth_setup_constraints(ClothModifierData *clmd)
{
  Cloth *cloth = clmd->clothObject;
  Implicit_Data *data = cloth->implicit;
  ClothVertex *verts = cloth->verts;
  int mvert_num = cloth->mvert_num;
  int v;
 
  const float ZERO[3] = {0.0f, 0.0f, 0.0f};
 
  SIM_mass_spring_clear_constraints(data);
 
  for (v = 0; v < mvert_num; v++) {
    if (verts[v].flags & CLOTH_VERT_FLAG_PINNED) {
      /* pinned vertex constraints */
      SIM_mass_spring_add_constraint_ndof0(data, v, ZERO); /* velocity is defined externally */
    }
 
    verts[v].impulse_count = 0;
  }
}

static int UNUSED_FUNCTION(cloth_calc_helper_forces)(
    Object * /*ob*/, ClothModifierData *clmd, float (*initial_cos)[3], float /*step*/, float dt)
{
  Cloth *cloth = clmd->clothObject;
  float (*cos)[3] = MEM_calloc_arrayN<float[3]>(cloth->mvert_num, "cos cloth_calc_helper_forces");
  float *masses = MEM_calloc_arrayN<float>(cloth->mvert_num, "cos cloth_calc_helper_forces");
  LinkNode *node;
  ClothSpring *spring;
  ClothVertex *cv;
  int i, steps;
 
  cv = cloth->verts;
  for (i = 0; i < cloth->mvert_num; i++, cv++) {
    copy_v3_v3(cos[i], cv->tx);
 
    if (cv->goal == 1.0f || len_squared_v3v3(initial_cos[i], cv->tx) != 0.0f) {
      masses[i] = 1e+10;
    }
    else {
      masses[i] = cv->mass;
    }
  }
 
  steps = 55;
  for (i = 0; i < steps; i++) {
    for (node = cloth->springs; node; node = node->next) {
      // ClothVertex *cv1, *cv2; /* UNUSED */
      int v1, v2;
      float len, c, l, vec[3];
 
      spring = (ClothSpring *)node->link;
      if (!ELEM(spring->type, CLOTH_SPRING_TYPE_STRUCTURAL, CLOTH_SPRING_TYPE_SHEAR)) {
        continue;
      }
 
      v1 = spring->ij;
      v2 = spring->kl;
      // cv1 = cloth->verts + v1; /* UNUSED. */
      // cv2 = cloth->verts + v2; /* UNUSED. */
      len = len_v3v3(cos[v1], cos[v2]);
 
      sub_v3_v3v3(vec, cos[v1], cos[v2]);
      normalize_v3(vec);
 
      c = (len - spring->restlen);
      if (c == 0.0f) {
        continue;
      }
 
      l = c / ((1.0f / masses[v1]) + (1.0f / masses[v2]));
 
      mul_v3_fl(vec, -(1.0f / masses[v1]) * l);
      add_v3_v3(cos[v1], vec);
 
      sub_v3_v3v3(vec, cos[v2], cos[v1]);
      normalize_v3(vec);
 
      mul_v3_fl(vec, -(1.0f / masses[v2]) * l);
      add_v3_v3(cos[v2], vec);
    }
  }
 
  cv = cloth->verts;
  for (i = 0; i < cloth->mvert_num; i++, cv++) {
    float vec[3];
 
    /* Compute forces. */
    sub_v3_v3v3(vec, cos[i], cv->tx);
    mul_v3_fl(vec, cv->mass * dt * 20.0f);
    add_v3_v3(cv->tv, vec);
    // copy_v3_v3(cv->tx, cos[i]);
  }
 
  MEM_freeN(cos);
  MEM_freeN(masses);
 
  return 1;
}
 
BLI_INLINE void cloth_calc_spring_force(ClothModifierData *clmd, ClothSpring *s)
{
  Cloth *cloth = clmd->clothObject;
  ClothSimSettings *parms = clmd->sim_parms;
  Implicit_Data *data = cloth->implicit;
  bool using_angular = parms->bending_model == CLOTH_BENDING_ANGULAR;
  bool resist_compress = (parms->flags & CLOTH_SIMSETTINGS_FLAG_RESIST_SPRING_COMPRESS) &&
                         !using_angular;
 
  s->flags &= ~CLOTH_SPRING_FLAG_NEEDED;
 
  /* Calculate force of bending springs. */
  if ((s->type & CLOTH_SPRING_TYPE_BENDING) && using_angular) {
#ifdef CLOTH_FORCE_SPRING_BEND
    float k, scaling;
 
    s->flags |= CLOTH_SPRING_FLAG_NEEDED;
 
    scaling = parms->bending + s->ang_stiffness * fabsf(parms->max_bend - parms->bending);
    /* Multiplying by 0.1, just to scale the forces to more reasonable values. */
    k = scaling * s->restlen * 0.1f;
 
    SIM_mass_spring_force_spring_angular(
        data, s->ij, s->kl, s->pa, s->pb, s->la, s->lb, s->restang, k, parms->bending_damping);
#endif
  }
 
