¿Cómo puedo dibujar líneas en ángulo en LaTeX para crear una plantilla reglada para caligrafía?

Solución:

Puede utilizar coordenadas polares como (55:100cm). En el siguiente código, calculo el número exacto de líneas oblicuas para dibujar en función del ángulo elegido myAngle y la distancia myDist entre dos líneas oblicuas consecutivas. Mi código también calcula la mayor longitud necesaria para estas líneas.

documentclass[a4paper]article
usepackagetikz
usetikzlibrarycalc

pagestyleempty

newcommand*myDist1cm % distance between consecutive oblique lines
newcommand*myAngle55 % angle of said lines wrt horizontal, in degrees
% Distance between consecutive oblique lines, projected on the horizontal axis
pgfmathsetlengthmacrohorizIntervWidthmyDist/sin(myAngle)

% Length of the longest oblique lines we'll need. I add 10pt to be 100% safe
% with respect to rounding errors (the lines will be clipped anyway).
pgfmathsetlengthmacromaxLength10pt + paperheight/sin(myAngle)

% Number of oblique lines to draw
pgfmathtruncatemacromaxIndex
  round((paperheight/tan(myAngle) + paperwidth)/horizIntervWidth)

begindocument

begintikzpicture[remember picture, overlay]
% Just to be sure we don't paint outside the page. :-)
clip (current page.south west) rectangle (current page.north east);

foreach i in 1,2,...,30 
  draw[black] ($(current page.north west)+(0,-i)$) --
               ($(current page.north east)+(0,-i)$);


foreach i in 0.5,1.5,...,60 
  draw[lightgray] ($(current page.north west)+(0,-i)$) --
                   ($(current page.north east)+(0,-i)$);


foreach i in 1,2,...,maxIndex 
  draw[red] ([xshift=-i*horizIntervWidth]current page.south east) --
            +(myAngle:maxLength);

endtikzpicture

enddocument

Esto hace no responder a su pregunta específica, pero se puede adaptar para su uso con muchas otras opciones integradas. Intenté establecer los valores predeterminados según sus requisitos (a la izquierda en las líneas verticales, pero puede deshabilitar eso indlugin draw=none hasta el final de Vertical Line Style y Vertical Line Style Alternate.

Notas:

• Hay tres tipos diferentes de líneas: horizontal, vertical y horizontal.
• El ángulo de inclinación se puede configurar mediante SlantAngle.
• Cada estilo de línea tiene un tikzset tener un estilo alternativo aplicado a cada enésima línea y cada uno tiene dos estilos de líneas asociados: el estilo principal y un estilo de línea alternativo.
• El borde es opcional y se puede desactivar configurando MarginTop, MarginBottom, MarginLeft y MarginRight para 0.0cm.

Código:

%% Calligraphy Guide Lines
%% Peter Grill
%%
%% ---------------------- Note: May need to run this twice ---------------------
%%
%% --------------------------------------------------- Select Lines 
%% ---------------------------------------------------------------- Horizontal Lines
defVerticalSkip1.0cm%               0.10cm through 2cm
defUseAltStyleEveryNthHorizontalLine2%

%% ---------------------------------------------------------------- Vertical Slant Lines
defHorizontalSlantSkip1.0cm%    
defSlantAngle55%                    Degrees >30, < 60
defUseAltStyleEveryNthSlantLine4%

%% ---------------------------------------------------------------- Vertical Lines
defHorizontalSkip2.66625cm%     
defUseAltStyleEveryNthVerticalLine5%


%% ---------------------------------------------------------------- Select Margins
defMarginTop0.25cm
defMarginBottom0.25cm
defMarginLeft0.25cm 
defMarginRight0.25cm 
%% ---------------------------------------------------------------- Select Paper 
defPapera4paper%        letter | a4paper | a5paper, ....
defOrientationportrait%% portrait | landscape
%% -----------------------
documentclass[Paper, Orientation]article% Version 1.1


usepackagetikz
usepackagexstring

pagestyleempty

%% Select the line style. I prefer using the second one here and using the output underneath
%% the actual paper as guide lines. The first is better if you want to actually write on 
%% top of the guide lines
%%
%% Few other options that can be applied here (last applied options override earlier ones).
%%     solid
%%     dotted,          densely dotted,     loosely dotted,
%%     dashed,          densely dashed,     loosely dashed,
%%     dash dot dot,    densely dash dot dot,   loosely dash dot dot,
%%     loosely dashed,
%%
%% Custom line styles can be defined also be specifying the on/off patter:
%%     dash pattern=on 2pt off 3pt on 4pt off 4pt
%%
%% To disable ANY lines use the draw=none as the last style.

