blender-archive/source/blender/python/mathutils/mathutils_Quaternion.c

/*
 * 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.
 */

/** \file
 * \ingroup pymathutils
 */

#include <Python.h>

#include "mathutils.h"

#include "BLI_math.h"
#include "BLI_utildefines.h"

#include "../generic/python_utildefines.h"
#include "../generic/py_capi_utils.h"

#ifndef MATH_STANDALONE
#  include "BLI_dynstr.h"
#endif

#define QUAT_SIZE 4

static PyObject *quat__apply_to_copy(PyNoArgsFunction quat_func, QuaternionObject *self);
static void quat__axis_angle_sanitize(float axis[3], float *angle);
static PyObject *Quaternion_copy(QuaternionObject *self);
static PyObject *Quaternion_deepcopy(QuaternionObject *self, PyObject *args);

/* -----------------------------METHODS------------------------------ */

/* note: BaseMath_ReadCallback must be called beforehand */
static PyObject *Quaternion_to_tuple_ext(QuaternionObject *self, int ndigits)
{
  PyObject *ret;
  int i;

  ret = PyTuple_New(QUAT_SIZE);

  if (ndigits >= 0) {
    for (i = 0; i < QUAT_SIZE; i++) {
      PyTuple_SET_ITEM(ret, i, PyFloat_FromDouble(double_round((double)self->quat[i], ndigits)));
    }
  }
  else {
    for (i = 0; i < QUAT_SIZE; i++) {
      PyTuple_SET_ITEM(ret, i, PyFloat_FromDouble(self->quat[i]));
    }
  }

  return ret;
}

PyDoc_STRVAR(Quaternion_to_euler_doc,
             ".. method:: to_euler(order, euler_compat)\n"
             "\n"
             "   Return Euler representation of the quaternion.\n"
             "\n"
             "   :arg order: Optional rotation order argument in\n"
             "      ['XYZ', 'XZY', 'YXZ', 'YZX', 'ZXY', 'ZYX'].\n"
             "   :type order: string\n"
             "   :arg euler_compat: Optional euler argument the new euler will be made\n"
             "      compatible with (no axis flipping between them).\n"
             "      Useful for converting a series of matrices to animation curves.\n"
             "   :type euler_compat: :class:`Euler`\n"
             "   :return: Euler representation of the quaternion.\n"
             "   :rtype: :class:`Euler`\n");
static PyObject *Quaternion_to_euler(QuaternionObject *self, PyObject *args)
{
  float tquat[4];
  float eul[3];
  const char *order_str = NULL;
  short order = EULER_ORDER_XYZ;
  EulerObject *eul_compat = NULL;

  if (!PyArg_ParseTuple(args, "|sO!:to_euler", &order_str, &euler_Type, &eul_compat)) {
    return NULL;
  }

  if (BaseMath_ReadCallback(self) == -1) {
    return NULL;
  }

  if (order_str) {
    order = euler_order_from_string(order_str, "Matrix.to_euler()");

    if (order == -1) {
      return NULL;
    }
  }

  normalize_qt_qt(tquat, self->quat);

  if (eul_compat) {
    if (BaseMath_ReadCallback(eul_compat) == -1) {
      return NULL;
    }

    if (order == EULER_ORDER_XYZ) {
      quat_to_compatible_eul(eul, eul_compat->eul, tquat);
    }
    else {
      quat_to_compatible_eulO(eul, eul_compat->eul, order, tquat);
    }
  }
  else {
    if (order == EULER_ORDER_XYZ) {
      quat_to_eul(eul, tquat);
    }
    else {
      quat_to_eulO(eul, order, tquat);
    }
  }

  return Euler_CreatePyObject(eul, order, NULL);
}

PyDoc_STRVAR(Quaternion_to_matrix_doc,
             ".. method:: to_matrix()\n"
             "\n"
             "   Return a matrix representation of the quaternion.\n"
             "\n"
             "   :return: A 3x3 rotation matrix representation of the quaternion.\n"
             "   :rtype: :class:`Matrix`\n");
static PyObject *Quaternion_to_matrix(QuaternionObject *self)
{
  float mat[9]; /* all values are set */

  if (BaseMath_ReadCallback(self) == -1) {
    return NULL;
  }

  quat_to_mat3((float(*)[3])mat, self->quat);
  return Matrix_CreatePyObject(mat, 3, 3, NULL);
}

PyDoc_STRVAR(Quaternion_to_axis_angle_doc,
             ".. method:: to_axis_angle()\n"
             "\n"
             "   Return the axis, angle representation of the quaternion.\n"
             "\n"
             "   :return: axis, angle.\n"
             "   :rtype: (:class:`Vector`, float) pair\n");
static PyObject *Quaternion_to_axis_angle(QuaternionObject *self)
{
  PyObject *ret;

  float tquat[4];

  float axis[3];
  float angle;

  if (BaseMath_ReadCallback(self) == -1) {
    return NULL;
  }

  normalize_qt_qt(tquat, self->quat);
  quat_to_axis_angle(axis, &angle, tquat);

  quat__axis_angle_sanitize(axis, &angle);

  ret = PyTuple_New(2);
  PyTuple_SET_ITEMS(ret, Vector_CreatePyObject(axis, 3, NULL), PyFloat_FromDouble(angle));
  return ret;
}

PyDoc_STRVAR(
    Quaternion_to_exponential_map_doc,
    ".. method:: to_exponential_map()\n"
    "\n"
    "   Return the exponential map representation of the quaternion.\n"
    "\n"
    "   This representation consist of the rotation axis multiplied by the rotation angle."
    "   Such a representation is useful for interpolation between multiple orientations.\n"
    "\n"
    "   :return: exponential map.\n"
    "   :rtype: :class:`Vector` of size 3\n"
    "\n"
    "   To convert back to a quaternion, pass it to the :class:`Quaternion` constructor.\n");
static PyObject *Quaternion_to_exponential_map(QuaternionObject *self)
{
  float expmap[3];

  if (BaseMath_ReadCallback(self) == -1) {
    return NULL;
  }

  quat_to_expmap(expmap, self->quat);
  return Vector_CreatePyObject(expmap, 3, NULL);
}

PyDoc_STRVAR(Quaternion_cross_doc,
             ".. method:: cross(other)\n"
             "\n"
             "   Return the cross product of this quaternion and another.\n"
             "\n"
             "   :arg other: The other quaternion to perform the cross product with.\n"
             "   :type other: :class:`Quaternion`\n"
             "   :return: The cross product.\n"
             "   :rtype: :class:`Quaternion`\n");
static PyObject *Quaternion_cross(QuaternionObject *self, PyObject *value)
{
  float quat[QUAT_SIZE], tquat[QUAT_SIZE];

  if (BaseMath_ReadCallback(self) == -1) {
    return NULL;
  }

  if (mathutils_array_parse(
          tquat, QUAT_SIZE, QUAT_SIZE, value, "Quaternion.cross(other), invalid 'other' arg") ==
      -1) {
    return NULL;
  }

  mul_qt_qtqt(quat, self->quat, tquat);
  return Quaternion_CreatePyObject(quat, Py_TYPE(self));
}

