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List: lilypond-user
Subject: Re: Slur with left and/or right arrow head
From: Thomas Morley <thomasmorley65 () gmail ! com>
Date: 2019-04-19 21:03:31
Message-ID: CABsfGyVY5+X5BsYq085TF6R0XuhBB5eo_yfLfXuzpHErsuqieA () mail ! gmail ! com
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Am Di., 16. Apr. 2019 um 23:45 Uhr schrieb Aaron Hill
<lilypond@hillvisions.com>:
>
> On 2019-04-16 10:37 am, Thomas Morley wrote:
> > Am Mo., 15. Apr. 2019 um 19:26 Uhr schrieb Lukas-Fabian Moser
> > <lfm@gmx.de>:
> >>
> >> Folks,
> >>
> >> in
> >> https://archiv.lilypondforum.de/index.php?topic=1744.msg9669#msg9669,
> >> Harm invented a truly wonderful new feature allowing to add an arrow
> >> head to the right end of a Slur (or, for that matter, a Tie,
> >> PhrasingSlur etc.). I reproduce it here with only trivial changes
> >> (mainly omitting parser/location).
> >>
> >> Now I also need slurs with arrows pointing to the left (and ideally,
> >> also the option to have an arrow tip at both ends of the Slur). At
> >> first
> >> glance the asymmetry favoring the right hand side of a Slur seems to
> >> be
> >> hard-coded pretty deeply in Harm's code. Is there a cheap way to add a
> >> choice of "left or right end" (if not even the "or/and" possibility)?
> >>
> >> Best
> >> Lukas
> >
> > Hi Lukas,
> >
> > I started to implement the functionality, finally I more or less
> > rewrote anything.
> > As David K once said: rewriting all means at least knowing where the
> > bugs are...
>
> Harm,
>
> There is an annoying optical issue where using the angle of the curve at
> the end points does not work well for an arrow head that partially
> overlaps the curve. Instead, one needs to consider the slope of the
> curve a little inwards from the ends so that the arrow appears to be
> aligned properly.
>
> I took a stab at patching your code to address this. This involved some
> additional computational work for various metrics of a Bezier curve.
> See the attached files.
>
> Among the things I changed is that the code that adds the arrows to the
> ends of the curve no longer applies an offset. This offset was strictly
> horizontal which did not work well for more heavily rotated arrows.
> Instead, the offset is done within the code that computes and rotates
> the arrow, so that the center of rotation is properly defined.
Hi Aaron,
meanwhile I think I understand more about Beziers, many thanks for
your and David's explanations.
Also, I looked entirely through your code and probably understood how
you do things.
As already said I stumbled across some procedures being called over
and over, also I asked myself why we need the entire length of the
Bezier, if we are interested only in a short part at start/end.
So I wrote a procedure (relying on `split-bezier ´ from
bezier-tools.scm), where the Bezier is splitted, i.e. two sets of new
control-points are returned.
For those new control-points the direct line between first and last
point is calculated. If this is lower than a certain treshold, we have
control-points for a Bezier where we can calculate the angle,
otherwise it continues to recurse until the goal is reached. Relying
on start/end of the original Bezier it's first or last of the new
points, which now can serve for calculating the angle.
Function-calls are drastically reduced, performance time is reduced
and code simplified imho.
One thing I noticed are not so nice printed arrows for short Beziers
like Repeat/LaissezVibrerTie.
Likely due to the width of the arrowhead, _within_ this width the
Bezier is "too active", so to speak.
In general I've found your function to calculate a point on the Bezier
and to calculate an angle at a certain point of the Bezier _very_
helpful.
What do you think adding it to bezier-tools.scm?
Attached the newest code.
WYT?
Thanks,
Harm
@ Lukas
Up to now I didn't tackle the arrow-left/right LEFT/RIGHT thing, I
first wanted to fight my way through the code for Beziers.
Probably tomorrow, hopefuly ...
["arrow-slur-04.ly" (text/x-lilypond)]
\version "2.19.82"
%% Thanks to Aaron Hill
%% http://lists.gnu.org/archive/html/lilypond-user/2019-04/msg00240.html
%% Does not work for 2.18.2 because of
%% - grob::name (could be replaced by grob-name, see p.e. LSR)
%% - minimum-length-after-break (no replacement possible, only used in
%% the examples, though)
#(ly:load "bezier-tools.scm")
#(define (note-column-bounded? dir grob)
"Checks wether @var{grob} is a spanner and whether the spanner is bounded in
@var{dir}-direction by a note-column."
