/*
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
 *
 * The Original Code is Copyright (C) 2001-2002 by NaN Holding BV.
 * All rights reserved.
 */

/** \file
 * \ingroup bke
 */

#include <ctype.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#include <stdio.h>
#include <float.h>

#include "MEM_guardedalloc.h"

#include "BLI_math.h"
#include "BLI_listbase.h"
#include "BLI_string.h"
#include "BLI_ghash.h"
#include "BLI_task.h"
#include "BLI_utildefines.h"
#include "BLI_alloca.h"

#include "DNA_anim_types.h"
#include "DNA_armature_types.h"
#include "DNA_constraint_types.h"
#include "DNA_gpencil_types.h"
#include "DNA_mesh_types.h"
#include "DNA_lattice_types.h"
#include "DNA_listBase.h"
#include "DNA_meshdata_types.h"
#include "DNA_scene_types.h"
#include "DNA_object_types.h"

#include "BKE_animsys.h"
#include "BKE_armature.h"
#include "BKE_action.h"
#include "BKE_anim.h"
#include "BKE_constraint.h"
#include "BKE_curve.h"
#include "BKE_deform.h"
#include "BKE_displist.h"
#include "BKE_idprop.h"
#include "BKE_library.h"
#include "BKE_lattice.h"
#include "BKE_main.h"
#include "BKE_object.h"
#include "BKE_scene.h"

#include "DEG_depsgraph_build.h"

#include "BIK_api.h"

#include "atomic_ops.h"

#include "CLG_log.h"

static CLG_LogRef LOG = {"bke.armature"};

/* **************** Generic Functions, data level *************** */

bArmature *BKE_armature_add(Main *bmain, const char *name)
{
  bArmature *arm;

  arm = BKE_libblock_alloc(bmain, ID_AR, name, 0);
  arm->deformflag = ARM_DEF_VGROUP | ARM_DEF_ENVELOPE;
  arm->flag = ARM_COL_CUSTOM; /* custom bone-group colors */
  arm->layer = 1;
  return arm;
}

bArmature *BKE_armature_from_object(Object *ob)
{
  if (ob->type == OB_ARMATURE) {
    return (bArmature *)ob->data;
  }
  return NULL;
}

int BKE_armature_bonelist_count(ListBase *lb)
{
  int i = 0;
  for (Bone *bone = lb->first; bone; bone = bone->next) {
    i += 1 + BKE_armature_bonelist_count(&bone->childbase);
  }

  return i;
}

void BKE_armature_bonelist_free(ListBase *lb)
{
  Bone *bone;

  for (bone = lb->first; bone; bone = bone->next) {
    if (bone->prop) {
      IDP_FreeProperty(bone->prop);
    }
    BKE_armature_bonelist_free(&bone->childbase);
  }

  BLI_freelistN(lb);
}

/** Free (or release) any data used by this armature (does not free the armature itself). */
void BKE_armature_free(bArmature *arm)
{
  BKE_animdata_free(&arm->id, false);

  BKE_armature_bone_hash_free(arm);
  BKE_armature_bonelist_free(&arm->bonebase);

  /* free editmode data */
  if (arm->edbo) {
    BLI_freelistN(arm->edbo);

    MEM_freeN(arm->edbo);
    arm->edbo = NULL;
  }
}

void BKE_armature_make_local(Main *bmain, bArmature *arm, const bool lib_local)
{
  BKE_id_make_local_generic(bmain, &arm->id, true, lib_local);
}

static void copy_bonechildren(Bone *bone_dst,
                              const Bone *bone_src,
                              const Bone *bone_src_act,
                              Bone **r_bone_dst_act,
                              const int flag)
{
  Bone *bone_src_child, *bone_dst_child;

  if (bone_src == bone_src_act) {
    *r_bone_dst_act = bone_dst;
  }

  if (bone_src->prop) {
    bone_dst->prop = IDP_CopyProperty_ex(bone_src->prop, flag);
  }

  /* Copy this bone's list */
  BLI_duplicatelist(&bone_dst->childbase, &bone_src->childbase);

  /* For each child in the list, update it's children */
  for (bone_src_child = bone_src->childbase.first, bone_dst_child = bone_dst->childbase.first;
       bone_src_child;
       bone_src_child = bone_src_child->next, bone_dst_child = bone_dst_child->next) {
    bone_dst_child->parent = bone_dst;
    copy_bonechildren(bone_dst_child, bone_src_child, bone_src_act, r_bone_dst_act, flag);
  }
}

static void copy_bonechildren_custom_handles(Bone *bone_dst, bArmature *arm_dst)
{
  Bone *bone_dst_child;

  if (bone_dst->bbone_prev) {
    bone_dst->bbone_prev = BKE_armature_find_bone_name(arm_dst, bone_dst->bbone_prev->name);
  }
  if (bone_dst->bbone_next) {
    bone_dst->bbone_next = BKE_armature_find_bone_name(arm_dst, bone_dst->bbone_next->name);
  }

  for (bone_dst_child = bone_dst->childbase.first; bone_dst_child;
       bone_dst_child = bone_dst_child->next) {
    copy_bonechildren_custom_handles(bone_dst_child, arm_dst);
  }
}

/**
 * Only copy internal data of Armature ID from source
 * to already allocated/initialized destination.
 * You probably never want to use that directly,
 * use #BKE_id_copy or #BKE_id_copy_ex for typical needs.
 *
 * WARNING! This function will not handle ID user count!
 *
 * \param flag: Copying options (see BKE_library.h's LIB_ID_COPY_... flags for more).
 */
void BKE_armature_copy_data(Main *UNUSED(bmain),
                            bArmature *arm_dst,
                            const bArmature *arm_src,
                            const int flag)
{
  Bone *bone_src, *bone_dst;
  Bone *bone_dst_act = NULL;

  /* We never handle usercount here for own data. */
  const int flag_subdata = flag | LIB_ID_CREATE_NO_USER_REFCOUNT;

  arm_dst->bonehash = NULL;

  BLI_duplicatelist(&arm_dst->bonebase, &arm_src->bonebase);

  /* Duplicate the childrens' lists */
  bone_dst = arm_dst->bonebase.first;
  for (bone_src = arm_src->bonebase.first; bone_src; bone_src = bone_src->next) {
    bone_dst->parent = NULL;
    copy_bonechildren(bone_dst, bone_src, arm_src->act_bone, &bone_dst_act, flag_subdata);
    bone_dst = bone_dst->next;
  }

  arm_dst->act_bone = bone_dst_act;

  BKE_armature_bone_hash_make(arm_dst);

  /* Fix custom handle references. */
  for (bone_dst = arm_dst->bonebase.first; bone_dst; bone_dst = bone_dst->next) {
    copy_bonechildren_custom_handles(bone_dst, arm_dst);
  }

  arm_dst->edbo = NULL;
  arm_dst->act_edbone = NULL;
}

bArmature *BKE_armature_copy(Main *bmain, const bArmature *arm)
{
  bArmature *arm_copy;
  BKE_id_copy(bmain, &arm->id, (ID **)&arm_copy);
  return arm_copy;
}

static Bone *get_named_bone_bonechildren(ListBase *lb, const char *name)
{
  Bone *curBone, *rbone;

  for (curBone = lb->first; curBone; curBone = curBone->next) {
    if (STREQ(curBone->name, name)) {
      return curBone;
    }

    rbone = get_named_bone_bonechildren(&curBone->childbase, name);
    if (rbone) {
      return rbone;
    }
  }

  return NULL;
}

/**
 * Walk the list until the bone is found (slow!),
 * use #BKE_armature_bone_from_name_map for multiple lookups.
 */
Bone *BKE_armature_find_bone_name(bArmature *arm, const char *name)
{
  if (!arm) {
    return NULL;
  }

  if (arm->bonehash) {
    return BLI_ghash_lookup(arm->bonehash, name);
  }

  return get_named_bone_bonechildren(&arm->bonebase, name);
}

static void armature_bone_from_name_insert_recursive(GHash *bone_hash, ListBase *lb)
{
  for (Bone *bone = lb->first; bone; bone = bone->next) {
    BLI_ghash_insert(bone_hash, bone->name, bone);
    armature_bone_from_name_insert_recursive(bone_hash, &bone->childbase);
  }
}

/**
 * Create a (name -> bone) map.
 *
 * \note typically #bPose.chanhash us used via #BKE_pose_channel_find_name
 * this is for the cases we can't use pose channels.
 */
static GHash *armature_bone_from_name_map(bArmature *arm)
{
  const int bones_count = BKE_armature_bonelist_count(&arm->bonebase);
  GHash *bone_hash = BLI_ghash_str_new_ex(__func__, bones_count);
  armature_bone_from_name_insert_recursive(bone_hash, &arm->bonebase);
  return bone_hash;
}

void BKE_armature_bone_hash_make(bArmature *arm)
{
  if (!arm->bonehash) {
    arm->bonehash = armature_bone_from_name_map(arm);
  }
}

void BKE_armature_bone_hash_free(bArmature *arm)
{
  if (arm->bonehash) {
    BLI_ghash_free(arm->bonehash, NULL, NULL);
    arm->bonehash = NULL;
  }
}

bool BKE_armature_bone_flag_test_recursive(const Bone *bone, int flag)
{
  if (bone->flag & flag) {
    return true;
  }
  else if (bone->parent) {
    return BKE_armature_bone_flag_test_recursive(bone->parent, flag);
  }
  else {
    return false;
  }
}

static void armature_refresh_layer_used_recursive(bArmature *arm, ListBase *bones)
{
  for (Bone *bone = bones->first; bone; bone = bone->next) {
    arm->layer_used |= bone->layer;
    armature_refresh_layer_used_recursive(arm, &bone->childbase);
  }
}

/* Update the layers_used variable after bones are moved between layer
 * NOTE: Used to be done in drawing code in 2.7, but that won't work with
 *       Copy-on-Write, as drawing uses evaluated copies.
 */
void BKE_armature_refresh_layer_used(bArmature *arm)
{
  arm->layer_used = 0;
  armature_refresh_layer_used_recursive(arm, &arm->bonebase);
}

/* Finds the best possible extension to the name on a particular axis. (For renaming, check for
 * unique names afterwards) strip_number: removes number extensions  (TODO: not used)
 * axis: the axis to name on
 * head/tail: the head/tail co-ordinate of the bone on the specified axis */
int bone_autoside_name(
    char name[MAXBONENAME], int UNUSED(strip_number), short axis, float head, float tail)
{
  unsigned int len;
  char basename[MAXBONENAME] = "";
  char extension[5] = "";

  len = strlen(name);
  if (len == 0) {
    return 0;
  }
  BLI_strncpy(basename, name, sizeof(basename));

  /* Figure out extension to append:
   * - The extension to append is based upon the axis that we are working on.
   * - If head happens to be on 0, then we must consider the tail position as well to decide
   *   which side the bone is on
   *   -> If tail is 0, then it's bone is considered to be on axis, so no extension should be added
   *   -> Otherwise, extension is added from perspective of object based on which side tail goes to
   * - If head is non-zero, extension is added from perspective of object based on side head is on
   */
  if (axis == 2) {
    /* z-axis - vertical (top/bottom) */
    if (IS_EQF(head, 0.0f)) {
      if (tail < 0) {
        strcpy(extension, "Bot");
      }
      else if (tail > 0) {
        strcpy(extension, "Top");
      }
    }
    else {
      if (head < 0) {
        strcpy(extension, "Bot");
      }
      else {
        strcpy(extension, "Top");
      }
    }
  }
  else if (axis == 1) {
    /* y-axis - depth (front/back) */
    if (IS_EQF(head, 0.0f)) {
      if (tail < 0) {
        strcpy(extension, "Fr");
      }
      else if (tail > 0) {
        strcpy(extension, "Bk");
      }
    }
    else {
      if (head < 0) {
        strcpy(extension, "Fr");
      }
      else {
        strcpy(extension, "Bk");
      }
    }
  }
  else {
    /* x-axis - horizontal (left/right) */
    if (IS_EQF(head, 0.0f)) {
      if (tail < 0) {
        strcpy(extension, "R");
      }
      else if (tail > 0) {
        strcpy(extension, "L");
      }
    }
    else {
      if (head < 0) {
        strcpy(extension, "R");
        /* XXX Shouldn't this be simple else, as for z and y axes? */
      }
      else if (head > 0) {
        strcpy(extension, "L");
      }
    }
  }