PyDoc_STRVAR(Quaternion_dot_doc,
             ".. method:: dot(other)\n"
             "\n"
             "   Return the dot product of this quaternion and another.\n"
             "\n"
             "   :arg other: The other quaternion to perform the dot product with.\n"
             "   :type other: :class:`Quaternion`\n"
             "   :return: The dot product.\n"
             "   :rtype: float\n");
static PyObject *Quaternion_dot(QuaternionObject *self, PyObject *value)
{
  float tquat[QUAT_SIZE];

  if (BaseMath_ReadCallback(self) == -1) {
    return NULL;
  }

  if (mathutils_array_parse(
          tquat, QUAT_SIZE, QUAT_SIZE, value, "Quaternion.dot(other), invalid 'other' arg") ==
      -1) {
    return NULL;
  }

  return PyFloat_FromDouble(dot_qtqt(self->quat, tquat));
}

PyDoc_STRVAR(Quaternion_rotation_difference_doc,
             ".. function:: rotation_difference(other)\n"
             "\n"
             "   Returns a quaternion representing the rotational difference.\n"
             "\n"
             "   :arg other: second quaternion.\n"
             "   :type other: :class:`Quaternion`\n"
             "   :return: the rotational difference between the two quat rotations.\n"
             "   :rtype: :class:`Quaternion`\n");
static PyObject *Quaternion_rotation_difference(QuaternionObject *self, PyObject *value)
{
  float tquat[QUAT_SIZE], quat[QUAT_SIZE];

  if (BaseMath_ReadCallback(self) == -1) {
    return NULL;
  }

  if (mathutils_array_parse(tquat,
                            QUAT_SIZE,
                            QUAT_SIZE,
                            value,
                            "Quaternion.difference(other), invalid 'other' arg") == -1) {
    return NULL;
  }

  rotation_between_quats_to_quat(quat, self->quat, tquat);

  return Quaternion_CreatePyObject(quat, Py_TYPE(self));
}

PyDoc_STRVAR(Quaternion_slerp_doc,
             ".. function:: slerp(other, factor)\n"
             "\n"
             "   Returns the interpolation of two quaternions.\n"
             "\n"
             "   :arg other: value to interpolate with.\n"
             "   :type other: :class:`Quaternion`\n"
             "   :arg factor: The interpolation value in [0.0, 1.0].\n"
             "   :type factor: float\n"
             "   :return: The interpolated rotation.\n"
             "   :rtype: :class:`Quaternion`\n");
static PyObject *Quaternion_slerp(QuaternionObject *self, PyObject *args)
{
  PyObject *value;
  float tquat[QUAT_SIZE], quat[QUAT_SIZE], fac;

  if (!PyArg_ParseTuple(args, "Of:slerp", &value, &fac)) {
    PyErr_SetString(PyExc_TypeError,
                    "quat.slerp(): "
                    "expected Quaternion types and float");
    return NULL;
  }

  if (BaseMath_ReadCallback(self) == -1) {
    return NULL;
  }

  if (mathutils_array_parse(
          tquat, QUAT_SIZE, QUAT_SIZE, value, "Quaternion.slerp(other), invalid 'other' arg") ==
      -1) {
    return NULL;
  }

  if (fac > 1.0f || fac < 0.0f) {
    PyErr_SetString(PyExc_ValueError,
                    "quat.slerp(): "
                    "interpolation factor must be between 0.0 and 1.0");
    return NULL;
  }

  interp_qt_qtqt(quat, self->quat, tquat, fac);

  return Quaternion_CreatePyObject(quat, Py_TYPE(self));
}

PyDoc_STRVAR(Quaternion_rotate_doc,
             ".. method:: rotate(other)\n"
             "\n"
             "   Rotates the quaternion by another mathutils value.\n"
             "\n"
             "   :arg other: rotation component of mathutils value\n"
             "   :type other: :class:`Euler`, :class:`Quaternion` or :class:`Matrix`\n");
static PyObject *Quaternion_rotate(QuaternionObject *self, PyObject *value)
{
  float self_rmat[3][3], other_rmat[3][3], rmat[3][3];
  float tquat[4], length;

  if (BaseMath_ReadCallback_ForWrite(self) == -1) {
    return NULL;
  }

  if (mathutils_any_to_rotmat(other_rmat, value, "Quaternion.rotate(value)") == -1) {
    return NULL;
  }

  length = normalize_qt_qt(tquat, self->quat);
  quat_to_mat3(self_rmat, tquat);
  mul_m3_m3m3(rmat, other_rmat, self_rmat);

  mat3_to_quat(self->quat, rmat);
  mul_qt_fl(self->quat, length); /* maintain length after rotating */

  (void)BaseMath_WriteCallback(self);
  Py_RETURN_NONE;
}

/* ----------------------------Quaternion.normalize()---------------- */
/* Normalize the quaternion. This may change the angle as well as the
 * rotation axis, as all of (w, x, y, z) are scaled. */
PyDoc_STRVAR(Quaternion_normalize_doc,
             ".. function:: normalize()\n"
             "\n"
             "   Normalize the quaternion.\n");
static PyObject *Quaternion_normalize(QuaternionObject *self)
{
  if (BaseMath_ReadCallback_ForWrite(self) == -1) {
    return NULL;
  }

  normalize_qt(self->quat);

  (void)BaseMath_WriteCallback(self);
  Py_RETURN_NONE;
}
PyDoc_STRVAR(Quaternion_normalized_doc,
             ".. function:: normalized()\n"
             "\n"
             "   Return a new normalized quaternion.\n"
             "\n"
             "   :return: a normalized copy.\n"
             "   :rtype: :class:`Quaternion`\n");
static PyObject *Quaternion_normalized(QuaternionObject *self)
{
  return quat__apply_to_copy((PyNoArgsFunction)Quaternion_normalize, self);
}

PyDoc_STRVAR(Quaternion_invert_doc,
             ".. function:: invert()\n"
             "\n"
             "   Set the quaternion to its inverse.\n");
static PyObject *Quaternion_invert(QuaternionObject *self)
{
  if (BaseMath_ReadCallback_ForWrite(self) == -1) {
    return NULL;
  }

  invert_qt(self->quat);

  (void)BaseMath_WriteCallback(self);
  Py_RETURN_NONE;
}
PyDoc_STRVAR(Quaternion_inverted_doc,
             ".. function:: inverted()\n"
             "\n"
             "   Return a new, inverted quaternion.\n"
             "\n"
             "   :return: the inverted value.\n"
             "   :rtype: :class:`Quaternion`\n");
static PyObject *Quaternion_inverted(QuaternionObject *self)
{
  return quat__apply_to_copy((PyNoArgsFunction)Quaternion_invert, self);
}

