X-Git-Url: https://git.donarmstrong.com/?a=blobdiff_plain;f=lily%2Ftuplet-bracket.cc;h=29d9916497baa66a0a9f3a47acb6633fda11b5e3;hb=26380ed75fbd7b32781715c043dfa5dd96dfbe4a;hp=bfcc48bfdb3e160938ba1c05b5db9e4babe600a0;hpb=da5ebcb20a260914bc71260f68c38559a344016c;p=lilypond.git diff --git a/lily/tuplet-bracket.cc b/lily/tuplet-bracket.cc index bfcc48bfdb..29d9916497 100644 --- a/lily/tuplet-bracket.cc +++ b/lily/tuplet-bracket.cc @@ -1,9 +1,10 @@ /* - plet-spanner.cc -- implement Tuplet_bracket + tuplet-bracket.cc -- implement Tuplet_bracket source file of the GNU LilyPond music typesetter - (c) 1997--2002 Jan Nieuwenhuizen + (c) 1997--2005 Jan Nieuwenhuizen + Han-Wen Nienhuys */ /* @@ -15,23 +16,28 @@ - There is no support for kneed brackets, or nested brackets. - number placement for parallel beams should be much more advanced: - for sloped beams some extra horizontal offset must be introduced. + for sloped beams some extra horizontal offset must be introduced. - number placement is usually done over the center note, not the - graphical center. - - */ + graphical center. +*/ + +/* + TODO: quantise, we don't want to collide with staff lines. + (or should we be above staff?) + + todo: handle breaking elegantly. +*/ #include +#include "tuplet-bracket.hh" +#include "line-interface.hh" #include "beam.hh" -#include "box.hh" -#include "debug.hh" +#include "warn.hh" #include "font-interface.hh" -#include "molecule.hh" -#include "paper-def.hh" -#include "text-item.hh" -#include "tuplet-bracket.hh" +#include "output-def.hh" +#include "text-interface.hh" #include "stem.hh" #include "note-column.hh" #include "group-interface.hh" @@ -40,421 +46,488 @@ #include "staff-symbol-referencer.hh" #include "lookup.hh" - -static Real -get_x_offset (Grob *g, Grob *common, Direction my_dir) +static Grob * +get_x_bound_grob (Grob *g, Direction my_dir) { - if (Note_column::stem_l (g) + if (Note_column::get_stem (g) && Note_column::dir (g) == my_dir) { - g = Note_column::stem_l (g); + g = Note_column::get_stem (g); } - return g->relative_coordinate (common, X_AXIS); + return g; } - - -Grob* -Tuplet_bracket::parallel_beam (Grob *me, Link_array cols, bool *equally_long) +Grob * +Tuplet_bracket::parallel_beam (Grob *me, Link_array const &cols, bool *equally_long) { /* - ugh: code dup. + ugh: code dup. */ - Grob *s1 = Note_column::stem_l (cols[0]); - Grob *s2 = Note_column::stem_l (cols.top()); + Grob *s1 = Note_column::get_stem (cols[0]); + Grob *s2 = Note_column::get_stem (cols.top ()); - Grob*b1 = s1 ? Stem::beam_l (s1) : 0; - Grob*b2 = s2 ? Stem::beam_l (s2) : 0; - - Spanner*sp = dynamic_cast (me); + Grob *b1 = s1 ? Stem::get_beam (s1) : 0; + Grob *b2 = s2 ? Stem::get_beam (s2) : 0; - *equally_long= false; - if (! ( b1 && (b1 == b2) && !sp->broken_b() )) - return 0; + Spanner *sp = dynamic_cast (me); + + *equally_long = false; + if (! (b1 && (b1 == b2) && !sp->is_broken ())) + return 0; - Link_array beam_stems = Pointer_group_interface__extract_grobs - (b1, (Grob*)0, "stems"); + Link_array beam_stems = extract_grob_array (b1, ly_symbol2scm ("stems")); + if (beam_stems.size () == 0) + { + programming_error ("beam under tuplet bracket has no stems"); + *equally_long = 0; + return 0; + } - - *equally_long = (beam_stems[0] == s1 && beam_stems.top() == s2); + *equally_long = (beam_stems[0] == s1 && beam_stems.top () == s2); return b1; } - /* TODO: in the case that there is no bracket, but there is a (single) beam, follow beam precisely for determining tuplet number location. - - */ -MAKE_SCHEME_CALLBACK (Tuplet_bracket,brew_molecule,1); +*/ +MAKE_SCHEME_CALLBACK (Tuplet_bracket, print, 1); SCM -Tuplet_bracket::brew_molecule (SCM smob) +Tuplet_bracket::print (SCM smob) { - Grob *me= unsmob_grob (smob); - Molecule mol; - Link_array column_arr= - Pointer_group_interface__extract_grobs (me, (Grob*)0, "note-columns"); + Grob *me = unsmob_grob (smob); + Stencil mol; + Link_array columns + = extract_grob_array (me, ly_symbol2scm ("note-columns")); - if (!column_arr.size ()) + if (!columns.size ()) return mol.smobbed_copy (); + { + SCM lp = me->get_property ("left-position"); + SCM rp = me->get_property ("right-position"); + + if (!scm_is_number (rp) || !scm_is_number (lp)) + after_line_breaking (smob); + } + + Real ly = robust_scm2double (me->get_property ("left-position"), 0); + Real ry = robust_scm2double (me->get_property ("right-position"), 0); + bool equally_long = false; - Grob * par_beam = parallel_beam (me, column_arr, &equally_long); + Grob *par_beam = parallel_beam (me, columns, &equally_long); - Spanner*sp = dynamic_cast (me); + Spanner *sp = dynamic_cast (me); bool bracket_visibility = !(par_beam && equally_long); bool number_visibility = true; /* Fixme: the type of this prop is sucky. - */ - SCM bracket = me->get_grob_property ("bracket-visibility"); - if (gh_boolean_p (bracket)) + */ + SCM bracket = me->get_property ("bracket-visibility"); + if (scm_is_bool (bracket)) { - bracket_visibility = gh_scm2bool (bracket); + bracket_visibility = ly_scm2bool (bracket); } else if (bracket == ly_symbol2scm ("if-no-beam")) bracket_visibility = !par_beam; - SCM numb = me->get_grob_property ("number-visibility"); - if (gh_boolean_p (numb)) + SCM numb = me->get_property ("number-visibility"); + if (scm_is_bool (numb)) { - number_visibility = gh_scm2bool (numb); + number_visibility = ly_scm2bool (numb); } else if (numb == ly_symbol2scm ("if-no-beam")) number_visibility = !par_beam; - - Grob * commonx = column_arr[0]->common_refpoint (column_arr.top (),X_AXIS); - Direction dir = Directional_element_interface::get (me); - - Real x0 = get_x_offset (column_arr[0], commonx, dir); - Real x1 = get_x_offset (column_arr.top(), commonx, dir); + + Grob *commonx = columns[0]->common_refpoint (columns.top (), X_AXIS); + + /* + Tuplet brackets are normally not broken, but we shouldn't crash if + they are. + */ + commonx = commonx->common_refpoint (sp->get_bound (LEFT), X_AXIS); + commonx = commonx->common_refpoint (sp->get_bound (RIGHT), X_AXIS); + + Direction dir = get_grob_direction (me); + + Grob *lgr = get_x_bound_grob (columns[0], dir); + Grob *rgr = get_x_bound_grob (columns.top (), dir); + + Real x0 = robust_relative_extent (lgr, commonx, X_AXIS)[LEFT]; + Real x1 = robust_relative_extent (rgr, commonx, X_AXIS)[RIGHT]; Real w = x1 -x0; - Real ly = gh_scm2double (me->get_grob_property ("left-position")); - Real ry = gh_scm2double (me->get_grob_property ("right-position")); - SCM number = me->get_grob_property ("text"); - - if (gh_string_p (number) && number_visibility) + SCM number = me->get_property ("text"); + + Output_def *pap = me->get_layout (); + Stencil num; + if (scm_is_string (number) && number_visibility) { - SCM properties = Font_interface::font_alist_chain (me); - Molecule num = Text_item::text2molecule (me, number, properties); + SCM properties = Font_interface::text_font_alist_chain (me); + SCM snum = Text_interface::interpret_markup (pap->self_scm (), properties, number); + num = *unsmob_stencil (snum); num.align_to (X_AXIS, CENTER); - num.translate_axis (w/2, X_AXIS); + num.translate_axis (w / 2, X_AXIS); num.align_to (Y_AXIS, CENTER); - - num.translate_axis ((ry-ly)/2, Y_AXIS); - mol.add_molecule (num); + num.translate_axis ((ry - ly) / 2, Y_AXIS); + + mol.add_stencil (num); } - - if (bracket_visibility) + + /* + No bracket when it would be smaller than the number. + + TODO: should use GAP in calculation too. + */ + if (bracket_visibility && number_visibility + && mol.extent (X_AXIS).length () > w) + { + bracket_visibility = false; + } + + if (bracket_visibility) { - Real lt = me->paper_l ()->get_var ("linethickness"); - - SCM thick = me->get_grob_property ("thickness"); - if (gh_number_p (thick)) - lt *= gh_scm2double (thick); - - SCM gap = me->get_grob_property ("gap"); - - Real prot_size = 0.7; // magic. - - Molecule brack = make_bracket (Y_AXIS, - w, ry-ly, lt, - -prot_size*dir, -prot_size*dir, - gh_scm2double (gap), - 0.0, 0.0); - mol.add_molecule (brack); + Real ss = Staff_symbol_referencer::staff_space (me); + Real gap = 0.; + + if (!num.extent (X_AXIS).is_empty ()) + gap = num.extent (X_AXIS).length () + 1.0; + + SCM fl = me->get_property ("bracket-flare"); + SCM eh = me->get_property ("edge-height"); + SCM sp = me->get_property ("shorten-pair"); + + Direction d = LEFT; + Drul_array height, flare, shorten; + do + { + flare[d] = height[d] = shorten[d] = 0.0; + if (is_number_pair (fl)) + flare[d] += ss * scm_to_double (index_get_cell (fl, d)); + if (is_number_pair (eh)) + height[d] += -dir * ss * scm_to_double (index_get_cell (eh, d)); + if (is_number_pair (sp)) + shorten[d] += ss * scm_to_double (index_get_cell (sp, d)); + } + while (flip (&d) != LEFT); + + Stencil brack = make_bracket (me, Y_AXIS, + Offset (w, ry - ly), + height, + /* + 0.1 = more space at right due to italics + TODO: use italic correction of font. + */ + Interval (-0.5, 0.5) * gap + 0.1, + flare, shorten); + mol.add_stencil (brack); } mol.translate_axis (ly, Y_AXIS); - mol.translate_axis (x0 - sp->get_bound (LEFT)->relative_coordinate (commonx,X_AXIS),X_AXIS); + mol.translate_axis (x0 - sp->get_bound (LEFT)->relative_coordinate (commonx, X_AXIS), X_AXIS); return mol.smobbed_copy (); } /* should move to lookup? - */ -Molecule -Tuplet_bracket::make_bracket (Axis protusion_axis, - Real dx, Real dy, Real thick, Real lprotrusion, - Real rprotrusion, Real gap, Real left_widen, - Real right_widen) + + TODO: this will fail for very short (shorter than the flare) + brackets. +*/ +Stencil +Tuplet_bracket::make_bracket (Grob *me, // for line properties. + Axis protusion_axis, + Offset dz, + Drul_array height, + Interval gap, + Drul_array flare, + Drul_array shorten) { - Real len = Offset (dx,dy).length (); - Real gapx = dx* (gap / len); - Real gapy = dy* (gap / len); - Axis other = other_axis (protusion_axis); - - Molecule l1 = Lookup::line (thick, Offset(0,0), - Offset ( (dx - gapx)/2, (dy - gapy)/2 )); - Molecule l2 = Lookup::line (thick, Offset((dx + gapx) / 2,(dy + gapy) / 2), - - Offset (dx,dy)); - - Offset protusion; - protusion[other] = left_widen; - protusion[protusion_axis] = lprotrusion; - - Molecule p1 = Lookup::line (thick, Offset(0,0), protusion); - - protusion[other] = right_widen; - protusion[protusion_axis] = rprotrusion; - Molecule p2 = Lookup::line (thick, Offset(dx,dy),Offset(dx,dy) + protusion); - - - Molecule m; - m.add_molecule (p1); - m.add_molecule (p2); - m.add_molecule (l1); - m.add_molecule (l2); - - return m; -} + Drul_array corners (Offset (0, 0), dz); + Real length = dz.length (); + Drul_array gap_corners; + + Axis