Setup Tutorial for 2D Problems

from lsdo_genie import Genie2D

Generate your point cloud

Begin by importing your point cloud \(\mathcal{P}=\{(\mathbf{p}_i,\vec{\mathbf{n}}_i):i=1,\dots, N_\Gamma\}\). Genie requires your points and normals to be in a numpy array of shape \((N_\Gamma,2)\). In this example, we will consider an ellipse with 100 points in the point cloud

from lsdo_genie.utils.geometric_shapes import Ellipse
num_points = 100
geom_shape = Ellipse(7,4)
surface_points = geom_shape.surface_points(num_points)
surface_normals = geom_shape.unit_normals(num_points)

Define the domain of interest

Depending on your optimization problem, you will need to define a rectangular domain for the constraint function. This domain is shapped as follows:

import numpy as np
x_domain = np.array([-10.0,10.0])
y_domain = np.array([-5.6, 5.6])
custom_domain = np.array([
    x_domain,
    y_domain,
])

Initialize Genie instance

Next, we will initialize an instance of Genie. We can use python verbose=True for Genie to print out steps as we go

genie = Genie2D(verbose=True)

Input your data

We will now input the point cloud to be saved in the genie instance.

genie.input_point_cloud(
    surface_points=surface_points,
    surface_normals=surface_normals,
)

Minimum bbox: 
 [[-7.  7.]
 [-4.  4.]]
Minimum bbox diagonal:  16.1245154965971
num_surface_points:  100 

Initialize the Bspline

Finally, we will define the Bspline for our non-interference constraint function. The python genie.config() command will input the number of control points and the domain of the function and automtically distribution the Bspline control points spatially throughout the domain AND initialize their values \(\mathbf{C}^\phi\) according to Hicken and Kaur’s explicit formulation [HK22]

genie.config(
    domain=custom_domain,
    max_control_points=70,
    min_ratio=0.75,
)

Bspline box: 
 [[-10.   10. ]
 [ -5.6   5.6]]
Control point grid:  [70 52] = 3640
Number of quadrature points:  3400
Initial min distance:  -5.667319111986389
Initial max distance:  3.906473470307496
Bspline order:  4 

We can now visualize the initialized Bspline

genie.visualize()