  /* Simple name truncation
   * - truncate if there is an extension and it wouldn't be able to fit
   * - otherwise, just append to end
   */
  if (extension[0]) {
    bool changed = true;

    while (changed) { /* remove extensions */
      changed = false;
      if (len > 2 && basename[len - 2] == '.') {
        if (basename[len - 1] == 'L' || basename[len - 1] == 'R') { /* L R */
          basename[len - 2] = '\0';
          len -= 2;
          changed = true;
        }
      }
      else if (len > 3 && basename[len - 3] == '.') {
        if ((basename[len - 2] == 'F' && basename[len - 1] == 'r') || /* Fr */
            (basename[len - 2] == 'B' && basename[len - 1] == 'k'))   /* Bk */
        {
          basename[len - 3] = '\0';
          len -= 3;
          changed = true;
        }
      }
      else if (len > 4 && basename[len - 4] == '.') {
        if ((basename[len - 3] == 'T' && basename[len - 2] == 'o' &&
             basename[len - 1] == 'p') || /* Top */
            (basename[len - 3] == 'B' && basename[len - 2] == 'o' &&
             basename[len - 1] == 't')) /* Bot */
        {
          basename[len - 4] = '\0';
          len -= 4;
          changed = true;
        }
      }
    }

    if ((MAXBONENAME - len) < strlen(extension) + 1) { /* add 1 for the '.' */
      strncpy(name, basename, len - strlen(extension));
    }

    BLI_snprintf(name, MAXBONENAME, "%s.%s", basename, extension);

    return 1;
  }

  else {
    return 0;
  }
}

/* ************* B-Bone support ******************* */

/* Compute a set of bezier parameter values that produce approximately equally spaced points. */
static void equalize_cubic_bezier(const float control[4][3],
                                  int temp_segments,
                                  int final_segments,
                                  float *r_t_points)
{
  float(*coords)[3] = BLI_array_alloca(coords, temp_segments + 1);
  float *pdist = BLI_array_alloca(pdist, temp_segments + 1);

  /* Compute the first pass of bezier point coordinates. */
  for (int i = 0; i < 3; i++) {
    BKE_curve_forward_diff_bezier(control[0][i],
                                  control[1][i],
                                  control[2][i],
                                  control[3][i],
                                  &coords[0][i],
                                  temp_segments,
                                  sizeof(*coords));
  }

  /* Calculate the length of the polyline at each point. */
  pdist[0] = 0.0f;

  for (int i = 0; i < temp_segments; i++) {
    pdist[i + 1] = pdist[i] + len_v3v3(coords[i], coords[i + 1]);
  }

  /* Go over distances and calculate new parameter values. */
  float dist_step = pdist[temp_segments] / final_segments;

  r_t_points[0] = 0.0f;

  for (int i = 1, nr = 1; i <= final_segments; i++) {
    float dist = i * dist_step;

    /* We're looking for location (distance) 'dist' in the array. */
    while ((nr < temp_segments) && (dist >= pdist[nr])) {
      nr++;
    }

    float fac = (pdist[nr] - dist) / (pdist[nr] - pdist[nr - 1]);

    r_t_points[i] = (nr - fac) / temp_segments;
  }

  r_t_points[final_segments] = 1.0f;
}

/* Evaluate bezier position and tangent at a specific parameter value
 * using the De Casteljau algorithm. */
static void evaluate_cubic_bezier(const float control[4][3],
                                  float t,
                                  float r_pos[3],
                                  float r_tangent[3])
{
  float layer1[3][3];
  interp_v3_v3v3(layer1[0], control[0], control[1], t);
  interp_v3_v3v3(layer1[1], control[1], control[2], t);
  interp_v3_v3v3(layer1[2], control[2], control[3], t);

  float layer2[2][3];
  interp_v3_v3v3(layer2[0], layer1[0], layer1[1], t);
  interp_v3_v3v3(layer2[1], layer1[1], layer1[2], t);

  sub_v3_v3v3(r_tangent, layer2[1], layer2[0]);
  madd_v3_v3v3fl(r_pos, layer2[0], r_tangent, t);
}

/* Get "next" and "prev" bones - these are used for handle calculations. */
void BKE_pchan_bbone_handles_get(bPoseChannel *pchan, bPoseChannel **r_prev, bPoseChannel **r_next)
{
  if (pchan->bone->bbone_prev_type == BBONE_HANDLE_AUTO) {
    /* Use connected parent. */
    if (pchan->bone->flag & BONE_CONNECTED) {
      *r_prev = pchan->parent;
    }
    else {
      *r_prev = NULL;
    }
  }
  else {
    /* Use the provided bone as prev - leave blank to eliminate this effect altogether. */
    *r_prev = pchan->bbone_prev;
  }

  if (pchan->bone->bbone_next_type == BBONE_HANDLE_AUTO) {
    /* Use connected child. */
    *r_next = pchan->child;
  }
  else {
    /* Use the provided bone as next - leave blank to eliminate this effect altogether. */
    *r_next = pchan->bbone_next;
  }
}

/* Compute B-Bone spline parameters for the given channel. */
void BKE_pchan_bbone_spline_params_get(struct bPoseChannel *pchan,
                                       const bool rest,
                                       struct BBoneSplineParameters *param)
{
  bPoseChannel *next, *prev;
  Bone *bone = pchan->bone;
  float imat[4][4], posemat[4][4];
  float delta[3];

  memset(param, 0, sizeof(*param));

  param->segments = bone->segments;
  param->length = bone->length;

  if (!rest) {
    float scale[3];

    /* Check if we need to take non-uniform bone scaling into account. */
    mat4_to_size(scale, pchan->pose_mat);

    if (fabsf(scale[0] - scale[1]) > 1e-6f || fabsf(scale[1] - scale[2]) > 1e-6f) {
      param->do_scale = true;
      copy_v3_v3(param->scale, scale);
    }
  }

  BKE_pchan_bbone_handles_get(pchan, &prev, &next);

  /* Find the handle points, since this is inside bone space, the
   * first point = (0, 0, 0)
   * last point =  (0, length, 0) */
  if (rest) {
    invert_m4_m4(imat, pchan->bone->arm_mat);
  }
  else if (param->do_scale) {
    copy_m4_m4(posemat, pchan->pose_mat);
    normalize_m4(posemat);
    invert_m4_m4(imat, posemat);
  }
  else {
    invert_m4_m4(imat, pchan->pose_mat);
  }

  if (prev) {
    float h1[3];
    bool done = false;

    param->use_prev = true;

    /* Transform previous point inside this bone space. */
    if (bone->bbone_prev_type == BBONE_HANDLE_RELATIVE) {
      /* Use delta movement (from restpose), and apply this relative to the current bone's head. */
      if (rest) {
        /* In restpose, arm_head == pose_head */
        zero_v3(param->prev_h);
        done = true;
      }
      else {
        sub_v3_v3v3(delta, prev->pose_head, prev->bone->arm_head);
        sub_v3_v3v3(h1, pchan->pose_head, delta);
      }
    }
    else if (bone->bbone_prev_type == BBONE_HANDLE_TANGENT) {
      /* Use bone direction by offsetting so that its tail meets current bone's head */
      if (rest) {
        sub_v3_v3v3(delta, prev->bone->arm_tail, prev->bone->arm_head);
        sub_v3_v3v3(h1, bone->arm_head, delta);
      }
      else {
        sub_v3_v3v3(delta, prev->pose_tail, prev->pose_head);
        sub_v3_v3v3(h1, pchan->pose_head, delta);
      }
    }
    else {
      /* Apply special handling for smoothly joining B-Bone chains */
      param->prev_bbone = (prev->bone->segments > 1);

      /* Use bone head as absolute position. */
      copy_v3_v3(h1, rest ? prev->bone->arm_head : prev->pose_head);
    }

    if (!done) {
      mul_v3_m4v3(param->prev_h, imat, h1);
    }

    if (!param->prev_bbone) {
      /* Find the previous roll to interpolate. */
      mul_m4_m4m4(param->prev_mat, imat, rest ? prev->bone->arm_mat : prev->pose_mat);
    }
  }

  if (next) {
    float h2[3];
    bool done = false;

    param->use_next = true;

    /* Transform next point inside this bone space. */
    if (bone->bbone_next_type == BBONE_HANDLE_RELATIVE) {
      /* Use delta movement (from restpose), and apply this relative to the current bone's tail. */
      if (rest) {
        /* In restpose, arm_head == pose_head */
        copy_v3_fl3(param->next_h, 0.0f, param->length, 0.0);
        done = true;
      }
      else {
        sub_v3_v3v3(delta, next->pose_head, next->bone->arm_head);
        add_v3_v3v3(h2, pchan->pose_tail, delta);
      }
    }
    else if (bone->bbone_next_type == BBONE_HANDLE_TANGENT) {
      /* Use bone direction by offsetting so that its head meets current bone's tail */
      if (rest) {
        sub_v3_v3v3(delta, next->bone->arm_tail, next->bone->arm_head);
        add_v3_v3v3(h2, bone->arm_tail, delta);
      }
      else {
        sub_v3_v3v3(delta, next->pose_tail, next->pose_head);
        add_v3_v3v3(h2, pchan->pose_tail, delta);
      }
    }
    else {
      /* Apply special handling for smoothly joining B-Bone chains */
      param->next_bbone = (next->bone->segments > 1);

      /* Use bone tail as absolute position. */
      copy_v3_v3(h2, rest ? next->bone->arm_tail : next->pose_tail);
    }

    if (!done) {
      mul_v3_m4v3(param->next_h, imat, h2);
    }

    /* Find the next roll to interpolate as well. */
    mul_m4_m4m4(param->next_mat, imat, rest ? next->bone->arm_mat : next->pose_mat);
  }

  /* Add effects from bbone properties over the top
   * - These properties allow users to hand-animate the
   *   bone curve/shape, without having to resort to using
   *   extra bones
   * - The "bone" level offsets are for defining the restpose
   *   shape of the bone (e.g. for curved eyebrows for example).
   *   -> In the viewport, it's needed to define what the rest pose
   *      looks like
   *   -> For "rest == 0", we also still need to have it present
   *      so that we can "cancel out" this restpose when it comes
   *      time to deform some geometry, it won't cause double transforms.
   * - The "pchan" level offsets are the ones that animators actually
   *   end up animating
   */
  {
    param->ease1 = bone->ease1 + (!rest ? pchan->ease1 : 0.0f);
    param->ease2 = bone->ease2 + (!rest ? pchan->ease2 : 0.0f);

    param->roll1 = bone->roll1 + (!rest ? pchan->roll1 : 0.0f);
    param->roll2 = bone->roll2 + (!rest ? pchan->roll2 : 0.0f);

    if (bone->flag & BONE_ADD_PARENT_END_ROLL) {
      if (prev) {
        if (prev->bone) {
          param->roll1 += prev->bone->roll2;
        }

        if (!rest) {
          param->roll1 += prev->roll2;
        }
      }
    }

    param->scale_in_x = bone->scale_in_x * (!rest ? pchan->scale_in_x : 1.0f);
    param->scale_in_y = bone->scale_in_y * (!rest ? pchan->scale_in_y : 1.0f);
    param->scale_out_x = bone->scale_out_x * (!rest ? pchan->scale_out_x : 1.0f);
    param->scale_out_y = bone->scale_out_y * (!rest ? pchan->scale_out_y : 1.0f);

    /* Extra curve x / y */
    param->curve_in_x = bone->curve_in_x + (!rest ? pchan->curve_in_x : 0.0f);
    param->curve_in_y = bone->curve_in_y + (!rest ? pchan->curve_in_y : 0.0f);

    param->curve_out_x = bone->curve_out_x + (!rest ? pchan->curve_out_x : 0.0f);
    param->curve_out_y = bone->curve_out_y + (!rest ? pchan->curve_out_y : 0.0f);
  }
}

/* Fills the array with the desired amount of bone->segments elements.
 * This calculation is done within unit bone space. */
void BKE_pchan_bbone_spline_setup(bPoseChannel *pchan,
                                  const bool rest,
                                  const bool for_deform,
                                  Mat4 *result_array)
{
  BBoneSplineParameters param;

  BKE_pchan_bbone_spline_params_get(pchan, rest, &param);

  pchan->bone->segments = BKE_pchan_bbone_spline_compute(&param, for_deform, result_array);
}

/* Computes the bezier handle vectors and rolls coming from custom handles. */
void BKE_pchan_bbone_handles_compute(const BBoneSplineParameters *param,
                                     float h1[3],
                                     float *r_roll1,
                                     float h2[3],
                                     float *r_roll2,
                                     bool ease,
                                     bool offsets)
{
  float mat3[3][3];
  float length = param->length;
  float epsilon = 1e-5 * length;

  if (param->do_scale) {
    length *= param->scale[1];
  }

  *r_roll1 = *r_roll2 = 0.0f;

  if (param->use_prev) {
    copy_v3_v3(h1, param->prev_h);

    if (param->prev_bbone) {
      /* If previous bone is B-bone too, use average handle direction. */
      h1[1] -= length;
    }

    if (normalize_v3(h1) < epsilon) {
      copy_v3_fl3(h1, 0.0f, -1.0f, 0.0f);
    }

    negate_v3(h1);

    if (!param->prev_bbone) {
      /* Find the previous roll to interpolate. */
      copy_m3_m4(mat3, param->prev_mat);
      mat3_vec_to_roll(mat3, h1, r_roll1);
    }
  }
  else {
    h1[0] = 0.0f;
    h1[1] = 1.0;
    h1[2] = 0.0f;
  }

  if (param->use_next) {
    copy_v3_v3(h2, param->next_h);