  /* Calculate force of structural + shear springs. */
  if (s->type &
      (CLOTH_SPRING_TYPE_STRUCTURAL | CLOTH_SPRING_TYPE_SEWING | CLOTH_SPRING_TYPE_INTERNAL))
  {
#ifdef CLOTH_FORCE_SPRING_STRUCTURAL
    float k_tension, scaling_tension;
 
    s->flags |= CLOTH_SPRING_FLAG_NEEDED;
 
    scaling_tension = parms->tension +
                      s->lin_stiffness * fabsf(parms->max_tension - parms->tension);
    k_tension = scaling_tension / (parms->avg_spring_len + FLT_EPSILON);
 
    if (s->type & CLOTH_SPRING_TYPE_SEWING) {
      /* TODO: verify, half verified (couldn't see error)
       * sewing springs usually have a large distance at first so clamp the force so we don't get
       * tunneling through collision objects. */
      SIM_mass_spring_force_spring_linear(data,
                                          s->ij,
                                          s->kl,
                                          s->restlen,
                                          k_tension,
                                          parms->tension_damp,
                                          0.0f,
                                          0.0f,
                                          false,
                                          false,
                                          parms->max_sewing);
    }
    else if (s->type & CLOTH_SPRING_TYPE_STRUCTURAL) {
      float k_compression, scaling_compression;
      scaling_compression = parms->compression +
                            s->lin_stiffness * fabsf(parms->max_compression - parms->compression);
      k_compression = scaling_compression / (parms->avg_spring_len + FLT_EPSILON);
 
      SIM_mass_spring_force_spring_linear(data,
                                          s->ij,
                                          s->kl,
                                          s->restlen,
                                          k_tension,
                                          parms->tension_damp,
                                          k_compression,
                                          parms->compression_damp,
                                          resist_compress,
                                          using_angular,
                                          0.0f);
    }
    else {
      /* CLOTH_SPRING_TYPE_INTERNAL */
      BLI_assert(s->type & CLOTH_SPRING_TYPE_INTERNAL);
 
      scaling_tension = parms->internal_tension +
                        s->lin_stiffness *
                            fabsf(parms->max_internal_tension - parms->internal_tension);
      k_tension = scaling_tension / (parms->avg_spring_len + FLT_EPSILON);
      float scaling_compression = parms->internal_compression +
                                  s->lin_stiffness * fabsf(parms->max_internal_compression -
                                                           parms->internal_compression);
      float k_compression = scaling_compression / (parms->avg_spring_len + FLT_EPSILON);
 
      float k_tension_damp = parms->tension_damp;
      float k_compression_damp = parms->compression_damp;
 
      if (k_tension == 0.0f) {
        /* No damping so it behaves as if no tension spring was there at all. */
        k_tension_damp = 0.0f;
      }
 
      if (k_compression == 0.0f) {
        /* No damping so it behaves as if no compression spring was there at all. */
        k_compression_damp = 0.0f;
      }
 
      SIM_mass_spring_force_spring_linear(data,
                                          s->ij,
                                          s->kl,
                                          s->restlen,
                                          k_tension,
                                          k_tension_damp,
                                          k_compression,
                                          k_compression_damp,
                                          resist_compress,
                                          using_angular,
                                          0.0f);
    }
#endif
  }
  else if (s->type & CLOTH_SPRING_TYPE_SHEAR) {
#ifdef CLOTH_FORCE_SPRING_SHEAR
    float k, scaling;
 
    s->flags |= CLOTH_SPRING_FLAG_NEEDED;
 
    scaling = parms->shear + s->lin_stiffness * fabsf(parms->max_shear - parms->shear);
    k = scaling / (parms->avg_spring_len + FLT_EPSILON);
 
    SIM_mass_spring_force_spring_linear(data,
                                        s->ij,
                                        s->kl,
                                        s->restlen,
                                        k,
                                        parms->shear_damp,
                                        0.0f,
                                        0.0f,
                                        resist_compress,
                                        false,
                                        0.0f);
#endif
  }
  else if (s->type & CLOTH_SPRING_TYPE_BENDING) { /* calculate force of bending springs */
#ifdef CLOTH_FORCE_SPRING_BEND
    float kb, cb, scaling;
 
    s->flags |= CLOTH_SPRING_FLAG_NEEDED;
 
    scaling = parms->bending + s->lin_stiffness * fabsf(parms->max_bend - parms->bending);
    kb = scaling / (20.0f * (parms->avg_spring_len + FLT_EPSILON));
 
    /* Fix for #45084 for cloth stiffness must have cb proportional to kb */
    cb = kb * parms->bending_damping;
 
    SIM_mass_spring_force_spring_bending(data, s->ij, s->kl, s->restlen, kb, cb);
#endif
  }
  else if (s->type & CLOTH_SPRING_TYPE_BENDING_HAIR) {
#ifdef CLOTH_FORCE_SPRING_BEND
    float kb, cb, scaling;
 
    s->flags |= CLOTH_SPRING_FLAG_NEEDED;
 
    /* XXX WARNING: angular bending springs for hair apply stiffness factor as an overall factor,
     * unlike cloth springs! this is crap, but needed due to cloth/hair mixing ... max_bend factor
     * is not even used for hair, so ...
     */
    scaling = s->lin_stiffness * parms->bending;
    kb = scaling / (20.0f * (parms->avg_spring_len + FLT_EPSILON));
 
    /* Fix for #45084 for cloth stiffness must have cb proportional to kb */
    cb = kb * parms->bending_damping;
 
    /* XXX assuming same restlen for ij and jk segments here,
     * this can be done correctly for hair later. */
    SIM_mass_spring_force_spring_bending_hair(data, s->ij, s->kl, s->mn, s->target, kb, cb);
 
