mathutils_geometry.c

Go to the documentation of this file.

/*
 * $Id: mathutils_geometry.c 38409 2011-07-15 04:01:47Z campbellbarton $
 *
 * ***** 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.
 *
 * This is a new part of Blender.
 *
 * Contributor(s): Joseph Gilbert, Campbell Barton
 *
 * ***** END GPL LICENSE BLOCK *****
 */

#include <Python.h>

#include "mathutils_geometry.h"

/* Used for PolyFill */
#ifndef MATH_STANDALONE /* define when building outside blender */
#  include "MEM_guardedalloc.h"
#  include "BLI_blenlib.h"
#  include "BLI_boxpack2d.h"
#  include "BKE_displist.h"
#  include "BKE_curve.h"
#endif

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

#define SWAP_FLOAT(a, b, tmp) tmp=a; a=b; b=tmp
#define eps 0.000001


/*-------------------------DOC STRINGS ---------------------------*/
PyDoc_STRVAR(M_Geometry_doc,
"The Blender geometry module"
);

//---------------------------------INTERSECTION FUNCTIONS--------------------

PyDoc_STRVAR(M_Geometry_intersect_ray_tri_doc,
".. function:: intersect_ray_tri(v1, v2, v3, ray, orig, clip=True)\n"
"\n"
"   Returns the intersection between a ray and a triangle, if possible, returns None otherwise.\n"
"\n"
"   :arg v1: Point1\n"
"   :type v1: :class:`mathutils.Vector`\n"
"   :arg v2: Point2\n"
"   :type v2: :class:`mathutils.Vector`\n"
"   :arg v3: Point3\n"
"   :type v3: :class:`mathutils.Vector`\n"
"   :arg ray: Direction of the projection\n"
"   :type ray: :class:`mathutils.Vector`\n"
"   :arg orig: Origin\n"
"   :type orig: :class:`mathutils.Vector`\n"
"   :arg clip: When False, don't restrict the intersection to the area of the triangle, use the infinite plane defined by the triangle.\n"
"   :type clip: boolean\n"
"   :return: The point of intersection or None if no intersection is found\n"
"   :rtype: :class:`mathutils.Vector` or None\n"
);
static PyObject *M_Geometry_intersect_ray_tri(PyObject *UNUSED(self), PyObject* args)
{
        VectorObject *ray, *ray_off, *vec1, *vec2, *vec3;
        float dir[3], orig[3], v1[3], v2[3], v3[3], e1[3], e2[3], pvec[3], tvec[3], qvec[3];
        float det, inv_det, u, v, t;
        int clip= 1;

        if(!PyArg_ParseTuple(args, "O!O!O!O!O!|i:intersect_ray_tri", &vector_Type, &vec1, &vector_Type, &vec2, &vector_Type, &vec3, &vector_Type, &ray, &vector_Type, &ray_off , &clip)) {
                return NULL;
        }
        if(vec1->size != 3 || vec2->size != 3 || vec3->size != 3 || ray->size != 3 || ray_off->size != 3) {
                PyErr_SetString(PyExc_ValueError,
                                "only 3D vectors for all parameters");
                return NULL;
        }

        if(BaseMath_ReadCallback(vec1) == -1 || BaseMath_ReadCallback(vec2) == -1 || BaseMath_ReadCallback(vec3) == -1 || BaseMath_ReadCallback(ray) == -1 || BaseMath_ReadCallback(ray_off) == -1)
                return NULL;

        VECCOPY(v1, vec1->vec);
        VECCOPY(v2, vec2->vec);
        VECCOPY(v3, vec3->vec);

        VECCOPY(dir, ray->vec);
        normalize_v3(dir);

        VECCOPY(orig, ray_off->vec);

        /* find vectors for two edges sharing v1 */
        sub_v3_v3v3(e1, v2, v1);
        sub_v3_v3v3(e2, v3, v1);

        /* begin calculating determinant - also used to calculated U parameter */
        cross_v3_v3v3(pvec, dir, e2);

        /* if determinant is near zero, ray lies in plane of triangle */
        det= dot_v3v3(e1, pvec);

        if (det > -0.000001f && det < 0.000001f) {
                Py_RETURN_NONE;
        }

        inv_det= 1.0f / det;

        /* calculate distance from v1 to ray origin */
        sub_v3_v3v3(tvec, orig, v1);

        /* calculate U parameter and test bounds */
        u= dot_v3v3(tvec, pvec) * inv_det;
        if (clip && (u < 0.0f || u > 1.0f)) {
                Py_RETURN_NONE;
        }

        /* prepare to test the V parameter */
        cross_v3_v3v3(qvec, tvec, e1);

        /* calculate V parameter and test bounds */
        v= dot_v3v3(dir, qvec) * inv_det;

        if (clip && (v < 0.0f || u + v > 1.0f)) {
                Py_RETURN_NONE;
        }

        /* calculate t, ray intersects triangle */
        t= dot_v3v3(e2, qvec) * inv_det;

        mul_v3_fl(dir, t);
        add_v3_v3v3(pvec, orig, dir);

        return newVectorObject(pvec, 3, Py_NEW, NULL);
}

/* Line-Line intersection using algorithm from mathworld.wolfram.com */

PyDoc_STRVAR(M_Geometry_intersect_line_line_doc,
".. function:: intersect_line_line(v1, v2, v3, v4)\n"
"\n"
"   Returns a tuple with the points on each line respectively closest to the other.\n"
"\n"
"   :arg v1: First point of the first line\n"
"   :type v1: :class:`mathutils.Vector`\n"
"   :arg v2: Second point of the first line\n"
"   :type v2: :class:`mathutils.Vector`\n"
"   :arg v3: First point of the second line\n"
"   :type v3: :class:`mathutils.Vector`\n"
"   :arg v4: Second point of the second line\n"
"   :type v4: :class:`mathutils.Vector`\n"
"   :rtype: tuple of :class:`mathutils.Vector`'s\n"
);
static PyObject *M_Geometry_intersect_line_line(PyObject *UNUSED(self), PyObject *args)
{
        PyObject *tuple;
        VectorObject *vec1, *vec2, *vec3, *vec4;
        float v1[3], v2[3], v3[3], v4[3], i1[3], i2[3];