    /* If next bone is B-bone too, use average handle direction. */
    if (param->next_bbone) {
      /* pass */
    }
    else {
      h2[1] -= length;
    }

    if (normalize_v3(h2) < epsilon) {
      copy_v3_fl3(h2, 0.0f, 1.0f, 0.0f);
    }

    /* Find the next roll to interpolate as well. */
    copy_m3_m4(mat3, param->next_mat);
    mat3_vec_to_roll(mat3, h2, r_roll2);
  }
  else {
    h2[0] = 0.0f;
    h2[1] = 1.0f;
    h2[2] = 0.0f;
  }

  if (ease) {
    const float circle_factor = length * (cubic_tangent_factor_circle_v3(h1, h2) / 0.75f);

    const float hlength1 = param->ease1 * circle_factor;
    const float hlength2 = param->ease2 * circle_factor;

    /* and only now negate h2 */
    mul_v3_fl(h1, hlength1);
    mul_v3_fl(h2, -hlength2);
  }

  /* Add effects from bbone properties over the top
   * - These properties allow users to hand-animate the
   *   bone curve/shape, without having to resort to using
   *   extra bones
   * - The "bone" level offsets are for defining the restpose
   *   shape of the bone (e.g. for curved eyebrows for example).
   *   -> In the viewport, it's needed to define what the rest pose
   *      looks like
   *   -> For "rest == 0", we also still need to have it present
   *      so that we can "cancel out" this restpose when it comes
   *      time to deform some geometry, it won't cause double transforms.
   * - The "pchan" level offsets are the ones that animators actually
   *   end up animating
   */
  if (offsets) {
    /* Add extra rolls. */
    *r_roll1 += param->roll1;
    *r_roll2 += param->roll2;

    /* Extra curve x / y */
    /* NOTE:
     * Scale correction factors here are to compensate for some random floating-point glitches
     * when scaling up the bone or it's parent by a factor of approximately 8.15/6, which results
     * in the bone length getting scaled up too (from 1 to 8), causing the curve to flatten out.
     */
    const float xscale_correction = (param->do_scale) ? param->scale[0] : 1.0f;
    const float yscale_correction = (param->do_scale) ? param->scale[2] : 1.0f;

    h1[0] += param->curve_in_x * xscale_correction;
    h1[2] += param->curve_in_y * yscale_correction;

    h2[0] += param->curve_out_x * xscale_correction;
    h2[2] += param->curve_out_y * yscale_correction;
  }
}

static void make_bbone_spline_matrix(BBoneSplineParameters *param,
                                     float scalemats[2][4][4],
                                     float pos[3],
                                     float axis[3],
                                     float roll,
                                     float scalex,
                                     float scaley,
                                     float result[4][4])
{
  float mat3[3][3];

  vec_roll_to_mat3(axis, roll, mat3);

  copy_m4_m3(result, mat3);
  copy_v3_v3(result[3], pos);

  if (param->do_scale) {
    /* Correct for scaling when this matrix is used in scaled space. */
    mul_m4_series(result, scalemats[0], result, scalemats[1]);
  }

  /* BBone scale... */
  mul_v3_fl(result[0], scalex);
  mul_v3_fl(result[2], scaley);
}

/* Fade from first to second derivative when the handle is very short. */
static void ease_handle_axis(const float deriv1[3], const float deriv2[3], float r_axis[3])
{
  const float gap = 0.1f;

  copy_v3_v3(r_axis, deriv1);

  float len1 = len_squared_v3(deriv1), len2 = len_squared_v3(deriv2);
  float ratio = len1 / len2;

  if (ratio < gap * gap) {
    madd_v3_v3fl(r_axis, deriv2, gap - sqrtf(ratio));
  }
}

/* Fills the array with the desired amount of bone->segments elements.
 * This calculation is done within unit bone space. */
int BKE_pchan_bbone_spline_compute(BBoneSplineParameters *param,
                                   const bool for_deform,
                                   Mat4 *result_array)
{
  float scalemats[2][4][4];
  float bezt_controls[4][3];
  float h1[3], roll1, h2[3], roll2, prev[3], cur[3], axis[3];
  float length = param->length;

  if (param->do_scale) {
    size_to_mat4(scalemats[1], param->scale);
    invert_m4_m4(scalemats[0], scalemats[1]);

    length *= param->scale[1];
  }

  BKE_pchan_bbone_handles_compute(param, h1, &roll1, h2, &roll2, true, true);

  /* Make curve. */
  CLAMP_MAX(param->segments, MAX_BBONE_SUBDIV);

  copy_v3_fl3(bezt_controls[3], 0.0f, length, 0.0f);
  add_v3_v3v3(bezt_controls[2], bezt_controls[3], h2);
  copy_v3_v3(bezt_controls[1], h1);
  zero_v3(bezt_controls[0]);

  float bezt_points[MAX_BBONE_SUBDIV + 1];

  equalize_cubic_bezier(bezt_controls, MAX_BBONE_SUBDIV, param->segments, bezt_points);

  /* Deformation uses N+1 matrices computed at points between the segments. */
  if (for_deform) {
    /* Bezier derivatives. */
    float bezt_deriv1[3][3], bezt_deriv2[2][3];

    for (int i = 0; i < 3; i++) {
      sub_v3_v3v3(bezt_deriv1[i], bezt_controls[i + 1], bezt_controls[i]);
    }
    for (int i = 0; i < 2; i++) {
      sub_v3_v3v3(bezt_deriv2[i], bezt_deriv1[i + 1], bezt_deriv1[i]);
    }

    /* End points require special handling to fix zero length handles. */
    ease_handle_axis(bezt_deriv1[0], bezt_deriv2[0], axis);
    make_bbone_spline_matrix(param,
                             scalemats,
                             bezt_controls[0],
                             axis,
                             roll1,
                             param->scale_in_x,
                             param->scale_in_y,
                             result_array[0].mat);

    for (int a = 1; a < param->segments; a++) {
      evaluate_cubic_bezier(bezt_controls, bezt_points[a], cur, axis);

      float fac = ((float)a) / param->segments;
      float roll = interpf(roll2, roll1, fac);
      float scalex = interpf(param->scale_out_x, param->scale_in_x, fac);
      float scaley = interpf(param->scale_out_y, param->scale_in_y, fac);

      make_bbone_spline_matrix(
          param, scalemats, cur, axis, roll, scalex, scaley, result_array[a].mat);
    }

    negate_v3(bezt_deriv2[1]);
    ease_handle_axis(bezt_deriv1[2], bezt_deriv2[1], axis);
    make_bbone_spline_matrix(param,
                             scalemats,
                             bezt_controls[3],
                             axis,
                             roll2,
                             param->scale_out_x,
                             param->scale_out_y,
                             result_array[param->segments].mat);
  }
  /* Other code (e.g. display) uses matrices for the segments themselves. */
  else {
    zero_v3(prev);

    for (int a = 0; a < param->segments; a++) {
      evaluate_cubic_bezier(bezt_controls, bezt_points[a + 1], cur, axis);

      sub_v3_v3v3(axis, cur, prev);

      float fac = (a + 0.5f) / param->segments;
      float roll = interpf(roll2, roll1, fac);
      float scalex = interpf(param->scale_out_x, param->scale_in_x, fac);
      float scaley = interpf(param->scale_out_y, param->scale_in_y, fac);

      make_bbone_spline_matrix(
          param, scalemats, prev, axis, roll, scalex, scaley, result_array[a].mat);
      copy_v3_v3(prev, cur);
    }
  }

  return param->segments;
}

/* ************ Armature Deform ******************* */

static void allocate_bbone_cache(bPoseChannel *pchan, int segments)
{
  bPoseChannel_Runtime *runtime = &pchan->runtime;

  if (runtime->bbone_segments != segments) {
    BKE_pose_channel_free_bbone_cache(runtime);

    runtime->bbone_segments = segments;
    runtime->bbone_rest_mats = MEM_malloc_arrayN(
        sizeof(Mat4), 1 + (uint)segments, "bPoseChannel_Runtime::bbone_rest_mats");
    runtime->bbone_pose_mats = MEM_malloc_arrayN(
        sizeof(Mat4), 1 + (uint)segments, "bPoseChannel_Runtime::bbone_pose_mats");
    runtime->bbone_deform_mats = MEM_malloc_arrayN(
        sizeof(Mat4), 2 + (uint)segments, "bPoseChannel_Runtime::bbone_deform_mats");
    runtime->bbone_dual_quats = MEM_malloc_arrayN(
        sizeof(DualQuat), 1 + (uint)segments, "bPoseChannel_Runtime::bbone_dual_quats");
  }
}

/** Compute and cache the B-Bone shape in the channel runtime struct. */
void BKE_pchan_bbone_segments_cache_compute(bPoseChannel *pchan)
{
  bPoseChannel_Runtime *runtime = &pchan->runtime;
  Bone *bone = pchan->bone;
  int segments = bone->segments;

  BLI_assert(segments > 1);

  /* Allocate the cache if needed. */
  allocate_bbone_cache(pchan, segments);

  /* Compute the shape. */
  Mat4 *b_bone = runtime->bbone_pose_mats;
  Mat4 *b_bone_rest = runtime->bbone_rest_mats;
  Mat4 *b_bone_mats = runtime->bbone_deform_mats;
  DualQuat *b_bone_dual_quats = runtime->bbone_dual_quats;
  int a;

  BKE_pchan_bbone_spline_setup(pchan, false, true, b_bone);
  BKE_pchan_bbone_spline_setup(pchan, true, true, b_bone_rest);

  /* Compute deform matrices. */
  /* first matrix is the inverse arm_mat, to bring points in local bone space
   * for finding out which segment it belongs to */
  invert_m4_m4(b_bone_mats[0].mat, bone->arm_mat);

  /* then we make the b_bone_mats:
   * - first transform to local bone space
   * - translate over the curve to the bbone mat space
   * - transform with b_bone matrix
   * - transform back into global space */

  for (a = 0; a <= bone->segments; a++) {
    float tmat[4][4];

    invert_m4_m4(tmat, b_bone_rest[a].mat);
    mul_m4_series(b_bone_mats[a + 1].mat,
                  pchan->chan_mat,
                  bone->arm_mat,
                  b_bone[a].mat,
                  tmat,
                  b_bone_mats[0].mat);

    mat4_to_dquat(&b_bone_dual_quats[a], bone->arm_mat, b_bone_mats[a + 1].mat);
  }
}

/** Copy cached B-Bone segments from one channel to another */
void BKE_pchan_bbone_segments_cache_copy(bPoseChannel *pchan, bPoseChannel *pchan_from)
{
  bPoseChannel_Runtime *runtime = &pchan->runtime;
  bPoseChannel_Runtime *runtime_from = &pchan_from->runtime;
  int segments = runtime_from->bbone_segments;

  if (segments <= 1) {
    BKE_pose_channel_free_bbone_cache(&pchan->runtime);
  }
  else {
    allocate_bbone_cache(pchan, segments);

    memcpy(runtime->bbone_rest_mats, runtime_from->bbone_rest_mats, sizeof(Mat4) * (1 + segments));
    memcpy(runtime->bbone_pose_mats, runtime_from->bbone_pose_mats, sizeof(Mat4) * (1 + segments));
    memcpy(runtime->bbone_deform_mats,
           runtime_from->bbone_deform_mats,
           sizeof(Mat4) * (2 + segments));
    memcpy(runtime->bbone_dual_quats,
           runtime_from->bbone_dual_quats,
           sizeof(DualQuat) * (1 + segments));
  }
}

/** Calculate index and blend factor for the two B-Bone segment nodes
 * affecting the point at 0 <= pos <= 1. */
void BKE_pchan_bbone_deform_segment_index(const bPoseChannel *pchan,
                                          float pos,
                                          int *r_index,
                                          float *r_blend_next)
{
  int segments = pchan->bone->segments;

  CLAMP(pos, 0.0f, 1.0f);

  /* Calculate the indices of the 2 affecting b_bone segments.
   * Integer part is the first segment's index.
   * Integer part plus 1 is the second segment's index.
   * Fractional part is the blend factor. */
  float pre_blend = pos * (float)segments;

  int index = (int)floorf(pre_blend);
  float blend = pre_blend - index;

  CLAMP(index, 0, segments);
  CLAMP(blend, 0.0f, 1.0f);