PyDoc_STRVAR(Quaternion_identity_doc,
             ".. function:: identity()\n"
             "\n"
             "   Set the quaternion to an identity quaternion.\n"
             "\n"
             "   :rtype: :class:`Quaternion`\n");
static PyObject *Quaternion_identity(QuaternionObject *self)
{
  if (BaseMath_ReadCallback_ForWrite(self) == -1) {
    return NULL;
  }

  unit_qt(self->quat);

  (void)BaseMath_WriteCallback(self);
  Py_RETURN_NONE;
}

PyDoc_STRVAR(Quaternion_negate_doc,
             ".. function:: negate()\n"
             "\n"
             "   Set the quaternion to its negative.\n"
             "\n"
             "   :rtype: :class:`Quaternion`\n");
static PyObject *Quaternion_negate(QuaternionObject *self)
{
  if (BaseMath_ReadCallback_ForWrite(self) == -1) {
    return NULL;
  }

  mul_qt_fl(self->quat, -1.0f);

  (void)BaseMath_WriteCallback(self);
  Py_RETURN_NONE;
}

PyDoc_STRVAR(Quaternion_conjugate_doc,
             ".. function:: conjugate()\n"
             "\n"
             "   Set the quaternion to its conjugate (negate x, y, z).\n");
static PyObject *Quaternion_conjugate(QuaternionObject *self)
{
  if (BaseMath_ReadCallback_ForWrite(self) == -1) {
    return NULL;
  }

  conjugate_qt(self->quat);

  (void)BaseMath_WriteCallback(self);
  Py_RETURN_NONE;
}
PyDoc_STRVAR(Quaternion_conjugated_doc,
             ".. function:: conjugated()\n"
             "\n"
             "   Return a new conjugated quaternion.\n"
             "\n"
             "   :return: a new quaternion.\n"
             "   :rtype: :class:`Quaternion`\n");
static PyObject *Quaternion_conjugated(QuaternionObject *self)
{
  return quat__apply_to_copy((PyNoArgsFunction)Quaternion_conjugate, self);
}

PyDoc_STRVAR(Quaternion_copy_doc,
             ".. function:: copy()\n"
             "\n"
             "   Returns a copy of this quaternion.\n"
             "\n"
             "   :return: A copy of the quaternion.\n"
             "   :rtype: :class:`Quaternion`\n"
             "\n"
             "   .. note:: use this to get a copy of a wrapped quaternion with\n"
             "      no reference to the original data.\n");
static PyObject *Quaternion_copy(QuaternionObject *self)
{
  if (BaseMath_ReadCallback(self) == -1) {
    return NULL;
  }

  return Quaternion_CreatePyObject(self->quat, Py_TYPE(self));
}
static PyObject *Quaternion_deepcopy(QuaternionObject *self, PyObject *args)
{
  if (!PyC_CheckArgs_DeepCopy(args)) {
    return NULL;
  }
  return Quaternion_copy(self);
}

/* print the object to screen */
static PyObject *Quaternion_repr(QuaternionObject *self)
{
  PyObject *ret, *tuple;

  if (BaseMath_ReadCallback(self) == -1) {
    return NULL;
  }

  tuple = Quaternion_to_tuple_ext(self, -1);

  ret = PyUnicode_FromFormat("Quaternion(%R)", tuple);

  Py_DECREF(tuple);
  return ret;
}

#ifndef MATH_STANDALONE
static PyObject *Quaternion_str(QuaternionObject *self)
{
  DynStr *ds;

  if (BaseMath_ReadCallback(self) == -1) {
    return NULL;
  }

  ds = BLI_dynstr_new();

  BLI_dynstr_appendf(ds,
                     "<Quaternion (w=%.4f, x=%.4f, y=%.4f, z=%.4f)>",
                     self->quat[0],
                     self->quat[1],
                     self->quat[2],
                     self->quat[3]);

  return mathutils_dynstr_to_py(ds); /* frees ds */
}
#endif

static PyObject *Quaternion_richcmpr(PyObject *a, PyObject *b, int op)
{
  PyObject *res;
  int ok = -1; /* zero is true */

  if (QuaternionObject_Check(a) && QuaternionObject_Check(b)) {
    QuaternionObject *quatA = (QuaternionObject *)a;
    QuaternionObject *quatB = (QuaternionObject *)b;

    if (BaseMath_ReadCallback(quatA) == -1 || BaseMath_ReadCallback(quatB) == -1) {
      return NULL;
    }

    ok = (EXPP_VectorsAreEqual(quatA->quat, quatB->quat, QUAT_SIZE, 1)) ? 0 : -1;
  }

  switch (op) {
    case Py_NE:
      ok = !ok;
      ATTR_FALLTHROUGH;
    case Py_EQ:
      res = ok ? Py_False : Py_True;
      break;

    case Py_LT:
    case Py_LE:
    case Py_GT:
    case Py_GE:
      res = Py_NotImplemented;
      break;
    default:
      PyErr_BadArgument();
      return NULL;
  }

  return Py_INCREF_RET(res);
}

static Py_hash_t Quaternion_hash(QuaternionObject *self)
{
  if (BaseMath_ReadCallback(self) == -1) {
    return -1;
  }

  if (BaseMathObject_Prepare_ForHash(self) == -1) {
    return -1;
  }

  return mathutils_array_hash(self->quat, QUAT_SIZE);
}

/* ---------------------SEQUENCE PROTOCOLS------------------------ */
/* ----------------------------len(object)------------------------ */
/* sequence length */
static int Quaternion_len(QuaternionObject *UNUSED(self))
{
  return QUAT_SIZE;
}
/* ----------------------------object[]--------------------------- */
/* sequence accessor (get) */
static PyObject *Quaternion_item(QuaternionObject *self, int i)
{
  if (i < 0) {
    i = QUAT_SIZE - i;
  }

  if (i < 0 || i >= QUAT_SIZE) {
    PyErr_SetString(PyExc_IndexError,
                    "quaternion[attribute]: "
                    "array index out of range");
    return NULL;
  }

  if (BaseMath_ReadIndexCallback(self, i) == -1) {
    return NULL;
  }

  return PyFloat_FromDouble(self->quat[i]);
}
/* ----------------------------object[]------------------------- */
/* sequence accessor (set) */
static int Quaternion_ass_item(QuaternionObject *self, int i, PyObject *ob)
{
  float f;

  if (BaseMath_Prepare_ForWrite(self) == -1) {
    return -1;
  }

  f = (float)PyFloat_AsDouble(ob);

  if (f == -1.0f && PyErr_Occurred()) { /* parsed item not a number */
    PyErr_SetString(PyExc_TypeError,
                    "quaternion[index] = x: "
                    "assigned value not a number");
    return -1;
  }