        if(!PyArg_ParseTuple(args, "O!O!O!O!:intersect_line_line", &vector_Type, &vec1, &vector_Type, &vec2, &vector_Type, &vec3, &vector_Type, &vec4)) {
                return NULL;
        }
        if(vec1->size != vec2->size || vec1->size != vec3->size || vec3->size != vec2->size) {
                PyErr_SetString(PyExc_ValueError,
                                "vectors must be of the same size");
                return NULL;
        }

        if(BaseMath_ReadCallback(vec1) == -1 || BaseMath_ReadCallback(vec2) == -1 || BaseMath_ReadCallback(vec3) == -1 || BaseMath_ReadCallback(vec4) == -1)
                return NULL;

        if(vec1->size == 3 || vec1->size == 2) {
                int result;

                if (vec1->size == 3) {
                        VECCOPY(v1, vec1->vec);
                        VECCOPY(v2, vec2->vec);
                        VECCOPY(v3, vec3->vec);
                        VECCOPY(v4, vec4->vec);
                }
                else {
                        v1[0]= vec1->vec[0];
                        v1[1]= vec1->vec[1];
                        v1[2]= 0.0f;

                        v2[0]= vec2->vec[0];
                        v2[1]= vec2->vec[1];
                        v2[2]= 0.0f;

                        v3[0]= vec3->vec[0];
                        v3[1]= vec3->vec[1];
                        v3[2]= 0.0f;

                        v4[0]= vec4->vec[0];
                        v4[1]= vec4->vec[1];
                        v4[2]= 0.0f;
                }

                result= isect_line_line_v3(v1, v2, v3, v4, i1, i2);

                if (result == 0) {
                        /* colinear */
                        Py_RETURN_NONE;
                }
                else {
                        tuple= PyTuple_New(2);
                        PyTuple_SET_ITEM(tuple, 0, newVectorObject(i1, vec1->size, Py_NEW, NULL));
                        PyTuple_SET_ITEM(tuple, 1, newVectorObject(i2, vec1->size, Py_NEW, NULL));
                        return tuple;
                }
        }
        else {
                PyErr_SetString(PyExc_ValueError,
                                "2D/3D vectors only");
                return NULL;
        }
}




//----------------------------geometry.normal() -------------------
PyDoc_STRVAR(M_Geometry_normal_doc,
".. function:: normal(v1, v2, v3, v4=None)\n"
"\n"
"   Returns the normal of the 3D tri or quad.\n"
"\n"
"   :arg v1: Point1\n"
"   :type v1: :class:`mathutils.Vector`\n"
"   :arg v2: Point2\n"
"   :type v2: :class:`mathutils.Vector`\n"
"   :arg v3: Point3\n"
"   :type v3: :class:`mathutils.Vector`\n"
"   :arg v4: Point4 (optional)\n"
"   :type v4: :class:`mathutils.Vector`\n"
"   :rtype: :class:`mathutils.Vector`\n"
);
static PyObject *M_Geometry_normal(PyObject *UNUSED(self), PyObject* args)
{
        VectorObject *vec1, *vec2, *vec3, *vec4;
        float n[3];

        if(PyTuple_GET_SIZE(args) == 3) {
                if(!PyArg_ParseTuple(args, "O!O!O!:normal", &vector_Type, &vec1, &vector_Type, &vec2, &vector_Type, &vec3)) {
                        return NULL;
                }
                if(vec1->size != vec2->size || vec1->size != vec3->size) {
                        PyErr_SetString(PyExc_ValueError,
                                        "vectors must be of the same size");
                        return NULL;
                }
                if(vec1->size < 3) {
                        PyErr_SetString(PyExc_ValueError,
                                        "2D vectors unsupported");
                        return NULL;
                }

                if(BaseMath_ReadCallback(vec1) == -1 || BaseMath_ReadCallback(vec2) == -1 || BaseMath_ReadCallback(vec3) == -1)
                        return NULL;

                normal_tri_v3(n, vec1->vec, vec2->vec, vec3->vec);
        }
        else {
                if(!PyArg_ParseTuple(args, "O!O!O!O!:normal", &vector_Type, &vec1, &vector_Type, &vec2, &vector_Type, &vec3, &vector_Type, &vec4)) {
                        return NULL;
                }
                if(vec1->size != vec2->size || vec1->size != vec3->size || vec1->size != vec4->size) {
                        PyErr_SetString(PyExc_ValueError,
                                        "vectors must be of the same size");
                        return NULL;
                }
                if(vec1->size < 3) {
                        PyErr_SetString(PyExc_ValueError,
                                        "2D vectors unsupported");
                        return NULL;
                }

                if(BaseMath_ReadCallback(vec1) == -1 || BaseMath_ReadCallback(vec2) == -1 || BaseMath_ReadCallback(vec3) == -1 || BaseMath_ReadCallback(vec4) == -1)
                        return NULL;

                normal_quad_v3(n, vec1->vec, vec2->vec, vec3->vec, vec4->vec);
        }

        return newVectorObject(n, 3, Py_NEW, NULL);
}

//--------------------------------- AREA FUNCTIONS--------------------

PyDoc_STRVAR(M_Geometry_area_tri_doc,
".. function:: area_tri(v1, v2, v3)\n"
"\n"
"   Returns the area size of the 2D or 3D triangle defined.\n"
"\n"
"   :arg v1: Point1\n"
"   :type v1: :class:`mathutils.Vector`\n"
"   :arg v2: Point2\n"
"   :type v2: :class:`mathutils.Vector`\n"
"   :arg v3: Point3\n"
"   :type v3: :class:`mathutils.Vector`\n"
"   :rtype: float\n"
);
static PyObject *M_Geometry_area_tri(PyObject *UNUSED(self), PyObject* args)
{
        VectorObject *vec1, *vec2, *vec3;

        if(!PyArg_ParseTuple(args, "O!O!O!:area_tri", &vector_Type, &vec1, &vector_Type, &vec2, &vector_Type, &vec3)) {
                return NULL;
        }

        if(vec1->size != vec2->size || vec1->size != vec3->size) {
                PyErr_SetString(PyExc_ValueError,
                                "vectors must be of the same size");
                return NULL;
        }

        if(BaseMath_ReadCallback(vec1) == -1 || BaseMath_ReadCallback(vec2) == -1 || BaseMath_ReadCallback(vec3) == -1)
                return NULL;

        if (vec1->size == 3) {
                return PyFloat_FromDouble(area_tri_v3(vec1->vec, vec2->vec, vec3->vec));
        }
        else if (vec1->size == 2) {
                return PyFloat_FromDouble(area_tri_v2(vec1->vec, vec2->vec, vec3->vec));
        }
        else {
                PyErr_SetString(PyExc_ValueError,
                                "only 2D,3D vectors are supported");
                return NULL;
        }
}