  *r_index = index;
  *r_blend_next = blend;
}

/* Add the effect of one bone or B-Bone segment to the accumulated result. */
static void pchan_deform_accumulate(const DualQuat *deform_dq,
                                    const float deform_mat[4][4],
                                    const float co_in[3],
                                    float weight,
                                    float co_accum[3],
                                    DualQuat *dq_accum,
                                    float mat_accum[3][3])
{
  if (weight == 0.0f) {
    return;
  }

  if (dq_accum) {
    BLI_assert(!co_accum);

    add_weighted_dq_dq(dq_accum, deform_dq, weight);
  }
  else {
    float tmp[3];
    mul_v3_m4v3(tmp, deform_mat, co_in);

    sub_v3_v3(tmp, co_in);
    madd_v3_v3fl(co_accum, tmp, weight);

    if (mat_accum) {
      float tmpmat[3][3];
      copy_m3_m4(tmpmat, deform_mat);

      madd_m3_m3m3fl(mat_accum, mat_accum, tmpmat, weight);
    }
  }
}

static void b_bone_deform(const bPoseChannel *pchan,
                          const float co[3],
                          float weight,
                          float vec[3],
                          DualQuat *dq,
                          float defmat[3][3])
{
  const DualQuat *quats = pchan->runtime.bbone_dual_quats;
  const Mat4 *mats = pchan->runtime.bbone_deform_mats;
  const float(*mat)[4] = mats[0].mat;
  float blend, y;
  int index;

  /* Transform co to bone space and get its y component. */
  y = mat[0][1] * co[0] + mat[1][1] * co[1] + mat[2][1] * co[2] + mat[3][1];

  /* Calculate the indices of the 2 affecting b_bone segments. */
  BKE_pchan_bbone_deform_segment_index(pchan, y / pchan->bone->length, &index, &blend);

  pchan_deform_accumulate(
      &quats[index], mats[index + 1].mat, co, weight * (1.0f - blend), vec, dq, defmat);
  pchan_deform_accumulate(
      &quats[index + 1], mats[index + 2].mat, co, weight * blend, vec, dq, defmat);
}

/* using vec with dist to bone b1 - b2 */
float distfactor_to_bone(
    const float vec[3], const float b1[3], const float b2[3], float rad1, float rad2, float rdist)
{
  float dist_sq;
  float bdelta[3];
  float pdelta[3];
  float hsqr, a, l, rad;

  sub_v3_v3v3(bdelta, b2, b1);
  l = normalize_v3(bdelta);

  sub_v3_v3v3(pdelta, vec, b1);

  a = dot_v3v3(bdelta, pdelta);
  hsqr = len_squared_v3(pdelta);

  if (a < 0.0f) {
    /* If we're past the end of the bone, do a spherical field attenuation thing */
    dist_sq = len_squared_v3v3(b1, vec);
    rad = rad1;
  }
  else if (a > l) {
    /* If we're past the end of the bone, do a spherical field attenuation thing */
    dist_sq = len_squared_v3v3(b2, vec);
    rad = rad2;
  }
  else {
    dist_sq = (hsqr - (a * a));

    if (l != 0.0f) {
      rad = a / l;
      rad = rad * rad2 + (1.0f - rad) * rad1;
    }
    else {
      rad = rad1;
    }
  }

  a = rad * rad;
  if (dist_sq < a) {
    return 1.0f;
  }
  else {
    l = rad + rdist;
    l *= l;
    if (rdist == 0.0f || dist_sq >= l) {
      return 0.0f;
    }
    else {
      a = sqrtf(dist_sq) - rad;
      return 1.0f - (a * a) / (rdist * rdist);
    }
  }
}

static float dist_bone_deform(
    bPoseChannel *pchan, float vec[3], DualQuat *dq, float mat[3][3], const float co[3])
{
  Bone *bone = pchan->bone;
  float fac, contrib = 0.0;

  if (bone == NULL) {
    return 0.0f;
  }

  fac = distfactor_to_bone(
      co, bone->arm_head, bone->arm_tail, bone->rad_head, bone->rad_tail, bone->dist);

  if (fac > 0.0f) {
    fac *= bone->weight;
    contrib = fac;
    if (contrib > 0.0f) {
      if (bone->segments > 1 && pchan->runtime.bbone_segments == bone->segments) {
        b_bone_deform(pchan, co, fac, vec, dq, mat);
      }
      else {
        pchan_deform_accumulate(
            &pchan->runtime.deform_dual_quat, pchan->chan_mat, co, fac, vec, dq, mat);
      }
    }
  }

  return contrib;
}

static void pchan_bone_deform(bPoseChannel *pchan,
                              float weight,
                              float vec[3],
                              DualQuat *dq,
                              float mat[3][3],
                              const float co[3],
                              float *contrib)
{
  Bone *bone = pchan->bone;

  if (!weight) {
    return;
  }

  if (bone->segments > 1 && pchan->runtime.bbone_segments == bone->segments) {
    b_bone_deform(pchan, co, weight, vec, dq, mat);
  }
  else {
    pchan_deform_accumulate(
        &pchan->runtime.deform_dual_quat, pchan->chan_mat, co, weight, vec, dq, mat);
  }

  (*contrib) += weight;
}

typedef struct ArmatureUserdata {
  Object *armOb;
  Object *target;
  const Mesh *mesh;
  float (*vertexCos)[3];
  float (*defMats)[3][3];
  float (*prevCos)[3];

  bool use_envelope;
  bool use_quaternion;
  bool invert_vgroup;
  bool use_dverts;

  int armature_def_nr;

  int target_totvert;
  MDeformVert *dverts;

  int defbase_tot;
  bPoseChannel **defnrToPC;

  float premat[4][4];
  float postmat[4][4];
} ArmatureUserdata;

static void armature_vert_task(void *__restrict userdata,
                               const int i,
                               const ParallelRangeTLS *__restrict UNUSED(tls))
{
  const ArmatureUserdata *data = userdata;
  float(*const vertexCos)[3] = data->vertexCos;
  float(*const defMats)[3][3] = data->defMats;
  float(*const prevCos)[3] = data->prevCos;
  const bool use_envelope = data->use_envelope;
  const bool use_quaternion = data->use_quaternion;
  const bool use_dverts = data->use_dverts;
  const int armature_def_nr = data->armature_def_nr;

  MDeformVert *dvert;
  DualQuat sumdq, *dq = NULL;
  bPoseChannel *pchan;
  float *co, dco[3];
  float sumvec[3], summat[3][3];
  float *vec = NULL, (*smat)[3] = NULL;
  float contrib = 0.0f;
  float armature_weight = 1.0f; /* default to 1 if no overall def group */
  float prevco_weight = 1.0f;   /* weight for optional cached vertexcos */

  if (use_quaternion) {
    memset(&sumdq, 0, sizeof(DualQuat));
    dq = &sumdq;
  }
  else {
    sumvec[0] = sumvec[1] = sumvec[2] = 0.0f;
    vec = sumvec;

    if (defMats) {
      zero_m3(summat);
      smat = summat;
    }
  }

  if (use_dverts || armature_def_nr != -1) {
    if (data->mesh) {
      BLI_assert(i < data->mesh->totvert);
      if (data->mesh->dvert != NULL) {
        dvert = data->mesh->dvert + i;
      }
      else {
        dvert = NULL;
      }
    }
    else if (data->dverts && i < data->target_totvert) {
      dvert = data->dverts + i;
    }
    else {
      dvert = NULL;
    }
  }
  else {
    dvert = NULL;
  }

  if (armature_def_nr != -1 && dvert) {
    armature_weight = defvert_find_weight(dvert, armature_def_nr);

    if (data->invert_vgroup) {
      armature_weight = 1.0f - armature_weight;
    }

    /* hackish: the blending factor can be used for blending with prevCos too */
    if (prevCos) {
      prevco_weight = armature_weight;
      armature_weight = 1.0f;
    }
  }

  /* check if there's any  point in calculating for this vert */
  if (armature_weight == 0.0f) {
    return;
  }

  /* get the coord we work on */
  co = prevCos ? prevCos[i] : vertexCos[i];

  /* Apply the object's matrix */
  mul_m4_v3(data->premat, co);

  if (use_dverts && dvert && dvert->totweight) { /* use weight groups ? */
    MDeformWeight *dw = dvert->dw;
    int deformed = 0;
    unsigned int j;
    float acum_weight = 0;
    for (j = dvert->totweight; j != 0; j--, dw++) {
      const int index = dw->def_nr;
      if (index >= 0 && index < data->defbase_tot && (pchan = data->defnrToPC[index])) {
        float weight = dw->weight;
        Bone *bone = pchan->bone;

        deformed = 1;

        if (bone && bone->flag & BONE_MULT_VG_ENV) {
          weight *= distfactor_to_bone(
              co, bone->arm_head, bone->arm_tail, bone->rad_head, bone->rad_tail, bone->dist);
        }

        /* check limit of weight */
        if (data->target->type == OB_GPENCIL) {
          if (acum_weight + weight >= 1.0f) {
            weight = 1.0f - acum_weight;
          }
          acum_weight += weight;
        }

        pchan_bone_deform(pchan, weight, vec, dq, smat, co, &contrib);

        /* if acumulated weight limit exceed, exit loop */
        if ((data->target->type == OB_GPENCIL) && (acum_weight >= 1.0f)) {
          break;
        }
      }
    }
    /* if there are vertexgroups but not groups with bones
     * (like for softbody groups) */
    if (deformed == 0 && use_envelope) {
      for (pchan = data->armOb->pose->chanbase.first; pchan; pchan = pchan->next) {
        if (!(pchan->bone->flag & BONE_NO_DEFORM)) {
          contrib += dist_bone_deform(pchan, vec, dq, smat, co);
        }
      }
    }
  }
  else if (use_envelope) {
    for (pchan = data->armOb->pose->chanbase.first; pchan; pchan = pchan->next) {
      if (!(pchan->bone->flag & BONE_NO_DEFORM)) {
        contrib += dist_bone_deform(pchan, vec, dq, smat, co);
      }
    }
  }

  /* actually should be EPSILON? weight values and contrib can be like 10e-39 small */
  if (contrib > 0.0001f) {
    if (use_quaternion) {
      normalize_dq(dq, contrib);

      if (armature_weight != 1.0f) {
        copy_v3_v3(dco, co);
        mul_v3m3_dq(dco, (defMats) ? summat : NULL, dq);
        sub_v3_v3(dco, co);
        mul_v3_fl(dco, armature_weight);
        add_v3_v3(co, dco);
      }
      else {
        mul_v3m3_dq(co, (defMats) ? summat : NULL, dq);
      }

      smat = summat;
    }
    else {
      mul_v3_fl(vec, armature_weight / contrib);
      add_v3_v3v3(co, vec, co);
    }

    if (defMats) {
      float pre[3][3], post[3][3], tmpmat[3][3];

      copy_m3_m4(pre, data->premat);
      copy_m3_m4(post, data->postmat);
      copy_m3_m3(tmpmat, defMats[i]);

      if (!use_quaternion) { /* quaternion already is scale corrected */
        mul_m3_fl(smat, armature_weight / contrib);
      }

      mul_m3_series(defMats[i], post, smat, pre, tmpmat);
    }
  }

  /* always, check above code */
  mul_m4_v3(data->postmat, co);

  /* interpolate with previous modifier position using weight group */
  if (prevCos) {
    float mw = 1.0f - prevco_weight;
    vertexCos[i][0] = prevco_weight * vertexCos[i][0] + mw * co[0];
    vertexCos[i][1] = prevco_weight * vertexCos[i][1] + mw * co[1];
    vertexCos[i][2] = prevco_weight * vertexCos[i][2] + mw * co[2];
  }
}

void armature_deform_verts(Object *armOb,
                           Object *target,
                           const Mesh *mesh,
                           float (*vertexCos)[3],
                           float (*defMats)[3][3],
                           int numVerts,
                           int deformflag,
                           float (*prevCos)[3],
                           const char *defgrp_name,
                           bGPDstroke *gps)
{
  bArmature *arm = armOb->data;
  bPoseChannel **defnrToPC = NULL;
  MDeformVert *dverts = NULL;
  bDeformGroup *dg;
  const bool use_envelope = (deformflag & ARM_DEF_ENVELOPE) != 0;
  const bool use_quaternion = (deformflag & ARM_DEF_QUATERNION) != 0;
  const bool invert_vgroup = (deformflag & ARM_DEF_INVERT_VGROUP) != 0;
  int defbase_tot = 0;       /* safety for vertexgroup index overflow */
  int i, target_totvert = 0; /* safety for vertexgroup overflow */
  bool use_dverts = false;
  int armature_def_nr;

