Basic usage of geo3d

from geo3d import frame_wizard, Vector, Point, RotationMatrix, Frame, transformation_between_frames

Frame creation

Manual Frame cration

Manually create frame from given rotation Euler angles and translation vector.

rot = RotationMatrix.from_euler_angles('xyz', [-70.89339465, -74.20683095,  45], degrees=True)
vec = Vector([3,4,6])
Frame(rot,vec)

rotation matrix	Fixed angles (xyz, extr., deg.)	Euler angles (xyz, intr., deg.)	translation
0.19245009 0.41147560 -0.89087081 0.19245009 0.87438565 0.44543540 0.96225045 -0.25717225 0.08908708	θx -70.89339 θy -74.20683 θz 45.00000	θx -78.69007 θy -62.98288 θz -64.93417	x 3.00000 y 4.00000 z 6.00000

The Frame Wizard

Create two frames using a Frame Wizard (comparable to the one in Spatial Analyzer). Frames are defined as transformations starting from a unit frame (no translation and rotation).

# rotation only from UnitFrame
fa = frame_wizard(Vector([1, 1, 0]), Vector([1, -1, 0]), "x", "y", origin=[0, 0, 0])
# translation only from UnitFrame
fb = frame_wizard(Vector([1, 0, 0]), Vector([0, 1, 0]), "x", "y", origin=[1, 1, 4])
# rotation and translation from UnitFrame
fc = frame_wizard(Vector([1, 1, 0]), Vector([1, -1, 0]), "x", "y", origin=[1, 1, 4])

fa

rotation matrix	Fixed angles (xyz, extr., deg.)	Euler angles (xyz, intr., deg.)	translation
0.70710678 0.70710678 0.00000000 0.70710678 -0.70710678 0.00000000 0.00000000 -0.00000000 -1.00000000	θx 180.00000 θy 0.00000 θz 45.00000	θx 180.00000 θy 0.00000 θz -45.00000	x 0.00000 y 0.00000 z 0.00000

print(fb)

<Frame instance at 4508522128>
rotation
[[ 1. -0.  0.]
 [ 0.  1.  0.]
 [ 0. -0.  1.]]
Fixed angles (xyz, extrinsic, deg.)
[0. 0. 0.]
Euler angles (XYZ, intrinsic, deg.)
[0. 0. 0.]
translation
[1 1 4]

They have a rotation and translation component:

fc.translation

x	1.00000
y	1.00000
z	4.00000

fc.rotation

0.70710678	0.70710678	0.00000000
0.70710678	-0.70710678	0.00000000
0.00000000	-0.00000000	-1.00000000

The rotation can be expressed as Euler angles.

fc.euler_angles('xyz', degrees='True')

array([180.,   0.,  45.])

Frame from 4x4 matrix string

Construct Frame from 4x4 matrix (SA style)

frame_from_SA = Frame.from_SA_pastable_string(
    "0.0000000344 0.0000002614 -1.0000000000 634.9997932029 -0.1305702435 -0.9914390609 -0.0000002637 784.0319609308 -0.9914390609 0.1305702435 0.0000000000 747.5060850385 0.0000000000 0.0000000000 0.0000000000 1.0000000000 "
)
frame_from_SA

rotation matrix	Fixed angles (xyz, extr., deg.)	Euler angles (xyz, intr., deg.)	translation
0.00000003 0.00000026 -1.00000000 -0.13057024 -0.99143906 -0.00000026 -0.99143906 0.13057024 0.00000000	θx 90.00000 θy 82.49745 θz -89.99998	θx 89.99689 θy -89.99998 θz -82.50056	x 634.99979 y 784.03196 z 747.50609

Convert Frame back to 4x4 matrix string

print(frame_from_SA.SA_pastable_string())

0.000000034400 0.000000261400 -1.000000000000 634.999793202900
-0.130570243500 -0.991439060900 -0.000000263700 784.031960930800
-0.991439060900 0.130570243500 0.000000000000 747.506085038500
0.000000000000 0.000000000000 0.000000000000 1.000000000000

Frame to frame transformations

A frame can be expressed in a different frame.

fb.express_in_frame(fa)

rotation matrix	Fixed angles (xyz, extr., deg.)	Euler angles (xyz, intr., deg.)	translation
0.70710678 0.70710678 0.00000000 0.70710678 -0.70710678 0.00000000 0.00000000 0.00000000 -1.00000000	θx 180.00000 θy 0.00000 θz 45.00000	θx 180.00000 θy 0.00000 θz -45.00000	x 1.41421 y 0.00000 z -4.00000

This yields the frame-to-frame transformation from fA to fB, represented in fA.

The same frame-to-frame transformation matrix, but given in the original (unit) frame is

transformation_between_frames(fa, fb)

rotation matrix	Fixed angles (xyz, extr., deg.)	Euler angles (xyz, intr., deg.)	translation
0.70710678 0.70710678 0.00000000 0.70710678 -0.70710678 0.00000000 0.00000000 0.00000000 -1.00000000	θx 180.00000 θy 0.00000 θz 45.00000	θx 180.00000 θy 0.00000 θz -45.00000	x 1.00000 y 1.00000 z 4.00000

Expression of vectors and points in frames

Express a vector given in original_frame in a new frame.

Vector([1,3,0]).express_in_frame(fa, original_frame=fb)

x	2.82843
y	-1.41421
z	0.00000

Express a point given in original_frame in a new frame.

Point([5,3,20]).express_in_frame(fa, original_frame=fb)

x	7.07107
y	1.41421
z	-24.00000