PyDoc_STRVAR(M_Geometry_intersect_line_line_2d_doc,
".. function:: intersect_line_line_2d(lineA_p1, lineA_p2, lineB_p1, lineB_p2)\n"
"\n"
"   Takes 2 lines (as 4 vectors) and returns a vector for their point of intersection or None.\n"
"\n"
"   :arg lineA_p1: First point of the first line\n"
"   :type lineA_p1: :class:`mathutils.Vector`\n"
"   :arg lineA_p2: Second point of the first line\n"
"   :type lineA_p2: :class:`mathutils.Vector`\n"
"   :arg lineB_p1: First point of the second line\n"
"   :type lineB_p1: :class:`mathutils.Vector`\n"
"   :arg lineB_p2: Second point of the second line\n"
"   :type lineB_p2: :class:`mathutils.Vector`\n"
"   :return: The point of intersection or None when not found\n"
"   :rtype: :class:`mathutils.Vector` or None\n"
);
static PyObject *M_Geometry_intersect_line_line_2d(PyObject *UNUSED(self), PyObject* args)
{
        VectorObject *line_a1, *line_a2, *line_b1, *line_b2;
        float vi[2];
        if(!PyArg_ParseTuple(args, "O!O!O!O!:intersect_line_line_2d",
          &vector_Type, &line_a1,
          &vector_Type, &line_a2,
          &vector_Type, &line_b1,
          &vector_Type, &line_b2)
        ) {
                return NULL;
        }
        
        if(BaseMath_ReadCallback(line_a1) == -1 || BaseMath_ReadCallback(line_a2) == -1 || BaseMath_ReadCallback(line_b1) == -1 || BaseMath_ReadCallback(line_b2) == -1)
                return NULL;

        if(isect_seg_seg_v2_point(line_a1->vec, line_a2->vec, line_b1->vec, line_b2->vec, vi) == 1) {
                return newVectorObject(vi, 2, Py_NEW, NULL);
        }
        else {
                Py_RETURN_NONE;
        }
}


PyDoc_STRVAR(M_Geometry_intersect_line_plane_doc,
".. function:: intersect_line_plane(line_a, line_b, plane_co, plane_no, no_flip=False)\n"
"\n"
"   Takes 2 lines (as 4 vectors) and returns a vector for their point of intersection or None.\n"
"\n"
"   :arg line_a: First point of the first line\n"
"   :type line_a: :class:`mathutils.Vector`\n"
"   :arg line_b: Second point of the first line\n"
"   :type line_b: :class:`mathutils.Vector`\n"
"   :arg plane_co: A point on the plane\n"
"   :type plane_co: :class:`mathutils.Vector`\n"
"   :arg plane_no: The direction the plane is facing\n"
"   :type plane_no: :class:`mathutils.Vector`\n"
"   :arg no_flip: Always return an intersection on the directon defined bt line_a -> line_b\n"
"   :type no_flip: :boolean\n"
"   :return: The point of intersection or None when not found\n"
"   :rtype: :class:`mathutils.Vector` or None\n"
);
static PyObject *M_Geometry_intersect_line_plane(PyObject *UNUSED(self), PyObject* args)
{
        VectorObject *line_a, *line_b, *plane_co, *plane_no;
        int no_flip= 0;
        float isect[3];
        if(!PyArg_ParseTuple(args, "O!O!O!O!|i:intersect_line_plane",
          &vector_Type, &line_a,
          &vector_Type, &line_b,
          &vector_Type, &plane_co,
          &vector_Type, &plane_no,
          &no_flip)
        ) {
                return NULL;
        }

        if(             BaseMath_ReadCallback(line_a) == -1 ||
                BaseMath_ReadCallback(line_b) == -1 ||
                BaseMath_ReadCallback(plane_co) == -1 ||
                BaseMath_ReadCallback(plane_no) == -1
        ) {
                return NULL;
        }

        if(ELEM4(2, line_a->size, line_b->size, plane_co->size, plane_no->size)) {
                PyErr_SetString(PyExc_ValueError,
                                "geometry.intersect_line_plane(...): "
                                " can't use 2D Vectors");
                return NULL;
        }

        if(isect_line_plane_v3(isect, line_a->vec, line_b->vec, plane_co->vec, plane_no->vec, no_flip) == 1) {
                return newVectorObject(isect, 3, Py_NEW, NULL);
        }
        else {
                Py_RETURN_NONE;
        }
}