#  if 0
    {
      float x_kl[3], x_mn[3], v[3], d[3];
 
      SIM_mass_spring_get_motion_state(data, s->kl, x_kl, v);
      SIM_mass_spring_get_motion_state(data, s->mn, x_mn, v);
 
      BKE_sim_debug_data_add_dot(clmd->debug_data, x_kl, 0.9, 0.9, 0.9, "target", 7980, s->kl);
      BKE_sim_debug_data_add_line(
          clmd->debug_data, x_kl, x_mn, 0.8, 0.8, 0.8, "target", 7981, s->kl);
 
      copy_v3_v3(d, s->target);
      BKE_sim_debug_data_add_vector(
          clmd->debug_data, x_kl, d, 0.8, 0.8, 0.2, "target", 7982, s->kl);
 
      // copy_v3_v3(d, s->target_ij);
      // BKE_sim_debug_data_add_vector(clmd->debug_data, x, d, 1, 0.4, 0.4, "target", 7983, s->kl);
    }
#  endif
#endif
  }
}
 
static void hair_get_boundbox(ClothModifierData *clmd,
                              blender::float3 &gmin,
                              blender::float3 &gmax)
{
  Cloth *cloth = clmd->clothObject;
  Implicit_Data *data = cloth->implicit;
  uint mvert_num = cloth->mvert_num;
  int i;
 
  INIT_MINMAX(gmin, gmax);
  for (i = 0; i < mvert_num; i++) {
    blender::float3 x;
    SIM_mass_spring_get_motion_state(data, i, x, nullptr);
    blender::math::min_max(x, gmin, gmax);
  }
}
 
static void cloth_calc_force(
    Scene *scene, ClothModifierData *clmd, float /*frame*/, ListBase *effectors, float time)
{
  /* Collect forces and derivatives: F, dFdX, dFdV. */
  Cloth *cloth = clmd->clothObject;
  ClothSimSettings *parms = clmd->sim_parms;
  Implicit_Data *data = cloth->implicit;
  uint i = 0;
  float drag = clmd->sim_parms->Cvi * 0.01f; /* viscosity of air scaled in percent */
  float gravity[3] = {0.0f, 0.0f, 0.0f};
  const blender::int3 *vert_tris = cloth->vert_tris;
  uint mvert_num = cloth->mvert_num;
  ClothVertex *vert;
 
#ifdef CLOTH_FORCE_GRAVITY
  /* global acceleration (gravitation) */
  if (scene->physics_settings.flag & PHYS_GLOBAL_GRAVITY) {
    /* scale gravity force */
    mul_v3_v3fl(gravity,
                scene->physics_settings.gravity,
                0.001f * clmd->sim_parms->effector_weights->global_gravity);
  }
 
  vert = cloth->verts;
  for (i = 0; i < cloth->mvert_num; i++, vert++) {
    SIM_mass_spring_force_gravity(data, i, vert->mass, gravity);
 
    /* Vertex goal springs */
    if (!(vert->flags & CLOTH_VERT_FLAG_PINNED) && (vert->goal > FLT_EPSILON)) {
      float goal_x[3], goal_v[3];
      float k;
 
      /* divide by time_scale to prevent goal vertices' delta locations from being multiplied */
      interp_v3_v3v3(goal_x, vert->xold, vert->xconst, time / clmd->sim_parms->time_scale);
      sub_v3_v3v3(goal_v, vert->xconst, vert->xold); /* distance covered over dt==1 */
 
      k = vert->goal * clmd->sim_parms->goalspring /
          (clmd->sim_parms->avg_spring_len + FLT_EPSILON);
 
      SIM_mass_spring_force_spring_goal(
          data, i, goal_x, goal_v, k, clmd->sim_parms->goalfrict * 0.01f);
    }
  }
#endif
 
  // cloth_calc_volume_force(clmd);
 
#ifdef CLOTH_FORCE_DRAG
  SIM_mass_spring_force_drag(data, drag);
#endif
  /* handle pressure forces (making sure that this never gets computed for hair). */
  if ((parms->flags & CLOTH_SIMSETTINGS_FLAG_PRESSURE) && (clmd->hairdata == nullptr)) {
    /* The difference in pressure between the inside and outside of the mesh. */
    float pressure_difference = 0.0f;
    float volume_factor = 1.0f;
 
    float init_vol;
    if (parms->flags & CLOTH_SIMSETTINGS_FLAG_PRESSURE_VOL) {
      init_vol = clmd->sim_parms->target_volume;
    }
    else {
      init_vol = cloth->initial_mesh_volume;
    }
 
    /* Check if we need to calculate the volume of the mesh. */
    if (init_vol > 1E-6f) {
      float f;
      float vol = cloth_calc_volume(clmd);
 
      /* If the volume is the same don't apply any pressure. */
      volume_factor = init_vol / vol;
      pressure_difference = volume_factor - 1;
 
      /* Calculate an artificial maximum value for cloth pressure. */
      f = fabs(clmd->sim_parms->uniform_pressure_force) + 200.0f;
 
      /* Clamp the cloth pressure to the calculated maximum value. */
      CLAMP_MAX(pressure_difference, f);
    }
 
    pressure_difference += clmd->sim_parms->uniform_pressure_force;
    pressure_difference *= clmd->sim_parms->pressure_factor;
 
