mathutils_Quaternion.c

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/*
 * ***** BEGIN GPL LICENSE BLOCK *****
 *
 * 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.
 *
 *
 * Contributor(s): Joseph Gilbert
 *
 * ***** END GPL LICENSE BLOCK *****
 */

#include <Python.h>

#include "mathutils.h"

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

#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);

//-----------------------------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) {
        float mat[3][3];

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

        quat_to_mat3(mat, tquat);

        if (order == EULER_ORDER_XYZ)   mat3_to_compatible_eul(eul, eul_compat->eul, mat);
        else                            mat3_to_compatible_eulO(eul, eul_compat->eul, order, mat);
    }
    else {
        if (order == EULER_ORDER_XYZ)   quat_to_eul(eul, tquat);
        else                            quat_to_eulO(eul, order, tquat);
    }

    return Euler_CreatePyObject(eul, order, Py_NEW, NULL);
}
//----------------------------Quaternion.toMatrix()------------------
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, Py_NEW, NULL);
}

//----------------------------Quaternion.toMatrix()------------------
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_ITEM(ret, 0, Vector_CreatePyObject(axis, 3, Py_NEW, NULL));
    PyTuple_SET_ITEM(ret, 1, PyFloat_FromDouble(angle));
    return ret;
}


//----------------------------Quaternion.cross(other)------------------
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_NEW, Py_TYPE(self));
}

//----------------------------Quaternion.dot(other)------------------
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: :class:`Quaternion`\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_NEW, 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_NEW, Py_TYPE(self));
}

PyDoc_STRVAR(Quaternion_rotate_doc,
".. method:: rotate(other)\n"
"\n"
"   Rotates the quaternion a 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(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 axis of rotation of [theta, vector]
PyDoc_STRVAR(Quaternion_normalize_doc,
".. function:: normalize()\n"
"\n"
"   Normalize the quaternion.\n"
);
static PyObject *Quaternion_normalize(QuaternionObject *self)
{
    if (BaseMath_ReadCallback(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);
}

//----------------------------Quaternion.invert()------------------
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(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);
}

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

    unit_qt(self->quat);

    (void)BaseMath_WriteCallback(self);
    Py_RETURN_NONE;
}
//----------------------------Quaternion.negate()-------------------
PyDoc_STRVAR(Quaternion_negate_doc,
".. function:: negate()\n"
"\n"
"   Set the quaternion to its negative.\n"
"\n"
"   :return: an instance of itself.\n"
"   :rtype: :class:`Quaternion`\n"
);
static PyObject *Quaternion_negate(QuaternionObject *self)
{
    if (BaseMath_ReadCallback(self) == -1)
        return NULL;

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

    (void)BaseMath_WriteCallback(self);
    Py_RETURN_NONE;
}
//----------------------------Quaternion.conjugate()----------------
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(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);
}

//----------------------------Quaternion.copy()----------------
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_NEW, Py_TYPE(self));
}

//----------------------------print object (internal)--------------
//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;
}

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 */
}

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; /* pass through */
    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(res), res;
}

//---------------------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 scalar = (float)PyFloat_AsDouble(ob);
    if (scalar == -1.0f && PyErr_Occurred()) { /* parsed item not a number */
        PyErr_SetString(PyExc_TypeError,
                        "quaternion[index] = x: "
                        "index argument 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] = scalar;

    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(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((void *)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((void *)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_NEW, 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_NEW, 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_NEW, Py_TYPE(quat));
}

//------------------------obj * obj------------------------------
//mulplication
static PyObject *Quaternion_mul(PyObject *q1, PyObject *q2)
{
    float quat[QUAT_SIZE], 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 (cross product) */
        mul_qt_qtqt(quat, quat1->quat, quat2->quat);
        return Quaternion_CreatePyObject(quat, Py_NEW, Py_TYPE(q1));
    }
    /* 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 * 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_NEW, Py_TYPE(vec2));
        }
        /* QUAT * FLOAT */
        else if ((((scalar = PyFloat_AsDouble(q2)) == -1.0f && PyErr_Occurred()) == 0)) {
            return quat_mul_float(quat1, scalar);
        }
    }
    else {
        BLI_assert(!"internal error");
    }

    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
  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_NEW, 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)     0,  /*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 */
    NULL,               /* 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 */
};

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, GET_INT_FROM_POINTER(type));
}

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

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

    return PyFloat_FromDouble(sqrt(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(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, Py_NEW, 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(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] = {0.0f, 0.0f, 0.0f, 0.0f};

    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:
        if (mathutils_array_parse(quat, QUAT_SIZE, QUAT_SIZE, seq, "mathutils.Quaternion()") == -1)
            return NULL;
        break;
    case 2:
        if (mathutils_array_parse(quat, 3, 3, seq, "mathutils.Quaternion()") == -1)
            return NULL;
        angle = angle_wrap_rad(angle); /* clamp because of precision issues */
        axis_angle_to_quat(quat, quat, angle);
        break;
    /* PyArg_ParseTuple assures no more then 2 */
    }
    return Quaternion_CreatePyObject(quat, Py_NEW, 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 precission errors, use this function to ensure */
static void quat__axis_angle_sanitize(float axis[3], float *angle)
{
    if (axis) {
        if ( !finite(axis[0]) ||
             !finite(axis[1]) ||
             !finite(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 (!finite(*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},

    /* 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},

    {"__copy__", (PyCFunction) Quaternion_copy, METH_NOARGS, Quaternion_copy_doc},
    {"copy", (PyCFunction) Quaternion_copy, METH_NOARGS, 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 *)"owner", (getter)BaseMathObject_owner_get, (setter)NULL, BaseMathObject_owner_doc, NULL},
    {NULL, NULL, NULL, NULL, NULL}  /* Sentinel */
};

//------------------PY_OBECT DEFINITION--------------------------
PyDoc_STRVAR(quaternion_doc,
"This object gives access to Quaternions in Blender."
);
PyTypeObject quaternion_Type = {
    PyVarObject_HEAD_INIT(NULL, 0)
    "mathutils.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
    NULL,                               //tp_hash
    NULL,                               //tp_call
    (reprfunc) Quaternion_str,          //tp_str
    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
};
//------------------------Quaternion_CreatePyObject (internal)-------------
//creates a new quaternion object
/*pass Py_WRAP - if vector is a WRAPPER for data allocated by BLENDER
 (i.e. it was allocated elsewhere by MEM_mallocN())
  pass Py_NEW - if vector is not a WRAPPER and managed by PYTHON
 (i.e. it must be created here with PyMEM_malloc())*/
PyObject *Quaternion_CreatePyObject(float *quat, int type, PyTypeObject *base_type)
{
    QuaternionObject *self;

    self = base_type ? (QuaternionObject *)base_type->tp_alloc(base_type, 0) :
                       (QuaternionObject *)PyObject_GC_New(QuaternionObject, &quaternion_Type);

    if (self) {
        /* init callbacks as NULL */
        self->cb_user = NULL;
        self->cb_type = self->cb_subtype = 0;

        if (type == Py_WRAP) {
            self->quat = quat;
            self->wrapped = Py_WRAP;
        }
        else if (type == Py_NEW) {
            self->quat = PyMem_Malloc(QUAT_SIZE * sizeof(float));
            if (!quat) { //new empty
                unit_qt(self->quat);
            }
            else {
                copy_qt_qt(self->quat, quat);
            }
            self->wrapped = Py_NEW;
        }
        else {
            Py_FatalError("Quaternion(): invalid type!");
        }
    }
    return (PyObject *) self;
}

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

    return (PyObject *)self;
}