  if (i < 0) {
    i = QUAT_SIZE - i;
  }

  if (i < 0 || i >= QUAT_SIZE) {
    PyErr_SetString(PyExc_IndexError,
                    "quaternion[attribute] = x: "
                    "array assignment index out of range");
    return -1;
  }
  self->quat[i] = f;

  if (BaseMath_WriteIndexCallback(self, i) == -1) {
    return -1;
  }

  return 0;
}
/* ----------------------------object[z:y]------------------------ */
/* sequence slice (get) */
static PyObject *Quaternion_slice(QuaternionObject *self, int begin, int end)
{
  PyObject *tuple;
  int count;

  if (BaseMath_ReadCallback(self) == -1) {
    return NULL;
  }

  CLAMP(begin, 0, QUAT_SIZE);
  if (end < 0) {
    end = (QUAT_SIZE + 1) + end;
  }
  CLAMP(end, 0, QUAT_SIZE);
  begin = MIN2(begin, end);

  tuple = PyTuple_New(end - begin);
  for (count = begin; count < end; count++) {
    PyTuple_SET_ITEM(tuple, count - begin, PyFloat_FromDouble(self->quat[count]));
  }

  return tuple;
}
/* ----------------------------object[z:y]------------------------ */
/* sequence slice (set) */
static int Quaternion_ass_slice(QuaternionObject *self, int begin, int end, PyObject *seq)
{
  int i, size;
  float quat[QUAT_SIZE];

  if (BaseMath_ReadCallback_ForWrite(self) == -1) {
    return -1;
  }

  CLAMP(begin, 0, QUAT_SIZE);
  if (end < 0) {
    end = (QUAT_SIZE + 1) + end;
  }
  CLAMP(end, 0, QUAT_SIZE);
  begin = MIN2(begin, end);

  if ((size = mathutils_array_parse(
           quat, 0, QUAT_SIZE, seq, "mathutils.Quaternion[begin:end] = []")) == -1) {
    return -1;
  }

  if (size != (end - begin)) {
    PyErr_SetString(PyExc_ValueError,
                    "quaternion[begin:end] = []: "
                    "size mismatch in slice assignment");
    return -1;
  }

  /* parsed well - now set in vector */
  for (i = 0; i < size; i++) {
    self->quat[begin + i] = quat[i];
  }

  (void)BaseMath_WriteCallback(self);
  return 0;
}

static PyObject *Quaternion_subscript(QuaternionObject *self, PyObject *item)
{
  if (PyIndex_Check(item)) {
    Py_ssize_t i;
    i = PyNumber_AsSsize_t(item, PyExc_IndexError);
    if (i == -1 && PyErr_Occurred()) {
      return NULL;
    }
    if (i < 0) {
      i += QUAT_SIZE;
    }
    return Quaternion_item(self, i);
  }
  else if (PySlice_Check(item)) {
    Py_ssize_t start, stop, step, slicelength;

    if (PySlice_GetIndicesEx(item, QUAT_SIZE, &start, &stop, &step, &slicelength) < 0) {
      return NULL;
    }

    if (slicelength <= 0) {
      return PyTuple_New(0);
    }
    else if (step == 1) {
      return Quaternion_slice(self, start, stop);
    }
    else {
      PyErr_SetString(PyExc_IndexError, "slice steps not supported with quaternions");
      return NULL;
    }
  }
  else {
    PyErr_Format(PyExc_TypeError,
                 "quaternion indices must be integers, not %.200s",
                 Py_TYPE(item)->tp_name);
    return NULL;
  }
}

static int Quaternion_ass_subscript(QuaternionObject *self, PyObject *item, PyObject *value)
{
  if (PyIndex_Check(item)) {
    Py_ssize_t i = PyNumber_AsSsize_t(item, PyExc_IndexError);
    if (i == -1 && PyErr_Occurred()) {
      return -1;
    }
    if (i < 0) {
      i += QUAT_SIZE;
    }
    return Quaternion_ass_item(self, i, value);
  }
  else if (PySlice_Check(item)) {
    Py_ssize_t start, stop, step, slicelength;

    if (PySlice_GetIndicesEx(item, QUAT_SIZE, &start, &stop, &step, &slicelength) < 0) {
      return -1;
    }

    if (step == 1) {
      return Quaternion_ass_slice(self, start, stop, value);
    }
    else {
      PyErr_SetString(PyExc_IndexError, "slice steps not supported with quaternion");
      return -1;
    }
  }
  else {
    PyErr_Format(PyExc_TypeError,
                 "quaternion indices must be integers, not %.200s",
                 Py_TYPE(item)->tp_name);
    return -1;
  }
}

/* ------------------------NUMERIC PROTOCOLS---------------------- */
/* ------------------------obj + obj------------------------------ */
/* addition */
static PyObject *Quaternion_add(PyObject *q1, PyObject *q2)
{
  float quat[QUAT_SIZE];
  QuaternionObject *quat1 = NULL, *quat2 = NULL;

  if (!QuaternionObject_Check(q1) || !QuaternionObject_Check(q2)) {
    PyErr_Format(PyExc_TypeError,
                 "Quaternion addition: (%s + %s) "
                 "invalid type for this operation",
                 Py_TYPE(q1)->tp_name,
                 Py_TYPE(q2)->tp_name);
    return NULL;
  }
  quat1 = (QuaternionObject *)q1;
  quat2 = (QuaternionObject *)q2;

  if (BaseMath_ReadCallback(quat1) == -1 || BaseMath_ReadCallback(quat2) == -1) {
    return NULL;
  }

  add_qt_qtqt(quat, quat1->quat, quat2->quat, 1.0f);
  return Quaternion_CreatePyObject(quat, Py_TYPE(q1));
}
/* ------------------------obj - obj------------------------------ */
/* subtraction */
static PyObject *Quaternion_sub(PyObject *q1, PyObject *q2)
{
  int x;
  float quat[QUAT_SIZE];
  QuaternionObject *quat1 = NULL, *quat2 = NULL;

  if (!QuaternionObject_Check(q1) || !QuaternionObject_Check(q2)) {
    PyErr_Format(PyExc_TypeError,
                 "Quaternion subtraction: (%s - %s) "
                 "invalid type for this operation",
                 Py_TYPE(q1)->tp_name,
                 Py_TYPE(q2)->tp_name);
    return NULL;
  }

  quat1 = (QuaternionObject *)q1;
  quat2 = (QuaternionObject *)q2;

  if (BaseMath_ReadCallback(quat1) == -1 || BaseMath_ReadCallback(quat2) == -1) {
    return NULL;
  }

  for (x = 0; x < QUAT_SIZE; x++) {
    quat[x] = quat1->quat[x] - quat2->quat[x];
  }

  return Quaternion_CreatePyObject(quat, Py_TYPE(q1));
}

static PyObject *quat_mul_float(QuaternionObject *quat, const float scalar)
{
  float tquat[4];
  copy_qt_qt(tquat, quat->quat);
  mul_qt_fl(tquat, scalar);
  return Quaternion_CreatePyObject(tquat, Py_TYPE(quat));
}

