Shear markup
This superseeds snippet 1166 and snippet 1167.
\version "2.24.0"
%% Thabks to Arnold from the geman forum
%% https://lilypondforum.de/index.php/topic,1216.msg6404.html#msg6404
#(define-markup-command (pop-override layout props arg)
(markup?)
"pop the last override in the markup chain"
(let ((popped-props (if (> (length props) 1) (cdr props) props)))
(interpret-markup layout popped-props arg)))
#(define-markup-command (slant layout props phi arg)
(number? markup?)
#:category other
#:properties ((par #t)
(tilt 0.0)
(finalrotation 0.0)
(extrascaling '(1 . 1)))
"
A geometric transformation which may be described in two ways:
a) Shear Mapping: Cut your image in small stripes parallel to your
base axis (e.g. X axis), then move them parallel to your base axis,
the distance is proportional to the distance from the base axis.
b) Skew Coordinates: See your input image as a geometric list by the
cartesian coordiate system relative to your base axes (e.g. X axis
and perpendicular the Y axis) - name these axes U resp. V. Now the
V axis will be rotated to manipulate your image. Your U-V coordiante
system is no longer cartesian, because it's no longer pependicular.
Tranformation matrix for an angle @var{phi}, default tilt, type a
resp. property par = ##t:
xx = 1.0 xy = tan(w)
yx = 0.0 yy = 1.0
Tranformation matrix for an angle @var{phi}, default tilt, type b
resp. property par = ##f:
xx = 1.0 xy = sin(w)
yx = 0.0 yy = cos(w)
Relation from type b to type a: the original Y axis (V axis) is
scaled by factor 1/cos(w)
Properties for this markup:
@var{par} is #t for Type a (default), #f for Type b
@var{tilt} specifies the invariant axis, 0 for X axis (default),
90 for Y axis, other values possible
@var{finalrotation} specifies an additional rotation appended to this
shear / skew mapping
@var{extrascaling} will apply an extra scaling to the U and V axis
Arguments for this markup:
@var{phi} is the shear angle. (allmost) ±90° will force geometric
problems.
And finally the markup to be transformed.
Technically there is no SCHEME function available to apply a
ly:transform? object to a stencil. Therefore roation and scale
statements are used to fullfill the task.
Once the U and V axis are properly scaled, the stencil is rotated so
the U axis directs 45° up to the right and the V axis directs 45° up to
the left. A properly choosen scale factor pair will rotate both axes
together (or away from each other) by a specified angle without scaling
these axes. A final back rotation completes the sequence.
"
(let* ((half-phi (* 0.5 phi))
(phi-dir (ly:directed phi))
(cos-phi (car phi-dir))
(half-dir (ly:directed half-phi))
(sin-part (cdr half-dir))
(cos-part (car half-dir))
(px (- cos-part sin-part))
(py (+ cos-part sin-part))
(stil (interpret-markup layout props arg))
(need-first-rot (or par
(not (= (car extrascaling) 1))
(not (= (cdr extrascaling) 1))))
(first-scale (if par
(cons (car extrascaling) (/ (cdr extrascaling) cos-phi))
extrascaling)))
; for debugging:
; (for-each display (list "\n\\slant " phi " (par=" par " ori=" tilt " fin=" finalrotation " scl=" extrascaling ")\n"
; " cos-phi=" (ly:number->string cos-phi)
; " sin-part=" (ly:number->string sin-part)
; " cos-part=" (ly:number->string cos-part)
; " first-scale=" first-scale
; "\n"))
(if (< (abs cos-phi) 0.01) (ly:program-error
"slant markup with angle too close to 90° may cause runtime error!"))
