"""Bölüm 19: uzayda kesişim, açı, izdüşüm ve uzaklık laboratuvarı. Uygulama sentetik bir CAD datum düzlemi, delik ekseni ve ikinci doğru adayını sınar. Ölçülmüş veri, üretim toleransı veya kabul kararı içermez. """ from __future__ import annotations import numpy as np from agbook import ( canonical_array_sha256, line_line_diagnostics_3d, line_plane_diagnostics_3d, plane_plane_diagnostics_3d, project_point_to_line_3d, project_point_to_plane_3d, ) def main() -> None: length_unit = "mm" angular_tolerance = 1.0e-12 absolute_tolerance_mm = 1.0e-9 relative_tolerance = 1.0e-12 reference_scale_mm = 200.0 relation_options = { "angular_tolerance": angular_tolerance, "absolute_tolerance": absolute_tolerance_mm, "relative_tolerance": relative_tolerance, "reference_scale": reference_scale_mm, } point_a = np.array([120.0, 80.0, 35.0]) axis_direction = np.array([16.0, -12.0, 15.0]) point_q = np.array([115.2, 83.6, 43.0]) second_direction = np.array([12.0, 16.0, 0.0]) connector = point_q - point_a datum_plane = np.array([0.64, -0.48, 0.60, -59.4]) first_axis_normal = np.array([0.60, 0.80, 0.0]) second_axis_normal = np.array([-0.48, 0.36, 0.80]) first_axis_plane = np.append(first_axis_normal, -first_axis_normal @ point_a) second_axis_plane = np.append(second_axis_normal, -second_axis_normal @ point_a) line_pair = line_line_diagnostics_3d( point_a, axis_direction, point_q, second_direction, **relation_options, ) q_on_axis_projection = project_point_to_line_3d( point_a, axis_direction, point_q, ) a_on_second_projection = project_point_to_line_3d( point_q, second_direction, point_a, ) axis_datum = line_plane_diagnostics_3d( point_a, axis_direction, datum_plane, **relation_options, ) second_datum = line_plane_diagnostics_3d( point_q, second_direction, datum_plane, **relation_options, ) axis_plane_pair = plane_plane_diagnostics_3d( first_axis_plane, second_axis_plane, **relation_options, ) probe_point = point_a + 12.0 * datum_plane[:3] probe_projection = project_point_to_plane_3d(datum_plane, probe_point) scale = 1.0e-3 metre_options = { "angular_tolerance": angular_tolerance, "absolute_tolerance": scale * absolute_tolerance_mm, "relative_tolerance": relative_tolerance, "reference_scale": scale * reference_scale_mm, } metre_pair = line_line_diagnostics_3d( scale * point_a, scale * axis_direction, scale * point_q, scale * second_direction, **metre_options, ) loose_near_parallel = line_line_diagnostics_3d( [0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [1.0, 1.0e-8, 0.0], angular_tolerance=1.0e-7, absolute_tolerance=1.0e-7, relative_tolerance=0.0, reference_scale=1.0, ) strict_near_parallel = line_line_diagnostics_3d( [0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [1.0, 1.0e-8, 0.0], angular_tolerance=1.0e-10, absolute_tolerance=1.0e-7, relative_tolerance=0.0, reference_scale=1.0, ) np.testing.assert_allclose(np.dot(connector, axis_direction), 0.0, atol=3.0e-13) np.testing.assert_allclose(np.dot(connector, second_direction), 0.0, atol=3.0e-13) assert line_pair.relation == "skew" np.testing.assert_allclose(line_pair.closest_point_first, point_a, atol=3.0e-14) np.testing.assert_allclose(line_pair.closest_point_second, point_q, atol=3.0e-14) np.testing.assert_allclose(line_pair.distance, 10.0, atol=2.0e-14) np.testing.assert_allclose(q_on_axis_projection.foot, point_a, atol=3.0e-14) np.testing.assert_allclose(a_on_second_projection.foot, point_q, atol=3.0e-14) assert