def from_point_and_two_vectors(cls, point, u, v):
"""Construct a plane from a base point and two vectors.
Parameters
----------
point : [float, float, float] | :class:`compas.geometry.Point`
The base point.
u : [float, float, float] | :class:`compas.geometry.Vector`
The first vector.
v : [float, float, float] | :class:`compas.geometry.Vector`
The second vector.
Returns
-------
:class:`compas.geometry.Plane`
A plane with base point `point` and normal vector defined as the unitized
cross product of vectors `u` and `v`.
Examples
--------
>>> plane = Plane.from_three_points([0.0, 0.0, 0.0], [2.0, 1.0, 0.0], [0.0, 3.0, 0.0])
>>> plane.point
Point(0.000, 0.000, 0.000)
>>> plane.normal
Vector(0.000, 0.000, 1.000)
"""
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 : [float, float, float] | :class:`compas.geometry.Point`
The first point.
b : [float, float, float] | :class:`compas.geometry.Point`
The second point.
c : [float, float, float] | :class:`compas.geometry.Point`
The second point.
Returns
-------
:class:`compas.geometry.Plane`
A plane with base point `a` and normal vector defined as the unitized
cross product of the vectors `ab` and `ac`.
Examples
--------
>>> plane = Plane.from_three_points([0.0, 0.0, 0.0], [2.0, 1.0, 0.0], [0.0, 3.0, 0.0])
>>> plane.point
Point(0.000, 0.000, 0.000)
>>> plane.normal
Vector(0.000, 0.000, 1.000)
"""
a = Point(*a)
b = Point(*b)
c = Point(*c)
normal = Vector.cross(b - a, c - a)
return cls(a, normal)
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)
zaxis.unitize()
self._yaxis = Vector.cross(zaxis, self.xaxis)