  /* in editmode, or not an armature */
  if (arm->edbo || (armOb->pose == NULL)) {
    return;
  }

  if ((armOb->pose->flag & POSE_RECALC) != 0) {
    CLOG_ERROR(&LOG,
               "Trying to evaluate influence of armature '%s' which needs Pose recalc!",
               armOb->id.name);
    BLI_assert(0);
  }

  /* get the def_nr for the overall armature vertex group if present */
  armature_def_nr = defgroup_name_index(target, defgrp_name);

  if (ELEM(target->type, OB_MESH, OB_LATTICE, OB_GPENCIL)) {
    defbase_tot = BLI_listbase_count(&target->defbase);

    if (target->type == OB_MESH) {
      Mesh *me = target->data;
      dverts = me->dvert;
      if (dverts) {
        target_totvert = me->totvert;
      }
    }
    else if (target->type == OB_LATTICE) {
      Lattice *lt = target->data;
      dverts = lt->dvert;
      if (dverts) {
        target_totvert = lt->pntsu * lt->pntsv * lt->pntsw;
      }
    }
    else if (target->type == OB_GPENCIL) {
      dverts = gps->dvert;
      if (dverts) {
        target_totvert = gps->totpoints;
      }
    }
  }

  /* get a vertex-deform-index to posechannel array */
  if (deformflag & ARM_DEF_VGROUP) {
    if (ELEM(target->type, OB_MESH, OB_LATTICE, OB_GPENCIL)) {
      /* if we have a Mesh, only use dverts if it has them */
      if (mesh) {
        use_dverts = (mesh->dvert != NULL);
      }
      else if (dverts) {
        use_dverts = true;
      }

      if (use_dverts) {
        defnrToPC = MEM_callocN(sizeof(*defnrToPC) * defbase_tot, "defnrToBone");
        /* TODO(sergey): Some considerations here:
         *
         * - Check whether keeping this consistent across frames gives speedup.
         */
        for (i = 0, dg = target->defbase.first; dg; i++, dg = dg->next) {
          defnrToPC[i] = BKE_pose_channel_find_name(armOb->pose, dg->name);
          /* exclude non-deforming bones */
          if (defnrToPC[i]) {
            if (defnrToPC[i]->bone->flag & BONE_NO_DEFORM) {
              defnrToPC[i] = NULL;
            }
          }
        }
      }
    }
  }

  ArmatureUserdata data = {.armOb = armOb,
                           .target = target,
                           .mesh = mesh,
                           .vertexCos = vertexCos,
                           .defMats = defMats,
                           .prevCos = prevCos,
                           .use_envelope = use_envelope,
                           .use_quaternion = use_quaternion,
                           .invert_vgroup = invert_vgroup,
                           .use_dverts = use_dverts,
                           .armature_def_nr = armature_def_nr,
                           .target_totvert = target_totvert,
                           .dverts = dverts,
                           .defbase_tot = defbase_tot,
                           .defnrToPC = defnrToPC};

  float obinv[4][4];
  invert_m4_m4(obinv, target->obmat);

  mul_m4_m4m4(data.postmat, obinv, armOb->obmat);
  invert_m4_m4(data.premat, data.postmat);

  ParallelRangeSettings settings;
  BLI_parallel_range_settings_defaults(&settings);
  settings.min_iter_per_thread = 32;
  BLI_task_parallel_range(0, numVerts, &data, armature_vert_task, &settings);

  if (defnrToPC) {
    MEM_freeN(defnrToPC);
  }
}

/* ************ END Armature Deform ******************* */

void get_objectspace_bone_matrix(struct Bone *bone,
                                 float M_accumulatedMatrix[4][4],
                                 int UNUSED(root),
                                 int UNUSED(posed))
{
  copy_m4_m4(M_accumulatedMatrix, bone->arm_mat);
}

/* **************** Space to Space API ****************** */

/* Convert World-Space Matrix to Pose-Space Matrix */
void BKE_armature_mat_world_to_pose(Object *ob, float inmat[4][4], float outmat[4][4])
{
  float obmat[4][4];

  /* prevent crashes */
  if (ob == NULL) {
    return;
  }

  /* get inverse of (armature) object's matrix  */
  invert_m4_m4(obmat, ob->obmat);

  /* multiply given matrix by object's-inverse to find pose-space matrix */
  mul_m4_m4m4(outmat, inmat, obmat);
}

/* Convert World-Space Location to Pose-Space Location
 * NOTE: this cannot be used to convert to pose-space location of the supplied
 *       pose-channel into its local space (i.e. 'visual'-keyframing) */
void BKE_armature_loc_world_to_pose(Object *ob, const float inloc[3], float outloc[3])
{
  float xLocMat[4][4];
  float nLocMat[4][4];

  /* build matrix for location */
  unit_m4(xLocMat);
  copy_v3_v3(xLocMat[3], inloc);

  /* get bone-space cursor matrix and extract location */
  BKE_armature_mat_world_to_pose(ob, xLocMat, nLocMat);
  copy_v3_v3(outloc, nLocMat[3]);
}

/* Simple helper, computes the offset bone matrix.
 *     offs_bone = yoffs(b-1) + root(b) + bonemat(b). */
void BKE_bone_offset_matrix_get(const Bone *bone, float offs_bone[4][4])
{
  BLI_assert(bone->parent != NULL);

  /* Bone transform itself. */
  copy_m4_m3(offs_bone, bone->bone_mat);

  /* The bone's root offset (is in the parent's coordinate system). */
  copy_v3_v3(offs_bone[3], bone->head);

  /* Get the length translation of parent (length along y axis). */
  offs_bone[3][1] += bone->parent->length;
}

/* Construct the matrices (rot/scale and loc)
 * to apply the PoseChannels into the armature (object) space.
 * I.e. (roughly) the "pose_mat(b-1) * yoffs(b-1) * d_root(b) * bone_mat(b)" in the
 *     pose_mat(b)= pose_mat(b-1) * yoffs(b-1) * d_root(b) * bone_mat(b) * chan_mat(b)
 * ...function.
 *
 * This allows to get the transformations of a bone in its object space,
 * *before* constraints (and IK) get applied (used by pose evaluation code).
 * And reverse: to find pchan transformations needed to place a bone at a given loc/rot/scale
 * in object space (used by interactive transform, and snapping code).
 *
 * Note that, with the HINGE/NO_SCALE/NO_LOCAL_LOCATION options, the location matrix
 * will differ from the rotation/scale matrix...
 *
 * NOTE: This cannot be used to convert to pose-space transforms of the supplied
 *       pose-channel into its local space (i.e. 'visual'-keyframing).
 *       (note: I don't understand that, so I keep it :p --mont29).
 */
void BKE_bone_parent_transform_calc_from_pchan(const bPoseChannel *pchan,
                                               BoneParentTransform *r_bpt)
{
  const Bone *bone, *parbone;
  const bPoseChannel *parchan;

  /* set up variables for quicker access below */
  bone = pchan->bone;
  parbone = bone->parent;
  parchan = pchan->parent;

  if (parchan) {
    float offs_bone[4][4];
    /* yoffs(b-1) + root(b) + bonemat(b). */
    BKE_bone_offset_matrix_get(bone, offs_bone);

    BKE_bone_parent_transform_calc_from_matrices(
        bone->flag, offs_bone, parbone->arm_mat, parchan->pose_mat, r_bpt);
  }
  else {
    BKE_bone_parent_transform_calc_from_matrices(bone->flag, bone->arm_mat, NULL, NULL, r_bpt);
  }
}

/* Compute the parent transform using data decoupled from specific data structures.
 *
 * bone_flag: Bone->flag containing settings
 * offs_bone: delta from parent to current arm_mat (or just arm_mat if no parent)
 * parent_arm_mat, parent_pose_mat: arm_mat and pose_mat of parent, or NULL
 * r_bpt: OUTPUT parent transform */
void BKE_bone_parent_transform_calc_from_matrices(int bone_flag,
                                                  const float offs_bone[4][4],
                                                  const float parent_arm_mat[4][4],
                                                  const float parent_pose_mat[4][4],
                                                  BoneParentTransform *r_bpt)
{
  if (parent_pose_mat) {
    /* Compose the rotscale matrix for this bone. */
    if ((bone_flag & BONE_HINGE) && (bone_flag & BONE_NO_SCALE)) {
      /* Parent rest rotation and scale. */
      mul_m4_m4m4(r_bpt->rotscale_mat, parent_arm_mat, offs_bone);
    }
    else if (bone_flag & BONE_HINGE) {
      /* Parent rest rotation and pose scale. */
      float tmat[4][4], tscale[3];

      /* Extract the scale of the parent pose matrix. */
      mat4_to_size(tscale, parent_pose_mat);
      size_to_mat4(tmat, tscale);

      /* Applies the parent pose scale to the rest matrix. */
      mul_m4_m4m4(tmat, tmat, parent_arm_mat);

      mul_m4_m4m4(r_bpt->rotscale_mat, tmat, offs_bone);
    }
    else if (bone_flag & BONE_NO_SCALE) {
      /* Parent pose rotation and rest scale (i.e. no scaling). */
      float tmat[4][4];
      copy_m4_m4(tmat, parent_pose_mat);
      normalize_m4(tmat);
      mul_m4_m4m4(r_bpt->rotscale_mat, tmat, offs_bone);
    }
    else {
      mul_m4_m4m4(r_bpt->rotscale_mat, parent_pose_mat, offs_bone);
    }

    /* Compose the loc matrix for this bone. */
    /* NOTE: That version does not modify bone's loc when HINGE/NO_SCALE options are set. */

    /* In this case, use the object's space *orientation*. */
    if (bone_flag & BONE_NO_LOCAL_LOCATION) {
      /* XXX I'm sure that code can be simplified! */
      float bone_loc[4][4], bone_rotscale[3][3], tmat4[4][4], tmat3[3][3];
      unit_m4(bone_loc);
      unit_m4(r_bpt->loc_mat);
      unit_m4(tmat4);

      mul_v3_m4v3(bone_loc[3], parent_pose_mat, offs_bone[3]);

      unit_m3(bone_rotscale);
      copy_m3_m4(tmat3, parent_pose_mat);
      mul_m3_m3m3(bone_rotscale, tmat3, bone_rotscale);

      copy_m4_m3(tmat4, bone_rotscale);
      mul_m4_m4m4(r_bpt->loc_mat, bone_loc, tmat4);
    }
    /* Those flags do not affect position, use plain parent transform space! */
    else if (bone_flag & (BONE_HINGE | BONE_NO_SCALE)) {
      mul_m4_m4m4(r_bpt->loc_mat, parent_pose_mat, offs_bone);
    }
    /* Else (i.e. default, usual case),
     * just use the same matrix for rotation/scaling, and location. */
    else {
      copy_m4_m4(r_bpt->loc_mat, r_bpt->rotscale_mat);
    }
  }
  /* Root bones. */
  else {
    /* Rotation/scaling. */
    copy_m4_m4(r_bpt->rotscale_mat, offs_bone);
    /* Translation. */
    if (bone_flag & BONE_NO_LOCAL_LOCATION) {
      /* Translation of arm_mat, without the rotation. */
      unit_m4(r_bpt->loc_mat);
      copy_v3_v3(r_bpt->loc_mat[3], offs_bone[3]);
    }
    else {
      copy_m4_m4(r_bpt->loc_mat, r_bpt->rotscale_mat);
    }
  }
}

void BKE_bone_parent_transform_clear(struct BoneParentTransform *bpt)
{
  unit_m4(bpt->rotscale_mat);
  unit_m4(bpt->loc_mat);
}

void BKE_bone_parent_transform_invert(struct BoneParentTransform *bpt)
{
  invert_m4(bpt->rotscale_mat);
  invert_m4(bpt->loc_mat);
}

void BKE_bone_parent_transform_combine(const struct BoneParentTransform *in1,
                                       const struct BoneParentTransform *in2,
                                       struct BoneParentTransform *result)
{
  mul_m4_m4m4(result->rotscale_mat, in1->rotscale_mat, in2->rotscale_mat);
  mul_m4_m4m4(result->loc_mat, in1->loc_mat, in2->loc_mat);
}

void BKE_bone_parent_transform_apply(const struct BoneParentTransform *bpt,
                                     const float inmat[4][4],
                                     float outmat[4][4])
{
  /* in case inmat == outmat */
  float tmploc[3];
  copy_v3_v3(tmploc, inmat[3]);

  mul_m4_m4m4(outmat, bpt->rotscale_mat, inmat);
  mul_v3_m4v3(outmat[3], bpt->loc_mat, tmploc);
}

/* Convert Pose-Space Matrix to Bone-Space Matrix.
 * NOTE: this cannot be used to convert to pose-space transforms of the supplied
 *       pose-channel into its local space (i.e. 'visual'-keyframing) */
void BKE_armature_mat_pose_to_bone(bPoseChannel *pchan, float inmat[4][4], float outmat[4][4])
{
  BoneParentTransform bpt;

