/** This file is part of Shapes.
 **
 ** Shapes is free software: you can redistribute it and/or modify
 ** it under the terms of the GNU General Public License as published by
 ** the Free Software Foundation, either version 3 of the License, or
 ** any later version.
 **
 ** Shapes is distributed in the hope that it will be useful,
 ** but WITHOUT ANY WARRANTY; without even the implied warranty of
 ** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 ** GNU General Public License for more details.
 **
 ** You should have received a copy of the GNU General Public License
 ** along with Shapes.  If not, see <http://www.gnu.org/licenses/>.
 **
 ** Copyright 2009, 2010, 2014 Henrik Tidefelt
 **/

##needs ..Applications..Blockdraw
##needs ..Shapes..Geometry / pathmapping
##preamble \usepackage{amsmath}

##lookin ..Shapes
##lookin ..Shapes..Geometry
##lookin ..Applications..Blockdraw

lengthMarks: \ n p r:void a:75° →
{
  the_r: [if [typeof r]=Data..Type..§Void Traits..@width*10 r]
  d: 0.5 * the_r
  rot: [rotate a]
  l_p: (|p|)
  (>
     picture:
  [[Data..range '0 n-'1].foldl
   \ pile e →
     pile &
     {
       sl: [p 0.5*l_p + ( e*1 - 0.5*(n-'1) ) * d]
       [shift sl.p]*rot [] [Graphics..stroke the_r*sl.T--~the_r*sl.T]
     }
   Graphics..null]
     cut:0m
   <)
}

IO..•page << [shift (~4cm,~1cm)][][Layout..center [Graphics..TeX `
\begin{minipage}{6cm}
\begin{align*}
2\, \alpha &= \text{\texttt{frontAngle}}
\\
2\, \beta &= \text{\texttt{rearAngle}}
\\
2\, w &=
\begin{cases}
\text{\texttt{width}}, & \text{if \texttt{width} is a Data..Type..§Length}
\\
\max \left\{\, 3\,\mathrm{bp},\, \text{\texttt{width}}\, \text{\texttt{Traits..@width}} \,\right\}, & \text{if \texttt{width} is a Data..Type..§Float}
\end{cases}
\end{align*}
\end{minipage}
´] (~1,~1)]


Traits..@width:1cm
|
{
  pth: { c: [Geometry..circle 5cm]  [c 2.3]--[c 3.3] }

  /** First we set up variables that mirror the formal parameters of ShapesArrow.
   **/
  p: [Geometry..reverse pth]
  width:3
  frontAngle:40°
  rearAngle:150°

  /** Show the arrowhead.
   **/
  IO..•page << Traits..@stroking:[Traits..gray 0.7] | [Graphics..stroke pth head:[Graphics..ShapesArrow width:width frontAngle:frontAngle rearAngle:rearAngle ...]]

  /** Then we paste the implementation of ShapesArrow...
   **/
  z: p.begin.p
  lMax: 0.99*[Numeric..Math..abs p]
  w: 0.5*[if [typeof width]=Data..Type..§Float Traits..@width*width width]
  el: [Numeric..Math..min w/[Numeric..Math..sin 0.5*frontAngle] lMax]
  l: [Numeric..Math..min w * ( [Numeric..Math..cot 0.5*frontAngle] - [Numeric..Math..cot 0.5*rearAngle] ) lMax]
  e: [p 0]--[p el] >> [shift ~z]
  sl: [p l]
  pr: sl.p
  dr: e.end.p
  dra: [angle dr]
  drl: (|dr|)
  r: w / [Numeric..Math..sin 0.5*rearAngle]
  d1: sl.p + [[rotate 0.5*rearAngle] (r*sl.T)] - z
  d2: sl.p + [[rotate ~0.5*rearAngle] (r*sl.T)] - z

  /** The following paths are not bound to variables in the implementation, but we need them here.
   **/
  e1: [[shift z]*[rotate [angle d1]-dra]*[scale (|d1|)/drl] e]
  e2: [[shift z]*[rotate [angle d2]-dra]*[scale (|d2|)/drl] e]

  /** ... so that we can annotate the result!
   **/

  IO..•page << Traits..@width:3bp & Traits..@stroking:[Traits..gray 0.8] | [Graphics..stroke pth]

  Traits..@width:1.5bp & Traits..@stroking:Traits..RGB..BLUE
  |
  {
    IO..•page << [Graphics..stroke [shift z][]e]
          << [Graphics..stroke e1]
          << [Graphics..stroke e2]
  }