PyDoc_STRVAR(M_Geometry_intersect_line_sphere_doc,
".. function:: intersect_line_sphere(line_a, line_b, sphere_co, sphere_radius, clip=True)\n"
"\n"
"   Takes a lines (as 2 vectors), a sphere as a point and a radius and\n"
"   returns the intersection\n"
"\n"
"   :arg line_a: First point of the first line\n"
"   :type line_a: :class:`mathutils.Vector`\n"
"   :arg line_b: Second point of the first line\n"
"   :type line_b: :class:`mathutils.Vector`\n"
"   :arg sphere_co: The center of the sphere\n"
"   :type sphere_co: :class:`mathutils.Vector`\n"
"   :arg sphere_radius: Radius of the sphere\n"
"   :type sphere_radius: sphere_radius\n"
"   :return: The intersection points as a pair of vectors or None when there is no intersection\n"
"   :rtype: A tuple pair containing :class:`mathutils.Vector` or None\n"
);
static PyObject *M_Geometry_intersect_line_sphere(PyObject *UNUSED(self), PyObject* args)
{
        VectorObject *line_a, *line_b, *sphere_co;
        float sphere_radius;
        int clip= TRUE;

        float isect_a[3];
        float isect_b[3];

        if(!PyArg_ParseTuple(args, "O!O!O!f|i:intersect_line_sphere",
          &vector_Type, &line_a,
          &vector_Type, &line_b,
          &vector_Type, &sphere_co,
          &sphere_radius, &clip)
        ) {
                return NULL;
        }

        if(             BaseMath_ReadCallback(line_a) == -1 ||
                BaseMath_ReadCallback(line_b) == -1 ||
                BaseMath_ReadCallback(sphere_co) == -1
        ) {
                return NULL;
        }

        if(ELEM3(2, line_a->size, line_b->size, sphere_co->size)) {
                PyErr_SetString(PyExc_ValueError,
                                "geometry.intersect_line_sphere(...): "
                                " can't use 2D Vectors");
                return NULL;
        }
        else {
                short use_a= TRUE;
                short use_b= TRUE;
                float lambda;

                PyObject *ret= PyTuple_New(2);

                switch(isect_line_sphere_v3(line_a->vec, line_b->vec, sphere_co->vec, sphere_radius, isect_a, isect_b)) {
                case 1:
                        if(!(!clip || (((lambda= line_point_factor_v3(isect_a, line_a->vec, line_b->vec)) >= 0.0f) && (lambda <= 1.0f)))) use_a= FALSE;
                        use_b= FALSE;
                        break;
                case 2:
                        if(!(!clip || (((lambda= line_point_factor_v3(isect_a, line_a->vec, line_b->vec)) >= 0.0f) && (lambda <= 1.0f)))) use_a= FALSE;
                        if(!(!clip || (((lambda= line_point_factor_v3(isect_b, line_a->vec, line_b->vec)) >= 0.0f) && (lambda <= 1.0f)))) use_b= FALSE;
                        break;
                default:
                        use_a= FALSE;
                        use_b= FALSE;
                }

                if(use_a) { PyTuple_SET_ITEM(ret, 0,  newVectorObject(isect_a, 3, Py_NEW, NULL)); }
                else      { PyTuple_SET_ITEM(ret, 0,  Py_None); Py_INCREF(Py_None); }

                if(use_b) { PyTuple_SET_ITEM(ret, 1,  newVectorObject(isect_b, 3, Py_NEW, NULL)); }
                else      { PyTuple_SET_ITEM(ret, 1,  Py_None); Py_INCREF(Py_None); }

                return ret;
        }
}

/* keep in sync with M_Geometry_intersect_line_sphere */
PyDoc_STRVAR(M_Geometry_intersect_line_sphere_2d_doc,
".. function:: intersect_line_sphere_2d(line_a, line_b, sphere_co, sphere_radius, clip=True)\n"
"\n"
"   Takes a lines (as 2 vectors), a sphere as a point and a radius and\n"
"   returns the intersection\n"
"\n"
"   :arg line_a: First point of the first line\n"
"   :type line_a: :class:`mathutils.Vector`\n"
"   :arg line_b: Second point of the first line\n"
"   :type line_b: :class:`mathutils.Vector`\n"
"   :arg sphere_co: The center of the sphere\n"
"   :type sphere_co: :class:`mathutils.Vector`\n"
"   :arg sphere_radius: Radius of the sphere\n"
"   :type sphere_radius: sphere_radius\n"
"   :return: The intersection points as a pair of vectors or None when there is no intersection\n"
"   :rtype: A tuple pair containing :class:`mathutils.Vector` or None\n"
);
static PyObject *M_Geometry_intersect_line_sphere_2d(PyObject *UNUSED(self), PyObject* args)
{
        VectorObject *line_a, *line_b, *sphere_co;
        float sphere_radius;
        int clip= TRUE;

        float isect_a[3];
        float isect_b[3];

        if(!PyArg_ParseTuple(args, "O!O!O!f|i:intersect_line_sphere_2d",
          &vector_Type, &line_a,
          &vector_Type, &line_b,
          &vector_Type, &sphere_co,
          &sphere_radius, &clip)
        ) {
                return NULL;
        }

        if(             BaseMath_ReadCallback(line_a) == -1 ||
                BaseMath_ReadCallback(line_b) == -1 ||
                BaseMath_ReadCallback(sphere_co) == -1
        ) {
                return NULL;
        }
        else {
                short use_a= TRUE;
                short use_b= TRUE;
                float lambda;

                PyObject *ret= PyTuple_New(2);

                switch(isect_line_sphere_v2(line_a->vec, line_b->vec, sphere_co->vec, sphere_radius, isect_a, isect_b)) {
                case 1:
                        if(!(!clip || (((lambda= line_point_factor_v2(isect_a, line_a->vec, line_b->vec)) >= 0.0f) && (lambda <= 1.0f)))) use_a= FALSE;
                        use_b= FALSE;
                        break;
                case 2:
                        if(!(!clip || (((lambda= line_point_factor_v2(isect_a, line_a->vec, line_b->vec)) >= 0.0f) && (lambda <= 1.0f)))) use_a= FALSE;
                        if(!(!clip || (((lambda= line_point_factor_v2(isect_b, line_a->vec, line_b->vec)) >= 0.0f) && (lambda <= 1.0f)))) use_b= FALSE;
                        break;
                default:
                        use_a= FALSE;
                        use_b= FALSE;
                }

                if(use_a) { PyTuple_SET_ITEM(ret, 0,  newVectorObject(isect_a, 2, Py_NEW, NULL)); }
                else      { PyTuple_SET_ITEM(ret, 0,  Py_None); Py_INCREF(Py_None); }

                if(use_b) { PyTuple_SET_ITEM(ret, 1,  newVectorObject(isect_b, 2, Py_NEW, NULL)); }
                else      { PyTuple_SET_ITEM(ret, 1,  Py_None); Py_INCREF(Py_None); }