  BKE_bone_parent_transform_calc_from_pchan(pchan, &bpt);
  BKE_bone_parent_transform_invert(&bpt);
  BKE_bone_parent_transform_apply(&bpt, inmat, outmat);
}

/* Convert Bone-Space Matrix to Pose-Space Matrix. */
void BKE_armature_mat_bone_to_pose(bPoseChannel *pchan, float inmat[4][4], float outmat[4][4])
{
  BoneParentTransform bpt;

  BKE_bone_parent_transform_calc_from_pchan(pchan, &bpt);
  BKE_bone_parent_transform_apply(&bpt, inmat, outmat);
}

/* Convert Pose-Space Location to Bone-Space Location
 * NOTE: this cannot be used to convert to pose-space location of the supplied
 *       pose-channel into its local space (i.e. 'visual'-keyframing) */
void BKE_armature_loc_pose_to_bone(bPoseChannel *pchan, const float inloc[3], float outloc[3])
{
  float xLocMat[4][4];
  float nLocMat[4][4];

  /* build matrix for location */
  unit_m4(xLocMat);
  copy_v3_v3(xLocMat[3], inloc);

  /* get bone-space cursor matrix and extract location */
  BKE_armature_mat_pose_to_bone(pchan, xLocMat, nLocMat);
  copy_v3_v3(outloc, nLocMat[3]);
}

void BKE_armature_mat_pose_to_bone_ex(struct Depsgraph *depsgraph,
                                      Object *ob,
                                      bPoseChannel *pchan,
                                      float inmat[4][4],
                                      float outmat[4][4])
{
  bPoseChannel work_pchan = *pchan;

  /* recalculate pose matrix with only parent transformations,
   * bone loc/sca/rot is ignored, scene and frame are not used. */
  BKE_pose_where_is_bone(depsgraph, NULL, ob, &work_pchan, 0.0f, false);

  /* find the matrix, need to remove the bone transforms first so this is
   * calculated as a matrix to set rather then a difference ontop of what's
   * already there. */
  unit_m4(outmat);
  BKE_pchan_apply_mat4(&work_pchan, outmat, false);

  BKE_armature_mat_pose_to_bone(&work_pchan, inmat, outmat);
}

/**
 * Same as #BKE_object_mat3_to_rot().
 */
void BKE_pchan_mat3_to_rot(bPoseChannel *pchan, float mat[3][3], bool use_compat)
{
  BLI_ASSERT_UNIT_M3(mat);

  switch (pchan->rotmode) {
    case ROT_MODE_QUAT:
      mat3_normalized_to_quat(pchan->quat, mat);
      break;
    case ROT_MODE_AXISANGLE:
      mat3_normalized_to_axis_angle(pchan->rotAxis, &pchan->rotAngle, mat);
      break;
    default: /* euler */
      if (use_compat) {
        mat3_normalized_to_compatible_eulO(pchan->eul, pchan->eul, pchan->rotmode, mat);
      }
      else {
        mat3_normalized_to_eulO(pchan->eul, pchan->rotmode, mat);
      }
      break;
  }
}

/**
 * Same as #BKE_object_rot_to_mat3().
 */
void BKE_pchan_rot_to_mat3(const bPoseChannel *pchan, float mat[3][3])
{
  /* rotations may either be quats, eulers (with various rotation orders), or axis-angle */
  if (pchan->rotmode > 0) {
    /* euler rotations (will cause gimble lock,
     * but this can be alleviated a bit with rotation orders) */
    eulO_to_mat3(mat, pchan->eul, pchan->rotmode);
  }
  else if (pchan->rotmode == ROT_MODE_AXISANGLE) {
    /* axis-angle - not really that great for 3D-changing orientations */
    axis_angle_to_mat3(mat, pchan->rotAxis, pchan->rotAngle);
  }
  else {
    /* quats are normalized before use to eliminate scaling issues */
    float quat[4];

    /* NOTE: we now don't normalize the stored values anymore,
     * since this was kindof evil in some cases but if this proves to be too problematic,
     * switch back to the old system of operating directly on the stored copy. */
    normalize_qt_qt(quat, pchan->quat);
    quat_to_mat3(mat, quat);
  }
}

/**
 * Apply a 4x4 matrix to the pose bone,
 * similar to #BKE_object_apply_mat4().
 */
void BKE_pchan_apply_mat4(bPoseChannel *pchan, float mat[4][4], bool use_compat)
{
  float rot[3][3];
  mat4_to_loc_rot_size(pchan->loc, rot, pchan->size, mat);
  BKE_pchan_mat3_to_rot(pchan, rot, use_compat);
}

/**
 * Remove rest-position effects from pose-transform for obtaining
 * 'visual' transformation of pose-channel.
 * (used by the Visual-Keyframing stuff).
 */
void BKE_armature_mat_pose_to_delta(float delta_mat[4][4],
                                    float pose_mat[4][4],
                                    float arm_mat[4][4])
{
  float imat[4][4];

  invert_m4_m4(imat, arm_mat);
  mul_m4_m4m4(delta_mat, imat, pose_mat);
}

/* **************** Rotation Mode Conversions ****************************** */
/* Used for Objects and Pose Channels, since both can have multiple rotation representations */

/* Called from RNA when rotation mode changes
 * - the result should be that the rotations given in the provided pointers have had conversions
 *   applied (as appropriate), such that the rotation of the element hasn't 'visually' changed  */
void BKE_rotMode_change_values(
    float quat[4], float eul[3], float axis[3], float *angle, short oldMode, short newMode)
{
  /* check if any change - if so, need to convert data */
  if (newMode > 0) { /* to euler */
    if (oldMode == ROT_MODE_AXISANGLE) {
      /* axis-angle to euler */
      axis_angle_to_eulO(eul, newMode, axis, *angle);
    }
    else if (oldMode == ROT_MODE_QUAT) {
      /* quat to euler */
      normalize_qt(quat);
      quat_to_eulO(eul, newMode, quat);
    }
    /* else { no conversion needed } */
  }
  else if (newMode == ROT_MODE_QUAT) { /* to quat */
    if (oldMode == ROT_MODE_AXISANGLE) {
      /* axis angle to quat */
      axis_angle_to_quat(quat, axis, *angle);
    }
    else if (oldMode > 0) {
      /* euler to quat */
      eulO_to_quat(quat, eul, oldMode);
    }
    /* else { no conversion needed } */
  }
  else if (newMode == ROT_MODE_AXISANGLE) { /* to axis-angle */
    if (oldMode > 0) {
      /* euler to axis angle */
      eulO_to_axis_angle(axis, angle, eul, oldMode);
    }
    else if (oldMode == ROT_MODE_QUAT) {
      /* quat to axis angle */
      normalize_qt(quat);
      quat_to_axis_angle(axis, angle, quat);
    }

    /* When converting to axis-angle,
     * we need a special exception for the case when there is no axis. */
    if (IS_EQF(axis[0], axis[1]) && IS_EQF(axis[1], axis[2])) {
      /* for now, rotate around y-axis then (so that it simply becomes the roll) */
      axis[1] = 1.0f;
    }
  }
}

/* **************** The new & simple (but OK!) armature evaluation ********* */

/* ****************** And how it works! ****************************************
 *
 * This is the bone transformation trick; they're hierarchical so each bone(b)
 * is in the coord system of bone(b-1):
 *
 * arm_mat(b)= arm_mat(b-1) * yoffs(b-1) * d_root(b) * bone_mat(b)
 *
 * -> yoffs is just the y axis translation in parent's coord system
 * -> d_root is the translation of the bone root, also in parent's coord system
 *
 * pose_mat(b)= pose_mat(b-1) * yoffs(b-1) * d_root(b) * bone_mat(b) * chan_mat(b)
 *
 * we then - in init deform - store the deform in chan_mat, such that:
 *
 * pose_mat(b)= arm_mat(b) * chan_mat(b)
 *
 * *************************************************************************** */

/* Computes vector and roll based on a rotation.
 * "mat" must contain only a rotation, and no scaling. */
void mat3_to_vec_roll(const float mat[3][3], float r_vec[3], float *r_roll)
{
  if (r_vec) {
    copy_v3_v3(r_vec, mat[1]);
  }

  if (r_roll) {
    mat3_vec_to_roll(mat, mat[1], r_roll);
  }
}

/* Computes roll around the vector that best approximates the matrix.
 * If vec is the Y vector from purely rotational mat, result should be exact. */
void mat3_vec_to_roll(const float mat[3][3], const float vec[3], float *r_roll)
{
  float vecmat[3][3], vecmatinv[3][3], rollmat[3][3];

  vec_roll_to_mat3(vec, 0.0f, vecmat);
  invert_m3_m3(vecmatinv, vecmat);
  mul_m3_m3m3(rollmat, vecmatinv, mat);

  *r_roll = atan2f(rollmat[2][0], rollmat[2][2]);
}

/* Calculates the rest matrix of a bone based on its vector and a roll around that vector. */
/**
 * Given `v = (v.x, v.y, v.z)` our (normalized) bone vector, we want the rotation matrix M
 * from the Y axis (so that `M * (0, 1, 0) = v`).
 * - The rotation axis a lays on XZ plane, and it is orthonormal to v,
 *   hence to the projection of v onto XZ plane.
 * - `a = (v.z, 0, -v.x)`
 *
 * We know a is eigenvector of M (so M * a = a).
 * Finally, we have w, such that M * w = (0, 1, 0)
 * (i.e. the vector that will be aligned with Y axis once transformed).
 * We know w is symmetric to v by the Y axis.
 * - `w = (-v.x, v.y, -v.z)`
 *
 * Solving this, we get (x, y and z being the components of v):
 * <pre>
 *     ┌ (x^2 * y + z^2) / (x^2 + z^2),   x,   x * z * (y - 1) / (x^2 + z^2) ┐
 * M = │  x * (y^2 - 1)  / (x^2 + z^2),   y,    z * (y^2 - 1)  / (x^2 + z^2) │
 *     └ x * z * (y - 1) / (x^2 + z^2),   z,   (x^2 + z^2 * y) / (x^2 + z^2) ┘
 * </pre>
 *
 * This is stable as long as v (the bone) is not too much aligned with +/-Y
 * (i.e. x and z components are not too close to 0).
 *
 * Since v is normalized, we have `x^2 + y^2 + z^2 = 1`,
 * hence `x^2 + z^2 = 1 - y^2 = (1 - y)(1 + y)`.
 *
 * This allows to simplifies M like this:
 * <pre>
 *     ┌ 1 - x^2 / (1 + y),   x,     -x * z / (1 + y) ┐
 * M = │                -x,   y,                   -z │
 *     └  -x * z / (1 + y),   z,    1 - z^2 / (1 + y) ┘
 * </pre>
 *
 * Written this way, we see the case v = +Y is no more a singularity.
 * The only one
 * remaining is the bone being aligned with -Y.
 *
 * Let's handle
 * the asymptotic behavior when bone vector is reaching the limit of y = -1.
 * Each of the four corner elements can vary from -1 to 1,
 * depending on the axis a chosen for doing the rotation.
 * And the "rotation" here is in fact established by mirroring XZ plane by that given axis,
 * then inversing the Y-axis.
 * For sufficiently small x and z, and with y approaching -1,
 * all elements but the four corner ones of M will degenerate.
 * So let's now focus on these corner elements.
 *
 * We rewrite M so that it only contains its four corner elements,
 * and combine the `1 / (1 + y)` factor:
 * <pre>
 *                    ┌ 1 + y - x^2,        -x * z ┐
 * M* = 1 / (1 + y) * │                            │
 *                    └      -x * z,   1 + y - z^2 ┘
 * </pre>
 *
 * When y is close to -1, computing 1 / (1 + y) will cause severe numerical instability,
 * so we ignore it and normalize M instead.
 * We know `y^2 = 1 - (x^2 + z^2)`, and `y < 0`, hence `y = -sqrt(1 - (x^2 + z^2))`.
 *
 * Since x and z are both close to 0, we apply the binomial expansion to the first order:
 * `y = -sqrt(1 - (x^2 + z^2)) = -1 + (x^2 + z^2) / 2`. Which gives:
 * <pre>
 *                        ┌  z^2 - x^2,  -2 * x * z ┐
 * M* = 1 / (x^2 + z^2) * │                         │
 *                        └ -2 * x * z,   x^2 - z^2 ┘
 * </pre>
 */
void vec_roll_to_mat3_normalized(const float nor[3], const float roll, float mat[3][3])
{
#define THETA_THRESHOLD_NEGY 1.0e-9f
#define THETA_THRESHOLD_NEGY_CLOSE 1.0e-5f

  float theta;
  float rMatrix[3][3], bMatrix[3][3];

  BLI_ASSERT_UNIT_V3(nor);

  theta = 1.0f + nor[1];