    /* Compute the hydrostatic pressure gradient if enabled. */
    float fluid_density = clmd->sim_parms->fluid_density * 1000; /* kg/l -> kg/m3 */
    float *hydrostatic_pressure = nullptr;
 
    if (fabs(fluid_density) > 1e-6f) {
      float hydrostatic_vector[3];
      copy_v3_v3(hydrostatic_vector, gravity);
 
      /* When the fluid is inside the object, factor in the acceleration of
       * the object into the pressure field, as gravity is indistinguishable
       * from acceleration from the inside. */
      if (fluid_density > 0) {
        sub_v3_v3(hydrostatic_vector, cloth->average_acceleration);
 
        /* Preserve the total mass by scaling density to match the change in volume. */
        fluid_density *= volume_factor;
      }
 
      mul_v3_fl(hydrostatic_vector, fluid_density);
 
      /* Compute an array of per-vertex hydrostatic pressure, and subtract the average. */
      hydrostatic_pressure = MEM_malloc_arrayN<float>(mvert_num, "hydrostatic pressure gradient");
 
      cloth_calc_pressure_gradient(clmd, hydrostatic_vector, hydrostatic_pressure);
 
      pressure_difference -= cloth_calc_average_pressure(clmd, hydrostatic_pressure);
    }
 
    /* Apply pressure. */
    if (hydrostatic_pressure || fabs(pressure_difference) > 1E-6f) {
      float weights[3] = {1.0f, 1.0f, 1.0f};
 
      for (i = 0; i < cloth->primitive_num; i++) {
        const blender::int3 tri = vert_tris[i];
 
        if (cloth_get_pressure_weights(clmd, tri, weights)) {
          SIM_mass_spring_force_pressure(
              data, tri[0], tri[1], tri[2], pressure_difference, hydrostatic_pressure, weights);
        }
      }
    }
 
    if (hydrostatic_pressure) {
      MEM_freeN(hydrostatic_pressure);
    }
  }
 
  /* handle external forces like wind */
  if (effectors) {
    bool is_not_hair = (clmd->hairdata == nullptr) && (cloth->primitive_num > 0);
    bool has_wind = false, has_force = false;
 
    /* cache per-vertex forces to avoid redundant calculation */
    float (*winvec)[3] = MEM_calloc_arrayN<float[3]>(mvert_num * 2, "effector forces");
    float (*forcevec)[3] = is_not_hair ? winvec + mvert_num : winvec;
 
    for (i = 0; i < cloth->mvert_num; i++) {
      float x[3], v[3];
      EffectedPoint epoint;
 
      SIM_mass_spring_get_motion_state(data, i, x, v);
      pd_point_from_loc(scene, x, v, i, &epoint);
      BKE_effectors_apply(effectors,
                          nullptr,
                          clmd->sim_parms->effector_weights,
                          &epoint,
                          forcevec[i],
                          winvec[i],
                          nullptr);
 
      has_wind = has_wind || !is_zero_v3(winvec[i]);
      has_force = has_force || !is_zero_v3(forcevec[i]);
    }
 
    /* Hair has only edges. */
    if (is_not_hair) {
      for (i = 0; i < cloth->primitive_num; i++) {
        const blender::int3 tri = vert_tris[i];
        if (has_wind) {
          SIM_mass_spring_force_face_wind(data, tri[0], tri[1], tri[2], winvec);
        }
        if (has_force) {
          SIM_mass_spring_force_face_extern(data, tri[0], tri[1], tri[2], forcevec);
        }
      }
    }
    else {
#if 0
      ClothHairData *hairdata = clmd->hairdata;
      ClothHairData *hair_ij, *hair_kl;
 
      for (LinkNode *link = cloth->springs; link; link = link->next) {
        ClothSpring *spring = (ClothSpring *)link->link;
        if (spring->type == CLOTH_SPRING_TYPE_STRUCTURAL) {
          if (hairdata) {
            hair_ij = &hairdata[spring->ij];
            hair_kl = &hairdata[spring->kl];
            SIM_mass_spring_force_edge_wind(
                data, spring->ij, spring->kl, hair_ij->radius, hair_kl->radius, winvec);
          }
          else {
            SIM_mass_spring_force_edge_wind(data, spring->ij, spring->kl, 1.0f, 1.0f, winvec);
          }
        }
      }
#else
      ClothHairData *hairdata = clmd->hairdata;
 
      vert = cloth->verts;
      for (i = 0; i < cloth->mvert_num; i++, vert++) {
        if (hairdata) {
          ClothHairData *hair = &hairdata[i];
          SIM_mass_spring_force_vertex_wind(data, i, hair->radius, winvec);
        }
        else {
          SIM_mass_spring_force_vertex_wind(data, i, 1.0f, winvec);
        }
      }
#endif
    }
 
    MEM_freeN(winvec);
  }
 
  /* calculate spring forces */
  for (LinkNode *link = cloth->springs; link; link = link->next) {
    ClothSpring *spring = (ClothSpring *)link->link;
    /* only handle active springs */
    if (!(spring->flags & CLOTH_SPRING_FLAG_DEACTIVATE)) {
      cloth_calc_spring_force(clmd, spring);
    }
  }
}
 