(if (< (abs px) 0.00001)
(set! px (if (negative? px) -0.00001 0.00001)))
(if (< (abs py) 0.00001)
(set! py (if (negative? py) -0.00001 0.00001)))
(let* ((v-pos-stil
(if need-first-rot
(ly:stencil-rotate-absolute
(ly:stencil-scale
(if (= tilt 0.0)
stil
(ly:stencil-rotate-absolute
stil
(- tilt) 0.0 0.0))
(car first-scale) (cdr first-scale))
45.0 0.0 0.0)
(ly:stencil-rotate-absolute stil (- 45.0 tilt) 0.0 0.0)))
(final-stil
(ly:stencil-rotate-absolute
(ly:stencil-scale v-pos-stil px py)
(+ -45.0 (- half-phi) tilt finalrotation) 0.0 0.0))
(final-expr (ly:stencil-expr final-stil))
(final-X-ext (stencil-true-extent final-stil X))
(final-Y-ext (stencil-true-extent final-stil Y)))
(ly:make-stencil final-expr final-X-ext final-Y-ext))))
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
#(define di-wl 7.18)
#(define di-wr 41.41)
#(define bezier-round 0.551857)
#(define sz 16)
#(define (di-map size z x y)
(let ((dir-l (ly:directed di-wl size))
(dir-r (ly:directed di-wr size)))
(cons (- (* (car dir-l) x) (* (car dir-r) 0.5 z))
(- (* y size) (* (cdr dir-l) x) (* (cdr dir-r) 0.5 z)))))
DiRoofL = #(define-scheme-function (m) (markup?)
(let* ((h (sqrt 0.75))
(PP (di-map sz -0.5 0 h))
(lgs (/ (sqrt (+ (* (car PP) (car PP)) (* (cdr PP) (cdr PP)))) sz))
(w (ly:angle (car PP) (cdr PP))))
(make-override-markup `((finalrotation . ,(- di-wl))
(extrascaling . (1 . ,lgs))
(par . #f))
(make-slant-markup (- 90 w di-wl) m))))
DiRoofR = #(define-scheme-function (m) (markup?)
(let* ((h (sqrt 0.75))
(PP (di-map sz 0 -0.5 h))
(lgs (/ (sqrt (+ (* (car PP) (car PP)) (* (cdr PP) (cdr PP)))) sz))
(w (ly:angle (car PP) (cdr PP))))
(make-override-markup `((finalrotation . ,di-wr)
(extrascaling . (0.5 . ,lgs))
(par . #f))
(make-slant-markup (- 90 w (- di-wr)) m))))
DiPlaneL = #(define-scheme-function (m) (markup?)
(make-override-markup `((finalrotation . ,(- di-wl))
(par . #f))
(make-slant-markup (- di-wl) m)))
DiPlaneL¹ = #(define-scheme-function (m) (markup?)
(make-override-markup `((finalrotation . 90)
(par . #f))
(make-slant-markup di-wl m)))
DiPlaneR = #(define-scheme-function (m) (markup?)
(make-override-markup `((finalrotation . ,di-wr)
(extrascaling . (0.5 . 1))
(par . #f))
(make-slant-markup di-wr m)))
DiPlaneR¹ = #(define-scheme-function (m) (markup?)
(make-override-markup `((finalrotation . 90)
(extrascaling . (1 . 0.5))
(par . #f))
(make-slant-markup (- di-wr) m)))
DiPlaneT = #(define-scheme-function (m) (markup?)
(make-override-markup `((finalrotation . ,(- di-wl))
(extrascaling . (1 . 0.5))
(par . #f))
(make-slant-markup (- 90.0 di-wr di-wl) m)))
DiPlaneT¹ = #(define-scheme-function (m) (markup?)
(make-override-markup `((finalrotation . ,di-wr)
(extrascaling . (0.5 . 1))
(par . #f))
(make-slant-markup (+ di-wr di-wl -90.0) m)))
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
#(define roof-path `((moveto 0 0)
(lineto ,sz 0)
(lineto ,(* 0.5 sz) ,sz)
(closepath)))
#(define large-bow-path `((moveto 0 0)
(lineto ,sz 0)
(curveto ,sz ,(* sz bezier-round)
,(* sz (- 2 bezier-round)) ,sz
,(* sz 2) ,sz)
(curveto ,(* sz (+ 2 bezier-round)) ,sz
,(* sz 3) ,(* sz bezier-round)
,(* sz 3) 0)
(lineto ,(* sz 4) 0)
(lineto ,(* sz 4) ,(* sz 1.5))
(lineto 0 ,(* sz 1.5))
(closepath)))
#(define small-bow-path `((moveto 0 0)
(lineto ,sz 0)
(curveto ,sz ,(* sz bezier-round 0.5)
,(* sz 0.5 (- 3 bezier-round)) ,(* sz 0.5)
,(* sz 1.5) ,(* sz 0.5))
(curveto ,(* sz 0.5 (+ 3 bezier-round)) ,(* sz 0.5)
,(* sz 2) ,(* sz 0.5 bezier-round)
,(* sz 2) 0)
(lineto ,(* sz 3) 0)
(lineto ,(* sz 3) ,sz)
(lineto 0 ,sz)
(closepath)))
RoofPlane = #(define-scheme-function (r g b) (number? number? number?)
