# coding=utf-8
"""3D Arc"""
from __future__ import division
from .plane import Plane
from ..geometry2d.pointvector import Point2D, Vector2D
from ..geometry2d.ray import Ray2D
from ..geometry2d.arc import Arc2D
from .pointvector import Vector3D, Point3D
from .polyline import Polyline3D
import math
[docs]class Arc3D(object):
"""3D arc object.
Args:
plane: A Plane in which the arc lies with an origin representing the
center of the circle for the arc.
radius: A number representing the radius of the arc.
a1: A number between 0 and 2 * pi for the start angle of the arc.
a2: A number between 0 and 2 * pi for the end angle of the arc.
Properties:
* plane
* radius
* a1
* a2
* p1
* p2
* midpoint
* c
* min
* max
* length
* angle
* is_circle
* is_inverted
* arc2d
"""
__slots__ = ('_plane', '_arc2d', '_min', '_max')
def __init__(self, plane, radius, a1=0, a2=2 * math.pi):
"""Initialize Arc3D."""
assert isinstance(plane, Plane), "Expected Plane. Got {}.".format(type(plane))
self._plane = plane
self._arc2d = Arc2D(Point2D(0, 0), radius, a1, a2)
self._min = None
self._max = None
[docs] @classmethod
def from_dict(cls, data):
"""Create a Arc3D from a dictionary.
Args:
data: A python dictionary in the following format
.. code-block:: python
{
"type": "Arc3D"
"plane": {"n": (0, 0, 1), "o": (0, 10, 0), "x": (1, 0, 0)},
"radius": 5,
"a1": 0,
"a2": 3.14159
}
"""
return cls(Plane.from_dict(data['plane']), data['radius'],
data['a1'], data['a2'])
[docs] @classmethod
def from_start_mid_end(cls, p1, m, p2, circle=False):
"""Initialize a new arc from start, middle, and end points.
Note that input points will be assumed to be in counterclockwise order.
Args:
p1: The start point of the arc.
m: Any point along the length of the arc that is not the start or end.
p2: The end point of the arc.
circle: Set to True if you would like the output to be a full circle
defined by the three points instead of an arc with a start and end.
Default is False.
"""
plane = cls._plane_from_vertices(p1, m, p2)
p1_2d, m_2d, p2_2d = plane.xyz_to_xy(p1), plane.xyz_to_xy(m), plane.xyz_to_xy(p2)
arc_2d = Arc2D.from_start_mid_end(p1_2d, m_2d, p2_2d, circle)
return cls(Plane(plane.n, plane.xy_to_xyz(arc_2d.c), plane.x),
arc_2d.r, arc_2d.a1, arc_2d.a2)
[docs] @classmethod
def from_arc2d(cls, arc2d, z=0):
"""Initialize a new Arc3D from an Arc2D and a z value.
Args:
arc2d: An Arc2D to be used to generate the Arc3D.
z: A number for the Z coordinate value of the arc.
"""
plane = Plane(o=Point3D(arc2d.c.x, arc2d.c.y, z))
return cls(plane, arc2d.r, arc2d.a1, arc2d.a2)
@property
def plane(self):
"""A Plane in which the arc lies with an origin for the center of the arc."""
return self._plane
@property
def radius(self):
"""Radius of arc."""
return self._arc2d.r
@property
def a1(self):
"""Start angle of the arc in radians."""
return self._arc2d.a1
@property
def a2(self):
"""End angle of the arc in radians."""
return self._arc2d.a2
@property
def p1(self):
"""Start point."""
return self.plane.xy_to_xyz(self.arc2d.p1)
@property
def p2(self):
"""End point."""
return self.plane.xy_to_xyz(self.arc2d.p2)
@property
def midpoint(self):
"""Midpoint."""
return self.point_at(0.5)
@property
def c(self):
"""Center point of the circle on which the arc lies."""
return self.plane.o
@property
def min(self):
"""A Point3D for the minimum bounding box vertex around this geometry."""
if self._min is None:
self._calculate_min_max()
return self._min
@property
def max(self):
"""A Point3D for the maximum bounding box vertex around this geometry."""
if self._max is None:
self._calculate_min_max()
return self._max
@property
def length(self):
"""The length of the arc."""
return self.angle * self.radius
@property
def angle(self):
"""The total angle over the domain of the arc in radians."""