/* returns vertices' motion state */
BLI_INLINE void cloth_get_grid_location(Implicit_Data *data,
                                        float cell_scale,
                                        const float cell_offset[3],
                                        int index,
                                        float x[3],
                                        float v[3])
{
  SIM_mass_spring_get_position(data, index, x);
  SIM_mass_spring_get_new_velocity(data, index, v);
 
  mul_v3_fl(x, cell_scale);
  add_v3_v3(x, cell_offset);
}
 
/* returns next spring forming a continuous hair sequence */
BLI_INLINE LinkNode *hair_spring_next(LinkNode *spring_link)
{
  ClothSpring *spring = (ClothSpring *)spring_link->link;
  LinkNode *next = spring_link->next;
  if (next) {
    ClothSpring *next_spring = (ClothSpring *)next->link;
    if (next_spring->type == CLOTH_SPRING_TYPE_STRUCTURAL && next_spring->kl == spring->ij) {
      return next;
    }
  }
  return nullptr;
}
 
/* XXX this is nasty: cloth meshes do not explicitly store
 * the order of hair segments!
 * We have to rely on the spring build function for now,
 * which adds structural springs in reverse order:
 *   (3,4), (2,3), (1,2)
 * This is currently the only way to figure out hair geometry inside this code ...
 */
static LinkNode *cloth_continuum_add_hair_segments(HairGrid *grid,
                                                   const float cell_scale,
                                                   const float cell_offset[3],
                                                   Cloth *cloth,
                                                   LinkNode *spring_link)
{
  Implicit_Data *data = cloth->implicit;
  LinkNode *next_spring_link = nullptr; /* return value */
  ClothSpring *spring1, *spring2, *spring3;
  // ClothVertex *verts = cloth->verts;
  // ClothVertex *vert3, *vert4;
  float x1[3], v1[3], x2[3], v2[3], x3[3], v3[3], x4[3], v4[3];
  float dir1[3], dir2[3], dir3[3];
 
  spring1 = nullptr;
  spring2 = nullptr;
  spring3 = (ClothSpring *)spring_link->link;
 
  zero_v3(x1);
  zero_v3(v1);
  zero_v3(dir1);
  zero_v3(x2);
  zero_v3(v2);
  zero_v3(dir2);
 
  // vert3 = &verts[spring3->kl];
  cloth_get_grid_location(data, cell_scale, cell_offset, spring3->kl, x3, v3);
  // vert4 = &verts[spring3->ij];
  cloth_get_grid_location(data, cell_scale, cell_offset, spring3->ij, x4, v4);
  sub_v3_v3v3(dir3, x4, x3);
  normalize_v3(dir3);
 
  while (spring_link) {
    /* move on */
    spring1 = spring2;
    spring2 = spring3;
 
    // vert3 = vert4;
 
    copy_v3_v3(x1, x2);
    copy_v3_v3(v1, v2);
    copy_v3_v3(x2, x3);
    copy_v3_v3(v2, v3);
    copy_v3_v3(x3, x4);
    copy_v3_v3(v3, v4);
 
    copy_v3_v3(dir1, dir2);
    copy_v3_v3(dir2, dir3);
 
    /* read next segment */
    next_spring_link = spring_link->next;
    spring_link = hair_spring_next(spring_link);
 
    if (spring_link) {
      spring3 = (ClothSpring *)spring_link->link;
      // vert4 = &verts[spring3->ij];
      cloth_get_grid_location(data, cell_scale, cell_offset, spring3->ij, x4, v4);
      sub_v3_v3v3(dir3, x4, x3);
      normalize_v3(dir3);
    }
    else {
      spring3 = nullptr;
      // vert4 = nullptr;
      zero_v3(x4);
      zero_v3(v4);
      zero_v3(dir3);
    }
 
    SIM_hair_volume_add_segment(grid,
                                x1,
                                v1,
                                x2,
                                v2,
                                x3,
                                v3,
                                x4,
                                v4,
                                spring1 ? dir1 : nullptr,
                                dir2,
                                spring3 ? dir3 : nullptr);
  }
 
  return next_spring_link;
}
 
static void cloth_continuum_fill_grid(HairGrid *grid, Cloth *cloth)
{
#if 0
  Implicit_Data *data = cloth->implicit;
  int mvert_num = cloth->mvert_num;
  ClothVertex *vert;
  int i;
 
  for (i = 0, vert = cloth->verts; i < mvert_num; i++, vert++) {
    float x[3], v[3];
 
    cloth_get_vertex_motion_state(data, vert, x, v);
    SIM_hair_volume_add_vertex(grid, x, v);
  }
#else
  LinkNode *link;
  float cellsize, gmin[3], cell_scale, cell_offset[3];
 
  /* scale and offset for transforming vertex locations into grid space
   * (cell size is 0..1, gmin becomes origin)
   */
  SIM_hair_volume_grid_geometry(grid, &cellsize, nullptr, gmin, nullptr);
  cell_scale = cellsize > 0.0f ? 1.0f / cellsize : 0.0f;
  mul_v3_v3fl(cell_offset, gmin, cell_scale);
  negate_v3(cell_offset);
 
  link = cloth->springs;
  while (link) {
    ClothSpring *spring = (ClothSpring *)link->link;
    if (spring->type == CLOTH_SPRING_TYPE_STRUCTURAL) {
      link = cloth_continuum_add_hair_segments(grid, cell_scale, cell_offset, cloth, link);
    }
    else {
      link = link->next;
    }
  }
#endif
  SIM_hair_volume_normalize_vertex_grid(grid);
}
 
static void cloth_continuum_step(ClothModifierData *clmd, float dt)
{
  ClothSimSettings *parms = clmd->sim_parms;
  Cloth *cloth = clmd->clothObject;
  Implicit_Data *data = cloth->implicit;
  int mvert_num = cloth->mvert_num;
  ClothVertex *vert;
 
  const float fluid_factor = 0.95f; /* blend between PIC and FLIP methods */
  float smoothfac = parms->velocity_smooth;
  /* XXX FIXME arbitrary factor!!! this should be based on some intuitive value instead,
   * like number of hairs per cell and time decay instead of "strength"
   */
  float density_target = parms->density_target;
  float density_strength = parms->density_strength;
  blender::float3 gmin, gmax;
  int i;
 