(make-with-color-markup (list r g b)
(make-override-markup '(filled . #t)
(make-path-markup 0 roof-path))))
BowPlaneSmall = #(define-scheme-function (r g b) (number? number? number?)
(make-with-color-markup (list r g b)
(make-override-markup '(filled . #t)
(make-path-markup 0 small-bow-path))))
BowPlaneLarge = #(define-scheme-function (r g b) (number? number? number?)
(make-with-color-markup (list r g b)
(make-override-markup '(filled . #t)
(make-path-markup 0 large-bow-path))))
RectPlane = #(define-scheme-function (r g b x y) (number? number? number? number? number?)
(make-with-color-markup (list r g b)
(make-override-markup '(filled . #t)
(make-path-markup 0 `((moveto 0 0)
(lineto ,(* sz x) 0)
(lineto ,(* sz x) ,(* sz y))
(lineto 0 ,(* sz y))
(closepath))))))
RoofPlaneR = \markup \RoofPlane #1.0 #0.4 #0.4
RoofPlaneL = \markup \RoofPlane #0.9 #0.2 #0.2
BowPlaneLaRaw = \markup \BowPlaneLarge #0.2 #0.7 #0.2
BowPlaneLd = \markup \BowPlaneLarge #0.1 #0.5 #0.1
BowFeederL = \markup \RectPlane #0.1 #0.5 #0.1 #1 #1
BowSideL = \markup \RectPlane #0.5 #0.9 #0.5 #1 #1.5
BowTopLa = \markup \RectPlane #0.2 #0.6 #0.2 #4 #1
BowPlaneLbRaw = \markup \BowPlaneSmall #0.7 #0.7 #0.6
BowFeederSm = \markup \RectPlane #0.5 #0.5 #0.4 #1 #0.8
BowTopSm = \markup \RectPlane #0.6 #0.6 #0.5 #3 #1
RoofPlaneRV¹ = \markup \overlay {
\RoofPlaneR
\translate #(cons (* 0.5 sz) (* 0.4 sz))
\scale #(cons (* 0.1 sz) (* 0.1 sz))
\center-align \musicglyph #"clefs.F"
}
RoofPlaneLB¹ = \markup \overlay {
\RoofPlaneL
\translate #(cons (* 0.5 sz) (* 0.3 sz))
\scale #(cons (* 0.1 sz) (* 0.1 sz))
\center-align \musicglyph #"clefs.G"
}
RoofPlaneRV² = \markup \overlay {
\RoofPlaneR
\translate #(cons (* 0.5 sz) (* 0.1 sz))
\scale #(cons (* 0.17 sz) (* 0.17 sz))
\center-align \musicglyph #"pedal.Ped"
}
RoofPlaneLB² = \markup \overlay {
\RoofPlaneL
\translate #(cons (* 0.5 sz) (* 0.3 sz))
\scale #(cons (* 0.1 sz) (* 0.1 sz))
\center-align \musicglyph #"clefs.C"
}
RoofPlaneRV³ = \markup \overlay {
\RoofPlaneR
\translate #(cons (* 0.5 sz) (* 0.35 sz))
\scale #(cons (* 0.22 sz) (* 0.22 sz))
\center-align \musicglyph #"scripts.coda"
}
RoofPlaneLB³ = \markup \overlay {
\RoofPlaneL
\translate #(cons (* 0.5 sz) (* 0.35 sz))
\scale #(cons (* 0.15 sz) (* 0.15 sz))
\center-align \musicglyph #"scripts.segno"
}
LongPlane¹¹ = \markup \overlay {
\RectPlane #0.1 #0.1 #1.0 #4 #1
\translate #(cons (* sz 2) (* sz 0.6))
\scale #(cons (* sz 0.15) (* sz 0.15))
\bold \column {
\center-align "deutschsprachiges"
\center-align "Lilypondforum"
}
}
LongPlane¹² = \markup \overlay {