  /* With old algo, 1.0e-13f caused T23954 and T31333, 1.0e-6f caused T27675 and T30438,
   * so using 1.0e-9f as best compromise.
   *
   * New algo is supposed much more precise, since less complex computations are performed,
   * but it uses two different threshold values...
   *
   * Note: When theta is close to zero, we have to check we do have non-null X/Z components as well
   *       (due to float precision errors, we can have nor = (0.0, 0.99999994, 0.0)...).
   */
  if (theta > THETA_THRESHOLD_NEGY_CLOSE || ((nor[0] || nor[2]) && theta > THETA_THRESHOLD_NEGY)) {
    /* nor is *not* -Y.
     * We got these values for free... so be happy with it... ;)
     */
    bMatrix[0][1] = -nor[0];
    bMatrix[1][0] = nor[0];
    bMatrix[1][1] = nor[1];
    bMatrix[1][2] = nor[2];
    bMatrix[2][1] = -nor[2];
    if (theta > THETA_THRESHOLD_NEGY_CLOSE) {
      /* If nor is far enough from -Y, apply the general case. */
      bMatrix[0][0] = 1 - nor[0] * nor[0] / theta;
      bMatrix[2][2] = 1 - nor[2] * nor[2] / theta;
      bMatrix[2][0] = bMatrix[0][2] = -nor[0] * nor[2] / theta;
    }
    else {
      /* If nor is too close to -Y, apply the special case. */
      theta = nor[0] * nor[0] + nor[2] * nor[2];
      bMatrix[0][0] = (nor[0] + nor[2]) * (nor[0] - nor[2]) / -theta;
      bMatrix[2][2] = -bMatrix[0][0];
      bMatrix[2][0] = bMatrix[0][2] = 2.0f * nor[0] * nor[2] / theta;
    }
  }
  else {
    /* If nor is -Y, simple symmetry by Z axis. */
    unit_m3(bMatrix);
    bMatrix[0][0] = bMatrix[1][1] = -1.0;
  }

  /* Make Roll matrix */
  axis_angle_normalized_to_mat3(rMatrix, nor, roll);

  /* Combine and output result */
  mul_m3_m3m3(mat, rMatrix, bMatrix);

#undef THETA_THRESHOLD_NEGY
#undef THETA_THRESHOLD_NEGY_CLOSE
}

void vec_roll_to_mat3(const float vec[3], const float roll, float mat[3][3])
{
  float nor[3];

  normalize_v3_v3(nor, vec);
  vec_roll_to_mat3_normalized(nor, roll, mat);
}

/* recursive part, calculates restposition of entire tree of children */
/* used by exiting editmode too */
void BKE_armature_where_is_bone(Bone *bone, Bone *prevbone, const bool use_recursion)
{
  float vec[3];

  /* Bone Space */
  sub_v3_v3v3(vec, bone->tail, bone->head);
  bone->length = len_v3(vec);
  vec_roll_to_mat3(vec, bone->roll, bone->bone_mat);

  /* this is called on old file reading too... */
  if (bone->xwidth == 0.0f) {
    bone->xwidth = 0.1f;
    bone->zwidth = 0.1f;
    bone->segments = 1;
  }

  if (prevbone) {
    float offs_bone[4][4];
    /* yoffs(b-1) + root(b) + bonemat(b) */
    BKE_bone_offset_matrix_get(bone, offs_bone);

    /* Compose the matrix for this bone  */
    mul_m4_m4m4(bone->arm_mat, prevbone->arm_mat, offs_bone);
  }
  else {
    copy_m4_m3(bone->arm_mat, bone->bone_mat);
    copy_v3_v3(bone->arm_mat[3], bone->head);
  }

  /* and the kiddies */
  if (use_recursion) {
    prevbone = bone;
    for (bone = bone->childbase.first; bone; bone = bone->next) {
      BKE_armature_where_is_bone(bone, prevbone, use_recursion);
    }
  }
}

/* updates vectors and matrices on rest-position level, only needed
 * after editing armature itself, now only on reading file */
void BKE_armature_where_is(bArmature *arm)
{
  Bone *bone;

  /* hierarchical from root to children */
  for (bone = arm->bonebase.first; bone; bone = bone->next) {
    BKE_armature_where_is_bone(bone, NULL, true);
  }
}

/* if bone layer is protected, copy the data from from->pose
 * when used with linked libraries this copies from the linked pose into the local pose */
static void pose_proxy_synchronize(Object *ob, Object *from, int layer_protected)
{
  bPose *pose = ob->pose, *frompose = from->pose;
  bPoseChannel *pchan, *pchanp;
  bConstraint *con;
  int error = 0;

  if (frompose == NULL) {
    return;
  }

  /* in some cases when rigs change, we cant synchronize
   * to avoid crashing check for possible errors here */
  for (pchan = pose->chanbase.first; pchan; pchan = pchan->next) {
    if (pchan->bone->layer & layer_protected) {
      if (BKE_pose_channel_find_name(frompose, pchan->name) == NULL) {
        CLOG_ERROR(&LOG,
                   "failed to sync proxy armature because '%s' is missing pose channel '%s'",
                   from->id.name,
                   pchan->name);
        error = 1;
      }
    }
  }

  if (error) {
    return;
  }

  /* clear all transformation values from library */
  BKE_pose_rest(frompose);

  /* copy over all of the proxy's bone groups */
  /* TODO for later
   * - implement 'local' bone groups as for constraints
   * Note: this isn't trivial, as bones reference groups by index not by pointer,
   *       so syncing things correctly needs careful attention */
  BLI_freelistN(&pose->agroups);
  BLI_duplicatelist(&pose->agroups, &frompose->agroups);
  pose->active_group = frompose->active_group;

  for (pchan = pose->chanbase.first; pchan; pchan = pchan->next) {
    pchanp = BKE_pose_channel_find_name(frompose, pchan->name);

    if (UNLIKELY(pchanp == NULL)) {
      /* happens for proxies that become invalid because of a missing link
       * for regular cases it shouldn't happen at all */
    }
    else if (pchan->bone->layer & layer_protected) {
      ListBase proxylocal_constraints = {NULL, NULL};
      bPoseChannel pchanw;

      /* copy posechannel to temp, but restore important pointers */
      pchanw = *pchanp;
      pchanw.bone = pchan->bone;
      pchanw.prev = pchan->prev;
      pchanw.next = pchan->next;
      pchanw.parent = pchan->parent;
      pchanw.child = pchan->child;
      pchanw.custom_tx = pchan->custom_tx;
      pchanw.bbone_prev = pchan->bbone_prev;
      pchanw.bbone_next = pchan->bbone_next;

      pchanw.mpath = pchan->mpath;
      pchan->mpath = NULL;

      /* this is freed so copy a copy, else undo crashes */
      if (pchanw.prop) {
        pchanw.prop = IDP_CopyProperty(pchanw.prop);

        /* use the values from the existing props */
        if (pchan->prop) {
          IDP_SyncGroupValues(pchanw.prop, pchan->prop);
        }
      }

      /* Constraints - proxy constraints are flushed... local ones are added after
       * 1: extract constraints not from proxy (CONSTRAINT_PROXY_LOCAL) from pchan's constraints.
       * 2: copy proxy-pchan's constraints on-to new.
       * 3: add extracted local constraints back on top.
       *
       * Note for BKE_constraints_copy:
       * When copying constraints, disable 'do_extern' otherwise
       * we get the libs direct linked in this blend.
       */
      BKE_constraints_proxylocal_extract(&proxylocal_constraints, &pchan->constraints);
      BKE_constraints_copy(&pchanw.constraints, &pchanp->constraints, false);
      BLI_movelisttolist(&pchanw.constraints, &proxylocal_constraints);

      /* constraints - set target ob pointer to own object */
      for (con = pchanw.constraints.first; con; con = con->next) {
        const bConstraintTypeInfo *cti = BKE_constraint_typeinfo_get(con);
        ListBase targets = {NULL, NULL};
        bConstraintTarget *ct;

        if (cti && cti->get_constraint_targets) {
          cti->get_constraint_targets(con, &targets);

          for (ct = targets.first; ct; ct = ct->next) {
            if (ct->tar == from) {
              ct->tar = ob;
            }
          }

          if (cti->flush_constraint_targets) {
            cti->flush_constraint_targets(con, &targets, 0);
          }
        }
      }

      /* free stuff from current channel */
      BKE_pose_channel_free(pchan);

      /* copy data in temp back over to the cleaned-out (but still allocated) original channel */
      *pchan = pchanw;
      if (pchan->custom) {
        id_us_plus(&pchan->custom->id);
      }
    }
    else {
      /* always copy custom shape */
      pchan->custom = pchanp->custom;
      if (pchan->custom) {
        id_us_plus(&pchan->custom->id);
      }
      if (pchanp->custom_tx) {
        pchan->custom_tx = BKE_pose_channel_find_name(pose, pchanp->custom_tx->name);
      }

      /* ID-Property Syncing */
      {
        IDProperty *prop_orig = pchan->prop;
        if (pchanp->prop) {
          pchan->prop = IDP_CopyProperty(pchanp->prop);
          if (prop_orig) {
            /* copy existing values across when types match */
            IDP_SyncGroupValues(pchan->prop, prop_orig);
          }
        }
        else {
          pchan->prop = NULL;
        }
        if (prop_orig) {
          IDP_FreeProperty(prop_orig);
        }
      }
    }
  }
}

static int rebuild_pose_bone(bPose *pose, Bone *bone, bPoseChannel *parchan, int counter)
{
  bPoseChannel *pchan = BKE_pose_channel_verify(pose, bone->name); /* verify checks and/or adds */

  pchan->bone = bone;
  pchan->parent = parchan;

  counter++;

  for (bone = bone->childbase.first; bone; bone = bone->next) {
    counter = rebuild_pose_bone(pose, bone, pchan, counter);
    /* for quick detecting of next bone in chain, only b-bone uses it now */
    if (bone->flag & BONE_CONNECTED) {
      pchan->child = BKE_pose_channel_find_name(pose, bone->name);
    }
  }

  return counter;
}

/**
 * Clear pointers of object's pose
 * (needed in remap case, since we cannot always wait for a complete pose rebuild).
 */
void BKE_pose_clear_pointers(bPose *pose)
{
  for (bPoseChannel *pchan = pose->chanbase.first; pchan; pchan = pchan->next) {
    pchan->bone = NULL;
    pchan->child = NULL;
  }
}

void BKE_pose_remap_bone_pointers(bArmature *armature, bPose *pose)
{
  for (bPoseChannel *pchan = pose->chanbase.first; pchan; pchan = pchan->next) {
    pchan->bone = BKE_armature_find_bone_name(armature, pchan->name);
  }
}

/** Find the matching pose channel using the bone name, if not NULL. */
static bPoseChannel *pose_channel_find_bone(bPose *pose, Bone *bone)
{
  return (bone != NULL) ? BKE_pose_channel_find_name(pose, bone->name) : NULL;
}

/** Update the links for the B-Bone handles from Bone data. */
void BKE_pchan_rebuild_bbone_handles(bPose *pose, bPoseChannel *pchan)
{
  pchan->bbone_prev = pose_channel_find_bone(pose, pchan->bone->bbone_prev);
  pchan->bbone_next = pose_channel_find_bone(pose, pchan->bone->bbone_next);
}

/**
 * Only after leave editmode, duplicating, validating older files, library syncing.
 *
 * \note pose->flag is set for it.
 *
 * \param bmain: May be NULL, only used to tag depsgraph as being dirty...
 */
void BKE_pose_rebuild(Main *bmain, Object *ob, bArmature *arm, const bool do_id_user)
{
  Bone *bone;
  bPose *pose;
  bPoseChannel *pchan, *next;
  int counter = 0;

  /* only done here */
  if (ob->pose == NULL) {
    /* create new pose */
    ob->pose = MEM_callocN(sizeof(bPose), "new pose");

    /* set default settings for animviz */
    animviz_settings_init(&ob->pose->avs);
  }
  pose = ob->pose;

  /* clear */
  BKE_pose_clear_pointers(pose);

  /* first step, check if all channels are there */
  for (bone = arm->bonebase.first; bone; bone = bone->next) {
    counter = rebuild_pose_bone(pose, bone, NULL, counter);
  }

  /* and a check for garbage */
  for (pchan = pose->chanbase.first; pchan; pchan = next) {
    next = pchan->next;
    if (pchan->bone == NULL) {
      BKE_pose_channel_free_ex(pchan, do_id_user);
      BKE_pose_channels_hash_free(pose);
      BLI_freelinkN(&pose->chanbase, pchan);
    }
  }

  BKE_pose_channels_hash_make(pose);

  for (pchan = pose->chanbase.first; pchan; pchan = pchan->next) {
    /* Find the custom B-Bone handles. */
    BKE_pchan_rebuild_bbone_handles(pose, pchan);
  }

