path: root/source/blender/python/mathutils/mathutils_Euler.c

/* SPDX-License-Identifier: GPL-2.0-or-later */

/** \file
 * \ingroup pymathutils
 */

#include <Python.h>

#include "mathutils.h"

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

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

#define EULER_SIZE 3

/* -------------------------------------------------------------------- */
/** \name Utilities
 * \{ */

/** Internal use, assume read callback is done. */
static const char *euler_order_str(EulerObject *self)
{
  static const char order[][4] = {"XYZ", "XZY", "YXZ", "YZX", "ZXY", "ZYX"};
  return order[self->order - EULER_ORDER_XYZ];
}

short euler_order_from_string(const char *str, const char *error_prefix)
{
  if (str[0] && str[1] && str[2] && str[3] == '\0') {

#ifdef __LITTLE_ENDIAN__
#  define MAKE_ID3(a, b, c) ((a) | ((b) << 8) | ((c) << 16))
#else
#  define MAKE_ID3(a, b, c) (((a) << 24) | ((b) << 16) | ((c) << 8))
#endif

    switch (*((const PY_INT32_T *)str)) {
      case MAKE_ID3('X', 'Y', 'Z'):
        return EULER_ORDER_XYZ;
      case MAKE_ID3('X', 'Z', 'Y'):
        return EULER_ORDER_XZY;
      case MAKE_ID3('Y', 'X', 'Z'):
        return EULER_ORDER_YXZ;
      case MAKE_ID3('Y', 'Z', 'X'):
        return EULER_ORDER_YZX;
      case MAKE_ID3('Z', 'X', 'Y'):
        return EULER_ORDER_ZXY;
      case MAKE_ID3('Z', 'Y', 'X'):
        return EULER_ORDER_ZYX;
    }

#undef MAKE_ID3
  }

  PyErr_Format(PyExc_ValueError, "%s: invalid euler order '%s'", error_prefix, str);
  return -1;
}

/**
 * \note #BaseMath_ReadCallback must be called beforehand.
 */
static PyObject *Euler_to_tuple_ex(EulerObject *self, int ndigits)
{
  PyObject *ret;
  int i;

  ret = PyTuple_New(EULER_SIZE);

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

  return ret;
}

/** \} */

/* -------------------------------------------------------------------- */
/** \name Euler Type: `__new__` / `mathutils.Euler()`
 * \{ */

static PyObject *Euler_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
{
  PyObject *seq = NULL;
  const char *order_str = NULL;

  float eul[EULER_SIZE] = {0.0f, 0.0f, 0.0f};
  short order = EULER_ORDER_XYZ;

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

  if (!PyArg_ParseTuple(args, "|Os:mathutils.Euler", &seq, &order_str)) {
    return NULL;
  }

  switch (PyTuple_GET_SIZE(args)) {
    case 0:
      break;
    case 2:
      if ((order = euler_order_from_string(order_str, "mathutils.Euler()")) == -1) {
        return NULL;
      }
      ATTR_FALLTHROUGH;
    case 1:
      if (mathutils_array_parse(eul, EULER_SIZE, EULER_SIZE, seq, "mathutils.Euler()") == -1) {
        return NULL;
      }
      break;
  }
  return Euler_CreatePyObject(eul, order, type);
}

/** \} */

/* -------------------------------------------------------------------- */
/** \name Euler Methods
 * \{ */

PyDoc_STRVAR(Euler_to_quaternion_doc,
             ".. method:: to_quaternion()\n"
             "\n"
             "   Return a quaternion representation of the euler.\n"
             "\n"
             "   :return: Quaternion representation of the euler.\n"
             "   :rtype: :class:`Quaternion`\n");
static PyObject *Euler_to_quaternion(EulerObject *self)
{
  float quat[4];

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

  eulO_to_quat(quat, self->eul, self->order);

  return Quaternion_CreatePyObject(quat, NULL);
}

PyDoc_STRVAR(Euler_to_matrix_doc,
             ".. method:: to_matrix()\n"
             "\n"
             "   Return a matrix representation of the euler.\n"
             "\n"
             "   :return: A 3x3 rotation matrix representation of the euler.\n"
             "   :rtype: :class:`Matrix`\n");
static PyObject *Euler_to_matrix(EulerObject *self)
{
  float mat[9];

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

  eulO_to_mat3((float(*)[3])mat, self->eul, self->order);

  return Matrix_CreatePyObject(mat, 3, 3, NULL);
}

PyDoc_STRVAR(Euler_zero_doc,
             ".. method:: zero()\n"
             "\n"
             "   Set all values to zero.\n");
static PyObject *Euler_zero(EulerObject *self)
{
  if (BaseMath_Prepare_ForWrite(self) == -1) {
    return NULL;
  }

  zero_v3(self->eul);