_diff = self.a2 - self.a1
return _diff if not self.is_inverted else 2 * math.pi + _diff
@property
def area(self):
"""Area of the circle to which the arc belongs."""
assert self.is_circle, 'Arc must be a closed circle to access "area" property.'
return math.pi * self.radius ** 2
@property
def is_circle(self):
"""Boolean for whether the arc is a full circle (True) or not (False)."""
return self.a1 == 0 and self.a2 == 2 * math.pi
@property
def is_inverted(self):
"""Boolean noting whether the end angle a2 is smaller than the start angle a1."""
return self.a2 < self.a1
@property
def arc2d(self):
"""An Arc2D within the plane of the Arc3D."""
return self._arc2d
[docs] def move(self, moving_vec):
"""Get an arc that has been moved along a vector.
Args:
moving_vec: A Vector3D with the direction and distance to move the arc.
"""
return Arc3D(self.plane.move(moving_vec), self.radius, self.a1, self.a2)
[docs] def rotate(self, axis, angle, origin):
"""Rotate this arc 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 object will be rotated.
"""
return Arc3D(self.plane.rotate(axis, angle, origin),
self.radius, self.a1, self.a2)
[docs] def rotate_xy(self, angle, origin):
"""Get a arc that is rotated counterclockwise in the world XY plane by a certain angle.
Args:
angle: An angle for rotation in radians.
origin: A Point3D for the origin around which the arc will be rotated.
"""
return Arc3D(self.plane.rotate_xy(angle, origin), self.radius, self.a1, self.a2)
[docs] def reflect(self, normal, origin):
"""Get a arc reflected across a plane with the input normal vector and origin.
Args:
normal: A Vector3D representing the normal vector for the plane across
which the arc will be reflected. THIS VECTOR MUST BE NORMALIZED.
origin: A Point3D representing the origin from which to reflect.
"""
arc2d = self.arc2d.reflect(Vector2D(0, 1), Point2D(0, 0))
return Arc3D(self.plane.reflect(normal, origin), self.radius, arc2d.a1, arc2d.a2)
[docs] def scale(self, factor, origin=None):
"""Scale a arc by a factor from an origin point.
Args:
factor: A number representing how much the arc should be scaled.
origin: A Point2D representing the origin from which to scale.
If None, it will be scaled from the World origin (0, 0, 0).
"""
return Arc3D(self.plane.scale(factor, origin), self.radius * factor,
self.a1, self.a2)
[docs] def subdivide(self, distances):
"""Get Point3D values along the arc that subdivide it based on input distances.
Args:
distances: A list of distances along the arc at which to subdivide it.
This can also be a single number that will be repeated until the
end of the arc.
"""
return [self.plane.xy_to_xyz(pt) for pt in self.arc2d.subdivide(distances)]
[docs] def subdivide_evenly(self, number):
"""Get Point3D values along the arc that divide it into evenly-spaced segments.
Args:
number: The number of segments into which the arc will be divided.
"""
return [self.plane.xy_to_xyz(pt) for pt in self.arc2d.subdivide_evenly(number)]
[docs] def point_at(self, parameter):
"""Get a point at a given fraction along the arc.
Args:
parameter: The fraction between the start and end point where the
desired point lies. For example, 0.5 will yield the midpoint.
"""
return self.plane.xy_to_xyz(self.arc2d.point_at(parameter))
[docs] def point_at_angle(self, angle):
"""Get a point at a given angle along the arc.
Args:
angle: The angle in radians from the start point along the arc
to get the Point3D.
"""
return self.plane.xy_to_xyz(self.arc2d.point_at_angle(angle))
[docs] def point_at_length(self, length):
"""Get a point at a given distance along the arc segment.
Args:
length: The distance along the arc from the start point where the
desired point lies.
"""
return self.point_at(length / self.length)
[docs] def closest_point(self, point):
"""Get the closest Point3D on this object to another Point3D.
Args:
point: A Point3D object to which the closest point on this object
will be computed.
Returns:
Point3D for the closest point on this line to the input point.
"""
plane_pt = self.plane.closest_point(point)
return self.plane.xy_to_xyz(
self.arc2d.closest_point(self.plane.xyz_to_xy(plane_pt)))
[docs] def distance_to_point(self, point):
"""Get the minimum distance between this object and the input point.
Args:
point: A Point3D object to which the minimum distance will be computed.
Returns:
The distance to the input point.
"""
close_pt = self.closest_point(point)
return point.distance_to_point(close_pt)
[docs] def intersect_plane(self, plane):
"""Get the intersection between this Arc3D and a Plane.
Args:
plane: A Plane that will be intersected with this arc.
Returns:
A list of Point3D objects if the intersection was successful.
