# coding=utf-8
"""3D Polyline"""
from __future__ import division
from ..geometry2d.pointvector import Point2D
from ..geometry2d.polyline import Polyline2D
from ._2d import Base2DIn3D
from .pointvector import Point3D
from .line import LineSegment3D
from .plane import Plane
from ..intersection3d import intersect_line3d_plane
from .._polyline import _group_vertices
[docs]
class Polyline3D(Base2DIn3D):
"""3D polyline object.
Args:
vertices: A list of Point3D objects representing the vertices of the polyline.
interpolated: Boolean to note whether the polyline should be interpolated
between the input vertices when it is translated to other interfaces.
Note that this property has no bearing on the geometric calculations
performed by this library and is only present in order to assist with
display/translation.
Properties:
* vertices
* segments
* min
* max
* center
* p1
* p2
* length
* interpolated
"""
__slots__ = ('_interpolated', '_segments', '_length')
def __init__(self, vertices, interpolated=False):
"""Initialize Polyline3D."""
Base2DIn3D.__init__(self, vertices)
self._interpolated = interpolated
self._segments = None
self._length = None
[docs]
@classmethod
def from_dict(cls, data):
"""Create a Polyline3D from a dictionary.
Args:
data: A python dictionary in the following format.
.. code-block:: python
{
"type": "Polyline3D",
"vertices": [(0, 0, 0), (10, 0, 2), (0, 10, 4)]
}
"""
interp = data['interpolated'] if 'interpolated' in data else False
return cls(tuple(Point3D.from_array(pt) for pt in data['vertices']), interp)
[docs]
@classmethod
def from_array(cls, point_array):
"""Create a Polyline3D from a nested array of vertex coordinates.
Args:
point_array: nested array of point arrays.
"""
return Polyline3D(Point3D(*point) for point in point_array)
[docs]
@classmethod
def from_polyline2d(cls, polyline2d, plane=None):
"""Create a closed Polyline3D from a Polyline2D and a plane.
Args:
polyline2d: A Polyline2D object to be converted to a Polyline3D.
plane: A Plane in which the Polyline2D sits. If None, the WorldXY
plane will be used.
"""
plane = Plane() if plane is None else plane
return Polyline3D((plane.xy_to_xyz(pt) for pt in polyline2d.vertices),
polyline2d.interpolated)
@property
def segments(self):
"""Tuple of all line segments in the polyline."""
if self._segments is None:
self._segments = \
tuple(LineSegment3D.from_end_points(vert, self._vertices[i + 1])
for i, vert in enumerate(self._vertices[:-1]))
return self._segments
@property
def p1(self):
"""Starting point of the Polyline3D."""
return self._vertices[0]
@property
def p2(self):
"""End point of the Polyline3D."""
return self._vertices[-1]
@property
def length(self):
"""The length of the polyline."""
if self._length is None:
self._length = sum([seg.length for seg in self.segments])
return self._length
@property
def interpolated(self):
"""Boolean noting whether the polyline should be interpolated upon translation.
Note that this property has no bearing on the geometric calculations
performed by this library and is only present in order to assist with
display/translation.
"""
return self._interpolated
[docs]
def is_closed(self, tolerance):
"""Test whether this polyline is closed to within the tolerance.
Args:
tolerance: The minimum difference between vertices below which vertices
are considered the same.
"""
return self._vertices[0].is_equivalent(self._vertices[-1], tolerance)
[docs]
def remove_colinear_vertices(self, tolerance):
"""Get a version of this polyline without colinear or duplicate vertices.
Args:
tolerance: The minimum distance that a vertex can be from a line
before it is considered colinear.
"""
if len(self.vertices) == 3:
return self # Polyline3D cannot have fewer than 3 vertices
new_vertices = [self.vertices[0]] # first vertex is always ok
for i, _v in enumerate(self.vertices[1:-1]):
if (self[i] - _v).cross(self[i + 2] - _v).magnitude >= tolerance:
new_vertices.append(_v)
new_vertices.append(self[-1]) # last vertex is always ok
_new_poly = Polyline3D(new_vertices)
self._transfer_properties(_new_poly)
return _new_poly
[docs]
def reverse(self):
"""Get a copy of this polyline where the vertices are reversed."""
_new_poly = Polyline3D(tuple(pt for pt in reversed(self.vertices)))
self._transfer_properties(_new_poly)
return _new_poly
[docs]
def move(self, moving_vec):
"""Get a polyline that has been moved along a vector.
Args:
moving_vec: A Vector3D with the direction and distance to move the polyline.
"""
_new_poly = Polyline3D(tuple(pt.move(moving_vec) for pt in self.vertices))
self._transfer_properties(_new_poly)
return _new_poly
[docs]
def rotate(self, axis, angle, origin):
"""Rotate a polyline by a certain angle around an axis and origin.
Right hand rule applies:
If axis has a positive orientation, rotation will be clockwise.
If axis has a negative orientation, rotation will be counterclockwise.
Args:
axis: A Vector3D axis representing the axis of rotation.
angle: An angle for rotation in radians.
origin: A Point3D for the origin around which the point will be rotated.