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

  Py_RETURN_NONE;
}

PyDoc_STRVAR(Euler_rotate_axis_doc,
             ".. method:: rotate_axis(axis, angle)\n"
             "\n"
             "   Rotates the euler a certain amount and returning a unique euler rotation\n"
             "   (no 720 degree pitches).\n"
             "\n"
             "   :arg axis: single character in ['X, 'Y', 'Z'].\n"
             "   :type axis: string\n"
             "   :arg angle: angle in radians.\n"
             "   :type angle: float\n");
static PyObject *Euler_rotate_axis(EulerObject *self, PyObject *args)
{
  float angle = 0.0f;
  int axis; /* actually a character */

  if (!PyArg_ParseTuple(args, "Cf:rotate_axis", &axis, &angle)) {
    PyErr_SetString(PyExc_TypeError,
                    "Euler.rotate_axis(): "
                    "expected an axis 'X', 'Y', 'Z' and an angle (float)");
    return NULL;
  }

  if (!ELEM(axis, 'X', 'Y', 'Z')) {
    PyErr_SetString(PyExc_ValueError,
                    "Euler.rotate_axis(): "
                    "expected axis to be 'X', 'Y' or 'Z'");
    return NULL;
  }

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

  rotate_eulO(self->eul, self->order, (char)axis, angle);

  (void)BaseMath_WriteCallback(self);

  Py_RETURN_NONE;
}

PyDoc_STRVAR(Euler_rotate_doc,
             ".. method:: rotate(other)\n"
             "\n"
             "   Rotates the euler 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 *Euler_rotate(EulerObject *self, PyObject *value)
{
  float self_rmat[3][3], other_rmat[3][3], rmat[3][3];

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

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

  eulO_to_mat3(self_rmat, self->eul, self->order);
  mul_m3_m3m3(rmat, other_rmat, self_rmat);

  mat3_to_compatible_eulO(self->eul, self->eul, self->order, rmat);

  (void)BaseMath_WriteCallback(self);
  Py_RETURN_NONE;
}

PyDoc_STRVAR(Euler_make_compatible_doc,
             ".. method:: make_compatible(other)\n"
             "\n"
             "   Make this euler compatible with another,\n"
             "   so interpolating between them works as intended.\n"
             "\n"
             "   .. note:: the rotation order is not taken into account for this function.\n");
static PyObject *Euler_make_compatible(EulerObject *self, PyObject *value)
{
  float teul[EULER_SIZE];

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

  if (mathutils_array_parse(teul,
                            EULER_SIZE,
                            EULER_SIZE,
                            value,
                            "euler.make_compatible(other), invalid 'other' arg") == -1) {
    return NULL;
  }

  compatible_eul(self->eul, teul);

  (void)BaseMath_WriteCallback(self);

  Py_RETURN_NONE;
}

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

  return Euler_CreatePyObject(self->eul, self->order, Py_TYPE(self));
}
static PyObject *Euler_deepcopy(EulerObject *self, PyObject *args)
{
  if (!PyC_CheckArgs_DeepCopy(args)) {
    return NULL;
  }
  return Euler_copy(self);
}

/** \} */

/* -------------------------------------------------------------------- */
/** \name Euler Type: `__repr__` & `__str__`
 * \{ */

static PyObject *Euler_repr(EulerObject *self)
{
  PyObject *ret, *tuple;

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

  tuple = Euler_to_tuple_ex(self, -1);

  ret = PyUnicode_FromFormat("Euler(%R, '%s')", tuple, euler_order_str(self));

  Py_DECREF(tuple);
  return ret;
}

#ifndef MATH_STANDALONE
static PyObject *Euler_str(EulerObject *self)
{
  DynStr *ds;

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

  ds = BLI_dynstr_new();

  BLI_dynstr_appendf(ds,
                     "<Euler (x=%.4f, y=%.4f, z=%.4f), order='%s'>",
                     self->eul[0],
                     self->eul[1],
                     self->eul[2],
                     euler_order_str(self));

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

/** \} */

/* -------------------------------------------------------------------- */
/** \name Euler Type: Rich Compare
 * \{ */