None if no intersection exists.
"""
_plane_int_ray = plane.intersect_plane(self.plane)
if _plane_int_ray is not None:
_p12d = self.plane.xyz_to_xy(_plane_int_ray.p)
_p22d = self.plane.xyz_to_xy(_plane_int_ray.p + _plane_int_ray.v)
_v2d = _p22d - _p12d
_int_ray2d = Ray2D(_p12d, _v2d)
_int_pt2d = self.arc2d.intersect_line_infinite(_int_ray2d)
if _int_pt2d is not None:
return [self.plane.xy_to_xyz(pt) for pt in _int_pt2d]
return None
[docs] def split_with_plane(self, plane):
"""Split this Arc3D in 2 or 3 smaller arcs using a Plane.
Args:
plane: A Plane that will be used to split this arc.
Returns:
A list with two or three Arc3D objects if the split was successful.
Will be a list with 1 Arc3D if no intersection exists.
"""
_plane_int_ray = plane.intersect_plane(self.plane)
if _plane_int_ray is not None:
_p12d = self.plane.xyz_to_xy(_plane_int_ray.p)
_p22d = self.plane.xyz_to_xy(_plane_int_ray.p + _plane_int_ray.v)
_v2d = _p22d - _p12d
_int_ray2d = Ray2D(_p12d, _v2d)
_int_pt2d = self.arc2d.split_line_infinite(_int_ray2d)
if len(_int_pt2d) != 1:
return [Arc3D(self.plane, self.radius, arc.a1, arc.a2)
for arc in _int_pt2d]
return [self]
[docs] def to_polyline(self, divisions, interpolated=True):
"""Get this Arc3D as an approximated Polyline3D.
Args:
divisions: The number of segments into which the arc will be divided.
interpolated: Boolean to note whether the polyline should be interpolated
between the input vertices when it is translated to other interfaces.
This property has no effect on the geometric calculations performed
by this library and is only present in order to assist with
display/translation. (Default: True)
"""
pts = self.subdivide_evenly(divisions)
return Polyline3D(pts, interpolated)
[docs] def to_dict(self):
"""Get Arc3D as a dictionary."""
return {'type': 'Arc3D', 'plane': self.plane.to_dict(),
'radius': self.radius, 'a1': self.a1, 'a2': self.a2}
[docs] def duplicate(self):
"""Get a copy of this object."""
return self.__copy__()
def _calculate_min_max(self):
"""Calculate maximum and minimum Point3D for this object.
At this point in time, this method only calculates the bounding box
around the circle of the arc using the formula here.
https://stackoverflow.com/questions/2592011/\
bounding-boxes-for-circle-and-arcs-in-3d
"""
if self.is_circle:
o, r = self._plane.o, self.radius
ax = self._plane.n.angle(Vector3D(1, 0, 0))
ay = self._plane.n.angle(Vector3D(0, 1, 0))
az = self._plane.n.angle(Vector3D(0, 0, 1))
r_vec = (math.sin(ax) * r, math.sin(ay) * r, math.sin(az) * r)
self._min = Point3D(o.x - r_vec[0], o.y - r_vec[1], o.z - r_vec[2])
self._max = Point3D(o.x + r_vec[0], o.y + r_vec[1], o.z + r_vec[2])
else: # get the min and max of the Arc2D
min_pt2d, max_pt2d = self._arc2d.min, self._arc2d.max
self._min = self.plane.xy_to_xyz(min_pt2d)
self._max = self.plane.xy_to_xyz(max_pt2d)
@staticmethod
def _plane_from_vertices(pt1, pt2, pt3):
"""Get a plane from three vertices."""
try:
v1 = pt2 - pt1
v2 = pt3 - pt1
n = v1.cross(v2)
except Exception as e:
raise ValueError('Incorrect Point3D input for Arc3D:\n\t{}'.format(e))
return Plane(n, pt1)
def __copy__(self):
return Arc3D(self.plane, self.radius, self.a1, self.a2)
def __key(self):
"""A tuple based on the object properties, useful for hashing."""
return (hash(self.plane), self.radius, self.a1, self.a2)
def __hash__(self):
return hash(self.__key())
def __eq__(self, other):
return isinstance(other, Arc3D) and self.__key() == other.__key()
def __ne__(self, other):
return not self.__eq__(other)
[docs] def ToString(self):
"""Overwrite .NET ToString."""
return self.__repr__()
def __repr__(self):
return 'Arc3D (center {}) (radius {}) (length {})'.format(
self.plane.o, self.radius, self.length)