math func to find the intersection(s) between a segment and a sphere for C/python.

from python:
  i1, i2 = mathutils.geometry.intersect_line_sphere(l1, l2, sphere, radius)

source/blender/blenlib/BLI_math_geom.h

@@ -79,6 +79,7 @@ void closest_to_line_segment_v3(float r[3], const float p[3], const float l1[3],
 int isect_line_line_v2(const float a1[2], const float a2[2], const float b1[2], const float b2[2]);
 int isect_line_line_v2_int(const int a1[2], const int a2[2], const int b1[2], const int b2[2]);
 int isect_seg_seg_v2_point(const float v1[2], const float v2[2], const float v3[2], const float v4[2], float vi[2]);
+int isect_seg_sphere_v3(const float l1[3], const float l2[3], const float sp[3], const float r, float r_p1[3], float r_p2[3]);
 
 /* Returns the number of point of interests
  * 0 - lines are colinear

source/blender/blenlib/intern/math_geom.c

@@ -349,6 +349,79 @@ int isect_seg_seg_v2_point(const float v1[2], const float v2[2], const float v3[
 	return -1;
 }
 
+int isect_seg_sphere_v3(const float l1[3], const float l2[3],
+                        const float sp[3], const float r,
+                        float r_p1[3], float r_p2[3])
+{
+	/* l1:         coordinates (point of line)
+	 * l2:         coordinates (point of line)
+	 * sp, r:      coordinates and radius (sphere)
+	 * r_p1, r_p2: return intersection coordinates
+	 */
+
+
+	/* adapted for use in blender by Campbell Barton - 2011
+	 *
+	 * atelier iebele abel - 2001
+	 * atelier@iebele.nl
+	 * http://www.iebele.nl
+	 *
+	 * sphere_line_intersection function adapted from:
+	 * http://astronomy.swin.edu.au/pbourke/geometry/sphereline
+	 * Paul Bourke pbourke@swin.edu.au
+	 */
+
+	const float ldir[3]= {
+	    l2[0] - l1[0],
+	    l2[1] - l1[1],
+	    l2[2] - l1[2]
+	};
+
+	const float a= dot_v3v3(ldir, ldir);
+
+	const float b= 2.0f *
+	        (ldir[0] * (l1[0] - sp[0]) +
+	         ldir[1] * (l1[1] - sp[1]) +
+	         ldir[2] * (l1[2] - sp[2]));
+
+	const float c=
+	        dot_v3v3(sp, sp) +
+	        dot_v3v3(l1, l1) -
+	        (2.0f * dot_v3v3(sp, l1)) -
+	        (r * r);
+
+	const float i = b * b - 4.0f * a * c;
+
+	float mu;
+
+	if (i < 0.0f) {
+		/* no intersections */
+		return 0;
+	}
+	else if (i == 0.0f) {
+		/* one intersection */
+		mu = -b / (2.0f * a);
+		madd_v3_v3v3fl(r_p1, l1, ldir, mu);
+		return 1;
+	}
+	else if (i > 0.0) {
+		const float i_sqrt= sqrt(i); /* avoid calc twice */
+
+		/* first intersection */
+		mu = (-b + i_sqrt) / (2.0f * a);
+		madd_v3_v3v3fl(r_p1, l1, ldir, mu);
+
+		/* second intersection */
+		mu = (-b - i_sqrt) / (2.0f * a);
+		madd_v3_v3v3fl(r_p2, l1, ldir, mu);
+		return 2;
+	}
+	else {
+		/* math domain error - nan */
+		return -1;
+	}
+}
+
 /*
 -1: colliniar
  1: intersection

source/blender/python/generic/mathutils_geometry.c

@@ -553,6 +553,73 @@ static PyObject *M_Geometry_intersect_line_plane(PyObject *UNUSED(self), PyObjec
 	}
 }
 
+
+PyDoc_STRVAR(M_Geometry_intersect_line_sphere_doc,
+".. function:: intersect_line_sphere(line_a, line_b, sphere_co, sphere_radius)\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)
+{
+	PyObject *ret;
+	VectorObject *line_a, *line_b, *sphere_co;
+	float sphere_radius;
+
+	float isect_a[3];
+	float isect_b[3];
+
+	if(!PyArg_ParseTuple(args, "O!O!O!f:intersect_line_sphere",
+	  &vector_Type, &line_a,
+	  &vector_Type, &line_b,
+	  &vector_Type, &sphere_co,
+	  &sphere_radius)
+	) {
+		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_RuntimeError, "geometry.intersect_line_sphere(...) can't use 2D Vectors");
+		return NULL;
+	}
+
+	ret= PyTuple_New(2);
+
+	switch(isect_seg_sphere_v3(line_a->vec, line_b->vec, sphere_co->vec, sphere_radius, isect_a, isect_b)) {
+	case 1:
+		PyTuple_SET_ITEM(ret, 0,  newVectorObject(isect_a, 3, Py_NEW, NULL));
+		PyTuple_SET_ITEM(ret, 1,  Py_None); Py_INCREF(Py_None);
+		break;
+	case 2:
+		PyTuple_SET_ITEM(ret, 0,  newVectorObject(isect_a, 3, Py_NEW, NULL));
+		PyTuple_SET_ITEM(ret, 1,  newVectorObject(isect_b, 3, Py_NEW, NULL));
+		break;
+	default:
+		PyTuple_SET_ITEM(ret, 0,  Py_None); Py_INCREF(Py_None);
+		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"
@@ -917,6 +984,7 @@ static PyMethodDef M_Geometry_methods[]= {
 	{"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},
 	{"interpolate_bezier", (PyCFunction) M_Geometry_interpolate_bezier, METH_VARARGS, M_Geometry_interpolate_bezier_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},