bracket_axis = other_axis (protusion_axis); + + Drul_array straight_corners = corners; + + Direction d = LEFT; + do + { + straight_corners[d] += -d * shorten[d] / length * dz; + } + while (flip (&d) != LEFT); + + if (gap.is_empty ()) + gap = Interval (0, 0); + do + { + gap_corners[d] = (dz * 0.5) + gap[d] / length * dz; + } + while (flip (&d) != LEFT); + + Drul_array flare_corners = straight_corners; + do + { + flare_corners[d][bracket_axis] = straight_corners[d][bracket_axis]; + flare_corners[d][protusion_axis] += height[d]; + straight_corners[d][bracket_axis] += -d * flare[d]; + } + while (flip (&d) != LEFT); + + Stencil m; + do + { + m.add_stencil (Line_interface::line (me, straight_corners[d], + gap_corners[d])); + + m.add_stencil (Line_interface::line (me, straight_corners[d], + flare_corners[d])); + } + while (flip (&d) != LEFT); + + return m; +} /* use first -> last note for slope, and then correct for disturbing notes in between. */ void -Tuplet_bracket::calc_position_and_height (Grob*me,Real *offset, Real * dy) +Tuplet_bracket::calc_position_and_height (Grob *me, Real *offset, Real *dy) { - Link_array column_arr= - Pointer_group_interface__extract_grobs (me, (Grob*)0, "note-columns"); + Link_array columns + = extract_grob_array (me, ly_symbol2scm ("note-columns")); + + SCM cols = me->get_property ("note-columns"); + Grob *commony = common_refpoint_of_list (cols, me, Y_AXIS); + Grob *commonx = common_refpoint_of_list (cols, me, X_AXIS); + Interval staff; + if (Grob *st = Staff_symbol_referencer::get_staff_symbol (me)) + staff = st->extent (commony, Y_AXIS); - Grob * commony = me->common_refpoint (me->get_grob_property ("note-columns"), Y_AXIS); - Grob * commonx = me->common_refpoint (me->get_grob_property ("note-columns"), X_AXIS); - - Direction d = Directional_element_interface::get (me); + Direction dir = get_grob_direction (me); /* Use outer non-rest columns to determine slope - */ + */ int l = 0; - while (l = l && Note_column::rest_b (column_arr[r])) + int r = columns.size ()- 1; + while (r >= l && Note_column::has_rests (columns[r])) r--; - + if (l < r) { - *dy = column_arr[r]->extent (commony, Y_AXIS) [d] - - column_arr[l]->extent (commony, Y_AXIS) [d] ; + Interval rv = columns[r]->extent (commony, Y_AXIS); + Interval lv = columns[l]->extent (commony, Y_AXIS); + rv.unite (staff); + lv.unite (staff); + Real graphical_dy = rv[dir] - lv[dir]; + + Slice ls = Note_column::head_positions_interval (columns[l]); + Slice rs = Note_column::head_positions_interval (columns[r]); + + Interval musical_dy; + musical_dy[UP] = rs[UP] - ls[UP]; + musical_dy[DOWN] = rs[DOWN] - ls[DOWN]; + if (sign (musical_dy[UP]) != sign (musical_dy[DOWN])) + *dy = 0.0; + else if (sign (graphical_dy) != sign (musical_dy[DOWN])) + *dy = 0.0; + else + *dy = graphical_dy; } else * dy = 0; + *offset = -dir * infinity_f; - *offset = - d * infinity_f; - - if (!column_arr.size ()) + if (!columns.size ()) return; + Grob *lgr = get_x_bound_grob (columns[0], dir); + Grob *rgr = get_x_bound_grob (columns.top (), dir); + Real x0 = robust_relative_extent (lgr, commonx, X_AXIS)[LEFT]; + Real x1 = robust_relative_extent (rgr, commonx, X_AXIS)[RIGHT]; - - Real x0 = get_x_offset (column_arr[0], commonx, d); - Real x1 = get_x_offset (column_arr.top(), commonx, d); + /* + Slope. + */ + Real factor = columns.size () > 1 ? 1 / (x1 - x0) : 1.0; - /* - Slope. - */ - Real factor = column_arr.size () > 1 ? 