"""
_new_poly = Polyline3D(tuple(pt.rotate(axis, angle, origin)
for pt in self.vertices))
self._transfer_properties(_new_poly)
return _new_poly
[docs]
def rotate_xy(self, angle, origin):
"""Get a polyline rotated counterclockwise in the XY plane by a certain angle.
Args:
angle: An angle in radians.
origin: A Point3D for the origin around which the object will be rotated.
"""
_new_p = Polyline3D(tuple(pt.rotate_xy(angle, origin) for pt in self.vertices))
self._transfer_properties(_new_p)
return _new_p
[docs]
def reflect(self, normal, origin):
"""Get a polyline reflected across a plane with the input normal and origin.
Args:
normal: A Vector3D representing the normal vector for the plane across
which the polyline will be reflected. THIS VECTOR MUST BE NORMALIZED.
origin: A Point3D representing the origin from which to reflect.
"""
_new_poly = Polyline3D(tuple(pt.reflect(normal, origin) for pt in self.vertices))
self._transfer_properties(_new_poly)
return _new_poly
[docs]
def scale(self, factor, origin=None):
"""Scale a polyline by a factor from an origin point.
Args:
factor: A number representing how much the polyline should be scaled.
origin: A Point3D representing the origin from which to scale.
If None, it will be scaled from the World origin (0, 0, 0).
"""
if origin is None:
_new_poly = Polyline3D(tuple(
Point3D(pt.x * factor, pt.y * factor, pt.z * factor)
for pt in self.vertices))
else:
_new_poly = Polyline3D(tuple(
pt.scale(factor, origin) for pt in self.vertices))
_new_poly._interpolated = self._interpolated
return _new_poly
[docs]
def intersect_plane(self, plane):
"""Get the intersections between this polyline and a Plane.
Args:
plane: A Plane that will be intersected with this object.
Returns:
A list with Point3D objects for the intersections.
List will be empty if no intersection exists.
"""
intersections = []
for _s in self.segments:
inters = intersect_line3d_plane(_s, plane)
if inters is not None:
intersections.append(inters)
return intersections
[docs]
def split_with_plane(self, plane):
"""Split this Polyline3D into Polyline3Ds and LineSegment3Ds using a Plane.
Args:
plane: A Plane that will be used to split this polyline.
Returns:
A list of Polyline3D and LineSegment3D objects if the split was successful.
Will be a list with 1 Polyline3D if no intersection exists.
"""
# group the vertices based on when they cross the plane
grouped_verts = [[self._vertices[0]]]
for _s in self.segments:
inters = intersect_line3d_plane(_s, plane)
if inters is None:
grouped_verts[-1].append(_s.p2)
else: # intersection; start a new group
grouped_verts[-1].append(inters)
grouped_verts.append([inters, _s.p2])
# make new Polyline3D and LineSegment3D objects based on the groups
return self._grouped_verts_to_objs(grouped_verts, self._interpolated)
[docs]
def to_dict(self):
"""Get Polyline3D as a dictionary."""
base = {'type': 'Polyline3D',
'vertices': [pt.to_array() for pt in self.vertices]}
if self.interpolated:
base['interpolated'] = self.interpolated
return base
[docs]
def to_array(self):
"""Get a list of lists where each sub-list represents a Point3D vertex."""
return tuple(pt.to_array() for pt in self.vertices)
[docs]
def to_polyline2d(self):
"""Get a Polyline2D in the XY plane derived from this 3D polyline."""
return Polyline2D(
(Point2D(pt.x, pt.y) for pt in self.vertices), self.interpolated)
[docs]
@staticmethod
def join_segments(segments, tolerance):
"""Get an array of Polyline3Ds from a list of LineSegment3Ds.
Args:
segments: An array of LineSegment3D objects.
tolerance: The minimum difference in X, Y, and Z values at which Point2Ds
are considered equivalent. Segments with points that match within the
tolerance will be joined.
Returns:
An array of Polyline3D and LineSegment3D objects assembled from the
joined segments.
"""
# group the vertices that make up polylines
grouped_verts = _group_vertices(segments, tolerance)
# create the Polyline3D and LineSegment3D objects
return Polyline3D._grouped_verts_to_objs(grouped_verts)
def _transfer_properties(self, new_polyline):
"""Transfer properties from this polyline to a new polyline."""
new_polyline._interpolated = self._interpolated
new_polyline._length = self._length
@staticmethod
def _grouped_verts_to_objs(grouped_verts, interpolated=False):
joined_lines = []
for v_list in grouped_verts:
if len(v_list) == 2:
joined_lines.append(LineSegment3D.from_end_points(v_list[0], v_list[1]))
else:
joined_lines.append(Polyline3D(v_list, interpolated))
return joined_lines
def __copy__(self):
return Polyline3D(self._vertices, self._interpolated)
def __key(self):
"""A tuple based on the object properties, useful for hashing."""
return tuple(hash(pt) for pt in self._vertices) + (self._interpolated,)
def __hash__(self):
return hash(self.__key())
def __eq__(self, other):
return isinstance(other, Polyline3D) and self.__key() == other.__key()
def __repr__(self):
return 'Polyline3D ({} vertices)'.format(len(self))