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

  if (EulerObject_Check(a) && EulerObject_Check(b)) {
    EulerObject *eulA = (EulerObject *)a;
    EulerObject *eulB = (EulerObject *)b;

    if (BaseMath_ReadCallback(eulA) == -1 || BaseMath_ReadCallback(eulB) == -1) {
      return NULL;
    }

    ok = ((eulA->order == eulB->order) &&
          EXPP_VectorsAreEqual(eulA->eul, eulB->eul, EULER_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);
}

/** \} */

/* -------------------------------------------------------------------- */
/** \name Euler Type: Hash (`__hash__`)
 * \{ */

static Py_hash_t Euler_hash(EulerObject *self)
{
  if (BaseMath_ReadCallback(self) == -1) {
    return -1;
  }

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

  return mathutils_array_hash(self->eul, EULER_SIZE);
}

/** \} */

/* -------------------------------------------------------------------- */
/** \name Euler Type: Sequence Protocol
 * \{ */

/** Sequence length: `len(object)`. */
static int Euler_len(EulerObject *UNUSED(self))
{
  return EULER_SIZE;
}

/** Sequence accessor (get): `x = object[i]`. */
static PyObject *Euler_item(EulerObject *self, int i)
{
  if (i < 0) {
    i = EULER_SIZE - i;
  }

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

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

  return PyFloat_FromDouble(self->eul[i]);
}

/** Sequence accessor (set): `object[i] = x`. */
static int Euler_ass_item(EulerObject *self, int i, PyObject *value)
{
  float f;

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

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

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

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

  self->eul[i] = f;

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

  return 0;
}

/** Sequence slice accessor (get): `x = object[i:j]`. */
static PyObject *Euler_slice(EulerObject *self, int begin, int end)
{
  PyObject *tuple;
  int count;

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

  CLAMP(begin, 0, EULER_SIZE);
  if (end < 0) {
    end = (EULER_SIZE + 1) + end;
  }
  CLAMP(end, 0, EULER_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->eul[count]));
  }

  return tuple;
}

/** Sequence slice accessor (set): `object[i:j] = x`. */
static int Euler_ass_slice(EulerObject *self, int begin, int end, PyObject *seq)
{
  int i, size;
  float eul[EULER_SIZE];

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

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

  if ((size = mathutils_array_parse(eul, 0, EULER_SIZE, seq, "mathutils.Euler[begin:end] = []")) ==
      -1) {
    return -1;
  }

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

  for (i = 0; i < EULER_SIZE; i++) {
    self->eul[begin + i] = eul[i];
  }

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

/** Sequence generic subscript (get): `x = object[...]`. */
static PyObject *Euler_subscript(EulerObject *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 += EULER_SIZE;
    }
    return Euler_item(self, i);
  }
  if (PySlice_Check(item)) {
    Py_ssize_t start, stop, step, slicelength;

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

    if (slicelength <= 0) {
      return PyTuple_New(0);
    }
    if (step == 1) {
      return Euler_slice(self, start, stop);
    }

    PyErr_SetString(PyExc_IndexError, "slice steps not supported with eulers");
    return NULL;
  }

  PyErr_Format(
      PyExc_TypeError, "euler indices must be integers, not %.200s", Py_TYPE(item)->tp_name);
  return NULL;
}

/** Sequence generic subscript (set): `object[...] = x`. */
static int Euler_ass_subscript(EulerObject *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 += EULER_SIZE;
    }
    return Euler_ass_item(self, i, value);
  }
  if (PySlice_Check(item)) {
    Py_ssize_t start, stop, step, slicelength;

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

    if (step == 1) {
      return Euler_ass_slice(self, start, stop, value);
    }

    PyErr_SetString(PyExc_IndexError, "slice steps not supported with euler");
    return -1;
  }

  PyErr_Format(
      PyExc_TypeError, "euler indices must be integers, not %.200s", Py_TYPE(item)->tp_name);
  return -1;
}

/** \} */

/* -------------------------------------------------------------------- */
/** \name Euler Type: Sequence & Mapping Protocol Declarations
 * \{ */

static PySequenceMethods Euler_SeqMethods = {
    (lenfunc)Euler_len,              /*sq_length*/
    (binaryfunc)NULL,                /*sq_concat*/
    (ssizeargfunc)NULL,              /*sq_repeat*/
    (ssizeargfunc)Euler_item,        /*sq_item*/
    (ssizessizeargfunc)NULL,         /*sq_slice(DEPRECATED)*/
    (ssizeobjargproc)Euler_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 Euler_AsMapping = {
    (lenfunc)Euler_len,
    (binaryfunc)Euler_subscript,
    (objobjargproc)Euler_ass_subscript,
};

