Vector Generators

For using the ReachabilityMap we need a Frame generator function. In a simple case, this can be only a list of frames. However, sometimes it makes sense to generate multiple frames at a certain location that deviate a bit in orientation. We provide 2 helper vector generators with very verbose names:

  • OrthonormalVectorsFromAxisGenerator

  • DeviationVectorsGenerator

Generate orthonormal vectors from an axis

The OrthonormalVectorsFromAxisGenerator generates vectors that are orthonormal a given axis.

In the example below, the given axis is visualized in red, and the generated vectors in black.

../../_images/03_ortho_vectors.jpg 
>>> import math
>>> from compas.geometry import Vector
>>> from compas_fab.robots import OrthonormalVectorsFromAxisGenerator
>>> zaxis = Vector(0, 0, 1)
>>> max_alpha = 60
>>> for xaxis in OrthonormalVectorsFromAxisGenerator(zaxis, math.radians(max_alpha)):
...     print(xaxis)
Vector(0.000, -1.000, 0.000)
Vector(0.866, -0.500, 0.000)
Vector(0.866, 0.500, 0.000)
Vector(0.000, 1.000, 0.000)
Vector(-0.866, 0.500, 0.000)
Vector(-0.866, -0.500, 0.000)

Generate vectors that deviate

The DeviationVectorsGenerator generates equally distributed vectors that deviate from the passed one by a maximal angle of max_alpha.

In the example below, the given axis is visualized in red, and the generated vectors in black.

../../_images/04_devi_vectors.jpg 
>>> import math
>>> from compas_fab.robots import DeviationVectorsGenerator
>>> zaxis = Vector(0, 0, 1)
>>> max_alpha = 40
>>> step = 1
>>> for axis in DeviationVectorsGenerator(zaxis, math.radians(max_alpha), step):
...     print(axis)
Vector(0.000, 0.000, 1.000)
Vector(-0.643, 0.000, 0.766)
Vector(-0.321, -0.557, 0.766)
Vector(0.321, -0.557, 0.766)
Vector(0.643, -0.000, 0.766)
Vector(0.321, 0.557, 0.766)
Vector(-0.321, 0.557, 0.766)

Or another example with using max_angle = 60 and step = 2.

../../_images/05_devi_vectors_2.jpg

Generate frames

Now having these two vector generators, we can combine them for generating frames.

from compas.geometry import Frame
from compas.geometry import Point
from compas.geometry import Vector
from compas_fab.robots import DeviationVectorsGenerator
from compas_fab.robots import OrthonormalVectorsFromAxisGenerator

def frame_generator():
    for i in range(6):
        pt = Point(0, 0, 0) + Vector(0, i, 0)
        zaxis = Vector(0, 0, 1)
        for axis in DeviationVectorsGenerator(zaxis, math.radians(40), 1):
            for xaxis in OrthonormalVectorsFromAxisGenerator(axis, math.radians(60)):
                yaxis = axis.cross(xaxis)
                yield Frame(pt, xaxis, yaxis)
../../_images/06_devi_frames.jpg