2 page-spacing.cc - implement routines for spacing
3 systems vertically on pages
5 source file of the GNU LilyPond music typesetter
7 (c) 2006 Joe Neeman <joeneeman@gmail.com>
10 #include "page-spacing.hh"
14 A much simplified rods-and-springs problem.
22 Real inverse_spring_k_;
24 Line_details last_line_;
26 Page_spacing (Real page_height)
28 page_height_ = page_height;
34 void append_system (const Line_details &line);
35 void prepend_system (const Line_details &line);
40 Page_spacing::calc_force ()
42 if (rod_height_ + last_line_.bottom_padding_ >= page_height_ || !inverse_spring_k_)
45 force_ = (page_height_ - rod_height_ - last_line_.bottom_padding_ - spring_len_) / inverse_spring_k_;
49 Page_spacing::append_system (const Line_details &line)
51 rod_height_ += last_line_.padding_;
53 rod_height_ += line.extent_.length ();
54 spring_len_ += line.space_;
55 inverse_spring_k_ += line.inverse_hooke_;
63 Page_spacing::prepend_system (const Line_details &line)
66 rod_height_ += line.padding_;
70 rod_height_ += line.extent_.length ();
71 spring_len_ += line.space_;
72 inverse_spring_k_ += line.inverse_hooke_;
78 Page_spacing::clear ()
80 force_ = rod_height_ = spring_len_ = 0;
81 inverse_spring_k_ = 0;
84 /* for each forbidden page break, merge the systems around it into one system. */
85 static vector<Line_details>
86 compress_lines (const vector<Line_details> &orig)
88 vector<Line_details> ret;
90 for (vsize i = 0; i < orig.size (); i++)
92 if (i < orig.size () - 1 && orig[i].page_permission_ == SCM_EOL)
94 Line_details compressed = orig[i+1];
95 compressed.extent_[DOWN] = orig[i].extent_[DOWN];
96 compressed.extent_[UP] = orig[i].extent_[UP] + orig[i+1].extent_.length () + orig[i].padding_;
97 compressed.space_ += orig[i].space_;
98 compressed.inverse_hooke_ += orig[i].inverse_hooke_;
100 /* we don't need the force_ field for the vertical spacing,
101 so we use force_ = -1 to signal that the line was compressed
102 (and force_ = +1 otherwise).
103 This makes uncompression much easier. */
104 compressed.force_ = -1;
105 ret.push_back (compressed);
110 ret.push_back (orig[i]);
111 ret.back ().force_ = 1;
117 /* translate the number of systems-per-page into something meaningful for
118 the uncompressed lines.
121 uncompress_solution (vector<vsize> const &systems_per_page,
122 vector<Line_details> const &compressed)
127 for (vsize i = 0; i < systems_per_page.size (); i++)
129 int compressed_count = 0;
130 for (vsize j = start_sys; j < start_sys + systems_per_page[i]; j++)
131 if (compressed[j].force_ < 0)
134 ret.push_back (systems_per_page[i] + compressed_count);
135 start_sys += systems_per_page[i];
140 /* the cases for page_count = 1 or 2 can be done in O(n) time. Since they
141 are by far the most common cases, we have special functions for them */
142 static Spacing_result
143 space_systems_on_1_page (vector<Line_details> const &lines, Real page_height)
145 Page_spacing space (page_height);
148 for (vsize i = 0; i < lines.size (); i++)
149 space.append_system (lines[i]);
151 ret.systems_per_page_.push_back (lines.size ());
152 ret.force_.push_back (space.force_);
153 ret.penalty_ = lines.back ().page_penalty_ + lines.back ().turn_penalty_;
154 ret.demerits_ = ret.force_.back () * ret.force_.back () + ret.penalty_;
159 static Spacing_result
160 space_systems_on_2_pages (vector<Line_details> const &lines, Real page_height)
162 /* if there is a forced break, this reduces to 2 1-page problems */