/*------------------------obj * obj------------------------------
 * multiplication */
static PyObject *Quaternion_mul(PyObject *q1, PyObject *q2)
{
  float scalar;
  QuaternionObject *quat1 = NULL, *quat2 = NULL;

  if (QuaternionObject_Check(q1)) {
    quat1 = (QuaternionObject *)q1;
    if (BaseMath_ReadCallback(quat1) == -1) {
      return NULL;
    }
  }
  if (QuaternionObject_Check(q2)) {
    quat2 = (QuaternionObject *)q2;
    if (BaseMath_ReadCallback(quat2) == -1) {
      return NULL;
    }
  }

  if (quat1 && quat2) { /* QUAT * QUAT (element-wise product) */
#ifdef USE_MATHUTILS_ELEM_MUL
    float quat[QUAT_SIZE];
    mul_vn_vnvn(quat, quat1->quat, quat2->quat, QUAT_SIZE);
    return Quaternion_CreatePyObject(quat, Py_TYPE(q1));
#endif
  }
  /* the only case this can happen (for a supported type is "FLOAT * QUAT") */
  else if (quat2) { /* FLOAT * QUAT */
    if (((scalar = PyFloat_AsDouble(q1)) == -1.0f && PyErr_Occurred()) == 0) {
      return quat_mul_float(quat2, scalar);
    }
  }
  else if (quat1) { /* QUAT * FLOAT */
    if ((((scalar = PyFloat_AsDouble(q2)) == -1.0f && PyErr_Occurred()) == 0)) {
      return quat_mul_float(quat1, scalar);
    }
  }

  PyErr_Format(PyExc_TypeError,
               "Element-wise multiplication: "
               "not supported between '%.200s' and '%.200s' types",
               Py_TYPE(q1)->tp_name,
               Py_TYPE(q2)->tp_name);
  return NULL;
}
/*------------------------obj *= obj------------------------------
 * in-place multiplication */
static PyObject *Quaternion_imul(PyObject *q1, PyObject *q2)
{
  float scalar;
  QuaternionObject *quat1 = NULL, *quat2 = NULL;

  if (QuaternionObject_Check(q1)) {
    quat1 = (QuaternionObject *)q1;
    if (BaseMath_ReadCallback(quat1) == -1) {
      return NULL;
    }
  }
  if (QuaternionObject_Check(q2)) {
    quat2 = (QuaternionObject *)q2;
    if (BaseMath_ReadCallback(quat2) == -1) {
      return NULL;
    }
  }

  if (quat1 && quat2) { /* QUAT *= QUAT (inplace element-wise product) */
#ifdef USE_MATHUTILS_ELEM_MUL
    mul_vn_vn(quat1->quat, quat2->quat, QUAT_SIZE);
#else
    PyErr_Format(PyExc_TypeError,
                 "Inplace element-wise multiplication: "
                 "not supported between '%.200s' and '%.200s' types",
                 Py_TYPE(q1)->tp_name,
                 Py_TYPE(q2)->tp_name);
    return NULL;
#endif
  }
  else if (quat1 && (((scalar = PyFloat_AsDouble(q2)) == -1.0f && PyErr_Occurred()) == 0)) {
    /* QUAT *= FLOAT */
    mul_qt_fl(quat1->quat, scalar);
  }
  else {
    PyErr_Format(PyExc_TypeError,
                 "Element-wise multiplication: "
                 "not supported between '%.200s' and '%.200s' types",
                 Py_TYPE(q1)->tp_name,
                 Py_TYPE(q2)->tp_name);
    return NULL;
  }

  (void)BaseMath_WriteCallback(quat1);
  Py_INCREF(q1);
  return q1;
}
/*------------------------obj @ obj------------------------------
 * quaternion multiplication */
static PyObject *Quaternion_matmul(PyObject *q1, PyObject *q2)
{
  float quat[QUAT_SIZE];
  QuaternionObject *quat1 = NULL, *quat2 = NULL;

  if (QuaternionObject_Check(q1)) {
    quat1 = (QuaternionObject *)q1;
    if (BaseMath_ReadCallback(quat1) == -1) {
      return NULL;
    }
  }
  if (QuaternionObject_Check(q2)) {
    quat2 = (QuaternionObject *)q2;
    if (BaseMath_ReadCallback(quat2) == -1) {
      return NULL;
    }
  }

  if (quat1 && quat2) { /* QUAT @ QUAT (cross product) */
    mul_qt_qtqt(quat, quat1->quat, quat2->quat);
    return Quaternion_CreatePyObject(quat, Py_TYPE(q1));
  }
  else if (quat1) {
    /* QUAT @ VEC */
    if (VectorObject_Check(q2)) {
      VectorObject *vec2 = (VectorObject *)q2;
      float tvec[3];

      if (vec2->size != 3) {
        PyErr_SetString(PyExc_ValueError,
                        "Vector multiplication: "
                        "only 3D vector rotations (with quats) "
                        "currently supported");
        return NULL;
      }
      if (BaseMath_ReadCallback(vec2) == -1) {
        return NULL;
      }

      copy_v3_v3(tvec, vec2->vec);
      mul_qt_v3(quat1->quat, tvec);

      return Vector_CreatePyObject(tvec, 3, Py_TYPE(vec2));
    }
  }

  PyErr_Format(PyExc_TypeError,
               "Quaternion multiplication: "
               "not supported between '%.200s' and '%.200s' types",
               Py_TYPE(q1)->tp_name,
               Py_TYPE(q2)->tp_name);
  return NULL;
}
/*------------------------obj @= obj------------------------------
 * inplace quaternion multiplication */
static PyObject *Quaternion_imatmul(PyObject *q1, PyObject *q2)
{
  float quat[QUAT_SIZE];
  QuaternionObject *quat1 = NULL, *quat2 = NULL;

  if (QuaternionObject_Check(q1)) {
    quat1 = (QuaternionObject *)q1;
    if (BaseMath_ReadCallback(quat1) == -1) {
      return NULL;
    }
  }
  if (QuaternionObject_Check(q2)) {
    quat2 = (QuaternionObject *)q2;
    if (BaseMath_ReadCallback(quat2) == -1) {
      return NULL;
    }
  }

  if (quat1 && quat2) { /* QUAT @ QUAT (cross product) */
    mul_qt_qtqt(quat, quat1->quat, quat2->quat);
    copy_qt_qt(quat1->quat, quat);
  }
  else {
    PyErr_Format(PyExc_TypeError,
                 "Inplace quaternion multiplication: "
                 "not supported between '%.200s' and '%.200s' types",
                 Py_TYPE(q1)->tp_name,
                 Py_TYPE(q2)->tp_name);
    return NULL;
  }