                return ret;
        }
}

PyDoc_STRVAR(M_Geometry_intersect_point_line_doc,
".. function:: intersect_point_line(pt, line_p1, line_p2)\n"
"\n"
"   Takes a point and a line and returns a tuple with the closest point on the line and its distance from the first point of the line as a percentage of the length of the line.\n"
"\n"
"   :arg pt: Point\n"
"   :type pt: :class:`mathutils.Vector`\n"
"   :arg line_p1: First point of the line\n"
"   :type line_p1: :class:`mathutils.Vector`\n"
"   :arg line_p1: Second point of the line\n"
"   :type line_p1: :class:`mathutils.Vector`\n"
"   :rtype: (:class:`mathutils.Vector`, float)\n"
);
static PyObject *M_Geometry_intersect_point_line(PyObject *UNUSED(self), PyObject* args)
{
        VectorObject *pt, *line_1, *line_2;
        float pt_in[3], pt_out[3], l1[3], l2[3];
        float lambda;
        PyObject *ret;
        
        if(!PyArg_ParseTuple(args, "O!O!O!:intersect_point_line",
                &vector_Type, &pt,
                &vector_Type, &line_1,
                &vector_Type, &line_2)
        ) {
                return NULL;
        }
        
        if(BaseMath_ReadCallback(pt) == -1 || BaseMath_ReadCallback(line_1) == -1 || BaseMath_ReadCallback(line_2) == -1)
                return NULL;
        
        /* accept 2d verts */
        if (pt->size==3) { VECCOPY(pt_in, pt->vec);}
        else { pt_in[2]=0.0;    VECCOPY2D(pt_in, pt->vec) }
        
        if (line_1->size==3) { VECCOPY(l1, line_1->vec);}
        else { l1[2]=0.0;       VECCOPY2D(l1, line_1->vec) }
        
        if (line_2->size==3) { VECCOPY(l2, line_2->vec);}
        else { l2[2]=0.0;       VECCOPY2D(l2, line_2->vec) }
        
        /* do the calculation */
        lambda= closest_to_line_v3(pt_out, pt_in, l1, l2);
        
        ret= PyTuple_New(2);
        PyTuple_SET_ITEM(ret, 0, newVectorObject(pt_out, 3, Py_NEW, NULL));
        PyTuple_SET_ITEM(ret, 1, PyFloat_FromDouble(lambda));
        return ret;
}

PyDoc_STRVAR(M_Geometry_intersect_point_tri_2d_doc,
".. function:: intersect_point_tri_2d(pt, tri_p1, tri_p2, tri_p3)\n"
"\n"
"   Takes 4 vectors (using only the x and y coordinates): one is the point and the next 3 define the triangle. Returns 1 if the point is within the triangle, otherwise 0.\n"
"\n"
"   :arg pt: Point\n"
"   :type v1: :class:`mathutils.Vector`\n"
"   :arg tri_p1: First point of the triangle\n"
"   :type tri_p1: :class:`mathutils.Vector`\n"
"   :arg tri_p2: Second point of the triangle\n"
"   :type tri_p2: :class:`mathutils.Vector`\n"
"   :arg tri_p3: Third point of the triangle\n"
"   :type tri_p3: :class:`mathutils.Vector`\n"
"   :rtype: int\n"
);
static PyObject *M_Geometry_intersect_point_tri_2d(PyObject *UNUSED(self), PyObject* args)
{
        VectorObject *pt_vec, *tri_p1, *tri_p2, *tri_p3;
        
        if(!PyArg_ParseTuple(args, "O!O!O!O!:intersect_point_tri_2d",
                  &vector_Type, &pt_vec,
                  &vector_Type, &tri_p1,
                  &vector_Type, &tri_p2,
                  &vector_Type, &tri_p3)
        ) {
                return NULL;
        }
        
        if(BaseMath_ReadCallback(pt_vec) == -1 || BaseMath_ReadCallback(tri_p1) == -1 || BaseMath_ReadCallback(tri_p2) == -1 || BaseMath_ReadCallback(tri_p3) == -1)
                return NULL;
        
        return PyLong_FromLong(isect_point_tri_v2(pt_vec->vec, tri_p1->vec, tri_p2->vec, tri_p3->vec));
}

PyDoc_STRVAR(M_Geometry_intersect_point_quad_2d_doc,
".. function:: intersect_point_quad_2d(pt, quad_p1, quad_p2, quad_p3, quad_p4)\n"
"\n"
"   Takes 5 vectors (using only the x and y coordinates): one is the point and the next 4 define the quad, only the x and y are used from the vectors. Returns 1 if the point is within the quad, otherwise 0.\n"
"\n"
"   :arg pt: Point\n"
"   :type v1: :class:`mathutils.Vector`\n"
"   :arg quad_p1: First point of the quad\n"
"   :type quad_p1: :class:`mathutils.Vector`\n"
"   :arg quad_p2: Second point of the quad\n"
"   :type quad_p2: :class:`mathutils.Vector`\n"
"   :arg quad_p3: Third point of the quad\n"
"   :type quad_p3: :class:`mathutils.Vector`\n"
"   :arg quad_p4: Forth point of the quad\n"
"   :type quad_p4: :class:`mathutils.Vector`\n"
"   :rtype: int\n"
);
static PyObject *M_Geometry_intersect_point_quad_2d(PyObject *UNUSED(self), PyObject* args)
{
        VectorObject *pt_vec, *quad_p1, *quad_p2, *quad_p3, *quad_p4;
        
        if(!PyArg_ParseTuple(args, "O!O!O!O!O!:intersect_point_quad_2d",
                  &vector_Type, &pt_vec,
                  &vector_Type, &quad_p1,
                  &vector_Type, &quad_p2,
                  &vector_Type, &quad_p3,
                  &vector_Type, &quad_p4)
        ) {
                return NULL;
        }
        
        if(BaseMath_ReadCallback(pt_vec) == -1 || BaseMath_ReadCallback(quad_p1) == -1 || BaseMath_ReadCallback(quad_p2) == -1 || BaseMath_ReadCallback(quad_p3) == -1 || BaseMath_ReadCallback(quad_p4) == -1)
                return NULL;
        
        return PyLong_FromLong(isect_point_quad_v2(pt_vec->vec, quad_p1->vec, quad_p2->vec, quad_p3->vec, quad_p4->vec));
}

