def frame(self):
"""The local coordinate frame."""
o = self.center
w = self.normal
p = self.points[0]
u = Vector.from_start_end(o, p)
u.unitize()
v = Vector.cross(w, u)
return o, u, v, w
def from_point_and_two_vectors(cls, point, v1, v2):
v1 = Vector(*v1)
v2 = Vector(*v2)
n = Vector.cross(v1, v2)
n.unitize()
plane = cls()
plane.point = Point(*point)
plane.normal = n
return plane
def from_three_points(cls, p1, p2, p3):
p1 = Point(*p1)
p2 = Point(*p2)
p3 = Point(*p3)
v1 = p2 - p1
v2 = p3 - p1
plane = cls()
plane.point = p1
plane.normal = Vector.cross(v1, v2)
plane.normal.unitize()
return plane
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)
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)
def yaxis(self, vector):
yaxis = Vector(*vector)
yaxis.unitize()
zaxis = Vector.cross(self.xaxis, yaxis)
self._yaxis = Vector.cross(zaxis, self.xaxis)