  (void)BaseMath_WriteCallback(quat1);
  Py_INCREF(q1);
  return q1;
}

/* -obj
 * returns the negative of this object*/
static PyObject *Quaternion_neg(QuaternionObject *self)
{
  float tquat[QUAT_SIZE];

  if (BaseMath_ReadCallback(self) == -1) {
    return NULL;
  }

  negate_v4_v4(tquat, self->quat);
  return Quaternion_CreatePyObject(tquat, Py_TYPE(self));
}

/* -----------------PROTOCOL DECLARATIONS-------------------------- */
static PySequenceMethods Quaternion_SeqMethods = {
    (lenfunc)Quaternion_len,              /* sq_length */
    (binaryfunc)NULL,                     /* sq_concat */
    (ssizeargfunc)NULL,                   /* sq_repeat */
    (ssizeargfunc)Quaternion_item,        /* sq_item */
    (ssizessizeargfunc)NULL,              /* sq_slice, deprecated */
    (ssizeobjargproc)Quaternion_ass_item, /* sq_ass_item */
    (ssizessizeobjargproc)NULL,           /* sq_ass_slice, deprecated */
    (objobjproc)NULL,                     /* sq_contains */
    (binaryfunc)NULL,                     /* sq_inplace_concat */
    (ssizeargfunc)NULL,                   /* sq_inplace_repeat */
};

static PyMappingMethods Quaternion_AsMapping = {
    (lenfunc)Quaternion_len,
    (binaryfunc)Quaternion_subscript,
    (objobjargproc)Quaternion_ass_subscript,
};

static PyNumberMethods Quaternion_NumMethods = {
    (binaryfunc)Quaternion_add,     /*nb_add*/
    (binaryfunc)Quaternion_sub,     /*nb_subtract*/
    (binaryfunc)Quaternion_mul,     /*nb_multiply*/
    NULL,                           /*nb_remainder*/
    NULL,                           /*nb_divmod*/
    NULL,                           /*nb_power*/
    (unaryfunc)Quaternion_neg,      /*nb_negative*/
    (unaryfunc)Quaternion_copy,     /*tp_positive*/
    (unaryfunc)0,                   /*tp_absolute*/
    (inquiry)0,                     /*tp_bool*/
    (unaryfunc)0,                   /*nb_invert*/
    NULL,                           /*nb_lshift*/
    (binaryfunc)0,                  /*nb_rshift*/
    NULL,                           /*nb_and*/
    NULL,                           /*nb_xor*/
    NULL,                           /*nb_or*/
    NULL,                           /*nb_int*/
    NULL,                           /*nb_reserved*/
    NULL,                           /*nb_float*/
    NULL,                           /* nb_inplace_add */
    NULL,                           /* nb_inplace_subtract */
    (binaryfunc)Quaternion_imul,    /* nb_inplace_multiply */
    NULL,                           /* nb_inplace_remainder */
    NULL,                           /* nb_inplace_power */
    NULL,                           /* nb_inplace_lshift */
    NULL,                           /* nb_inplace_rshift */
    NULL,                           /* nb_inplace_and */
    NULL,                           /* nb_inplace_xor */
    NULL,                           /* nb_inplace_or */
    NULL,                           /* nb_floor_divide */
    NULL,                           /* nb_true_divide */
    NULL,                           /* nb_inplace_floor_divide */
    NULL,                           /* nb_inplace_true_divide */
    NULL,                           /* nb_index */
    (binaryfunc)Quaternion_matmul,  /* nb_matrix_multiply */
    (binaryfunc)Quaternion_imatmul, /* nb_inplace_matrix_multiply */
};

PyDoc_STRVAR(Quaternion_axis_doc, "Quaternion axis value.\n\n:type: float");
static PyObject *Quaternion_axis_get(QuaternionObject *self, void *type)
{
  return Quaternion_item(self, POINTER_AS_INT(type));
}

static int Quaternion_axis_set(QuaternionObject *self, PyObject *value, void *type)
{
  return Quaternion_ass_item(self, POINTER_AS_INT(type), value);
}

PyDoc_STRVAR(Quaternion_magnitude_doc, "Size of the quaternion (read-only).\n\n:type: float");
static PyObject *Quaternion_magnitude_get(QuaternionObject *self, void *UNUSED(closure))
{
  if (BaseMath_ReadCallback(self) == -1) {
    return NULL;
  }

  return PyFloat_FromDouble(sqrtf(dot_qtqt(self->quat, self->quat)));
}

PyDoc_STRVAR(Quaternion_angle_doc, "Angle of the quaternion.\n\n:type: float");
static PyObject *Quaternion_angle_get(QuaternionObject *self, void *UNUSED(closure))
{
  float tquat[4];
  float angle;

  if (BaseMath_ReadCallback(self) == -1) {
    return NULL;
  }

  normalize_qt_qt(tquat, self->quat);

  angle = 2.0f * saacos(tquat[0]);

  quat__axis_angle_sanitize(NULL, &angle);

  return PyFloat_FromDouble(angle);
}

static int Quaternion_angle_set(QuaternionObject *self, PyObject *value, void *UNUSED(closure))
{
  float tquat[4];
  float len;

  float axis[3], angle_dummy;
  float angle;

  if (BaseMath_ReadCallback_ForWrite(self) == -1) {
    return -1;
  }

  len = normalize_qt_qt(tquat, self->quat);
  quat_to_axis_angle(axis, &angle_dummy, tquat);

  angle = PyFloat_AsDouble(value);

  if (angle == -1.0f && PyErr_Occurred()) { /* parsed item not a number */
    PyErr_SetString(PyExc_TypeError, "Quaternion.angle = value: float expected");
    return -1;
  }

  angle = angle_wrap_rad(angle);

  quat__axis_angle_sanitize(axis, &angle);

  axis_angle_to_quat(self->quat, axis, angle);
  mul_qt_fl(self->quat, len);

  if (BaseMath_WriteCallback(self) == -1) {
    return -1;
  }

  return 0;
}

PyDoc_STRVAR(Quaternion_axis_vector_doc, "Quaternion axis as a vector.\n\n:type: :class:`Vector`");
static PyObject *Quaternion_axis_vector_get(QuaternionObject *self, void *UNUSED(closure))
{
  float tquat[4];

  float axis[3];
  float angle_dummy;

  if (BaseMath_ReadCallback(self) == -1) {
    return NULL;
  }

  normalize_qt_qt(tquat, self->quat);
  quat_to_axis_angle(axis, &angle_dummy, tquat);

  quat__axis_angle_sanitize(axis, NULL);

  return Vector_CreatePyObject(axis, 3, NULL);
}

static int Quaternion_axis_vector_set(QuaternionObject *self,
                                      PyObject *value,
                                      void *UNUSED(closure))
{
  float tquat[4];
  float len;

  float axis[3];
  float angle;

  if (BaseMath_ReadCallback_ForWrite(self) == -1) {
    return -1;
  }

  len = normalize_qt_qt(tquat, self->quat);
  quat_to_axis_angle(axis, &angle, tquat); /* axis value is unused */