\RectPlane #0.3 #0.6 #1.0 #4 #1
\translate #(cons (* sz 2) (* sz 0.4))
\scale #(cons (* sz 0.15) (* sz 0.15))
\center-align "https://lilypondforum.de"
}
LongPlane²¹ = \markup \overlay {
\RectPlane #1.0 #0.5 #0.1 #2.5 #1
\translate #(cons (* sz 1.25) (* sz 0.35))
\scale #(cons (* sz 0.2) (* sz 0.2))
\bold \center-align "Lilypond"
}
LongPlane²² = \markup \overlay {
\RectPlane #1.0 #0.7 #0.5 #2.5 #1
\translate #(cons (* sz 1.25) (* sz 0.4))
\scale #(cons (* sz 0.12) (* sz 0.15))
\center-align "www.lilypond.org"
}
LongPlane³¹ = \markup \overlay {
\RectPlane #0.4 #0.2 #0.0 #2.5 #1
\translate #(cons (* sz 1.25) (* sz 0.55))
\scale #(cons (* sz 0.15) (* sz 0.15))
\with-color #yellow
\italic \override #'(baseline-skip . 2.5) \column {
\center-align "ein Notenbild,"
\center-align "mit dem man"
}
}
LongPlane³² = \markup \overlay {
\RectPlane #0.6 #0.3 #0.1 #2.5 #1
\translate #(cons (* sz 1.25) (* sz 0.55))
\scale #(cons (* sz 0.15) (* sz 0.15))
\with-color #'(1.0 1.0 0.5)
\italic \override #'(baseline-skip . 2.5) \column {
\center-align "gerne vom"
\center-align "Blatt spielt."
}
}
BowPlaneLa = \markup \overlay {
\BowPlaneLaRaw
\translate #(cons (* sz 0.2) (* sz 1.2))
% \scale #(cons (* sz 0.15) (* sz 0.15))
\score {
{ c'4 g' f' e'8 d' b'4. a'16 g' f'2
e''16( d'') c''-. b'-. \acciaccatura e'8 g' a'16 b'
\repeat tremolo 4 { c''16 a' }
b'8 g'4 f'8( ~ f'8 d'8 c'4)_\fermata \bar "|." }
\layout {
ragged-right = ##f
line-width = #(* 6.3 sz)
indent = 0
\context {
\Score
\override NonMusicalPaperColumn.line-break-permission = ##f
\override SpacingSpanner.common-shortest-duration = #(ly:make-moment 1/1)
}
}
}
\translate #(cons (* 0.5 sz) (* 0.5 sz))
\scale #(cons (* 0.22 sz) (* 0.22 sz))
\center-align \sharp
\translate #(cons (* 3.5 sz) (* 0.3 sz))
\scale #(cons (* 0.22 sz) (* 0.22 sz))
\center-align \flat
}
BowPlaneLb = \markup \overlay {
\BowPlaneLbRaw
\translate #(cons (* sz 0.2) (* sz 0.7))
% \scale #(cons (* sz 0.15) (* sz 0.15))
\score {
{ \clef alto
c'4. f8 g4 b d'\downbow f'2 e'8( d'
c'8 b a g f) e4.\trill
c1\fermata \bar "|." }
\layout {
ragged-right = ##f
line-width = #(* 4.7 sz)
indent = 0
\context {
\Score
\override NonMusicalPaperColumn.line-break-permission = ##f
\override SpacingSpanner.common-shortest-duration = #(ly:make-moment 1/1)
}
}
}
\translate #(cons (* 0.5 sz) (* 0.25 sz))
\scale #(cons (* 0.12 sz) (* 0.12 sz))
\center-align \natural
\translate #(cons (* 2.5 sz) (* 0.15 sz))
\scale #(cons (* 0.12 sz) (* 0.12 sz))
\center-align \doubleflat
}
% Check, no projection
%{
