def pcurve(self, face):
     """
     computes the 2d parametric spline that lies on the surface of the face
     :return: Geom2d_Curve, u, v
     """
     crv, u, v = BRep_Tool().CurveOnSurface(self, face)
     return crv.GetObject(), u, v
class Edge(TopoDS_Edge, BaseObject):
    def __init__(self, edge):
        assert isinstance(
            edge, TopoDS_Edge), 'need a TopoDS_Edge, got a %s' % edge.__class__
        assert not edge.IsNull()
        super(Edge, self).__init__()
        BaseObject.__init__(self, 'edge')
        # we need to copy the base shape using the following three
        # lines
        assert self.IsNull()
        self.TShape(edge.TShape())
        self.Location(edge.Location())
        self.Orientation(edge.Orientation())
        assert not self.IsNull()

        # tracking state
        self._local_properties_init = False
        self._curvature_init = False
        self._geometry_lookup_init = False
        self._curve_handle = None
        self._curve = None
        self._adaptor = None
        self._adaptor_handle = None

        # instantiating cooperative classes
        # cooperative classes are distinct through CamelCaps from
        # normal method -> pep8
        self.DiffGeom = DiffGeomCurve(self)
        self.Intersect = IntersectCurve(self)
        self.Construct = ConstructFromCurve(self)

        # GeomLProp object
        self._curvature = None

    def is_closed(self):
        return self.adaptor.IsClosed()

    def is_periodic(self):
        return self.adaptor.IsPeriodic()

    def is_rational(self):
        return self.adaptor.IsRational()

    def continuity(self):
        return self.adaptor.Continuity

    def degree(self):
        if 'line' in self.type:
            return 1
        elif 'curve' in self.type:
            return self.adaptor.Degree()
        else:
            # hyperbola, parabola, circle
            return 2

    def nb_knots(self):
        return self.adaptor.NbKnots()

    def nb_poles(self):
        return self.adaptor.NbPoles()

    @property
    def curve(self):
        if self._curve is not None and not self.is_dirty:
            pass
        else:
            self._curve_handle = BRep_Tool().Curve(self)[0]
            self._curve = self._curve_handle.GetObject()
        return self._curve

    @property
    def curve_handle(self):
        if self._curve_handle is not None and not self.is_dirty:
            return self._curve_handle
        else:
            return None

    @property
    def adaptor(self):
        if self._adaptor is not None and not self.is_dirty:
            pass
        else:
            self._adaptor = BRepAdaptor_Curve(self)
            self._adaptor_handle = BRepAdaptor_HCurve(self._adaptor)
        return self._adaptor

    @property
    def adaptor_handle(self):
        if self._adaptor_handle is not None and not self.is_dirty:
            pass
        else:
            self.adaptor
        return self._adaptor_handle

    @property
    def geom_curve_handle(self):
        """
        :return: Handle_Geom_Curve adapted from `self`
        """
        if self._adaptor_handle is not None and not self.is_dirty:
            return self._adaptor.Curve().Curve()
        else:
            return None

    @property
    def type(self):
        return geom_lut[self.adaptor.Curve().GetType()]

    def pcurve(self, face):
        """
        computes the 2d parametric spline that lies on the surface of the face
        :return: Geom2d_Curve, u, v
        """
        crv, u, v = BRep_Tool().CurveOnSurface(self, face)
        return crv.GetObject(), u, v

    def _local_properties(self):
        self._lprops_curve_tool = GeomLProp_CurveTool()
        self._local_properties_init = True

    def domain(self):
        '''returns the u,v domain of the curve'''
        return self.adaptor.FirstParameter(), self.adaptor.LastParameter()

#===========================================================================
#    Curve.GlobalProperties
#===========================================================================

    def length(self, lbound=None, ubound=None, tolerance=1e-5):
        '''returns the curve length
        if either lbound | ubound | both are given, than the length
        of the curve will be measured over that interval
        '''
        _min, _max = self.domain()
        if _min < self.adaptor.FirstParameter():
            raise ValueError(
                'the lbound argument is lower than the first parameter of the curve: %s '
                % (self.adaptor.FirstParameter()))
        if _max > self.adaptor.LastParameter():
            raise ValueError(
                'the ubound argument is greater than the last parameter of the curve: %s '
                % (self.adaptor.LastParameter()))

        lbound = _min if lbound is None else lbound
        ubound = _max if ubound is None else ubound
        return GCPnts_AbscissaPoint().Length(self.adaptor, lbound, ubound,
                                             tolerance)

