{"id":"W2170675451","doi":"10.1115/1.2735640","title":"A Distance Metric for Finite Sets of Rigid-Body Displacements via the Polar Decomposition","year":2006,"lang":"en","type":"article","venue":"Journal of Mechanical Design","topic":"Optical measurement and interference techniques","field":"Computer Science","cited_by":32,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"National Science Foundation","keywords":"Mathematics; Polar decomposition; Singular value decomposition; Invariant (physics); Metric (unit); Embedding; Homogeneous coordinates; Rigid body; Euclidean distance; Geometry; Mathematical analysis; Rotation group SO; Measure (data warehouse); Polar coordinate system; Pure mathematics; Combinatorics; Polar; Algorithm; Physics; Computer science; Classical mechanics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001388696,0.0007518081,0.0007309421,0.002033053,0.0005540634,0.002006576,0.001002433,0.0007371932,0.001857476],"category_scores_gemma":[0.004768583,0.0003522181,0.0005543488,0.001254809,0.002374931,0.003337191,0.002242854,0.001701168,0.0006795168],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008973979,"about_ca_system_score_gemma":0.000473182,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007851117,"about_ca_topic_score_gemma":0.0005285628,"domain_scores_codex":[0.9983854,0.0004831342,0.0001573481,0.0003493503,0.0005447111,0.00007999171],"domain_scores_gemma":[0.9978483,0.000648597,0.0003799073,0.0003542067,0.0005278389,0.0002411928],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0001154775,0.00002812255,0.0006102315,0.000147271,0.000025262,0.0001289152,0.0002544969,0.03451123,0.01014107,0.8832853,0.001799719,0.06895303],"study_design_scores_gemma":[0.00001761474,0.0001937471,0.001137201,0.00009210148,0.00001901931,0.0004003003,0.0002468056,0.2208913,0.005771228,0.7500849,0.02107514,0.00007066125],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02371225,0.0004648676,0.9709954,0.0002021251,0.0001144265,0.00003897939,0.000184216,0.00007363837,0.00421419],"genre_scores_gemma":[0.3270429,0.001284346,0.6648646,0.0001960408,0.0002185104,0.0002648162,0.0007443605,0.0001810113,0.005203391],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.002033053,"threshold_uncertainty_score":0.007344246,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03462605597211024,"score_gpt":0.3023986681595397,"score_spread":0.2677726121874294,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}