  /* printf("rebuild pose %s, %d bones\n", ob->id.name, counter); */

  /* synchronize protected layers with proxy */
  /* HACK! To preserve 2.7x behavior that you always can pose even locked bones,
   * do not do any restoration if this is a COW temp copy! */
  /* Switched back to just NO_MAIN tag, for some reasons (c)
   * using COW tag was working this morning, but not anymore... */
  if (ob->proxy != NULL && (ob->id.tag & LIB_TAG_NO_MAIN) == 0) {
    BKE_object_copy_proxy_drivers(ob, ob->proxy);
    pose_proxy_synchronize(ob, ob->proxy, arm->layer_protected);
  }

  BKE_pose_update_constraint_flags(pose); /* for IK detection for example */

  pose->flag &= ~POSE_RECALC;
  pose->flag |= POSE_WAS_REBUILT;

  /* Rebuilding poses forces us to also rebuild the dependency graph,
   * since there is one node per pose/bone. */
  if (bmain != NULL) {
    DEG_relations_tag_update(bmain);
  }
}

/* ********************** THE POSE SOLVER ******************* */

/* loc/rot/size to given mat4 */
void BKE_pchan_to_mat4(const bPoseChannel *pchan, float chan_mat[4][4])
{
  float smat[3][3];
  float rmat[3][3];
  float tmat[3][3];

  /* get scaling matrix */
  size_to_mat3(smat, pchan->size);

  /* get rotation matrix */
  BKE_pchan_rot_to_mat3(pchan, rmat);

  /* calculate matrix of bone (as 3x3 matrix, but then copy the 4x4) */
  mul_m3_m3m3(tmat, rmat, smat);
  copy_m4_m3(chan_mat, tmat);

  /* prevent action channels breaking chains */
  /* need to check for bone here, CONSTRAINT_TYPE_ACTION uses this call */
  if ((pchan->bone == NULL) || !(pchan->bone->flag & BONE_CONNECTED)) {
    copy_v3_v3(chan_mat[3], pchan->loc);
  }
}

/* loc/rot/size to mat4 */
/* used in constraint.c too */
void BKE_pchan_calc_mat(bPoseChannel *pchan)
{
  /* this is just a wrapper around the copy of this function which calculates the matrix
   * and stores the result in any given channel
   */
  BKE_pchan_to_mat4(pchan, pchan->chan_mat);
}

/* calculate tail of posechannel */
void BKE_pose_where_is_bone_tail(bPoseChannel *pchan)
{
  float vec[3];

  copy_v3_v3(vec, pchan->pose_mat[1]);
  mul_v3_fl(vec, pchan->bone->length);
  add_v3_v3v3(pchan->pose_tail, pchan->pose_head, vec);
}

/* The main armature solver, does all constraints excluding IK */
/* pchan is validated, as having bone and parent pointer
 * 'do_extra': when zero skips loc/size/rot, constraints and strip modifiers.
 */
void BKE_pose_where_is_bone(struct Depsgraph *depsgraph,
                            Scene *scene,
                            Object *ob,
                            bPoseChannel *pchan,
                            float ctime,
                            bool do_extra)
{
  /* This gives a chan_mat with actions (ipos) results. */
  if (do_extra) {
    BKE_pchan_calc_mat(pchan);
  }
  else {
    unit_m4(pchan->chan_mat);
  }

  /* Construct the posemat based on PoseChannels, that we do before applying constraints. */
  /* pose_mat(b) = pose_mat(b-1) * yoffs(b-1) * d_root(b) * bone_mat(b) * chan_mat(b) */
  BKE_armature_mat_bone_to_pose(pchan, pchan->chan_mat, pchan->pose_mat);

  /* Only rootbones get the cyclic offset (unless user doesn't want that). */
  /* XXX That could be a problem for snapping and other "reverse transform" features... */
  if (!pchan->parent) {
    if ((pchan->bone->flag & BONE_NO_CYCLICOFFSET) == 0) {
      add_v3_v3(pchan->pose_mat[3], ob->pose->cyclic_offset);
    }
  }

  if (do_extra) {
    /* Do constraints */
    if (pchan->constraints.first) {
      bConstraintOb *cob;
      float vec[3];

      /* make a copy of location of PoseChannel for later */
      copy_v3_v3(vec, pchan->pose_mat[3]);

      /* prepare PoseChannel for Constraint solving
       * - makes a copy of matrix, and creates temporary struct to use
       */
      cob = BKE_constraints_make_evalob(depsgraph, scene, ob, pchan, CONSTRAINT_OBTYPE_BONE);

      /* Solve PoseChannel's Constraints */
      BKE_constraints_solve(
          depsgraph, &pchan->constraints, cob, ctime); /* ctime doesn't alter objects */

      /* cleanup after Constraint Solving
       * - applies matrix back to pchan, and frees temporary struct used
       */
      BKE_constraints_clear_evalob(cob);

      /* prevent constraints breaking a chain */
      if (pchan->bone->flag & BONE_CONNECTED) {
        copy_v3_v3(pchan->pose_mat[3], vec);
      }
    }
  }

  /* calculate head */
  copy_v3_v3(pchan->pose_head, pchan->pose_mat[3]);
  /* calculate tail */
  BKE_pose_where_is_bone_tail(pchan);
}

/* This only reads anim data from channels, and writes to channels */
/* This is the only function adding poses */
void BKE_pose_where_is(struct Depsgraph *depsgraph, Scene *scene, Object *ob)
{
  bArmature *arm;
  Bone *bone;
  bPoseChannel *pchan;
  float imat[4][4];
  float ctime;

  if (ob->type != OB_ARMATURE) {
    return;
  }
  arm = ob->data;

  if (ELEM(NULL, arm, scene)) {
    return;
  }
  if ((ob->pose == NULL) || (ob->pose->flag & POSE_RECALC)) {
    /* WARNING! passing NULL bmain here means we won't tag depsgraph's as dirty -
     * hopefully this is OK. */
    BKE_pose_rebuild(NULL, ob, arm, true);
  }

  ctime = BKE_scene_frame_get(scene); /* not accurate... */

  /* In editmode or restposition we read the data from the bones */
  if (arm->edbo || (arm->flag & ARM_RESTPOS)) {
    for (pchan = ob->pose->chanbase.first; pchan; pchan = pchan->next) {
      bone = pchan->bone;
      if (bone) {
        copy_m4_m4(pchan->pose_mat, bone->arm_mat);
        copy_v3_v3(pchan->pose_head, bone->arm_head);
        copy_v3_v3(pchan->pose_tail, bone->arm_tail);
      }
    }
  }
  else {
    invert_m4_m4(ob->imat, ob->obmat); /* imat is needed */

    /* 1. clear flags */
    for (pchan = ob->pose->chanbase.first; pchan; pchan = pchan->next) {
      pchan->flag &= ~(POSE_DONE | POSE_CHAIN | POSE_IKTREE | POSE_IKSPLINE);
    }

    /* 2a. construct the IK tree (standard IK) */
    BIK_initialize_tree(depsgraph, scene, ob, ctime);

    /* 2b. construct the Spline IK trees
     * - this is not integrated as an IK plugin, since it should be able
     *   to function in conjunction with standard IK
     */
    BKE_pose_splineik_init_tree(scene, ob, ctime);

    /* 3. the main loop, channels are already hierarchical sorted from root to children */
    for (pchan = ob->pose->chanbase.first; pchan; pchan = pchan->next) {
      /* 4a. if we find an IK root, we handle it separated */
      if (pchan->flag & POSE_IKTREE) {
        BIK_execute_tree(depsgraph, scene, ob, pchan, ctime);
      }
      /* 4b. if we find a Spline IK root, we handle it separated too */
      else if (pchan->flag & POSE_IKSPLINE) {
        BKE_splineik_execute_tree(depsgraph, scene, ob, pchan, ctime);
      }
      /* 5. otherwise just call the normal solver */
      else if (!(pchan->flag & POSE_DONE)) {
        BKE_pose_where_is_bone(depsgraph, scene, ob, pchan, ctime, 1);
      }
    }
    /* 6. release the IK tree */
    BIK_release_tree(scene, ob, ctime);
  }

  /* calculating deform matrices */
  for (pchan = ob->pose->chanbase.first; pchan; pchan = pchan->next) {
    if (pchan->bone) {
      invert_m4_m4(imat, pchan->bone->arm_mat);
      mul_m4_m4m4(pchan->chan_mat, pchan->pose_mat, imat);
    }
  }
}

/************** Bounding box ********************/
static int minmax_armature(Object *ob, float r_min[3], float r_max[3])
{
  bPoseChannel *pchan;

  /* For now, we assume BKE_pose_where_is has already been called
   * (hence we have valid data in pachan). */
  for (pchan = ob->pose->chanbase.first; pchan; pchan = pchan->next) {
    minmax_v3v3_v3(r_min, r_max, pchan->pose_head);
    minmax_v3v3_v3(r_min, r_max, pchan->pose_tail);
  }

  return (BLI_listbase_is_empty(&ob->pose->chanbase) == false);
}

static void boundbox_armature(Object *ob)
{
  BoundBox *bb;
  float min[3], max[3];

  if (ob->runtime.bb == NULL) {
    ob->runtime.bb = MEM_callocN(sizeof(BoundBox), "Armature boundbox");
  }
  bb = ob->runtime.bb;

  INIT_MINMAX(min, max);
  if (!minmax_armature(ob, min, max)) {
    min[0] = min[1] = min[2] = -1.0f;
    max[0] = max[1] = max[2] = 1.0f;
  }

  BKE_boundbox_init_from_minmax(bb, min, max);

  bb->flag &= ~BOUNDBOX_DIRTY;
}

BoundBox *BKE_armature_boundbox_get(Object *ob)
{
  boundbox_armature(ob);

  return ob->runtime.bb;
}

bool BKE_pose_minmax(Object *ob, float r_min[3], float r_max[3], bool use_hidden, bool use_select)
{
  bool changed = false;

  if (ob->pose) {
    bArmature *arm = ob->data;
    bPoseChannel *pchan;

    for (pchan = ob->pose->chanbase.first; pchan; pchan = pchan->next) {
      /* XXX pchan->bone may be NULL for duplicated bones, see duplicateEditBoneObjects() comment
       *     (editarmature.c:2592)... Skip in this case too! */
      if (pchan->bone && (!((use_hidden == false) && (PBONE_VISIBLE(arm, pchan->bone) == false)) &&
                          !((use_select == true) && ((pchan->bone->flag & BONE_SELECTED) == 0)))) {
        bPoseChannel *pchan_tx = (pchan->custom && pchan->custom_tx) ? pchan->custom_tx : pchan;
        BoundBox *bb_custom = ((pchan->custom) && !(arm->flag & ARM_NO_CUSTOM)) ?
                                  BKE_object_boundbox_get(pchan->custom) :
                                  NULL;
        if (bb_custom) {
          float mat[4][4], smat[4][4];
          scale_m4_fl(smat, PCHAN_CUSTOM_DRAW_SIZE(pchan));
          mul_m4_series(mat, ob->obmat, pchan_tx->pose_mat, smat);
          BKE_boundbox_minmax(bb_custom, mat, r_min, r_max);
        }
        else {
          float vec[3];
          mul_v3_m4v3(vec, ob->obmat, pchan_tx->pose_head);
          minmax_v3v3_v3(r_min, r_max, vec);
          mul_v3_m4v3(vec, ob->obmat, pchan_tx->pose_tail);
          minmax_v3v3_v3(r_min, r_max, vec);
        }

        changed = true;
      }
    }
  }

  return changed;
}

/************** Graph evaluation ********************/

bPoseChannel *BKE_armature_ik_solver_find_root(bPoseChannel *pchan, bKinematicConstraint *data)
{
  bPoseChannel *rootchan = pchan;
  if (!(data->flag & CONSTRAINT_IK_TIP)) {
    /* Exclude tip from chain. */
    rootchan = rootchan->parent;
  }
  if (rootchan != NULL) {
    int segcount = 0;
    while (rootchan->parent) {
      /* Continue up chain, until we reach target number of items. */
      segcount++;
      if (segcount == data->rootbone) {
        break;
      }
      rootchan = rootchan->parent;
    }
  }
  return rootchan;
}

bPoseChannel *BKE_armature_splineik_solver_find_root(bPoseChannel *pchan,
                                                     bSplineIKConstraint *data)
{
  bPoseChannel *rootchan = pchan;
  int segcount = 0;
  BLI_assert(rootchan != NULL);
  while (rootchan->parent) {
    /* Continue up chain, until we reach target number of items. */
    segcount++;
    if (segcount == data->chainlen) {
      break;
    }
    rootchan = rootchan->parent;
  }
  return rootchan;
}