163 for (vsize i = 0; i < lines.size () - 1; i++)
164 if (lines[i].page_permission_ == ly_symbol2scm ("force"))
166 vector<Line_details> lines1 (lines.begin (), lines.begin () + i + 1);
167 vector<Line_details> lines2 (lines.begin () + i + 1, lines.end ());
168 Spacing_result p1 = space_systems_on_1_page (lines1, page_height);
169 Spacing_result p2 = space_systems_on_1_page (lines2, page_height);
171 p1.systems_per_page_.push_back (p2.systems_per_page_[0]);
172 p1.force_.push_back (p2.force_[0]);
173 p1.penalty_ += p2.penalty_ - lines[i].turn_penalty_;
174 p1.demerits_ += p2.demerits_ - lines[i].turn_penalty_;
178 vector<Real> page1_force;
179 vector<Real> page2_force;
180 Page_spacing page1 (page_height);
181 Page_spacing page2 (page_height);
183 page1_force.resize (lines.size () - 1, infinity_f);
184 page2_force.resize (lines.size () - 1, infinity_f);
186 for (vsize i = 0; i < page1_force.size (); i++)
188 page1.append_system (lines[i]);
189 page2.prepend_system (lines[lines.size () - 1 - i]);
190 page1_force[i] = page1.force_;
191 page2_force[page2_force.size () - 1 - i] = page2.force_;
194 vsize best_sys_count = 1;
195 Real best_demerits = infinity_f;
196 for (vsize i = 0; i < page1_force.size (); i++)
198 Real dem = page1_force[i] * page1_force[i]
199 + page2_force[i] * page2_force[i]
200 + lines[i+1].page_penalty_
201 + lines.back ().page_penalty_ + lines.back ().turn_penalty_;
202 if (dem < best_demerits)
205 best_sys_count = i+1;
210 ret.systems_per_page_.push_back (best_sys_count);
211 ret.systems_per_page_.push_back (lines.size () - best_sys_count);
212 ret.force_.push_back (page1_force[best_sys_count-1]);
213 ret.force_.push_back (page2_force[best_sys_count-1]);
214 ret.penalty_ = lines[best_sys_count-1].page_penalty_
215 + lines.back ().page_penalty_
216 + lines.back ().turn_penalty_;
217 ret.demerits_ = best_demerits;
222 /* for page_count > 2, we use a dynamic algorithm similar to
223 constrained-breaking -- we have a class that stores the intermediate
224 calculations so they can be reused for querying different page counts.
230 Page_spacer (vector<Line_details> const &lines, Real page_height);
231 Spacing_result solve (vsize page_count);
234 struct Page_spacing_node
238 demerits_ = infinity_f;
240 penalty_ = infinity_f;
251 vector<Line_details> lines_;
252 Matrix<Page_spacing_node> state_;
253 vsize max_page_count_;
255 void resize (vsize page_count);
256 bool calc_subproblem (vsize page, vsize lines);
259 Page_spacer::Page_spacer (vector<Line_details> const &lines, Real page_height)
262 page_height_ = page_height;
267 Page_spacer::solve (vsize page_count)
269 if (page_count > max_page_count_)
273 ret.force_.resize (page_count);
274 ret.systems_per_page_.resize (page_count);
276 vsize system = lines_.size () - 1;
278 ret.penalty_ = state_.at (system, page_count-1).penalty_
279 + lines_.back ().page_penalty_ + lines_.back ().turn_penalty_;
281 for (vsize p = page_count; p--;)
283 assert (system != VPOS);
285 Page_spacing_node const &ps = state_.at (system, p);
286 ret.force_[p] = ps.force_;
287 ret.demerits_ += ps.force_ * ps.force_;
289 ret.systems_per_page_[p] = system + 1;
291 ret.systems_per_page_[p] = system - ps.prev_;
294 ret.demerits_ += ret.penalty_;
299 Page_spacer::resize (vsize page_count)
301 assert (page_count > 0);
303 if (max_page_count_ >= page_count)
306 state_.resize (lines_.size (), page_count, Page_spacing_node ());
