Example 06: Fit real data of a concave ellipsoid

This example shows how to fit real data of a concave ellipsoid using the XMF library.

import os
from scipy.io import loadmat
import xmf

# Load the data
concave_ellipsoid_map = loadmat(os.path.join('..', '..', '..', 'real_data', 'sample_03_concave_ellipsoid_height_map.mat'))

p = concave_ellipsoid_map['params_target'][0][0][0][0][0]
q = concave_ellipsoid_map['params_target'][0][0][1][0][0]
theta = concave_ellipsoid_map['params_target'][0][0][2][0][0]
x_i = concave_ellipsoid_map['params_target'][0][0][3][0][0]
y_i = concave_ellipsoid_map['params_target'][0][0][4][0][0]
z_i = concave_ellipsoid_map['params_target'][0][0][5][0][0]
alpha = concave_ellipsoid_map['params_target'][0][0][6][0][0]
beta = concave_ellipsoid_map['params_target'][0][0][7][0][0]
gamma = concave_ellipsoid_map['params_target'][0][0][8][0][0]

x2d = concave_ellipsoid_map['x2d']
y2d = concave_ellipsoid_map['y2d']
z2d_measured = concave_ellipsoid_map['z2d']

# Target parameters as dictionary
target_params_dict = {
    'p': p,
    'q': q,
    'theta': theta,
    'x_i': x_i,
    'y_i': y_i,
    'z_i': z_i,
    'alpha': alpha,
    'beta': beta,
    'gamma': gamma
}

# Set input parameters as dictionary
input_params_dict = {
    'p': p,
    'q': q,
    'theta': theta
}

# Set the tolerance dictionary
opt_dict = {
    'p': 0,
    'q': 0,
    'theta': 0,
    'y_i': [-0.5e-3, 0.5e-3],
}

# Fit the surface shape
z2d_res, z2d_fit, opt_params_dict, opt_params_ci_dict, _ = xmf.fit_concave_ellipsoid_height(x2d, y2d, z2d_measured, input_params_dict, opt_dict)
# Show fitting results
xmf.fig_show_2d_fitting_map(x2d, y2d, z2d_measured, z2d_fit, z2d_res, target_params_dict, opt_params_dict, opt_params_ci_dict,'Concave Ellipsoid')