%tikzsetLine Style/.style=line width=1pt, densely dotted, gray, draw opacity=0.1
tikzsetLine Style/.style=
    line width=0.2pt, 
    solid, 
    gray, 
    draw opacity=0.5
 

tikzsetHorizontal Line Style/.style=
    Line Style, 
    solid,
 
tikzsetHorizontal Line Style Alternate/.style=
    Line Style, 
    line width=0.2pt, 
    dashed, 
    draw opacity=1.0, 


tikzsetSlant Line Style/.style=
    Line Style

tikzsetSlant Line Style Alternate/.style=
    Line Style, 
    line width=0.2pt, 
    solid, 
    draw opacity=1.0, 
    red



tikzsetVertical Line Style/.style=Line Style, line width=0.1pt
tikzsetVertical Line Style Alternate/.style=Line Style, line width=0.1pt


tikzsetBorder Line Style/.style=Line Style, thin


newlengthDeltaY
newlengthTempLength

pgfmathtruncatemacroMaxHorizontalLinespaperheight/VerticalSkip

pgfmathsetmacroTanSlantAngletan(SlantAngle)
pgfmathsetlengthDeltaYHorizontalSlantSkip*TanSlantAngle
pgfmathtruncatemacroMaxSlantLinesXpaperwidth/HorizontalSlantSkip
pgfmathtruncatemacroMaxSlantLinesYpaperheight/DeltaY

pgfmathtruncatemacroMaxVerticalLinespaperwidth/HorizontalSkip

newcommand*SetLineStyle[4]% 
    %% #1 = style name to set
    %% #2 = default line style
    %% #3 = line number
    %% #4 = which lines get the alternate line style
   pgfmathtruncatemacroRemaindermod(#3,#4)%
   ifnumRemainder=0relax
       tikzset#1/.style=#2 Alternate%
   else
       tikzset#1/.style=#2%
   fi
%

begindocument%
begintikzpicture[
    remember picture, 
    overlay, 
    shift=(current page.south west),% So that (0,0) is south west of paper
]
   %% Clip to create the border
   clip (MarginLeft,MarginBottom) rectangle 
         (paperwidth-MarginRight,paperheight-MarginTop);

   foreach y in 1,...,MaxHorizontalLines % Horizontal guide lines
       SetLineStyle
           This Horizontal Line StyleHorizontal Line Style
           yUseAltStyleEveryNthHorizontalLine

       beginscope[yshift=-MarginTop]
           draw[This Horizontal Line Style] 
               (0pt,paperheight-y*VerticalSkip) -- (paperwidth,paperheight-y*VerticalSkip) 
           ;
       endscope
   

   foreach x in 1,...,MaxVerticalLines % Vertical guide lines
       SetLineStyle
           This Vertical Line StyleVertical Line Style
           xUseAltStyleEveryNthVerticalLine

       beginscope[xshift=MarginLeft]
           draw[This Vertical Line Style] 
               (x*HorizontalSkip,0pt) -- (x*HorizontalSkip,paperheight) 
           ;
       endscope
   

   pgfmathsetlengthTempLengthpaperwidth*TanSlantAngle
   foreach x in 0,...,MaxSlantLinesX % Slant Lines starting along bottom of page
       SetLineStyle
           This Slant Line StyleSlant Line Style
           xUseAltStyleEveryNthSlantLine

       draw[This Slant Line Style] 
           (x*HorizontalSlantSkip,0pt) -- ++(paperwidth,TempLength)
       ;
   

   foreach y in 1,...,MaxSlantLinesY % Slant Lines starting along left of page
       SetLineStyle
           This Slant Line StyleSlant Line Style
           yUseAltStyleEveryNthSlantLine

       draw[This Slant Line Style] 
           (0pt,y*DeltaY) -- ++(paperwidth,TempLength)
       ;
   

   %% Draw border
   draw [Border Line Style]
         (MarginLeft,MarginBottom) rectangle 
         (paperwidth-MarginRight,paperheight-MarginTop);
endtikzpicture%
enddocument

Otra solucion sin calc.

documentclass[a4paper]article %do not include "draft" in order to render pictures
usepackagetikz
%usetikzlibrarycalc
usepackageverbatim

begindocument
pagestyleempty

begintikzpicture[remember picture,overlay]

foreach i in 1,2,3,...,30
    draw[black] ([yshift=-i cm]current page.north west) -- ++(0:paperwidth);

foreach i in 0.5,1.5,2.5,...,60
    draw[lightgray] ([yshift=-i cm]current page.north west) -- ++(0:paperwidth);

foreach i in 1,2,3,...,60
    draw[red] ([xshift=i cm]current page.north west) -- ++(235:2*paperheight);

endtikzpicture

enddocument

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