  /* clear grid info */
  zero_v3_int(clmd->hair_grid_res);
  zero_v3(clmd->hair_grid_min);
  zero_v3(clmd->hair_grid_max);
  clmd->hair_grid_cellsize = 0.0f;
 
  hair_get_boundbox(clmd, gmin, gmax);
 
  /* gather velocities & density */
  if (smoothfac > 0.0f || density_strength > 0.0f) {
    HairGrid *grid = SIM_hair_volume_create_vertex_grid(
        clmd->sim_parms->voxel_cell_size, gmin, gmax);
 
    cloth_continuum_fill_grid(grid, cloth);
 
    /* main hair continuum solver */
    SIM_hair_volume_solve_divergence(grid, dt, density_target, density_strength);
 
    for (i = 0, vert = cloth->verts; i < mvert_num; i++, vert++) {
      float x[3], v[3], nv[3];
 
      /* calculate volumetric velocity influence */
      SIM_mass_spring_get_position(data, i, x);
      SIM_mass_spring_get_new_velocity(data, i, v);
 
      SIM_hair_volume_grid_velocity(grid, x, v, fluid_factor, nv);
 
      interp_v3_v3v3(nv, v, nv, smoothfac);
 
      /* apply on hair data */
      SIM_mass_spring_set_new_velocity(data, i, nv);
    }
 
    /* store basic grid info in the modifier data */
    SIM_hair_volume_grid_geometry(grid,
                                  &clmd->hair_grid_cellsize,
                                  clmd->hair_grid_res,
                                  clmd->hair_grid_min,
                                  clmd->hair_grid_max);
 
#if 0 /* DEBUG hair velocity vector field */
    {
      const int size = 64;
      int i, j;
      float offset[3], a[3], b[3];
      const int axis = 0;
      const float shift = 0.0f;
 
      copy_v3_v3(offset, clmd->hair_grid_min);
      zero_v3(a);
      zero_v3(b);
 
      offset[axis] = shift * clmd->hair_grid_cellsize;
      a[(axis + 1) % 3] = clmd->hair_grid_max[(axis + 1) % 3] -
                          clmd->hair_grid_min[(axis + 1) % 3];
      b[(axis + 2) % 3] = clmd->hair_grid_max[(axis + 2) % 3] -
                          clmd->hair_grid_min[(axis + 2) % 3];
 
      BKE_sim_debug_data_clear_category(clmd->debug_data, "grid velocity");
      for (j = 0; j < size; j++) {
        for (i = 0; i < size; i++) {
          float x[3], v[3], gvel[3], gvel_smooth[3], gdensity;
 
          madd_v3_v3v3fl(x, offset, a, float(i) / float(size - 1));
          madd_v3_v3fl(x, b, float(j) / float(size - 1));
          zero_v3(v);
 
          SIM_hair_volume_grid_interpolate(
              grid, x, &gdensity, gvel, gvel_smooth, nullptr, nullptr);
 
#  if 0
          BKE_sim_debug_data_add_circle(
              clmd->debug_data, x, gdensity, 0.7, 0.3, 1, "grid density", i, j, 3111);
#  endif
          if (!is_zero_v3(gvel) || !is_zero_v3(gvel_smooth)) {
            float dvel[3];
            sub_v3_v3v3(dvel, gvel_smooth, gvel);
#  if 0
            BKE_sim_debug_data_add_vector(
                clmd->debug_data, x, gvel, 0.4, 0, 1, "grid velocity", i, j, 3112);
            BKE_sim_debug_data_add_vector(
                clmd->debug_data, x, gvel_smooth, 0.6, 1, 1, "grid velocity", i, j, 3113);
#  endif
            BKE_sim_debug_data_add_vector(
                clmd->debug_data, x, dvel, 0.4, 1, 0.7, "grid velocity", i, j, 3114);
#  if 0
            if (gdensity > 0.0f) {
              float col0[3] = {0.0, 0.0, 0.0};
              float col1[3] = {0.0, 1.0, 0.0};
              float col[3];
 
              interp_v3_v3v3(col,
                             col0,
                             col1,
                             std::clamp(gdensity * clmd->sim_parms->density_strength, 0.0, 1.0));
#    if 0
              BKE_sim_debug_data_add_circle(clmd->debug_data,
                                            x,
                                            gdensity * clmd->sim_parms->density_strength,
                                            0,
                                            1,
                                            0.4,
                                            "grid velocity",
                                            i,
                                            j,
                                            3115);
              BKE_sim_debug_data_add_dot(
                  clmd->debug_data, x, col[0], col[1], col[2], "grid velocity", i, j, 3115);
#    endif
              BKE_sim_debug_data_add_circle(
                  clmd->debug_data, x, 0.01f, col[0], col[1], col[2], "grid velocity", i, j, 3115);
            }
#  endif
          }
        }
      }
    }
#endif
 