/** \} */

/* -------------------------------------------------------------------- */
/** \name Euler Type: Get/Set Item Implementation
 * \{ */

/* Euler axis: `euler.x/y/z`. */

PyDoc_STRVAR(Euler_axis_doc, "Euler axis angle in radians.\n\n:type: float");
static PyObject *Euler_axis_get(EulerObject *self, void *type)
{
  return Euler_item(self, POINTER_AS_INT(type));
}

static int Euler_axis_set(EulerObject *self, PyObject *value, void *type)
{
  return Euler_ass_item(self, POINTER_AS_INT(type), value);
}

/* Euler rotation order: `euler.order`. */

PyDoc_STRVAR(
    Euler_order_doc,
    "Euler rotation order.\n\n:type: string in ['XYZ', 'XZY', 'YXZ', 'YZX', 'ZXY', 'ZYX']");
static PyObject *Euler_order_get(EulerObject *self, void *UNUSED(closure))
{
  if (BaseMath_ReadCallback(self) == -1) {
    /* can read order too */
    return NULL;
  }

  return PyUnicode_FromString(euler_order_str(self));
}

static int Euler_order_set(EulerObject *self, PyObject *value, void *UNUSED(closure))
{
  const char *order_str;
  short order;

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

  if (((order_str = PyUnicode_AsUTF8(value)) == NULL) ||
      ((order = euler_order_from_string(order_str, "euler.order")) == -1)) {
    return -1;
  }

  self->order = order;
  (void)BaseMath_WriteCallback(self); /* order can be written back */
  return 0;
}

/** \} */

/* -------------------------------------------------------------------- */
/** \name Euler Type: Get/Set Item Definitions
 * \{ */

static PyGetSetDef Euler_getseters[] = {
    {"x", (getter)Euler_axis_get, (setter)Euler_axis_set, Euler_axis_doc, (void *)0},
    {"y", (getter)Euler_axis_get, (setter)Euler_axis_set, Euler_axis_doc, (void *)1},
    {"z", (getter)Euler_axis_get, (setter)Euler_axis_set, Euler_axis_doc, (void *)2},
    {"order", (getter)Euler_order_get, (setter)Euler_order_set, Euler_order_doc, (void *)NULL},

    {"is_wrapped",
     (getter)BaseMathObject_is_wrapped_get,
     (setter)NULL,
     BaseMathObject_is_wrapped_doc,
     NULL},
    {"is_frozen",
     (getter)BaseMathObject_is_frozen_get,
     (setter)NULL,
     BaseMathObject_is_frozen_doc,
     NULL},
    {"is_valid",
     (getter)BaseMathObject_is_valid_get,
     (setter)NULL,
     BaseMathObject_is_valid_doc,
     NULL},
    {"owner", (getter)BaseMathObject_owner_get, (setter)NULL, BaseMathObject_owner_doc, NULL},
    {NULL, NULL, NULL, NULL, NULL} /* Sentinel */
};

/** \} */

/* -------------------------------------------------------------------- */
/** \name Euler Type: Method Definitions
 * \{ */

static struct PyMethodDef Euler_methods[] = {
    {"zero", (PyCFunction)Euler_zero, METH_NOARGS, Euler_zero_doc},
    {"to_matrix", (PyCFunction)Euler_to_matrix, METH_NOARGS, Euler_to_matrix_doc},
    {"to_quaternion", (PyCFunction)Euler_to_quaternion, METH_NOARGS, Euler_to_quaternion_doc},
    {"rotate_axis", (PyCFunction)Euler_rotate_axis, METH_VARARGS, Euler_rotate_axis_doc},
    {"rotate", (PyCFunction)Euler_rotate, METH_O, Euler_rotate_doc},
    {"make_compatible", (PyCFunction)Euler_make_compatible, METH_O, Euler_make_compatible_doc},
    {"copy", (PyCFunction)Euler_copy, METH_NOARGS, Euler_copy_doc},
    {"__copy__", (PyCFunction)Euler_copy, METH_NOARGS, Euler_copy_doc},
    {"__deepcopy__", (PyCFunction)Euler_deepcopy, METH_VARARGS, Euler_copy_doc},

    /* base-math methods */
    {"freeze", (PyCFunction)BaseMathObject_freeze, METH_NOARGS, BaseMathObject_freeze_doc},
    {NULL, NULL, 0, NULL},
};

/** \} */

/* -------------------------------------------------------------------- */
/** \name Euler Type: Python Object Definition
 * \{ */

