Enhancement: Page breaking to avoid widow lines

[b1]

Here is a proposed patch to add functionality to the Page Spacer. 

When typesetting large quantities of markup lines, Lilypond currently does not
try to avoid widowed/orphaned lines.  Some publishers will consider this an
unacceptable typographical error. 

I have added a few lines to the Page Spacer so it avoid having a line of markup
stand by itself.  There are two cases.  Case (1) is when the last line of a
markup paragraph is the first line on a page, and then there goes the start of
another paragraph (markuplines or music).  Case (2) is when there is nothing
after that lonely last line -- in other words, the last page of the book
consists of one line of markup. 

There are probably two things one would want to add to this functionality. 
First: The penalty associated with the widow should be made configurable. 
(Setting a Scheme variable in the source score, and then reading it in
Page_spacer::calc_subproblem() where it is now hardcoded to 
BAD_SPACING_PENALTY/2?)
Second: This definition of widow is oversimplified.  The Chicago Manual talks
about orphans/widows which are *too short*.  Right now, my code does not take
line length into consideration at all.  It should look at lines_[page_start] and
compare it to some configurable threshold.  I am not sure, however, how to read
the horizontal width, as Line_details only contains the Y extent. 
Also, if we consider line lengths, then we should address orphans as well --
right now we are only avoiding widows. 

Here is the proposed patch (against latest git head):

diff --git a/lily/constrained-breaking.cc b/lily/constrained-breaking.cc
index 2fead24..f5158b1 100644
--- a/lily/constrained-breaking.cc
+++ b/lily/constrained-breaking.cc
@@ -525,4 +525,6 @@ Line_details::Line_details (Prob *pb, Output_def *paper)
   title_ = to_boolean (pb->get_property ("is-title"));
   compressed_lines_count_ = 1;
   compressed_nontitle_lines_count_ = title_ ? 0 : 1;
+  SCM scmId = pb->get_property("markup-list-id");
+  markup_list_id = SCM_INUMP(scmId)? scm_num2int(scmId, 0, NULL) : 0;
 }
diff --git a/lily/include/constrained-breaking.hh
b/lily/include/constrained-breaking.hh
index bb8a1d0..9628492 100644
--- a/lily/include/constrained-breaking.hh
+++ b/lily/include/constrained-breaking.hh
@@ -52,6 +52,7 @@ struct Line_details {
      class. */
   int compressed_lines_count_;
   int compressed_nontitle_lines_count_;
+  int markup_list_id;
 
   Line_details ()
   {
@@ -71,6 +72,7 @@ struct Line_details {
     title_ = false;
     compressed_lines_count_ = 1;
     compressed_nontitle_lines_count_ = 1;
+    markup_list_id = 0;
   }
 
   Line_details (Prob *pb, Output_def *paper);
diff --git a/lily/page-spacing.cc b/lily/page-spacing.cc
index 8919257..be5f0e7 100644
--- a/lily/page-spacing.cc
+++ b/lily/page-spacing.cc
@@ -245,6 +245,24 @@ Page_spacer::calc_subproblem (vsize page, vsize line)
            penalty += lines_[page_start-1].page_penalty_
              + (page % 2 == 0) ? lines_[page_start-1].turn_penalty_ : 0;
 
+         /* Deal with widow lines */
+         /* The penalty should be made configurable from the source score */
+         Real widow_penalty = BAD_SPACING_PENALTY/2;
+         /* Avoid having a widow before start of next paragraph */
+         if ((page_start > 0) &&
+             (page_start+1 < lines_.size()) &&
+             (lines_[page_start-1].markup_list_id) &&
+             (lines_[page_start].markup_list_id) &&
+             // do not test for lines_[page_start+1].markup_list_id --
+             //    next paragraph may not be markup
+             (lines_[page_start].markup_list_id != 
lines_[page_start+1].markup_list_id) )
+                 penalty += widow_penalty;
+         /* Avoid having a widow as the very last line of the book */
+         if ((page_start > 0) &&
+                 (page_start == lines_.size()-1) &&
+                 (lines_[page_start].markup_list_id) )
+                 penalty += widow_penalty;
+
          demerits += penalty;
          if (demerits < cur.demerits_ || page_start == line)
            {
diff --git a/lily/paper-book.cc b/lily/paper-book.cc
index 79896e6..13bd955 100644
--- a/lily/paper-book.cc
+++ b/lily/paper-book.cc
@@ -430,6 +430,11 @@ Paper_book::get_score_title (SCM header)
 }
 
 
+static int current_int = 1;
+static int get_next_int() {
+       return current_int++;
+}
+
 SCM
 Paper_book::get_system_specs ()
 {
@@ -516,6 +521,7 @@ Paper_book::get_system_specs ()
                                  paper_->self_scm (),
                                  page_properties,
                                  scm_car (s));
+         int markup_list_id = get_next_int();
          for (SCM list = texts ; scm_is_pair (list) ; list = scm_cdr (list))
            {
              SCM t = scm_car (list);
@@ -525,6 +531,8 @@ Paper_book::get_system_specs ()
                                ly_symbol2scm ("allow"));
              ps->set_property ("page-turn-permission",
                                ly_symbol2scm ("allow"));
+             ps->set_property ("markup-list-id",
+                               scm_int2num (markup_list_id));
 
              paper_system_set_stencil (ps, *unsmob_stencil (t));
              ps->set_property ("is-title", SCM_BOOL_T);