    SIM_hair_volume_free_vertex_grid(grid);
  }
}
 
#if 0
static void cloth_calc_volume_force(ClothModifierData *clmd)
{
  ClothSimSettings *parms = clmd->sim_parms;
  Cloth *cloth = clmd->clothObject;
  Implicit_Data *data = cloth->implicit;
  int mvert_num = cloth->mvert_num;
  ClothVertex *vert;
 
  /* 2.0f is an experimental value that seems to give good results */
  float smoothfac = 2.0f * parms->velocity_smooth;
  float collfac = 2.0f * parms->collider_friction;
  float pressfac = parms->pressure;
  float minpress = parms->pressure_threshold;
  float gmin[3], gmax[3];
  int i;
 
  hair_get_boundbox(clmd, gmin, gmax);
 
  /* gather velocities & density */
  if (smoothfac > 0.0f || pressfac > 0.0f) {
    HairVertexGrid *vertex_grid = SIM_hair_volume_create_vertex_grid(
        clmd->sim_parms->voxel_res, gmin, gmax);
 
    vert = cloth->verts;
    for (i = 0; i < mvert_num; i++, vert++) {
      float x[3], v[3];
 
      if (vert->solver_index < 0) {
        copy_v3_v3(x, vert->x);
        copy_v3_v3(v, vert->v);
      }
      else {
        SIM_mass_spring_get_motion_state(data, vert->solver_index, x, v);
      }
      SIM_hair_volume_add_vertex(vertex_grid, x, v);
    }
    SIM_hair_volume_normalize_vertex_grid(vertex_grid);
 
    vert = cloth->verts;
    for (i = 0; i < mvert_num; i++, vert++) {
      float x[3], v[3], f[3], dfdx[3][3], dfdv[3][3];
 
      if (vert->solver_index < 0) {
        continue;
      }
 
      /* calculate volumetric forces */
      SIM_mass_spring_get_motion_state(data, vert->solver_index, x, v);
      SIM_hair_volume_vertex_grid_forces(
          vertex_grid, x, v, smoothfac, pressfac, minpress, f, dfdx, dfdv);
      /* apply on hair data */
      SIM_mass_spring_force_extern(data, vert->solver_index, f, dfdx, dfdv);
    }
 
    SIM_hair_volume_free_vertex_grid(vertex_grid);
  }
}
#endif
 
static void cloth_calc_average_acceleration(ClothModifierData *clmd, float dt)
{
  Cloth *cloth = clmd->clothObject;
  Implicit_Data *data = cloth->implicit;
  int i, mvert_num = cloth->mvert_num;
  float total[3] = {0.0f, 0.0f, 0.0f};
 
  for (i = 0; i < mvert_num; i++) {
    float v[3], nv[3];
 
    SIM_mass_spring_get_velocity(data, i, v);
    SIM_mass_spring_get_new_velocity(data, i, nv);
 
    sub_v3_v3(nv, v);
    add_v3_v3(total, nv);
  }
 
  mul_v3_fl(total, 1.0f / dt / mvert_num);
 
  /* Smooth the data using a running average to prevent instability.
   * This is effectively an abstraction of the wave propagation speed in fluid. */
  interp_v3_v3v3(cloth->average_acceleration, total, cloth->average_acceleration, powf(0.25f, dt));
}
 
static void cloth_solve_collisions(
    Depsgraph *depsgraph, Object *ob, ClothModifierData *clmd, float step, float dt)
{
  Cloth *cloth = clmd->clothObject;
  Implicit_Data *id = cloth->implicit;
  ClothVertex *verts = cloth->verts;
  int mvert_num = cloth->mvert_num;
  const float time_multiplier = 1.0f / (clmd->sim_parms->dt * clmd->sim_parms->timescale);
  int i;
 
  if (!(clmd->coll_parms->flags &
        (CLOTH_COLLSETTINGS_FLAG_ENABLED | CLOTH_COLLSETTINGS_FLAG_SELF)))
  {
    return;
  }
 
  if (!clmd->clothObject->bvhtree) {
    return;
  }
 
  SIM_mass_spring_solve_positions(id, dt);
 
  /* Update verts to current positions. */
  for (i = 0; i < mvert_num; i++) {
    SIM_mass_spring_get_new_position(id, i, verts[i].tx);
 
    sub_v3_v3v3(verts[i].tv, verts[i].tx, verts[i].txold);
    zero_v3(verts[i].dcvel);
  }
 
  if (cloth_bvh_collision(
          depsgraph, ob, clmd, step / clmd->sim_parms->timescale, dt / clmd->sim_parms->timescale))
  {
    for (i = 0; i < mvert_num; i++) {
      if ((clmd->sim_parms->vgroup_mass > 0) && (verts[i].flags & CLOTH_VERT_FLAG_PINNED)) {
        continue;
      }
 
