"""Example: 'point in frame'
The simple example above shows how to use a frame as a coordinate system:
Starting from a point `P` in the local (user-defined, relative) coordinate
system of frame `F`, i.e. its position is relative to the origin and orientation
of `F`, we want to get the position `P_` of `P` in the global (world, absolute)
coordinate system.
"""
from compas.geometry import Point
from compas.geometry import Vector
from compas.geometry import Frame
from compas.geometry import allclose
point = Point(146.00, 150.00, 161.50)
xaxis = Vector(0.9767, 0.0010, -0.214)
yaxis = Vector(0.1002, 0.8818, 0.4609)
F = Frame(point, xaxis, yaxis) # coordinate system F
P = Point(35., 35., 35.) # point in F (local coordinates)
P_ = F.to_world_coords(P) # point in global (world) coordinates
print("The point's world coordinates: {}".format(P_))
P2 = F.to_local_coords(P_)
print("The point's local coordinates: {}".format(P2)) # should equal P
print(allclose(P2, P))
"""Example: 'frame in frame' """ from compas.geometry import Point from compas.geometry import Vector from compas.geometry import Frame point = Point(146.00, 150.00, 161.50) xaxis = Vector(0.9767, 0.0010, -0.214) yaxis = Vector(0.1002, 0.8818, 0.4609) F0 = Frame(point, xaxis, yaxis) # coordinate system F0 point = Point(35., 35., 35.) xaxis = Vector(0.604, 0.430, 0.671) yaxis = Vector(-0.631, 0.772, 0.074) f_lcf = Frame(point, xaxis, yaxis) # frame f_lcf in F0 (local coordinates) # frame in global (world) coordinate system f_wcf = F0.to_world_coords(f_lcf) print(f_wcf) f_lcf2 = F0.to_local_coords(f_wcf) # world coords back to local coords print(f_lcf2) # should equal f_lcf print(f_lcf == f_lcf2)
"""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.change_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_coords(F1.point))