#===========================================================================
#    Curve.modify
#===========================================================================

    def trim(self, lbound, ubound):
        '''
        trim the curve
        @param lbound:
        @param ubound:
        '''
        a, b = sorted([lbound, ubound])
        tr = Geom_TrimmedCurve(self.adaptor.Curve().Curve(), a, b).GetHandle()
        return Edge(make_edge(tr))

    def extend_by_point(self, pnt, degree=3, beginning=True):
        '''extends the curve to point

        does not extend if the degree of self.curve > 3
        @param pnt:
        @param degree:
        @param beginning:
        '''
        if self.degree > 3:
            raise ValueError('to extend you self.curve should be <= 3, is %s' %
                             (self.degree))
        return geomlib.ExtendCurveToPoint(self.curve, pnt, degree, beginning)

#===========================================================================
#    Curve.
#===========================================================================

    def closest(self, other):
        return minimum_distance(self, other)

    def project_vertex(self, pnt_or_vertex):
        ''' returns the closest orthogonal project on `pnt` on edge
        '''
        if isinstance(pnt_or_vertex, TopoDS_Vertex):
            pnt_or_vertex = vertex2pnt(pnt_or_vertex)

        poc = GeomAPI_ProjectPointOnCurve(pnt_or_vertex, self.curve_handle)
        return poc.LowerDistanceParameter(), poc.NearestPoint()

    def distance_on_curve(self, distance, close_parameter, estimate_parameter):
        '''returns the parameter if there is a parameter
        on the curve with a distance length from u
        raises OutOfBoundary if no such parameter exists
        '''
        gcpa = GCPnts_AbscissaPoint(self.adaptor, distance, close_parameter,
                                    estimate_parameter, 1e-5)
        with assert_isdone(gcpa, 'couldnt compute distance on curve'):
            return gcpa.Parameter()

    def mid_point(self):
        """
        :return: the parameter at the mid point of the curve, and
        its corresponding gp_Pnt
        """
        _min, _max = self.domain()
        _mid = (_min + _max) / 2.
        return _mid, self.adaptor.Value(_mid)

    def divide_by_number_of_points(self, n_pts, lbound=None, ubound=None):
        '''returns a nested list of parameters and points on the edge
        at the requested interval [(param, gp_Pnt),...]
        '''
        _lbound, _ubound = self.domain()
        if lbound:
            _lbound = lbound
        elif ubound:
            _ubound = ubound

        # minimally two points or a Standard_ConstructionError is raised
        if n_pts <= 1:
            n_pts = 2

        try:
            npts = GCPnts_UniformAbscissa(self.adaptor, n_pts, _lbound,
                                          _ubound)
        except:
            print("Warning : GCPnts_UniformAbscissa failed")
        if npts.IsDone():
            tmp = []
            for i in xrange(1, npts.NbPoints() + 1):
                param = npts.Parameter(i)
                pnt = self.adaptor.Value(param)
                tmp.append((param, pnt))
            return tmp
        else:
            return None

    def __eq__(self, other):
        if hasattr(other, 'topo'):
            return self.IsEqual(other)
        else:
            return self.IsEqual(other)

    def __ne__(self, other):
        return not self.__eq__(other)

    def first_vertex(self):
        return topexp.FirstVertex(self)

    def last_vertex(self):
        return topexp.LastVertex(self)

    def common_vertex(self, edge):
        vert = TopoDS_Vertex()
        if topexp.CommonVertex(self, edge, vert):
            return vert
        else:
            return False

    def as_vec(self):
        if self.is_line():
            first, last = map(
                vertex2pnt,
                [self.first_vertex(), self.last_vertex()])
            return gp_Vec(first, last)
        else:
            raise ValueError(
                "edge is not a line, hence no meaningful vector can be returned"
            )

#===========================================================================
#    Curve.
#===========================================================================

    def parameter_to_point(self, u):
        '''returns the coordinate at parameter u
        '''
        return self.adaptor.Value(u)

    def fix_continuity(self, continuity):
        """
        splits an edge to achieve a level of continuity
        :param continuity: GeomAbs_C*
        """
        return fix_continuity(self, continuity)

    def continuity_from_faces(self, f1, f2):
        return BRep_Tool_Continuity(self, f1, f2)

#===========================================================================
#    Curve.
#===========================================================================

    def is_line(self):
        '''checks if the curve is planar
        '''
        if self.nb_knots() == 2 and self.nb_poles() == 2:
            return True
        else:
            return False

    def is_seam(self, face):
        """
        :return: True if the edge has two pcurves on one surface
        ( in the case of a sphere for example... )
        """
        sae = ShapeAnalysis_Edge()
        return sae.IsSeam(self, face)

    def is_edge_on_face(self, face):
        '''checks whether curve lies on a surface or a face
        '''
        return ShapeAnalysis_Edge().HasPCurve(self, face)


#===========================================================================
#    Curve.graphic
#===========================================================================

    def show(self):
        '''
        poles, knots, should render all slightly different.
        here's how...

        http://www.opencascade.org/org/forum/thread_1125/
        '''
        super(Edge, self).show()