1/ (x1 - x0) : 1.0; - - for (int i = 0; i < column_arr.size (); i++) + for (int i = 0; i < columns.size (); i++) { - Real notey = column_arr[i]->extent (commony, Y_AXIS)[d] - - me->relative_coordinate (commony, Y_AXIS); + Interval note_ext = columns[i]->extent (commony, Y_AXIS); + note_ext.unite (staff); + Real notey = note_ext[dir] - me->relative_coordinate (commony, Y_AXIS); - Real x = column_arr[i]->relative_coordinate (commonx, X_AXIS) - x0; - Real tuplety = *dy * x * factor; + Real x = columns[i]->relative_coordinate (commonx, X_AXIS) - x0; + Real tuplety = *dy * x * factor; - if (notey * d > (*offset + tuplety) * d) - *offset = notey - tuplety; + if (notey * dir > (*offset + tuplety) * dir) + *offset = notey - tuplety; } // padding - *offset += gh_scm2double (me->get_grob_property ("padding")) *d; + *offset += scm_to_double (me->get_property ("padding")) * dir; - /* horizontal brackets should not collide with staff lines. - */ - if (*dy == 0) + + */ + Real ss = Staff_symbol_referencer::staff_space (me); + if (*dy == 0 && fabs (*offset) < ss * Staff_symbol_referencer::staff_radius (me)) { // quantize, then do collision check. - Real ss= Staff_symbol_referencer::staff_space (me); *offset *= 2 / ss; - + *offset = rint (*offset); if (Staff_symbol_referencer::on_staffline (me, (int) rint (*offset))) - *offset += d; + *offset += dir; *offset *= 0.5 * ss; } - } -/* - use first -> last note for slope, -*/ -void -Tuplet_bracket::calc_dy (Grob*me,Real * dy) -{ - Link_array column_arr= - Pointer_group_interface__extract_grobs (me, (Grob*)0, "note-columns"); - - /* - ugh. refps. - */ - Direction d = Directional_element_interface::get (me); - *dy = column_arr.top ()->extent (column_arr.top (), Y_AXIS) [d] - - column_arr[0]->extent (column_arr[0], Y_AXIS) [d]; -} - - /* We depend on the beams if there are any. - */ -MAKE_SCHEME_CALLBACK (Tuplet_bracket,before_line_breaking,1); +*/ +MAKE_SCHEME_CALLBACK (Tuplet_bracket, before_line_breaking, 1); SCM Tuplet_bracket::before_line_breaking (SCM smob) { Grob *me = unsmob_grob (smob); - Link_array column_arr= - Pointer_group_interface__extract_grobs (me, (Grob*)0, "note-columns"); + Link_array columns + = extract_grob_array (me, ly_symbol2scm ("note-columns")); - - for (int i = column_arr.size(); i--;) + for (int i = columns.size (); i--;) { - Grob * s =Note_column::stem_l (column_arr[i]); - Grob * b = s ? Stem::beam_l (s): 0; + Grob *s = Note_column::get_stem (columns[i]); + Grob *b = s ? Stem::get_beam (s) : 0; if (b) me->add_dependency (b); } - return SCM_UNDEFINED; + return SCM_UNSPECIFIED; } -MAKE_SCHEME_CALLBACK (Tuplet_bracket,after_line_breaking,1); +MAKE_SCHEME_CALLBACK (Tuplet_bracket, after_line_breaking, 1); SCM Tuplet_bracket::after_line_breaking (SCM smob) { - Grob * me = unsmob_grob (smob); - Link_array column_arr= - Pointer_group_interface__extract_grobs (me, (Grob*)0, "note-columns"); + Grob *me = unsmob_grob (smob); + Link_array columns + = extract_grob_array (me, ly_symbol2scm ("note-columns")); - if (!column_arr.size ()) + if (!columns.size ()) { me->suicide (); return SCM_UNSPECIFIED; } - if (dynamic_cast (me)->broken_b ()) + if (dynamic_cast (me)->is_broken ()) { - me->warning ( "Tuplet_bracket was across linebreak. Farewell cruel world."); - me->suicide(); + me->warning (_ ("removing tuplet bracket across linebreak")); + me->suicide (); return SCM_UNSPECIFIED; } - - Direction dir = Directional_element_interface::get (me); + + Direction dir = get_grob_direction (me); if (!dir) { dir = Tuplet_bracket::get_default_dir (me); - Directional_element_interface::set (me, dir); + set_grob_direction (me, dir); } - + bool