PyDoc_STRVAR(M_Geometry_barycentric_transform_doc,
".. function:: barycentric_transform(point, tri_a1, tri_a2, tri_a3, tri_b1, tri_b2, tri_b3)\n"
"\n"
"   Return a transformed point, the transformation is defined by 2 triangles.\n"
"\n"
"   :arg point: The point to transform.\n"
"   :type point: :class:`mathutils.Vector`\n"
"   :arg tri_a1: source triangle vertex.\n"
"   :type tri_a1: :class:`mathutils.Vector`\n"
"   :arg tri_a2: source triangle vertex.\n"
"   :type tri_a2: :class:`mathutils.Vector`\n"
"   :arg tri_a3: source triangle vertex.\n"
"   :type tri_a3: :class:`mathutils.Vector`\n"
"   :arg tri_a1: target triangle vertex.\n"
"   :type tri_a1: :class:`mathutils.Vector`\n"
"   :arg tri_a2: target triangle vertex.\n"
"   :type tri_a2: :class:`mathutils.Vector`\n"
"   :arg tri_a3: target triangle vertex.\n"
"   :type tri_a3: :class:`mathutils.Vector`\n"
"   :return: The transformed point\n"
"   :rtype: :class:`mathutils.Vector`'s\n"
);
static PyObject *M_Geometry_barycentric_transform(PyObject *UNUSED(self), PyObject *args)
{
        VectorObject *vec_pt;
        VectorObject *vec_t1_tar, *vec_t2_tar, *vec_t3_tar;
        VectorObject *vec_t1_src, *vec_t2_src, *vec_t3_src;
        float vec[3];

        if(!PyArg_ParseTuple(args, "O!O!O!O!O!O!O!:barycentric_transform",
                  &vector_Type, &vec_pt,
                  &vector_Type, &vec_t1_src,
                  &vector_Type, &vec_t2_src,
                  &vector_Type, &vec_t3_src,
                  &vector_Type, &vec_t1_tar,
                  &vector_Type, &vec_t2_tar,
                  &vector_Type, &vec_t3_tar)
        ) {
                return NULL;
        }

        if(     vec_pt->size != 3 ||
                vec_t1_src->size != 3 ||
                vec_t2_src->size != 3 ||
                vec_t3_src->size != 3 ||
                vec_t1_tar->size != 3 ||
                vec_t2_tar->size != 3 ||
                vec_t3_tar->size != 3)
        {
                PyErr_SetString(PyExc_ValueError,
                                "One of more of the vector arguments wasn't a 3D vector");
                return NULL;
        }

        barycentric_transform(vec, vec_pt->vec,
                        vec_t1_tar->vec, vec_t2_tar->vec, vec_t3_tar->vec,
                        vec_t1_src->vec, vec_t2_src->vec, vec_t3_src->vec);

        return newVectorObject(vec, 3, Py_NEW, NULL);
}

#ifndef MATH_STANDALONE

PyDoc_STRVAR(M_Geometry_interpolate_bezier_doc,
".. function:: interpolate_bezier(knot1, handle1, handle2, knot2, resolution)\n"
"\n"
"   Interpolate a bezier spline segment.\n"
"\n"
"   :arg knot1: First bezier spline point.\n"
"   :type knot1: :class:`mathutils.Vector`\n"
"   :arg handle1: First bezier spline handle.\n"
"   :type handle1: :class:`mathutils.Vector`\n"
"   :arg handle2: Second bezier spline handle.\n"
"   :type handle2: :class:`mathutils.Vector`\n"
"   :arg knot2: Second bezier spline point.\n"
"   :type knot2: :class:`mathutils.Vector`\n"
"   :arg resolution: Number of points to return.\n"
"   :type resolution: int\n"
"   :return: The interpolated points\n"
"   :rtype: list of :class:`mathutils.Vector`'s\n"
);
static PyObject *M_Geometry_interpolate_bezier(PyObject *UNUSED(self), PyObject* args)
{
        VectorObject *vec_k1, *vec_h1, *vec_k2, *vec_h2;
        int resolu;
        int dims;
        int i;
        float *coord_array, *fp;
        PyObject *list;

        float k1[4]= {0.0, 0.0, 0.0, 0.0};
        float h1[4]= {0.0, 0.0, 0.0, 0.0};
        float k2[4]= {0.0, 0.0, 0.0, 0.0};
        float h2[4]= {0.0, 0.0, 0.0, 0.0};


        if(!PyArg_ParseTuple(args, "O!O!O!O!i:interpolate_bezier",
          &vector_Type, &vec_k1,
          &vector_Type, &vec_h1,
          &vector_Type, &vec_h2,
          &vector_Type, &vec_k2, &resolu)
        ) {
                return NULL;
        }

        if(resolu <= 1) {
                PyErr_SetString(PyExc_ValueError,
                                "resolution must be 2 or over");
                return NULL;
        }

        if(BaseMath_ReadCallback(vec_k1) == -1 || BaseMath_ReadCallback(vec_h1) == -1 || BaseMath_ReadCallback(vec_k2) == -1 || BaseMath_ReadCallback(vec_h2) == -1)
                return NULL;

        dims= MAX4(vec_k1->size, vec_h1->size, vec_h2->size, vec_k2->size);

        for(i=0; i < vec_k1->size; i++) k1[i]= vec_k1->vec[i];
        for(i=0; i < vec_h1->size; i++) h1[i]= vec_h1->vec[i];
        for(i=0; i < vec_k2->size; i++) k2[i]= vec_k2->vec[i];
        for(i=0; i < vec_h2->size; i++) h2[i]= vec_h2->vec[i];

        coord_array= MEM_callocN(dims * (resolu) * sizeof(float), "interpolate_bezier");
        for(i=0; i<dims; i++) {
                forward_diff_bezier(k1[i], h1[i], h2[i], k2[i], coord_array+i, resolu-1, sizeof(float)*dims);
        }

        list= PyList_New(resolu);
        fp= coord_array;
        for(i=0; i<resolu; i++, fp= fp+dims) {
                PyList_SET_ITEM(list, i, newVectorObject(fp, dims, Py_NEW, NULL));
        }
        MEM_freeN(coord_array);
        return list;
}