(if (ly:spanner? grob)
(grob::has-interface (ly:spanner-bound grob dir) 'note-column-interface)
#f))
#(define (offset-number-pair-list l1 l2)
"Offset the number-pairs of @var{l1} by the matching number-pairs of @var{l2}"
;; NB no type-checking or checking for equal lengths is done here
(map (lambda (p1 p2) (offset-add p1 p2)) l1 l2))
#(define (bezier::point control-points t)
"Given a Bezier curve of arbitrary degree specified by @var{control-points},
compute the point at the specified position @var{t}."
(if (< 1 (length control-points))
(let ((q0 (bezier::point (drop-right control-points 1) t))
(q1 (bezier::point (drop control-points 1) t)))
(cons
(+ (* (car q0) (- 1 t)) (* (car q1) t))
(+ (* (cdr q0) (- 1 t)) (* (cdr q1) t))))
(car control-points)))
#(define (bezier::angle control-points t)
"Given a Bezier curve of arbitrary degree specified by @var{control-points},
compute the slope at the specified position @var{t}."
(let ((q0 (bezier::point (drop-right control-points 1) t))
(q1 (bezier::point (drop control-points 1) t)))
(ly:angle (- (car q1) (car q0)) (- (cdr q1) (cdr q0)))))
#(define*
(bezier::approx-control-points-to-length
control-points dir length
#:optional (precision 0.01) (right-t 0.2) (left-t 0.8))
"Given a Bezier curve specified by @var{control-points}, return
new control-points where the length of the Bezier specified by them is approx
@var{length}.
The procedure returns if difference of the new calculated length and the given
@var{length} is lower than optional @var{precision}.
The optional @var{left-t} and @var{right-t} represent the steps where new
control-points are calculated relying on @var{dir}."
;; TODO
;; Do the values for precision, left-t, right-t cover all cases?
(let* ((frst-cp (car control-points))
(last-cp (last control-points))
(actual-length
(ly:length
(- (car frst-cp) (car last-cp))
(- (cdr frst-cp) (cdr last-cp))))
(diff (- (abs actual-length) (abs length))))
(if (< diff precision)
control-points
(bezier::approx-control-points-to-length
(if (positive? dir)
(cdr (split-bezier control-points right-t))
(car (split-bezier control-points left-t)))
dir
length))))
#(define (curve-adjusted-arrow-head dir control-points)
(lambda (curve)
"Returns a stencil build from an arrowhead-glyph, adjusted to fit at start/end
of a curve looking at the curve's @var{control-points}.
Relying on @var{dir} for looking at left or right side of the curve."
(if (not dir)
empty-stencil
(let* ((staff-space (ly:staff-symbol-staff-space curve))
;; reducing fs-from-staff-space a bit looks nicer
(fs-from-staff-space (1- (magnification->font-size staff-space)))
(grob-font
(ly:paper-get-font
(ly:grob-layout curve)
`(((font-encoding . fetaMusic)
(font-size . ,fs-from-staff-space)))))
(arrowhead-stil
(ly:font-get-glyph grob-font
(format #f "arrowheads.open.0~a1"
(if (positive? dir) "" "M"))))
(arrowhead-width
(interval-length (ly:stencil-extent arrowhead-stil X)))
(offset-stil
(ly:stencil-translate
arrowhead-stil
(cons (* dir 0.4 arrowhead-width) 0)))
(arrowhead-end
(interval-bound (ly:stencil-extent offset-stil X) (- dir)))
(offset (* 0.33 arrowhead-end))
(angle
(bezier::angle
(bezier::approx-control-points-to-length
control-points dir offset)
(if (positive? dir) 0 1))))
(ly:stencil-rotate-absolute offset-stil angle 0 0)))))
#(define modify-control-points-for-arrows
(lambda (grob)
"Returns a number-pair-list suitable for setting @code{control-points}-property.
The values are modified with respect to a probably printed arrowhead, which
is done by looking at the subproperties of @code{details}:
@code{arrow-left} and @code{arrow-right}."
(let* ((curve-dir (ly:grob-property grob 'direction))
(details (ly:grob-property grob 'details))
(arrow-left (assoc-get 'arrow-left details #f))
(arrow-right (assoc-get 'arrow-right details #f))
(nc-right-bound?