      SIM_mass_spring_get_new_velocity(id, i, verts[i].tv);
      madd_v3_v3fl(verts[i].tv, verts[i].dcvel, time_multiplier);
      SIM_mass_spring_set_new_velocity(id, i, verts[i].tv);
    }
  }
}
 
static void cloth_clear_result(ClothModifierData *clmd)
{
  ClothSolverResult *sres = clmd->solver_result;
 
  sres->status = 0;
  sres->max_error = sres->min_error = sres->avg_error = 0.0f;
  sres->max_iterations = sres->min_iterations = 0;
  sres->avg_iterations = 0.0f;
}
 
static void cloth_record_result(ClothModifierData *clmd, ImplicitSolverResult *result, float dt)
{
  ClothSolverResult *sres = clmd->solver_result;
 
  if (sres->status) { /* already initialized ? */
    /* error only makes sense for successful iterations */
    if (result->status == SIM_SOLVER_SUCCESS) {
      sres->min_error = min_ff(sres->min_error, result->error);
      sres->max_error = max_ff(sres->max_error, result->error);
      sres->avg_error += result->error * dt;
    }
 
    sres->min_iterations = min_ii(sres->min_iterations, result->iterations);
    sres->max_iterations = max_ii(sres->max_iterations, result->iterations);
    sres->avg_iterations += float(result->iterations) * dt;
  }
  else {
    /* error only makes sense for successful iterations */
    if (result->status == SIM_SOLVER_SUCCESS) {
      sres->min_error = sres->max_error = result->error;
      sres->avg_error += result->error * dt;
    }
 
    sres->min_iterations = sres->max_iterations = result->iterations;
    sres->avg_iterations += float(result->iterations) * dt;
  }
 
  sres->status |= result->status;
}
 
int SIM_cloth_solve(
    Depsgraph *depsgraph, Object *ob, float frame, ClothModifierData *clmd, ListBase *effectors)
{
  /* Hair currently is a cloth sim in disguise ...
   * Collision detection and volumetrics work differently then.
   * Bad design, TODO
   */
  Scene *scene = DEG_get_evaluated_scene(depsgraph);
  const bool is_hair = (clmd->hairdata != nullptr);
 
  uint i = 0;
  float step = 0.0f, tf = clmd->sim_parms->timescale;
  Cloth *cloth = clmd->clothObject;
  ClothVertex *verts = cloth->verts /*, *cv*/;
  uint mvert_num = cloth->mvert_num;
  float dt = clmd->sim_parms->dt * clmd->sim_parms->timescale;
  Implicit_Data *id = cloth->implicit;
 
  /* Hydrostatic pressure gradient of the fluid inside the object is affected by acceleration. */
  bool use_acceleration = (clmd->sim_parms->flags & CLOTH_SIMSETTINGS_FLAG_PRESSURE) &&
                          (clmd->sim_parms->fluid_density > 0);
 
  BKE_sim_debug_data_clear_category("collision");
 
  if (!clmd->solver_result) {
    clmd->solver_result = MEM_callocN<ClothSolverResult>("cloth solver result");
  }
  cloth_clear_result(clmd);
 
  if (clmd->sim_parms->vgroup_mass > 0) { /* Do goal stuff. */
    for (i = 0; i < mvert_num; i++) {
      /* update velocities with constrained velocities from pinned verts */
      if (verts[i].flags & CLOTH_VERT_FLAG_PINNED) {
        float v[3];
        sub_v3_v3v3(v, verts[i].xconst, verts[i].xold);
        // mul_v3_fl(v, clmd->sim_parms->stepsPerFrame);
        /* divide by time_scale to prevent constrained velocities from being multiplied */
        mul_v3_fl(v, 1.0f / clmd->sim_parms->time_scale);
        SIM_mass_spring_set_velocity(id, i, v);
      }
    }
  }
 
  if (!use_acceleration) {
    zero_v3(cloth->average_acceleration);
  }
 
  while (step < tf) {
    ImplicitSolverResult result;
 
    /* setup vertex constraints for pinned vertices */
    cloth_setup_constraints(clmd);
 
    /* initialize forces to zero */
    SIM_mass_spring_clear_forces(id);
 
    /* calculate forces */
    cloth_calc_force(scene, clmd, frame, effectors, step);
 
    /* calculate new velocity and position */
    SIM_mass_spring_solve_velocities(id, dt, &result);
    cloth_record_result(clmd, &result, dt);
 
    /* Calculate collision impulses. */
    cloth_solve_collisions(depsgraph, ob, clmd, step, dt);
 
    if (is_hair) {
      cloth_continuum_step(clmd, dt);
    }
 
    if (use_acceleration) {
      cloth_calc_average_acceleration(clmd, dt);
    }
 
    SIM_mass_spring_solve_positions(id, dt);
    SIM_mass_spring_apply_result(id);
 
    /* move pinned verts to correct position */
    for (i = 0; i < mvert_num; i++) {
      if (clmd->sim_parms->vgroup_mass > 0) {
        if (verts[i].flags & CLOTH_VERT_FLAG_PINNED) {
          float x[3];
          /* divide by time_scale to prevent pinned vertices'
           * delta locations from being multiplied */
          interp_v3_v3v3(
              x, verts[i].xold, verts[i].xconst, (step + dt) / clmd->sim_parms->time_scale);
          SIM_mass_spring_set_position(id, i, x);
        }
      }
 
      SIM_mass_spring_get_motion_state(id, i, verts[i].txold, nullptr);
    }
 
    step += dt;
  }
 
  /* copy results back to cloth data */
  for (i = 0; i < mvert_num; i++) {
    SIM_mass_spring_get_motion_state(id, i, verts[i].x, verts[i].v);
    copy_v3_v3(verts[i].txold, verts[i].x);
  }
 
  return 1;
}