AccessType Aglen args_string average_water_column_pressure axis_type_from_string AxisType backend_to_string bedrock_surface_temperature blatter_xy_exact blatter_xy_source blatter_xz_cfbc_base blatter_xz_cfbc_exact blatter_xz_cfbc_source blatter_xz_cfbc_surface blatter_xz_exact blatter_xz_halfar_exact blatter_xz_halfar_source blatter_xz_halfar_source_base blatter_xz_halfar_source_lateral blatter_xz_halfar_source_surface blatter_xz_source blatter_xz_source_bed blatter_xz_source_surface blatter_xz_vanderveen_beta blatter_xz_vanderveen_exact blatter_xz_vanderveen_source_lateral blatter_xz_vanderveen_source_surface blatter_xz_vanderveen_thickness Box c1 c2 calendar calendar_from_file check_c_call check_consistency_epsg check_forcing_duration check_input check_petsc_call choose_backend clear_fftw_array clip combine compute_cell_areas compute_coordinates compute_corrective_velocity compute_grounded_cell_fraction compute_horizontal_spacing compute_interface_velocity compute_lat_bounds compute_latitude compute_lon_bounds compute_lon_lat compute_lon_lat_bounds compute_longitude compute_node_types compute_nprocs compute_ownership_ranges compute_strain_heating_errors computeSurfaceVelocityErrors config_from_options ConfigSettingFlag context_from_options convert_vec convert_vec copy_fftw_array count_CFL_violations create_backend create_restriction criticalW diag_metadata DiagnosticList Direction effective_change end_time ends_with enthalpy_from_temperature_cold epsg_to_cf exactFG exactP exactP_list F F fftfreq filename_add_suffix find_json_value fletcher64 floating_ice_sheet_area_fraction_name funcP g generate_mound_topography generate_trough_topography get_all_arrays get_all_values get_projection_info get_real_part get_time get_value getsb getW GlobalMax GlobalMax GlobalMax GlobalMin GlobalMin GlobalReduce GlobalReduce GlobalSum GlobalSum GlobalSum GlobalSum GlobalSum Grid_FromFile grid_transpose grid_z grounded_area_fraction grounded_ice_sheet_area_fraction_name grounding_line_flux h0 handle_fatal_errors ice_area ice_area_floating ice_area_grounded ice_bottom_surface ice_volume ice_volume_not_displacing_seawater IceModelTerminationReason increment_date init_interpolation_indexes init_step initialconditionW InitializationType integration_weights integration_weights InterpolationType intersect_ab intersect_ac intersect_bc invalid is_increasing join join_impl k label_components label_components land_ice_area_fraction_name lapse_rate_correction limit_advective_flux limit_diffusive_flux logger_from_options LoggerLevel LonLat m0 make_nonnegative_preserving MaskValue max_timestep_cfl_2d max_timestep_cfl_3d max_timestep_diffusivity member Metadata nc_type_to_pism_type NodeType operator* operator< operator== operator> ownership_ranges p3 p4 pack_json_array parse_date parse_integer parse_number part_grid_threshold_thickness pism_is_valid_calendar_name pism_type_to_nc_type print_checksum print_config print_diagnostics print_diagnostics_json print_unused_parameters print_vector print_vector printf process_extra_shortcuts process_input_options process_ts_shortcuts psteady R1 reference_date reference_date_from_file regional_grid_from_options remove_narrow_tongues replace_character report_range reportErrors reporting_max_timestep restrict_data rhoi rhow same sea_level_rise_potential secondInvariant_2D set_config_from_options set_flag_from_option set_integer_from_option set_integer_list_from_option set_join set_keyword_from_option set_no_model_strip set_no_model_yield_stress set_number_from_option set_number_list_from_option set_parameter_from_options set_real_part set_split set_string_from_option set_value setInitStateF setup_level show_usage show_usage_check_req_opts SNESScalarProblem SNESVectorProblem special_parameter SperA split square start_time step step string_is_false string_is_true string_strip string_to_backend subset_extent subset_start_and_count TEMPORARY_STRING_LENGTH timestamp total_grounding_line_flux triangle_area ts_diag_metadata TSDiagnosticList UNOType unpack_json_array upwind username_prefix v0 validate_format_string validate_range vector_max vector_min version wall_clock_hours warn_about_missing weights_piecewise_constant weights_piecewise_linear Wr write write_mapping write_run_stats

triangle_area() static double pism::triangle_area ( const Point &  a, const Point &  b, const Point &  c  ) inlinestatic Consider the right triangle A(0,0) - B(1,0) - C(0,1). Define a linear function z = a + (b - a) * x + (c - a) * y, where a, b, and c are its values at points A, B, and C, respectively. Our goal is to find the fraction of the area of ABC in where z > 0. We note that z(x,y) is continuous, so unless a, b, and c have the same sign the line z = 0 will intersect exactly two of the sides (possibly at a node of ABC). So, if the line (z = 0) does not intersect BC, for example, then it has to intersect AB and AC. This method can be applied to arbitrary triangles. It does not even matter if values at triangle nodes (a, b, c) are listed in the same order. (For any two triangles on a plane there exists an affine map that takes one to the other. Also, affine maps preserve ratios of areas of figures.) Compute the area of a triangle on a plane using the "shoelace formula." Definition at line 62 of file grounded_cell_fraction.cc. References pism::Point::x, and pism::Point::y. Referenced by grounded_area_fraction().