"""Bölüm 18: uzayda doğru, düzlem ve rank tanısı laboratuvarı. Uygulama, sentetik bir CAD datum düzlemi ile delik ekseninin eşdeğer gösterimlerini sınar. Ölçülmüş veri, üretim toleransı, delik kalitesi veya kabul kararı içermez. """ from __future__ import annotations import numpy as np from agbook import ( affine_system_diagnostics_3d, canonical_array_sha256, canonical_plane_coefficients, parametric_line_points_3d, plane_from_points_3d, plane_membership_diagnostics_3d, plane_residuals_3d, ) def main() -> None: length_unit = "mm" rank_relative_tolerance = 1.0e-12 reference_scale_mm = 200.0 point_a = np.array([120.0, 80.0, 35.0]) point_b = np.array([156.0, 128.0, 35.0]) point_c = np.array([96.0, 98.0, 75.0]) datum_points_mm = np.vstack([point_a, point_b, point_c]) datum_plane_mm = plane_from_points_3d(point_a, point_b, point_c) expected_normal = np.array([0.64, -0.48, 0.60]) scaled_plane = canonical_plane_coefficients(-25.0 * datum_plane_mm) # Yön uzunluk birimindedir; t boyutsuzdur ve ||direction|| = 25 mm'dir. axis_direction_mm = np.array([16.0, -12.0, 15.0]) axis_parameters = np.array([-2.0, -1.0, 0.0, 1.0, 2.0]) axis_points_mm = parametric_line_points_3d( point_a, axis_direction_mm, axis_parameters, ) # İki birim normalin düzlemleri delik eksenini ortak çözüm olarak verir. tangent_1 = np.array([0.60, 0.80, 0.0]) tangent_2 = np.array([-0.48, 0.36, 0.80]) axis_matrix = np.vstack([tangent_1, tangent_2]) axis_rhs_mm = axis_matrix @ point_a axis_diagnosis_mm = affine_system_diagnostics_3d( axis_matrix, axis_rhs_mm, rank_relative_tolerance=rank_relative_tolerance, reference_scale=reference_scale_mm, ) axis_plane_residuals = np.column_stack( [ plane_residuals_3d( np.concatenate([axis_matrix[index], [-axis_rhs_mm[index]]]), axis_points_mm, ) for index in range(2) ] ) full_matrix = np.vstack([axis_matrix, expected_normal]) full_rhs_mm = full_matrix @ point_a anchor_diagnosis_mm = affine_system_diagnostics_3d( full_matrix, full_rhs_mm, rank_relative_tolerance=rank_relative_tolerance, reference_scale=reference_scale_mm, ) membership_b = plane_membership_diagnostics_3d( datum_plane_mm, point_b, absolute_tolerance=1.0e-12, relative_tolerance=0.0, reference_scale=reference_scale_mm, ) membership_c = plane_membership_diagnostics_3d( datum_plane_mm, point_c, absolute_tolerance=1.0e-12, relative_tolerance=0.0, reference_scale=reference_scale_mm, ) datum_points_m = datum_points_mm * 1.0e-3 datum_plane_m = plane_from_points_3d(*datum_points_m) axis_rhs_m = axis_matrix @ (point_a * 1.0e-3) axis_diagnosis_m = affine_system_diagnostics_3d( axis_matrix, axis_rhs_m, rank_relative_tolerance=rank_relative_tolerance, reference_scale=reference_scale_mm * 1.0e-3, ) # Aynı tam verinin iki açık rank eşiğinde farklı sayısal çözünürlüğü. perturbation = 1.0e-10 near_matrix = np.vstack([tangent_1, tangent_1 + perturbation * tangent_2]) near_rhs_mm = near_matrix @ point_a coarse_rank = affine_system_diagnostics_3d( near_matrix, near_rhs_mm, rank_relative_tolerance=1.0e-8, reference_scale=reference_scale_mm, ) fine_rank = affine_system_diagnostics_3d( near_matrix, near_rhs_mm, rank_relative_tolerance=1.0e-12, reference_scale=reference_scale_mm, ) np.testing.assert_allclose( datum_plane_mm, [0.64, -0.48, 0.60, -59.4], atol=2.0e-14, ) np.testing.assert_allclose(scaled_plane, datum_plane_mm, atol=2.0e-14) np.testing.assert_allclose(axis_direction_mm / 25.0, expected_normal) np.testing.assert_allclose(axis_points_mm[2], point_a) np.testing.assert_allclose(axis_plane_residuals, 0.0, atol=3.0e-14) assert axis_diagnosis_mm.classification == "line" assert axis_diagnosis_mm.coefficient_rank == 2 assert axis_diagnosis_mm.solution_dimension == 1 assert anchor_diagnosis_mm.classification == "point" assert anchor_diagnosis_mm.coefficient_rank == 3 np.testing.assert_allclose( anchor_diagnosis_mm.least_squares_point, point_a, atol=4.0e-14, ) assert membership_b.on_plane and membership_c.on_plane np.testing.assert_allclose(datum_plane_m[:3], datum_plane_mm[:3], atol=2.0e-15) np.testing.assert_allclose(datum_plane_m[3], 1.0e-3 * datum_plane_mm[3], atol=2.0e-16) assert axis_diagnosis_m.classification == axis_diagnosis_mm.classification np.testing.assert_allclose( axis_diagnosis_m.least_squares_point, 1.0e-3 * axis_diagnosis_mm.least_squares_point, atol=3.0e-16, ) assert coarse_rank.classification == "plane" assert fine_rank.classification == "line" signature_values = np.concatenate( [ datum_points_mm.ravel(), datum_plane_mm, axis_direction_mm, axis_parameters, axis_points_mm.ravel(), axis_matrix.ravel(), axis_rhs_mm, axis_diagnosis_mm.coefficient_singular_values, axis_diagnosis_mm.augmented_singular_values, full_matrix.ravel(), full_rhs_mm, anchor_diagnosis_mm.least_squares_point, datum_points_m.ravel(), datum_plane_m, axis_rhs_m, near_matrix.ravel(), near_rhs_mm, coarse_rank.coefficient_singular_values, fine_rank.coefficient_singular_values, np.array( [ rank_relative_tolerance, reference_scale_mm, perturbation, membership_b.normalized_residual, membership_c.normalized_residual, ] ), ] ) print("uzunluk_birimi:", length_unit) print("model: sentetik_cad_datum_duzlemi_ve_delik_ekseni") print("olculmus_veri_mi: False") print("uretim_toleransi_hesabi_mi: False") print("uretim_kabul_hesabi_mi: False") print("datum_noktalari_mm:") print(datum_points_mm) print("datum_duzlemi_kanonik:", datum_plane_mm) print("olceklenmis_denklem_ayni_duzlem_mi:", bool(np.allclose(scaled_plane, datum_plane_mm))) print("delik_ekseni_baslangici_mm:", point_a) print("delik_ekseni_yonu_mm:", axis_direction_mm) print("delik_ekseni_iki_duzlem_ranki:", axis_diagnosis_mm.coefficient_rank) print("delik_ekseni_cozum_boyutu:", axis_diagnosis_mm.solution_dimension) print("delik_ekseni_sinifi:", axis_diagnosis_mm.classification) print("uc_bagimsiz_duzlem_ranki:", anchor_diagnosis_mm.coefficient_rank) print("uc_bagimsiz_duzlem_sinifi:", anchor_diagnosis_mm.classification) print("tek_nokta_cozumu_mm:", anchor_diagnosis_mm.least_squares_point) print("B_ve_C_datum_duzleminde_mi:", membership_b.on_plane and membership_c.on_plane) print("metreye_geciste_normal_korundu_mu:", bool(np.allclose(datum_plane_m[:3], datum_plane_mm[:3]))) print("metreye_geciste_sabit_terim_olcegi:", f"{datum_plane_m[3] / datum_plane_mm[3]:.12f}") print("metreye_geciste_rank_sinifi_korundu_mu:", axis_diagnosis_m.classification == axis_diagnosis_mm.classification) print("yakin_bagimli_sistem_kaba_esik:", coarse_rank.classification) print("yakin_bagimli_sistem_ince_esik:", fine_rank.classification) print("rank_bagil_esigi:", f"{rank_relative_tolerance:.12e}") print("referans_uzunlugu_mm:", f"{reference_scale_mm:.12f}") print("bilimsel_imza:", canonical_array_sha256(signature_values)) if __name__ == "__main__": main()