axis_datum.relation == "intersecting" np.testing.assert_allclose(axis_datum.intersection_point, point_a, atol=2.0e-14) assert second_datum.relation == "contained" assert axis_plane_pair.relation == "intersecting" np.testing.assert_allclose( axis_plane_pair.line_direction, axis_direction / np.linalg.norm(axis_direction), atol=2.0e-15, ) np.testing.assert_allclose(probe_projection.foot, point_a, atol=3.0e-14) np.testing.assert_allclose(probe_projection.signed_distance, 12.0, atol=2.0e-14) assert metre_pair.relation == line_pair.relation np.testing.assert_allclose(metre_pair.distance, scale * line_pair.distance, atol=3.0e-17) assert loose_near_parallel.relation == "parallel" assert loose_near_parallel.numerically_ambiguous assert strict_near_parallel.relation == "intersecting" assert strict_near_parallel.condition_number > 1.0e8 signature_values = np.concatenate( [ point_a, axis_direction, point_q, second_direction, connector, datum_plane, first_axis_plane, second_axis_plane, line_pair.closest_point_first, line_pair.closest_point_second, line_pair.separation_vector, np.array( [ line_pair.distance, line_pair.small_angle, line_pair.condition_number, q_on_axis_projection.distance, a_on_second_projection.distance, axis_datum.line_plane_angle, second_datum.signed_anchor_distance, axis_plane_pair.small_angle, probe_projection.signed_distance, metre_pair.distance, loose_near_parallel.condition_number, strict_near_parallel.condition_number, angular_tolerance, absolute_tolerance_mm, relative_tolerance, reference_scale_mm, ] ), ] ) print("uzunluk_birimi:", length_unit) print("model: sentetik_cad_aykiri_dogrular_ve_datum_duzlemi") print("olculmus_veri_mi: False") print("uretim_toleransi_hesabi_mi: False") print("uretim_kabul_hesabi_mi: False") print("dogru_dogru_sinifi:", line_pair.relation) print("en_yakin_birinci_nokta_mm:", line_pair.closest_point_first) print("en_yakin_ikinci_nokta_mm:", line_pair.closest_point_second) print("ortak_dikme_uzunlugu_mm:", f"{line_pair.distance:.12f}") print("dogru_dogru_kucuk_aci_derece:", f"{np.degrees(line_pair.small_angle):.12f}") print("Q_noktasinin_eksen_izdusumu_mm:", q_on_axis_projection.foot) print("A_noktasinin_ikinci_dogru_izdusumu_mm:", a_on_second_projection.foot) print("delik_ekseni_datum_iliskisi:", axis_datum.relation) print("ikinci_dogru_datum_iliskisi:", second_datum.relation) print("eksen_duzlemleri_iliskisi:", axis_plane_pair.relation) print("eksen_duzlemleri_kesisim_yonu:", axis_plane_pair.line_direction) print("sonda_nokta_datum_uzakligi_mm:", f"{probe_projection.distance:.12f}") print("metreye_geciste_sinif_korundu_mu:", metre_pair.relation == line_pair.relation) print("metreye_geciste_uzaklik_orani:", f"{metre_pair.distance / line_pair.distance:.12f}") print("yakin_paralel_kaba_esik:", loose_near_parallel.relation) print("yakin_paralel_ince_esik:", strict_near_parallel.relation) print("yakin_paralel_kosul_sayisi:", f"{strict_near_parallel.condition_number:.6e}") print("acisal_esik:", f"{angular_tolerance:.12e}") print("mutlak_uzaklik_esigi_mm:", f"{absolute_tolerance_mm:.12e}") print("bagil_uzaklik_esigi:", f"{relative_tolerance:.12e}") print("referans_uzunlugu_mm:", f"{reference_scale_mm:.12f}") print("bilimsel_imza:", canonical_array_sha256(signature_values)) if __name__ == "__main__": main()