{"id":"W2055042442","doi":"10.1137/s0097539705447116","title":"Lines and Free Line Segments Tangent to Arbitrary Three-Dimensional Convex Polyhedra","year":2007,"lang":"en","type":"article","venue":"SIAM Journal on Computing","topic":"Computational Geometry and Mesh Generation","field":"Computer Science","cited_by":21,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"","keywords":"Polyhedron; Combinatorics; Tangent; Polytope; Regular polygon; Convex polytope; Mathematics; Line (geometry); Convex set; Connected component; Tangent space; Line segment; Convex hull; Integer points in convex polyhedra; Geometry; Algorithm; Linear programming; Convex optimization","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001169171,0.0001818558,0.0001901153,0.0003493592,0.0004265783,0.000237674,0.0004465527,0.00005619168,0.0000157446],"category_scores_gemma":[0.000108774,0.0001635322,0.00006795661,0.0004772508,0.00002238099,0.0002414012,0.0003647681,0.0003309054,0.00002770845],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006200888,"about_ca_system_score_gemma":0.00008993496,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004293262,"about_ca_topic_score_gemma":0.000008578267,"domain_scores_codex":[0.9982019,0.0000506914,0.0004635509,0.0003355983,0.0005877573,0.00036047],"domain_scores_gemma":[0.9987259,0.0003053179,0.0001826554,0.0002288267,0.0002028929,0.0003543984],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0002059225,0.0005048725,0.004271883,0.00003736706,0.0001722025,0.0007181959,0.0009460867,0.1333764,0.01177966,0.02870337,0.007648102,0.811636],"study_design_scores_gemma":[0.002849364,0.001713572,0.07951065,0.0004763155,0.00002538778,0.002457146,0.00004181749,0.8696003,0.01612052,0.01727703,0.008962304,0.0009655943],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.406796,0.00033653,0.5893268,0.002073908,0.001079124,0.00009359287,0.00000124875,0.00004834328,0.000244458],"genre_scores_gemma":[0.8043618,0.000005022168,0.1899493,0.004116034,0.001463061,4.979536e-7,0.000003191162,0.00001144309,0.00008965184],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8106704,"threshold_uncertainty_score":0.6668649,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02032279949089591,"score_gpt":0.2772758534224866,"score_spread":0.2569530539315907,"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."}}