PyDoc_STRVAR(M_Geometry_tesselate_polygon_doc,
".. function:: tesselate_polygon(veclist_list)\n"
"\n"
"   Takes a list of polylines (each point a vector) and returns the point indices for a polyline filled with triangles.\n"
"\n"
"   :arg veclist_list: list of polylines\n"
"   :rtype: list\n"
);
/* PolyFill function, uses Blenders scanfill to fill multiple poly lines */
static PyObject *M_Geometry_tesselate_polygon(PyObject *UNUSED(self), PyObject *polyLineSeq)
{
        PyObject *tri_list; /*return this list of tri's */
        PyObject *polyLine, *polyVec;
        int i, len_polylines, len_polypoints, ls_error= 0;

        /* display listbase */
        ListBase dispbase={NULL, NULL};
        DispList *dl;
        float *fp; /*pointer to the array of malloced dl->verts to set the points from the vectors */
        int index, *dl_face, totpoints=0;

        if(!PySequence_Check(polyLineSeq)) {
                PyErr_SetString(PyExc_TypeError,
                                "expected a sequence of poly lines");
                return NULL;
        }

        len_polylines= PySequence_Size(polyLineSeq);

        for(i= 0; i < len_polylines; ++i) {
                polyLine= PySequence_GetItem(polyLineSeq, i);
                if (!PySequence_Check(polyLine)) {
                        freedisplist(&dispbase);
                        Py_XDECREF(polyLine); /* may be null so use Py_XDECREF*/
                        PyErr_SetString(PyExc_TypeError,
                                        "One or more of the polylines is not a sequence of mathutils.Vector's");
                        return NULL;
                }

                len_polypoints= PySequence_Size(polyLine);
                if (len_polypoints>0) { /* dont bother adding edges as polylines */
#if 0
                        if (EXPP_check_sequence_consistency(polyLine, &vector_Type) != 1) {
                                freedisplist(&dispbase);
                                Py_DECREF(polyLine);
                                PyErr_SetString(PyExc_TypeError,
                                                "A point in one of the polylines is not a mathutils.Vector type");
                                return NULL;
                        }
#endif
                        dl= MEM_callocN(sizeof(DispList), "poly disp");
                        BLI_addtail(&dispbase, dl);
                        dl->type= DL_INDEX3;
                        dl->nr= len_polypoints;
                        dl->type= DL_POLY;
                        dl->parts= 1; /* no faces, 1 edge loop */
                        dl->col= 0; /* no material */
                        dl->verts= fp= MEM_callocN(sizeof(float)*3*len_polypoints, "dl verts");
                        dl->index= MEM_callocN(sizeof(int)*3*len_polypoints, "dl index");

                        for(index= 0; index<len_polypoints; ++index, fp+=3) {
                                polyVec= PySequence_GetItem(polyLine, index);
                                if(VectorObject_Check(polyVec)) {

                                        if(BaseMath_ReadCallback((VectorObject *)polyVec) == -1)
                                                ls_error= 1;

                                        fp[0]= ((VectorObject *)polyVec)->vec[0];
                                        fp[1]= ((VectorObject *)polyVec)->vec[1];
                                        if(((VectorObject *)polyVec)->size > 2)
                                                fp[2]= ((VectorObject *)polyVec)->vec[2];
                                        else
                                                fp[2]= 0.0f; /* if its a 2d vector then set the z to be zero */
                                }
                                else {
                                        ls_error= 1;
                                }

                                totpoints++;
                                Py_DECREF(polyVec);
                        }
                }
                Py_DECREF(polyLine);
        }

        if(ls_error) {
                freedisplist(&dispbase); /* possible some dl was allocated */
                PyErr_SetString(PyExc_TypeError,
                                "A point in one of the polylines "
                                "is not a mathutils.Vector type");
                return NULL;
        }
        else if (totpoints) {
                /* now make the list to return */
                filldisplist(&dispbase, &dispbase, 0);

                /* The faces are stored in a new DisplayList
                thats added to the head of the listbase */
                dl= dispbase.first;

                tri_list= PyList_New(dl->parts);
                if(!tri_list) {
                        freedisplist(&dispbase);
                        PyErr_SetString(PyExc_RuntimeError,
                                        "failed to make a new list");
                        return NULL;
                }

                index= 0;
                dl_face= dl->index;
                while(index < dl->parts) {
                        PyList_SET_ITEM(tri_list, index, Py_BuildValue("iii", dl_face[0], dl_face[1], dl_face[2]));
                        dl_face+= 3;
                        index++;
                }
                freedisplist(&dispbase);
        }
        else {
                /* no points, do this so scripts dont barf */
                freedisplist(&dispbase); /* possible some dl was allocated */
                tri_list= PyList_New(0);
        }

        return tri_list;
}


static int boxPack_FromPyObject(PyObject *value, boxPack **boxarray)
{
        int len, i;
        PyObject *list_item, *item_1, *item_2;
        boxPack *box;


        /* Error checking must already be done */
        if(!PyList_Check(value)) {
                PyErr_SetString(PyExc_TypeError,
                                "can only back a list of [x, y, w, h]");
                return -1;
        }

        len= PyList_Size(value);

        (*boxarray)= MEM_mallocN(len*sizeof(boxPack), "boxPack box");


        for(i= 0; i < len; i++) {
                list_item= PyList_GET_ITEM(value, i);
                if(!PyList_Check(list_item) || PyList_Size(list_item) < 4) {
                        MEM_freeN(*boxarray);
                        PyErr_SetString(PyExc_TypeError,
                                        "can only pack a list of [x, y, w, h]");
                        return -1;
                }

                box= (*boxarray)+i;

                item_1= PyList_GET_ITEM(list_item, 2);
                item_2= PyList_GET_ITEM(list_item, 3);

                box->w=  (float)PyFloat_AsDouble(item_1);
                box->h=  (float)PyFloat_AsDouble(item_2);
                box->index= i;

