def yaxis(self, vector):
yaxis = Vector(*vector)
yaxis.unitize()
zaxis = Vector.cross(self.xaxis, yaxis)
self._yaxis = Vector.cross(zaxis, self.xaxis)
class Plane(object):
"""A plane is defined by a base point and a normal vector.
Parameters
----------
point : point
The base point of the plane.
normal : vector
The normal vector of the plane.
Examples
--------
>>>
Notes
-----
For more info on lines and linear equations, see [1]_.
References
----------
.. [1] Wikipedia. *Plane (geometry)*.
Available at: https://en.wikipedia.org/wiki/Plane_(geometry).
"""
__slots__ = ['_point', '_normal']
def __init__(self, point, normal):
self._point = None
self._normal = None
self.point = point
self.normal = normal
# ==========================================================================
# factory
# ==========================================================================
@classmethod
def from_three_points(cls, a, b, c):
"""Construct a plane from three points in three-dimensional space.
Parameters
----------
a : point
The first point.
b : point
The second point.
c : point
The second point.
Returns
-------
Plane
A plane with base point ``a`` and normal vector defined as the unitized
cross product of the vectors ``ab`` and ``ac``.
"""
a = Point(*a)
b = Point(*b)
c = Point(*c)
normal = Vector.cross(b - a, c - a)
return cls(a, normal)
@classmethod
def from_point_and_two_vectors(cls, point, u, v):
"""Construct a plane from a base point and two vectors.
Parameters
----------
point : point
The base point.
u : vector
The first vector.
v : vector
The second vector.
Returns
-------
Plane
A plane with base point ``point`` and normal vector defined as the unitized
cross product of vectors ``u`` and ``v``.
"""
normal = Vector.cross(u, v)
return cls(point, normal)
@classmethod
def from_points(cls, points):
"""Construct the *best-fit* plane through more than three (non-coplanar) points.
Parameters
----------
points : list of point
List of points.
Returns
-------
Plane
A plane that minimizes the distance to each point in the list.
"""
raise NotImplementedError
# ==========================================================================
# descriptors
# ==========================================================================
@property
def point(self):
"""Point: The base point of the plane."""
return self._point
@point.setter
def point(self, point):
self._point = Point(*point)
@property
def normal(self):
"""Vector: The normal vector of the plane."""
return self._normal
@normal.setter
def normal(self, vector):
self._normal = Vector(*vector)
self._normal.unitize()
@property
def d(self):
""":obj:`float`: The *d* parameter of the linear equation describing the plane."""
a, b, c = self.normal
x, y, z = self.point
return - a * x - b * y - c * z
# @property
# def frame(self):
# """Frame: The frame that forms a basis for the local coordinates of all
# points in the half-spaces defined by the plane.
# """
# a, b, c = self.normal
# u = 1.0, 0.0, - a / c
# v = 0.0, 1.0, - b / c
# u, v = orthonormalize_vectors([u, v])
# u = Vector(*u)
# v = Vector(*v)
# u.unitize()
# v.unitize()
# return self.point, u, v
# ==========================================================================
# representation
# ==========================================================================
def __repr__(self):
return 'Plane({0}, {1})'.format(self.point, self.normal)
def __len__(self):
return 2
# ==========================================================================
# access
# ==========================================================================
def __getitem__(self, key):
if key == 0:
return self.point
if key == 1:
return self.normal
raise KeyError
def __setitem__(self, key, value):
if key == 0:
self.point = value
return
if key == 1:
self.normal = value
return
raise KeyError
def __iter__(self):
return iter([self.point, self.normal])
# ==========================================================================
# comparison
# ==========================================================================
def __eq__(self, other):
raise NotImplementedError
# ==========================================================================
# operators
# ==========================================================================
# ==========================================================================
# inplace operators
# ==========================================================================
# ==========================================================================
# helpers
# ==========================================================================
def copy(self):
"""Make a copy of this ``Plane``.
Returns
-------
Plane
The copy.
"""
cls = type(self)
return cls(self.point.copy(), self.normal.copy())
# ==========================================================================
# methods
# ==========================================================================
# ==========================================================================
# transformations
# ==========================================================================
def transform(self, matrix):
"""Transform this ``Plane`` using a given transformation matrix.
Parameters
----------
matrix : list of list
The transformation matrix.
"""
point = transform_points([self.point], matrix)
normal = transform_vectors([self.normal], matrix)
self.point.x = point[0]
self.point.y = point[1]
self.point.z = point[2]
self.normal.x = normal[0]
self.normal.y = normal[1]
self.normal.z = normal[2]
def xaxis(self, vector):
xaxis = Vector(*vector)
xaxis.unitize()
self._xaxis = xaxis