# coding=utf-8
"""Cone"""
from __future__ import division
from .pointvector import Point3D, Vector3D
from .plane import Plane
from .arc import Arc3D
import math
[docs]class Cone(object):
"""Cone object.
Args:
vertex: A Point3D at the tip of the cone.
axis: A Vector3D representing the direction and height of the cone.
The vector extends from the vertex to the center of the base.
angle: An angle in radians representing the half angle between
the axis and the surface.
Properties:
* vertex
* axis
* angle
* height
* slant_height
* radius
* area
* volume
* min
* max
* base
"""
__slots__ = ('_vertex', '_axis', '_angle', '_base', '_min', '_max')
def __init__(self, vertex, axis, angle):
"""Initialize Cone."""
assert isinstance(vertex, Point3D), \
"Expected Point3D. Got {}.".format(type(vertex))
assert isinstance(axis, Vector3D), \
"Expected Vector3D. Got {}.".format(type(axis))
assert angle > 0, 'Cone angle must be greater than 0. Got {}.'.format(angle)
self._vertex = vertex
self._axis = axis
self._angle = angle
self._base = None
self._min = None
self._max = None
[docs] @classmethod
def from_dict(cls, data):
"""Create a Cone from a dictionary.
Args:
data: A python dictionary in the following format
.. code-block:: python
{
"type": "Cone"
"vertex": (10, 0, 0),
"axis": (0, 0, 1),
"angle": 1.0
}
"""
return cls(Point3D.from_array(data['vertex']),
Vector3D.from_array(data['axis']),
data['angle'])
@property
def vertex(self):
"""Vertex of cone."""
return self._vertex
@property
def axis(self):
"""Axis of cone."""
return self._axis
@property
def angle(self):
"""Angle of cone"""
return self._angle
@property
def height(self):
"""Height of cone"""
return self.axis.magnitude
@property
def radius(self):
"""Radius of a cone"""
return self.height * math.tan(self.angle)
@property
def slant_height(self):
"""Slant height of a cone"""
return math.sqrt(self.radius ** 2 + self.height ** 2)
@property
def area(self):
"""Surface area of a cone"""
return math.pi * self.radius ** 2 + math.pi * self.radius * self.slant_height
@property
def volume(self):
"""Volume of a cone"""
return 1 / 3 * math.pi * self.radius ** 2 * self.height
@property
def base(self):
"""Get an Arc3D representing the circular base of the cone."""
if self._base is None:
plane = Plane(self.axis.reverse(), self.vertex + self.axis)
self._base = Arc3D(plane, self.radius)
return self._base
@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
[docs] def move(self, moving_vec):
"""Get a cone that has been moved along a vector.
Args:
moving_vec: A Vector3D with the direction and distance to move the cone.
"""
return Cone(self.vertex.move(moving_vec), self.axis, self.angle)
[docs] def rotate(self, axis, angle, origin):
"""Rotate this cone 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 cone will be rotated.
"""
return Cone(self.vertex.rotate(axis, angle, origin),
self.axis.rotate(axis, angle),
self.angle)
[docs] def rotate_xy(self, angle, origin):
"""Get a cone that is rotated counterclockwise in the world XY plane by an angle.
Args:
angle: An angle for rotation in radians.
origin: A Point3D for the origin around which the cone will be rotated.
"""
return Cone(self.vertex.rotate_xy(angle, origin),
self.axis.rotate_xy(angle),
self.angle)
[docs] def reflect(self, normal, origin):
"""Get a cone 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.
"""
return Cone(self.vertex.reflect(normal, origin),
self.axis.reflect(normal),
self.angle)
[docs] def scale(self, factor, origin=None):
"""Scale a cone by a factor from an origin point.
Args:
factor: A number representing how much the cone 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).
"""
return Cone(self.vertex.scale(factor, origin),
self.axis * factor,
self.angle)
[docs] def duplicate(self):
"""Get a copy of this object."""
return self.__copy__()
[docs] def to_dict(self):
"""Get Cone as a dictionary."""
return {
'type': 'Cone',
'vertex': self.vertex.to_array(),
'axis': self.axis.to_array(),
'angle': self.angle
}
def _calculate_min_max(self):
"""Calculate maximum and minimum Point3D for this object."""
base = self.base
bmn, bmx, ver = base.min, base.max, self.vertex
self._min = Point3D(min(bmn.x, ver.x), min(bmn.y, ver.y), min(bmn.z, ver.z))
self._max = Point3D(max(bmx.x, ver.x), max(bmx.y, ver.y), max(bmx.z, ver.z))
def __copy__(self):
return Cone(self.vertex, self.axis, self.angle)
def __key(self):
"""A tuple based on the object properties, useful for hashing."""
return (self._vertex, self._axis, self._angle)
def __hash__(self):
return hash(self.__key())
def __eq__(self, other):
return isinstance(other, Cone) 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 'Cone (vertex {}) (axis {}) (angle {}) (height {})'.\
format(self.vertex, self.axis, self.angle, self.height)