\markup {
\RoofPlaneRV¹ \RoofPlaneLB¹ \RoofPlaneRV² \RoofPlaneLB² \RoofPlaneRV³ \RoofPlaneLB³
}
\markup {
\BowPlaneLa
\BowPlaneLb
}
\markup \column {
\line { \LongPlane¹¹ \LongPlane²¹ }
\line { \LongPlane¹² \LongPlane²² }
\line { \LongPlane³¹ \LongPlane³² }
}
%}
% Simple Dimetric 3D image
\markup \left-align \overlay {
% Pilars
\translate #(di-map sz 0 1 0) \DiPlaneL¹ \LongPlane¹¹
\translate #(di-map sz -1 1 0) \DiPlaneR¹ \LongPlane¹²
\translate #(di-map sz -3 4 0) \DiPlaneL¹ \LongPlane³¹
\translate #(di-map sz -4 4 0) \DiPlaneR¹ \LongPlane³²
\translate #(di-map sz 0 4 0) \DiPlaneL¹ \LongPlane²¹
\translate #(di-map sz -1 4 0) \DiPlaneR¹ \LongPlane²²
% Bow brick on the right
\translate #(di-map sz -3 3 2.5) \DiPlaneL \BowFeederL
\translate #(di-map sz 0 4 2.5) \DiPlaneR \BowPlaneLa
\translate #(di-map sz 0 3 2.5) \DiPlaneL \RectPlane #0 #0.4 #0 #1 #1.5
\translate #(di-map sz 0 3 4) \DiPlaneT \RectPlane #0.2 #0.4 #0.1 #1 #4
% Small bow brick above
\translate #(di-map sz -3 3 4) \DiPlaneL \BowFeederSm
\translate #(di-map sz -1 4 4) \DiPlaneR \BowPlaneLb
\translate #(di-map sz -1 4 5) \DiPlaneT¹ \BowTopSm
% Bow brick to the left
\translate #(di-map sz -1 0 4) \DiPlaneL \BowPlaneLd
\translate #(di-map sz 0 1 4) \DiPlaneR \BowFeederL
\translate #(di-map sz 0 0 4) \DiPlaneL \BowPlaneLa
\translate #(di-map sz 0 4 4) \DiPlaneR \BowSideL
\translate #(di-map sz 0 0 5.5) \DiPlaneT \BowTopLa
% Roof
\translate #(di-map sz 0 0 5.5) \DiRoofL \RoofPlaneLB¹
\translate #(di-map sz 0 1 5.5) \DiRoofR \RoofPlaneRV¹
\translate #(di-map sz -3 3 5.0) \DiRoofL \RoofPlaneLB³
\translate #(di-map sz -3 4 5.0) \DiRoofR \RoofPlaneRV³
\translate #(di-map sz 0 3 5.5) \DiRoofL \RoofPlaneLB²
\translate #(di-map sz 0 4 5.5) \DiRoofR \RoofPlaneRV²
% Coordinate aid
%{
\translate #(di-map sz 0 0 0) \left-align ". 0 0 0"
\translate #(di-map sz 1 0 0) \left-align ". 1 0 0"
\translate #(di-map sz 2 0 0) \left-align ". 2 0 0"
\translate #(di-map sz 3 0 0) \left-align ". 3 0 0"
\translate #(di-map sz 0 1 0) \left-align ". 0 1 0"
\translate #(di-map sz 0 2 0) \left-align ". 0 2 0"
\translate #(di-map sz 0 3 0) \left-align ". 0 3 0"
\translate #(di-map sz 0 4 0) \left-align ". 0 4 0"
\translate #(di-map sz -4 4 0) \left-align ". -4 4 0"
\translate #(di-map sz 0 0 1) \left-align ". 0 0 1"
% \translate #(di-map sz 0 0 1.5) \left-align ". 0 0 1.5"
% \translate #(di-map sz 0 1 1.5) \left-align ". 0 1 1.5"
% \translate #(di-map sz -1 1 1.5) \left-align ". -1 1 1.5"
% \translate #(di-map sz -0.5 0.5 2.5) \left-align ". -0.5 0.5 2.5"
%}
}
