def local_to_local_coordinates(frame1, frame2, object_in_frame1):
"""Returns the object's coordinates in frame1 in the local coordinates of frame2.
Parameters
----------
frame1 : :class:`compas.geometry.Frame`
A frame representing one local coordinate system.
frame2 : :class:`compas.geometry.Frame`
A frame representing another local coordinate system.
object_in_frame1 : :class:`compas.geometry.Point` or :class:`compas.geometry.Vector` or :class:`compas.geometry.Frame` or list of float
An object in the coordinate frame1. If you pass a list of float, it is assumed to represent a point.
Returns
-------
:class:`compas.geometry.Point` or :class:`compas.geometry.Vector` or :class:`compas.geometry.Frame`
The object in the local coordinate system of frame2.
Examples
--------
>>> from compas.geometry import Point
>>> frame1 = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
>>> frame2 = Frame([2, 1, 3], [1., 0., 0.], [0., 1., 0.])
>>> p1 = Point(2, 2, 2) # point in frame1
>>> p2 = Frame.local_to_local_coordinates(frame1, frame2, p1) # point in frame2
>>> Frame.local_to_local_coordinates(frame2, frame1, p2)
Point(2.000, 2.000, 2.000)
"""
T = Transformation.from_change_of_basis(frame1, frame2)
if isinstance(object_in_frame1, list):
return Point(*object_in_frame1).transformed(T)
return object_in_frame1.transformed(T)
def to_world_coordinates(self, object_in_lcf):
"""Returns the object's coordinates in the global coordinate frame.
Parameters
----------
object_in_lcf : :class:`compas.geometry.Point` or :class:`compas.geometry.Vector` or :class:`compas.geometry.Frame` or list of float
An object in local coordinate system of the frame.
Returns
-------
:class:`compas.geometry.Point` or :class:`compas.geometry.Vector` or :class:`compas.geometry.Frame`
The object in the world coordinate frame.
Notes
-----
If you pass a list of float, it is assumed to represent a point.
Examples
--------
>>> from compas.geometry import Point
>>> frame = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
>>> pl = Point(1.632, -0.090, 0.573) # point in frame
>>> pw = frame.to_world_coordinates(pl) # point in wcf
>>> frame.to_local_coordinates(pw)
Point(1.632, -0.090, 0.573)
"""
T = Transformation.from_change_of_basis(self, Frame.worldXY())
if isinstance(object_in_lcf, list):
return Point(*object_in_lcf).transformed(T)
else:
return object_in_lcf.transformed(T)
def to_local_coordinates(self, obj_in_wcf):
"""Returns the object's coordinates in the local coordinate system of the frame.
Parameters
----------
obj_in_wcf : [float, float, float] | :class:`compas.geometry.Geometry`
An object in the world coordinate frame.
Returns
-------
:class:`compas.geometry.Geometry`
The object in the local coordinate system of the frame.
Notes
-----
If you pass a list of floats, it is assumed to represent a point.
Examples
--------
>>> from compas.geometry import Point
>>> frame = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
>>> pw = Point(2, 2, 2) # point in wcf
>>> pl = frame.to_local_coordinates(pw) # point in frame
>>> frame.to_world_coordinates(pl)
Point(2.000, 2.000, 2.000)
"""
T = Transformation.from_change_of_basis(Frame.worldXY(), self)
if isinstance(obj_in_wcf, (list, tuple)):
return Point(*obj_in_wcf).transformed(T)
return obj_in_wcf.transformed(T)
def contains(self, point):
"""Verify if the box contains a given point.
Parameters
----------
point : :class:`compas.geometry.Point` or (float, float, float)
Returns
-------
bool
"""
T = Transformation.from_change_of_basis(Frame.worldXY(), self.frame)
point = transform_points([point], T)[0]
if -0.5 * self.xsize < point[0] < + 0.5 * self.xsize:
if -0.5 * self.ysize < point[1] < +0.5 * self.ysize:
if -0.5 * self.zsize < point[2] < +0.5 * self.zsize:
return True
return False
from compas.geometry import Point, Box, Frame, Vector, Plane, scale_vector, normalize_vector, Polygon, Rotation, intersection_line_line from compas.geometry import Transformation frame1 = Frame(Point(0, 0), Vector(-1, 0), Vector(0, 1)) frame2 = Frame(Point(10, 0), Vector(-1, 0), Vector(0, 1)) frame3 = Frame(Point(0, 0), Vector(0, 1), Vector(1, 0)) F1 = Transformation.from_change_of_basis(frame1, frame2) frame4 = frame3.transformed(F1) print(frame4)
"""Change-basis transformation vs transformation between two frames. """ from compas.geometry import Point from compas.geometry import Frame from compas.geometry import Transformation F1 = Frame([2, 2, 2], [0.12, 0.58, 0.81], [-0.80, 0.53, -0.26]) F2 = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15]) # transformation between 2 frames F1, F2 Tf = Transformation.from_frame_to_frame(F1, F2) # change-basis transformation between two frames F1 and F2. Tc = Transformation.from_change_of_basis(F1, F2) # they are different print(Tf) print(Tc) # This is how to use Tf: transform geometry into another coordinate frame pt = Point(2, 2, 2) pt.transform(Tf) print(pt, "==", F2.point) # This is how to use Tc: represent geometry in another coordinate frame pt = Point(0, 0, 0) # local point in F1 pt.transform(Tc) print(pt, "==", F2.to_local_coordinates(F1.point))