                /* accounts for error case too and overwrites with own error */
                if (box->w < 0.0f || box->h < 0.0f) {
                        MEM_freeN(*boxarray);
                        PyErr_SetString(PyExc_TypeError,
                                        "error parsing width and height values from list: "
                                        "[x, y, w, h], not numbers or below zero");
                        return -1;
                }

                /* verts will be added later */
        }
        return 0;
}

static void boxPack_ToPyObject(PyObject *value, boxPack **boxarray)
{
        int len, i;
        PyObject *list_item;
        boxPack *box;

        len= PyList_Size(value);

        for(i= 0; i < len; i++) {
                box= (*boxarray)+i;
                list_item= PyList_GET_ITEM(value, box->index);
                PyList_SET_ITEM(list_item, 0, PyFloat_FromDouble(box->x));
                PyList_SET_ITEM(list_item, 1, PyFloat_FromDouble(box->y));
        }
        MEM_freeN(*boxarray);
}

PyDoc_STRVAR(M_Geometry_box_pack_2d_doc,
".. function:: box_pack_2d(boxes)\n"
"\n"
"   Returns the normal of the 3D tri or quad.\n"
"\n"
"   :arg boxes: list of boxes, each box is a list where the first 4 items are [x, y, width, height, ...] other items are ignored.\n"
"   :type boxes: list\n"
"   :return: the width and height of the packed bounding box\n"
"   :rtype: tuple, pair of floats\n"
);
static PyObject *M_Geometry_box_pack_2d(PyObject *UNUSED(self), PyObject *boxlist)
{
        float tot_width= 0.0f, tot_height= 0.0f;
        int len;

        PyObject *ret;

        if(!PyList_Check(boxlist)) {
                PyErr_SetString(PyExc_TypeError,
                                "expected a list of boxes [[x, y, w, h], ... ]");
                return NULL;
        }

        len= PyList_GET_SIZE(boxlist);
        if (len) {
                boxPack *boxarray= NULL;
                if(boxPack_FromPyObject(boxlist, &boxarray) == -1) {
                        return NULL; /* exception set */
                }

                /* Non Python function */
                boxPack2D(boxarray, len, &tot_width, &tot_height);

                boxPack_ToPyObject(boxlist, &boxarray);
        }

        ret= PyTuple_New(2);
        PyTuple_SET_ITEM(ret, 0, PyFloat_FromDouble(tot_width));
        PyTuple_SET_ITEM(ret, 1, PyFloat_FromDouble(tot_width));
        return ret;
}

#endif /* MATH_STANDALONE */


static PyMethodDef M_Geometry_methods[]= {
        {"intersect_ray_tri", (PyCFunction) M_Geometry_intersect_ray_tri, METH_VARARGS, M_Geometry_intersect_ray_tri_doc},
        {"intersect_point_line", (PyCFunction) M_Geometry_intersect_point_line, METH_VARARGS, M_Geometry_intersect_point_line_doc},
        {"intersect_point_tri_2d", (PyCFunction) M_Geometry_intersect_point_tri_2d, METH_VARARGS, M_Geometry_intersect_point_tri_2d_doc},
        {"intersect_point_quad_2d", (PyCFunction) M_Geometry_intersect_point_quad_2d, METH_VARARGS, M_Geometry_intersect_point_quad_2d_doc},
        {"intersect_line_line", (PyCFunction) M_Geometry_intersect_line_line, METH_VARARGS, M_Geometry_intersect_line_line_doc},
        {"intersect_line_line_2d", (PyCFunction) M_Geometry_intersect_line_line_2d, METH_VARARGS, M_Geometry_intersect_line_line_2d_doc},
        {"intersect_line_plane", (PyCFunction) M_Geometry_intersect_line_plane, METH_VARARGS, M_Geometry_intersect_line_plane_doc},
        {"intersect_line_sphere", (PyCFunction) M_Geometry_intersect_line_sphere, METH_VARARGS, M_Geometry_intersect_line_sphere_doc},
        {"intersect_line_sphere_2d", (PyCFunction) M_Geometry_intersect_line_sphere_2d, METH_VARARGS, M_Geometry_intersect_line_sphere_2d_doc},
        {"area_tri", (PyCFunction) M_Geometry_area_tri, METH_VARARGS, M_Geometry_area_tri_doc},
        {"normal", (PyCFunction) M_Geometry_normal, METH_VARARGS, M_Geometry_normal_doc},
        {"barycentric_transform", (PyCFunction) M_Geometry_barycentric_transform, METH_VARARGS, M_Geometry_barycentric_transform_doc},
#ifndef MATH_STANDALONE
        {"interpolate_bezier", (PyCFunction) M_Geometry_interpolate_bezier, METH_VARARGS, M_Geometry_interpolate_bezier_doc},
        {"tesselate_polygon", (PyCFunction) M_Geometry_tesselate_polygon, METH_O, M_Geometry_tesselate_polygon_doc},
        {"box_pack_2d", (PyCFunction) M_Geometry_box_pack_2d, METH_O, M_Geometry_box_pack_2d_doc},
#endif
        {NULL, NULL, 0, NULL}
};

static struct PyModuleDef M_Geometry_module_def= {
        PyModuleDef_HEAD_INIT,
        "mathutils.geometry",  /* m_name */
        M_Geometry_doc,  /* m_doc */
        0,  /* m_size */
        M_Geometry_methods,  /* m_methods */
        NULL,  /* m_reload */
        NULL,  /* m_traverse */
        NULL,  /* m_clear */
        NULL,  /* m_free */
};

/*----------------------------MODULE INIT-------------------------*/
PyMODINIT_FUNC PyInit_mathutils_geometry(void)
{
        PyObject *submodule= PyModule_Create(&M_Geometry_module_def);
        return submodule;
}