equally_long = false; - Grob * par_beam = parallel_beam (me, column_arr, &equally_long); + Grob *par_beam = parallel_beam (me, columns, &equally_long); + /* + We follow the beam only if there is one, and we are next to it. + */ Real dy, offset; - if (!par_beam) + if (!par_beam + || get_grob_direction (par_beam) != dir) { - calc_position_and_height (me,&offset,&dy); + calc_position_and_height (me, &offset, &dy); } else { - SCM ps = par_beam->get_grob_property ("positions"); + SCM ps = par_beam->get_property ("positions"); - Real lp = gh_scm2double (gh_car (ps)); - Real rp = gh_scm2double (gh_cdr (ps)); + Real lp = scm_to_double (scm_car (ps)); + Real rp = scm_to_double (scm_cdr (ps)); /* duh. magic. - */ - offset = lp + dir * (0.5 + gh_scm2double (me->get_grob_property ("padding"))); + */ + offset = lp + dir * (0.5 + scm_to_double (me->get_property ("padding"))); dy = rp- lp; } - - - SCM lp = me->get_grob_property ("left-position"); - SCM rp = me->get_grob_property ("right-position"); - - if (gh_number_p (lp) && !gh_number_p (rp)) + + SCM lp = me->get_property ("left-position"); + SCM rp = me->get_property ("right-position"); + + if (scm_is_number (lp) && !scm_is_number (rp)) { - rp = gh_double2scm (gh_scm2double (lp) + dy); + rp = scm_make_real (scm_to_double (lp) + dy); } - else if (gh_number_p (rp) && !gh_number_p (lp)) + else if (scm_is_number (rp) && !scm_is_number (lp)) { - lp = gh_double2scm (gh_scm2double (rp) - dy); + lp = scm_make_real (scm_to_double (rp) - dy); } - else if (!gh_number_p (rp) && !gh_number_p (lp)) + else if (!scm_is_number (rp) && !scm_is_number (lp)) { - lp = gh_double2scm (offset); - rp = gh_double2scm (offset +dy); + lp = scm_make_real (offset); + rp = scm_make_real (offset + dy); } - me->set_grob_property ("left-position", lp); - me->set_grob_property ("right-position", rp); + me->set_property ("left-position", lp); + me->set_property ("right-position", rp); return SCM_UNSPECIFIED; } - /* - similar to slur. - */ + similar to beam ? +*/ Direction -Tuplet_bracket::get_default_dir (Grob*me) +Tuplet_bracket::get_default_dir (Grob *me) { - Direction d = UP; - for (SCM s = me->get_grob_property ("note-columns"); gh_pair_p (s); s = ly_cdr (s)) + Drul_array dirs (0, 0); + for (SCM s = me->get_property ("note-columns"); scm_is_pair (s); s = scm_cdr (s)) { - Grob * nc = unsmob_grob (ly_car (s)); - if (Note_column::dir (nc) < 0) - { - d = DOWN; - break; - } + Grob *nc = unsmob_grob (scm_car (s)); + Direction d = Note_column::dir (nc); + if (d) + dirs[d]++; } - return d; + + return dirs[UP] >= dirs[DOWN] ? UP : DOWN; } void -Tuplet_bracket::add_column (Grob*me, Item*n) +Tuplet_bracket::add_column (Grob *me, Item *n) { Pointer_group_interface::add_grob (me, ly_symbol2scm ("note-columns"), n); me->add_dependency (n); - add_bound_item (dynamic_cast (me), n); + add_bound_item (dynamic_cast (me), n); } +ADD_INTERFACE (Tuplet_bracket, + "tuplet-bracket-interface", + "A bracket with a number in the middle, used for tuplets.", -bool -Tuplet_bracket::has_interface (Grob*me) -{ - return me->has_interface (ly_symbol2scm ("tuplet-bracket-interface")); -} - - - - -ADD_INTERFACE (Tuplet_bracket,"tuplet-bracket-interface", - "A bracket with a number in the middle, used for tuplets.", - "note-columns padding gap left-position right-position bracket-visibility number-visibility thickness direction"); + "note-columns bracket-flare edge-height shorten-pair " + "padding left-position right-position bracket-visibility " + "number-visibility thickness direction");