  if (mathutils_array_parse(axis, 3, 3, value, "quat.axis = other") == -1) {
    return -1;
  }

  quat__axis_angle_sanitize(axis, &angle);

  axis_angle_to_quat(self->quat, axis, angle);
  mul_qt_fl(self->quat, len);

  if (BaseMath_WriteCallback(self) == -1) {
    return -1;
  }

  return 0;
}

/* ----------------------------------mathutils.Quaternion() -------------- */
static PyObject *Quaternion_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
{
  PyObject *seq = NULL;
  double angle = 0.0f;
  float quat[QUAT_SIZE];
  unit_qt(quat);

  if (kwds && PyDict_Size(kwds)) {
    PyErr_SetString(PyExc_TypeError,
                    "mathutils.Quaternion(): "
                    "takes no keyword args");
    return NULL;
  }

  if (!PyArg_ParseTuple(args, "|Od:mathutils.Quaternion", &seq, &angle)) {
    return NULL;
  }

  switch (PyTuple_GET_SIZE(args)) {
    case 0:
      break;
    case 1: {
      int size;

      if ((size = mathutils_array_parse(quat, 3, QUAT_SIZE, seq, "mathutils.Quaternion()")) ==
          -1) {
        return NULL;
      }

      if (size == 4) {
        /* 4d: Quaternion (common case) */
      }
      else {
        /* 3d: Interpret as exponential map */
        BLI_assert(size == 3);
        expmap_to_quat(quat, quat);
      }

      break;
    }
    case 2: {
      float axis[3];
      if (mathutils_array_parse(axis, 3, 3, seq, "mathutils.Quaternion()") == -1) {
        return NULL;
      }
      angle = angle_wrap_rad(angle); /* clamp because of precision issues */
      axis_angle_to_quat(quat, axis, angle);
      break;
      /* PyArg_ParseTuple assures no more than 2 */
    }
  }
  return Quaternion_CreatePyObject(quat, type);
}

static PyObject *quat__apply_to_copy(PyNoArgsFunction quat_func, QuaternionObject *self)
{
  PyObject *ret = Quaternion_copy(self);
  PyObject *ret_dummy = quat_func(ret);
  if (ret_dummy) {
    Py_DECREF(ret_dummy);
    return ret;
  }
  else { /* error */
    Py_DECREF(ret);
    return NULL;
  }
}

/* axis vector suffers from precision errors, use this function to ensure */
static void quat__axis_angle_sanitize(float axis[3], float *angle)
{
  if (axis) {
    if (is_zero_v3(axis) || !isfinite(axis[0]) || !isfinite(axis[1]) || !isfinite(axis[2])) {
      axis[0] = 1.0f;
      axis[1] = 0.0f;
      axis[2] = 0.0f;
    }
    else if (EXPP_FloatsAreEqual(axis[0], 0.0f, 10) && EXPP_FloatsAreEqual(axis[1], 0.0f, 10) &&
             EXPP_FloatsAreEqual(axis[2], 0.0f, 10)) {
      axis[0] = 1.0f;
    }
  }

  if (angle) {
    if (!isfinite(*angle)) {
      *angle = 0.0f;
    }
  }
}

/* -----------------------METHOD DEFINITIONS ---------------------- */
static struct PyMethodDef Quaternion_methods[] = {
    /* in place only */
    {"identity", (PyCFunction)Quaternion_identity, METH_NOARGS, Quaternion_identity_doc},
    {"negate", (PyCFunction)Quaternion_negate, METH_NOARGS, Quaternion_negate_doc},

    /* operate on original or copy */
    {"conjugate", (PyCFunction)Quaternion_conjugate, METH_NOARGS, Quaternion_conjugate_doc},
    {"conjugated", (PyCFunction)Quaternion_conjugated, METH_NOARGS, Quaternion_conjugated_doc},

    {"invert", (PyCFunction)Quaternion_invert, METH_NOARGS, Quaternion_invert_doc},
    {"inverted", (PyCFunction)Quaternion_inverted, METH_NOARGS, Quaternion_inverted_doc},

    {"normalize", (PyCFunction)Quaternion_normalize, METH_NOARGS, Quaternion_normalize_doc},
    {"normalized", (PyCFunction)Quaternion_normalized, METH_NOARGS, Quaternion_normalized_doc},

    /* return converted representation */
    {"to_euler", (PyCFunction)Quaternion_to_euler, METH_VARARGS, Quaternion_to_euler_doc},
    {"to_matrix", (PyCFunction)Quaternion_to_matrix, METH_NOARGS, Quaternion_to_matrix_doc},
    {"to_axis_angle",
     (PyCFunction)Quaternion_to_axis_angle,
     METH_NOARGS,
     Quaternion_to_axis_angle_doc},
    {"to_exponential_map",
     (PyCFunction)Quaternion_to_exponential_map,
     METH_NOARGS,
     Quaternion_to_exponential_map_doc},

    /* operation between 2 or more types  */
    {"cross", (PyCFunction)Quaternion_cross, METH_O, Quaternion_cross_doc},
    {"dot", (PyCFunction)Quaternion_dot, METH_O, Quaternion_dot_doc},
    {"rotation_difference",
     (PyCFunction)Quaternion_rotation_difference,
     METH_O,
     Quaternion_rotation_difference_doc},
    {"slerp", (PyCFunction)Quaternion_slerp, METH_VARARGS, Quaternion_slerp_doc},
    {"rotate", (PyCFunction)Quaternion_rotate, METH_O, Quaternion_rotate_doc},

    /* base-math methods */
    {"freeze", (PyCFunction)BaseMathObject_freeze, METH_NOARGS, BaseMathObject_freeze_doc},

    {"copy", (PyCFunction)Quaternion_copy, METH_NOARGS, Quaternion_copy_doc},
    {"__copy__", (PyCFunction)Quaternion_copy, METH_NOARGS, Quaternion_copy_doc},
    {"__deepcopy__", (PyCFunction)Quaternion_deepcopy, METH_VARARGS, Quaternion_copy_doc},
    {NULL, NULL, 0, NULL},
};