(note-column-bounded? RIGHT grob))
(nc-left-bound?
(note-column-bounded? LEFT grob))
(c-ps (ly:grob-property grob 'control-points)))
(cond ((and (not arrow-left) (not arrow-right))
c-ps)
((eq? (grob::name grob) 'LaissezVibrerTie)
(if arrow-left ;; move a little to right
(offset-number-pair-list
c-ps
'((0.3 . 0) (0.3 . 0) (0.3 . 0) (0.3 . 0)))
c-ps))
((eq? (grob::name grob) 'RepeatTie)
(if arrow-right ;; move a little to left
(offset-number-pair-list
c-ps
'((-0.3 . 0) (-0.3 . 0) (-0.3 . 0) (-0.3 . 0)))
c-ps))
(else ;; Tie, Slur, PhrasingSlur
(let ((move-this-to-left
(if arrow-left
(if nc-left-bound? 0.4 0.5)
0))
(move-this-to-right
(if arrow-right
(if nc-right-bound? -0.4 -0.5)
0))
;; For Ties we want to keep a horizontal look
(move-Y-at-left
(if (or arrow-left
(grob::has-interface grob 'tie-interface))
(* 0.2 curve-dir)
0))
(move-Y-at-right
(if (or arrow-right
(grob::has-interface grob 'tie-interface))
(* 0.2 curve-dir)
0)))
(offset-number-pair-list
c-ps
(list
(cons move-this-to-left move-Y-at-left)
(cons move-this-to-left move-Y-at-left)
(cons move-this-to-right move-Y-at-right)
(cons move-this-to-right move-Y-at-right)))))))))
#(define add-arrow-head-to-curve
(lambda (grob)
"Returns a curve stencil with optional arrowheads at start/end.
Whether to print arrowheads is decided by looking at the subproperties of
@code{details}: @code{arrow-left} and @code{arrow-right}."
(let* ((orig (if (ly:spanner? grob)
(ly:grob-original grob)
#f))
(siblings (if (ly:grob? orig)
(ly:spanner-broken-into orig)
'()))
(control-points (modify-control-points-for-arrows grob))
(details (ly:grob-property grob 'details))
(arrow-left (assoc-get 'arrow-left details #f))
(arrow-right (assoc-get 'arrow-right details #f))
(function
(assoc-get 'stencil (reverse (ly:grob-basic-properties grob))))
(stil ;; Ugh, is there no better way to test that a grob has no
;; 'stencil and that no other previous procedure assigned
;; a stencil-value to said grob?
(if (and (procedure? function)
(not (eq? (procedure-name function)
'add-arrow-head-to-curve)))
(begin
(ly:grob-set-property! grob 'control-points control-points)
(function grob))
(begin
(ly:warning "~a has no stencil. Ignoring." grob)
#f))))
(cond ((and (not arrow-left) (not arrow-right))
stil)
(#t
;; TODO
;; For now arrowheads are printed as specified even for each
;; broken curve, should possibilities to limit behaviour at
;; line-break be implemented?
;(or (null? siblings)
; #t
; (equal? grob (car (last-pair siblings))))
(let* (;(control-points (modify-control-points-for-arrows grob))
(frst (car control-points))
(frth (cadddr control-points))
(arrow-right
((curve-adjusted-arrow-head arrow-right control-points)
grob))
(arrow-left
((curve-adjusted-arrow-head arrow-left control-points)
grob)))
(ly:stencil-add
(ly:stencil-translate arrow-left frst)
(ly:stencil-translate arrow-right frth)
(stencil-with-color stil red))))))))
pointing-curve =
#(define-music-function (p l curve) (string?)
"Set property @code{after-line-breaking} for grob @code{curve}. Finally setting
the @code{stencil} to @code{arrowed-curve}.
It's needed to go for @code{after-line-breaking}, otherwise changes to
@code{control-points} done by @code{shape} wouldn't be respected.
Whether or not arrows are printed should done by applying, p.e.
@lilypond[verbatim,quote]
\\override Tie.details.arrow-left = #LEFT
\\override Slur.details.arrow-left = #LEFT
@end lilypond
separately."