307 for (vsize page = max_page_count_; page < page_count; page++)
308 for (vsize line = page; line < lines_.size (); line++)
309 if (!calc_subproblem (page, line))
312 max_page_count_ = page_count;
316 Page_spacer::calc_subproblem (vsize page, vsize line)
318 Page_spacing space (page_height_);
319 Page_spacing_node &cur = state_.at (line, page);
321 for (vsize page_start = line+1; page_start > page && page_start--;)
323 Page_spacing_node const *prev = page > 0 ? &state_.at (page_start-1, page-1) : 0;
325 space.prepend_system (lines_[page_start]);
326 if (isinf (space.force_))
329 if (page == 0 && page_start > 0)
332 Real dem = fabs (space.force_) + (prev ? prev->demerits_ : 0);
335 penalty = lines_[page_start-1].page_penalty_
336 + (page % 2 == 0) ? lines_[page_start-1].turn_penalty_ : 0;
339 if (dem < cur.demerits_)
342 cur.force_ = space.force_;
343 cur.penalty_ = penalty + (prev ? prev->penalty_ : 0);
344 cur.prev_ = page_start - 1;
347 return !isinf (cur.demerits_);
351 min_page_count (vector<Line_details> const &lines, Real page_height)
354 Real cur_rod_height = 0;
356 for (vsize i = 0; i < lines.size (); i++)
358 Real next_height = cur_rod_height + lines[i].extent_.length ()
359 + ((i > 0 && cur_rod_height > 0) ? lines[i-1].padding_: 0);
361 if ((next_height > page_height && cur_rod_height > 0)
362 || (i > 0 && lines[i-1].page_permission_ == ly_symbol2scm ("force")))
365 cur_rod_height = lines[i].extent_.length ();
368 cur_rod_height = next_height;
374 space_systems_on_min_pages (vector<Line_details> const &lines,
376 Real odd_pages_penalty)
378 vector<Line_details> compressed_lines = compress_lines (lines);
379 vsize min_p_count = min_page_count (compressed_lines, page_height);
382 if (min_p_count == 1)
384 Spacing_result candidate1 = space_systems_on_1_page (compressed_lines, page_height);
385 candidate1.force_.back () += odd_pages_penalty;
386 candidate1.demerits_ += odd_pages_penalty;
387 if (compressed_lines.size () == 1)
391 Spacing_result candidate2 = space_systems_on_2_pages (compressed_lines, page_height);
392 ret = (candidate1.demerits_ < candidate2.demerits_) ?
393 candidate1 : candidate2;
396 else if (min_p_count == 2)
397 ret = space_systems_on_2_pages (compressed_lines, page_height);
400 Page_spacer ps (compressed_lines, page_height);
401 Spacing_result candidate1 = ps.solve (min_p_count);
402 if (min_p_count % 2 == 0)
406 candidate1.force_.back () += odd_pages_penalty;
407 candidate1.demerits_ += odd_pages_penalty;
409 if (min_p_count == compressed_lines.size ())
413 Spacing_result candidate2 = ps.solve (min_p_count + 1);
414 ret = (candidate1.demerits_ < candidate2.demerits_) ?
415 candidate1 : candidate2;
419 ret.systems_per_page_ = uncompress_solution (ret.systems_per_page_, compressed_lines);
424 space_systems_on_best_pages (vector<Line_details> const &lines,
426 Real odd_pages_penalty)
428 vector<Line_details> compressed_lines = compress_lines (lines);
429 vsize min_p_count = min_page_count (compressed_lines, page_height);
431 Page_spacer ps (compressed_lines, page_height);
432 Spacing_result best = ps.solve (min_p_count);
433 best.demerits_ += (min_p_count % 2) ? odd_pages_penalty : 0;
435 for (vsize i = min_p_count+1; i <= compressed_lines.size (); i++)
437 Spacing_result cur = ps.solve (i);
438 cur.demerits_ += (i % 2) ? odd_pages_penalty : 0;
439 if (cur.demerits_ < best.demerits_)
443 best.systems_per_page_ = uncompress_solution (best.systems_per_page_, compressed_lines);