PyDoc_STRVAR(
    euler_doc,
    ".. class:: Euler(angles, order='XYZ')\n"
    "\n"
    "   This object gives access to Eulers in Blender.\n"
    "\n"
    "   .. seealso:: `Euler angles <https://en.wikipedia.org/wiki/Euler_angles>`__ on Wikipedia.\n"
    "\n"
    "   :arg angles: Three angles, in radians.\n"
    "   :type angles: 3d vector\n"
    "   :arg order: Optional order of the angles, a permutation of ``XYZ``.\n"
    "   :type order: str\n");
PyTypeObject euler_Type = {
    PyVarObject_HEAD_INIT(NULL, 0) "Euler", /* tp_name */
    sizeof(EulerObject),                    /* tp_basicsize */
    0,                                      /* tp_itemsize */
    (destructor)BaseMathObject_dealloc,     /* tp_dealloc */
    (printfunc)NULL,                        /* tp_print */
    NULL,                                   /* tp_getattr */
    NULL,                                   /* tp_setattr */
    NULL,                                   /* tp_compare */
    (reprfunc)Euler_repr,                   /* tp_repr */
    NULL,                                   /* tp_as_number */
    &Euler_SeqMethods,                      /* tp_as_sequence */
    &Euler_AsMapping,                       /* tp_as_mapping */
    (hashfunc)Euler_hash,                   /* tp_hash */
    NULL,                                   /* tp_call */
#ifndef MATH_STANDALONE
    (reprfunc)Euler_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 */
    euler_doc,                                                     /* tp_doc */
    (traverseproc)BaseMathObject_traverse,                         /* tp_traverse */
    (inquiry)BaseMathObject_clear,                                 /* tp_clear */
    (richcmpfunc)Euler_richcmpr,                                   /* tp_richcompare */
    0,                                                             /* tp_weaklistoffset */
    NULL,                                                          /* tp_iter */
    NULL,                                                          /* tp_iternext */
    Euler_methods,                                                 /* tp_methods */
    NULL,                                                          /* tp_members */
    Euler_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 */
    Euler_new,                                                     /* tp_new */
    NULL,                                                          /* tp_free */
    (inquiry)BaseMathObject_is_gc,                                 /* tp_is_gc */
    NULL,                                                          /* tp_bases */
    NULL,                                                          /* tp_mro */
    NULL,                                                          /* tp_cache */
    NULL,                                                          /* tp_subclasses */
    NULL,                                                          /* tp_weaklist */
    NULL,                                                          /* tp_del */
};

/** \} */

/* -------------------------------------------------------------------- */
/** \name Euler Type: C/API Constructors
 * \{ */

PyObject *Euler_CreatePyObject(const float eul[3], const short order, PyTypeObject *base_type)
{
  EulerObject *self;
  float *eul_alloc;

  eul_alloc = PyMem_Malloc(EULER_SIZE * sizeof(float));
  if (UNLIKELY(eul_alloc == NULL)) {
    PyErr_SetString(PyExc_MemoryError,
                    "Euler(): "
                    "problem allocating data");
    return NULL;
  }

  self = BASE_MATH_NEW(EulerObject, euler_Type, base_type);
  if (self) {
    self->eul = eul_alloc;

    /* init callbacks as NULL */
    self->cb_user = NULL;
    self->cb_type = self->cb_subtype = 0;

    if (eul) {
      copy_v3_v3(self->eul, eul);
    }
    else {
      zero_v3(self->eul);
    }

    self->flag = BASE_MATH_FLAG_DEFAULT;
    self->order = order;
  }
  else {
    PyMem_Free(eul_alloc);
  }

  return (PyObject *)self;
}

PyObject *Euler_CreatePyObject_wrap(float eul[3], const short order, PyTypeObject *base_type)
{
  EulerObject *self;

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

    self->eul = eul;
    self->flag = BASE_MATH_FLAG_DEFAULT | BASE_MATH_FLAG_IS_WRAP;

    self->order = order;
  }

  return (PyObject *)self;
}

PyObject *Euler_CreatePyObject_cb(PyObject *cb_user,
                                  const short order,
                                  uchar cb_type,
                                  uchar cb_subtype)
{
  EulerObject *self = (EulerObject *)Euler_CreatePyObject(NULL, order, NULL);
  if (self) {
    Py_INCREF(cb_user);
    self->cb_user = cb_user;
    self->cb_type = cb_type;
    self->cb_subtype = cb_subtype;
    BLI_assert(!PyObject_GC_IsTracked((PyObject *)self));
    PyObject_GC_Track(self);
  }

  return (PyObject *)self;
}

/** \} */