#{
\temporary \override $curve . after-line-breaking =
#(lambda (grob)
(ly:grob-set-property! grob 'stencil (add-arrow-head-to-curve grob)))
#})
revert-pointing-curve =
#(define-music-function (p l curve) (string?)
"Revert the setting for @code{after-line-breaking} of grob @var{curve}."
#{
\revert $curve . after-line-breaking
#})
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% EXAMPLES
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\layout {
\override Tie.details.arrow-left = #LEFT
\override Slur.details.arrow-left = #LEFT
\override PhrasingSlur.details.arrow-left = #LEFT
\override RepeatTie.details.arrow-left = #LEFT
\override LaissezVibrerTie.details.arrow-left = #LEFT
\override Tie.details.arrow-right = #RIGHT
\override Slur.details.arrow-right = #RIGHT
\override PhrasingSlur.details.arrow-right = #RIGHT
\override RepeatTie.details.arrow-right = #RIGHT
\override LaissezVibrerTie.details.arrow-right = #RIGHT
}
% {
\new Staff \with { instrumentName = "Slurs" }
\relative c'' {
\pointing-curve Slur
c'( c
\bar "" \break
c c)
\slurDown
c( c c c)
\voiceOne
c,,4( c c c'')
<>^"default"
\revert-pointing-curve Slur
\oneVoice
c( c c c)
}
%}
% {
m = { c4( d e f e d des c) }
testI = {
\relative c \m
\relative c' \m
\relative c'' \m
\relative c''' \m
}
\new Staff \with { instrumentName = "Slurs" }
{
\pointing-curve Slur
<>^"no Slur-Stem-direction"
\testI
\break
<>^"Slur down, Stem up"
\slurDown
\stemUp
\testI
\break
<>^"Slur up, Stem down"
\slurUp
\stemDown
\testI
\break
<>^"Slur up, Stem up"
\slurUp
\stemUp
\testI
\break
<>^"Slur down, Stem down"
\slurDown
\stemDown
\testI
\break
<>^"default"
\stemNeutral
\slurNeutral
\revert-pointing-curve Slur
\testI
\break
}
%}
% {
\new Staff \with { instrumentName = "Ties" }
\relative c' {
\pointing-curve Tie
%% overriding TieColumn.tie-configuration works
<c e g c>1~
\once \override TieColumn.tie-configuration =
#'((3.0 . 1) (-1.0 . 1) (-5.0 . -1) (-8.0 . -1))
q
\once \override Tie.minimum-length-after-break = 8
<c e g c>1~
\break
q
<>^"default"
\revert-pointing-curve Tie
<c e g c>1~ q
}
%}
% {
\new Staff \with { instrumentName = "PhrasingSlur" }
\relative c' {
\pointing-curve PhrasingSlur
<c e g c>1^\( q q <g d' g b g'>\)
<>^"default"
\revert-pointing-curve PhrasingSlur
<c e g c>1^\( q q <g d' g b g'>\)
}
%}
% {
%% \shape works
\new Staff \with { instrumentName = "RepeatTie" }
\relative c' {
\pointing-curve RepeatTie
c1\repeatTie
%% If left _and_ right arrow is wished, the RepeatTie may be too
%% short, use \shape then
<>^"shaped"
\shape #'((-0.6 . 0) (-0.6 . -0.1) (0 . -0.1) (0 . 0)) RepeatTie
c1\repeatTie
<>^"default"
\revert-pointing-curve RepeatTie
c1\repeatTie
}
%}
% {
\new Staff \with { instrumentName = "LaissezVibrerTie" }
\relative c' {
\pointing-curve LaissezVibrerTie
c1\laissezVibrer
%% If left _and_ right arrow is wished, the LaissezVibrerTie may be too
%% short, use \shape then
<>^"shaped"
c1-\shape #'((0 . 0) (0 . -0.1) (0.6 . -0.1) (0.6 . 0))-\laissezVibrer
<>^"default"
\revert-pointing-curve LaissezVibrerTie
c1\laissezVibrer
}
%}
\paper { indent = 30 }
#(set-global-staff-size 18)
%% arrow-slur-04.ly
%% real 0m3,880s
%% user 0m3,595s
%% sys 0m0,286s
%% arrow-slur-03.ly
%% real 0m3,540s
%% user 0m3,323s
%% sys 0m0,216s
%% arrow-slur-03-patch.ly
%% real 0m4,191s
%% user 0m3,776s
%% sys 0m0,414s
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