/*****************************************************************************/
/* Python attributes get/set structure:                                      */
/*****************************************************************************/
static PyGetSetDef Quaternion_getseters[] = {
    {(char *)"w",
     (getter)Quaternion_axis_get,
     (setter)Quaternion_axis_set,
     Quaternion_axis_doc,
     (void *)0},
    {(char *)"x",
     (getter)Quaternion_axis_get,
     (setter)Quaternion_axis_set,
     Quaternion_axis_doc,
     (void *)1},
    {(char *)"y",
     (getter)Quaternion_axis_get,
     (setter)Quaternion_axis_set,
     Quaternion_axis_doc,
     (void *)2},
    {(char *)"z",
     (getter)Quaternion_axis_get,
     (setter)Quaternion_axis_set,
     Quaternion_axis_doc,
     (void *)3},
    {(char *)"magnitude",
     (getter)Quaternion_magnitude_get,
     (setter)NULL,
     Quaternion_magnitude_doc,
     NULL},
    {(char *)"angle",
     (getter)Quaternion_angle_get,
     (setter)Quaternion_angle_set,
     Quaternion_angle_doc,
     NULL},
    {(char *)"axis",
     (getter)Quaternion_axis_vector_get,
     (setter)Quaternion_axis_vector_set,
     Quaternion_axis_vector_doc,
     NULL},
    {(char *)"is_wrapped",
     (getter)BaseMathObject_is_wrapped_get,
     (setter)NULL,
     BaseMathObject_is_wrapped_doc,
     NULL},
    {(char *)"is_frozen",
     (getter)BaseMathObject_is_frozen_get,
     (setter)NULL,
     BaseMathObject_is_frozen_doc,
     NULL},
    {(char *)"owner",
     (getter)BaseMathObject_owner_get,
     (setter)NULL,
     BaseMathObject_owner_doc,
     NULL},
    {NULL, NULL, NULL, NULL, NULL} /* Sentinel */
};

/* ------------------PY_OBECT DEFINITION-------------------------- */
PyDoc_STRVAR(quaternion_doc,
             ".. class:: Quaternion([seq, [angle]])\n"
             "\n"
             "   This object gives access to Quaternions in Blender.\n"
             "\n"
             "   :param seq: size 3 or 4\n"
             "   :type seq: :class:`Vector`\n"
             "   :param angle: rotation angle, in radians\n"
             "   :type angle: float\n"
             "\n"
             "   The constructor takes arguments in various forms:\n"
             "\n"
             "   (), *no args*\n"
             "      Create an identity quaternion\n"
             "   (*wxyz*)\n"
             "      Create a quaternion from a ``(w, x, y, z)`` vector.\n"
             "   (*exponential_map*)\n"
             "      Create a quaternion from a 3d exponential map vector.\n"
             "\n"
             "      .. seealso:: :meth:`to_exponential_map`\n"
             "   (*axis, angle*)\n"
             "      Create a quaternion representing a rotation of *angle* radians over *axis*.\n"
             "\n"
             "      .. seealso:: :meth:`to_axis_angle`\n");
PyTypeObject quaternion_Type = {
    PyVarObject_HEAD_INIT(NULL, 0) "Quaternion", /* tp_name */
    sizeof(QuaternionObject),                    /* tp_basicsize */
    0,                                           /* tp_itemsize */
    (destructor)BaseMathObject_dealloc,          /* tp_dealloc */
    NULL,                                        /* tp_print */
    NULL,                                        /* tp_getattr */
    NULL,                                        /* tp_setattr */
    NULL,                                        /* tp_compare */
    (reprfunc)Quaternion_repr,                   /* tp_repr */
    &Quaternion_NumMethods,                      /* tp_as_number */
    &Quaternion_SeqMethods,                      /* tp_as_sequence */
    &Quaternion_AsMapping,                       /* tp_as_mapping */
    (hashfunc)Quaternion_hash,                   /* tp_hash */
    NULL,                                        /* tp_call */
#ifndef MATH_STANDALONE
    (reprfunc)Quaternion_str, /* tp_str */
#else
    NULL, /* tp_str */
#endif
    NULL,                                                          /* tp_getattro */
    NULL,                                                          /* tp_setattro */
    NULL,                                                          /* tp_as_buffer */
    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE | Py_TPFLAGS_HAVE_GC, /* tp_flags */
    quaternion_doc,                                                /* tp_doc */
    (traverseproc)BaseMathObject_traverse,                         /* tp_traverse */
    (inquiry)BaseMathObject_clear,                                 /* tp_clear */
    (richcmpfunc)Quaternion_richcmpr,                              /* tp_richcompare */
    0,                                                             /* tp_weaklistoffset */
    NULL,                                                          /* tp_iter */
    NULL,                                                          /* tp_iternext */
    Quaternion_methods,                                            /* tp_methods */
    NULL,                                                          /* tp_members */
    Quaternion_getseters,                                          /* tp_getset */
    NULL,                                                          /* tp_base */
    NULL,                                                          /* tp_dict */
    NULL,                                                          /* tp_descr_get */
    NULL,                                                          /* tp_descr_set */
    0,                                                             /* tp_dictoffset */
    NULL,                                                          /* tp_init */
    NULL,                                                          /* tp_alloc */
    Quaternion_new,                                                /* tp_new */
    NULL,                                                          /* tp_free */
    NULL,                                                          /* tp_is_gc */
    NULL,                                                          /* tp_bases */
    NULL,                                                          /* tp_mro */
    NULL,                                                          /* tp_cache */
    NULL,                                                          /* tp_subclasses */
    NULL,                                                          /* tp_weaklist */
    NULL,                                                          /* tp_del */
};

PyObject *Quaternion_CreatePyObject(const float quat[4], PyTypeObject *base_type)
{
  QuaternionObject *self;
  float *quat_alloc;

  quat_alloc = PyMem_Malloc(QUAT_SIZE * sizeof(float));
  if (UNLIKELY(quat_alloc == NULL)) {
    PyErr_SetString(PyExc_MemoryError,
                    "Quaternion(): "
                    "problem allocating data");
    return NULL;
  }

  self = BASE_MATH_NEW(QuaternionObject, quaternion_Type, base_type);
  if (self) {
    self->quat = quat_alloc;
    /* init callbacks as NULL */
    self->cb_user = NULL;
    self->cb_type = self->cb_subtype = 0;

    /* NEW */
    if (!quat) { /* new empty */
      unit_qt(self->quat);
    }
    else {
      copy_qt_qt(self->quat, quat);
    }
    self->flag = BASE_MATH_FLAG_DEFAULT;
  }
  else {
    PyMem_Free(quat_alloc);
  }

  return (PyObject *)self;
}

PyObject *Quaternion_CreatePyObject_wrap(float quat[4], PyTypeObject *base_type)
{
  QuaternionObject *self;

  self = BASE_MATH_NEW(QuaternionObject, quaternion_Type, base_type);
  if (self) {
    /* init callbacks as NULL */
    self->cb_user = NULL;
    self->cb_type = self->cb_subtype = 0;

    /* WRAP */
    self->quat = quat;
    self->flag = BASE_MATH_FLAG_DEFAULT | BASE_MATH_FLAG_IS_WRAP;
  }
  return (PyObject *)self;
}

PyObject *Quaternion_CreatePyObject_cb(PyObject *cb_user,
                                       unsigned char cb_type,
                                       unsigned char cb_subtype)
{
  QuaternionObject *self = (QuaternionObject *)Quaternion_CreatePyObject(NULL, NULL);
  if (self) {
    Py_INCREF(cb_user);
    self->cb_user = cb_user;
    self->cb_type = cb_type;
    self->cb_subtype = cb_subtype;
    PyObject_GC_Track(self);
  }

  return (PyObject *)self;
}