  Traits..@width:5bp & Traits..@stroking:Traits..RGB..RED
  |
  {
    IO..•page << [Graphics..spot pr] << [Graphics..spot z] << [Graphics..spot e1.end.p] << [Graphics..spot e2.end.p]
  }

  hStyle: Traits..@width:0.5bp & Traits..@stroking:[Traits..gray 0.2]
  angleHead: [Graphics..ShapesArrow width:2bp ...]

  hStyle
  |
  {
    r0: 1cm
    r1: 2.5cm
    r2: 3.5cm
    IO..•page << [Graphics..stroke [shift z][]( e1.begin.T*r0--e1.begin.T*~r1 )]
    IO..•page << [Graphics..stroke [shift z][]( e2.begin.T*r0--e2.begin.T*~r1 )]
    {
      rAngle: 0.8*r1
      arc: [shift z] [] [Geometry..ccw_arc (0m,0m) [rotate ~(5mm/rAngle)][]e2.begin.T*~r1 e2.begin.T*~r1 rAngle]
      IO..•page << [Graphics..stroke [shift z] [] [Geometry..ccw_arc (0m,0m) e2.begin.T*~r1 e1.begin.T*~r1 rAngle]]
            << [Graphics..stroke [shift z] [] [Geometry..cw_arc (0m,0m) [rotate (5mm/rAngle)][]e1.begin.T*~r1 e1.begin.T*~r1 rAngle]
                 head:angleHead]
            << [Graphics..stroke arc head:angleHead]
            << [putlabelRight [Graphics..TeX `$\approx 2\, \alpha$´] arc.begin.p ~1]
    }
    {
      arc1: [shift z] [] [Geometry..cw_arc (0m,0m) e1.begin.T*~r1 p.begin.T*~r1 0.5*(r1+r2)]
      arc2: [shift z] [] [Geometry..ccw_arc (0m,0m) e2.begin.T*~r1 p.begin.T*~r1 0.5*(r1+r2)]
      IO..•page << [Graphics..stroke z--(+~r2*p.begin.T)]
            << [Graphics..stroke [[shift z]*[rotate 0.5*frontAngle] ~(r1+1bp)*p.begin.T--(+(~(r2-r1)*p.begin.T))]]
            << [Graphics..stroke [[shift z]*[rotate ~0.5*frontAngle] ~(r1+1bp)*p.begin.T--(+(~(r2-r1)*p.begin.T))]]
            << [Graphics..stroke arc1 head:angleHead tail:angleHead]
            << [Graphics..stroke arc2 head:angleHead tail:angleHead]
            << [putlabelRight [Graphics..TeX `$\alpha$´] [Layout..mspoint arc1 0.5] ~1]
            << [putlabelRight [Graphics..TeX `$\alpha$´] [Layout..mspoint arc2 0.5] ~1]
    }
    {
      p: e1.end.p--pr
      IO..•page << [Graphics..stroke p]
            << [putlabelRight [Graphics..TeX `$r$´] [Layout..mspoint p 0.5] 0]
    }
    {
      p: pr--e2.end.p
      IO..•page << [Graphics..stroke p]
            << [putlabelRight [Graphics..TeX `$r$´] [Layout..mspoint p 0.5] 0]
    }
    {
      pw: pr + [Numeric..Math..cos 0.5*rearAngle]*r*sl.T
      p1: pw--e1.end.p
      p2: pw--e2.end.p
      IO..•page << [Graphics..stroke p1 head:angleHead tail:angleHead]
            << [putlabelLeft [Graphics..TeX `$w$´] [Layout..mspoint p1 0.5] 1]
            << [Graphics..stroke p2 head:angleHead tail:angleHead]
            << [putlabelLeft [Graphics..TeX `$w$´] [Layout..mspoint p2 0.5] ~1]
    }
    {
      hLine: pr--(+(1.2*r*sl.T))
      arc1: [Geometry..ccw_arc pr hLine.end.p e1.end.p 0.9*r]
      arc2: [Geometry..cw_arc pr hLine.end.p e2.end.p 0.9*r]
      IO..•page << [Graphics..stroke hLine]
            << [Graphics..stroke arc1 head:angleHead tail:angleHead]
            << [putlabelLeft [Graphics..TeX `$\beta$´] [Layout..mspoint arc1 0.5] 1]
            << [Graphics..stroke arc2 head:angleHead tail:angleHead]
            << [putlabelLeft [Graphics..TeX `$\beta$´] [Layout..mspoint arc2 0.5] ~1]
    }

    {
      offset: 5bp
      arc0: p.begin--[p l]
      arc: [Geometry..sidepath2 [Geometry..upsample_bends 20° arc0] offset]
      IO..•page << [Graphics..stroke arc head:angleHead tail:angleHead]
            << [Graphics..stroke arc0.begin.p--(+arc0.begin.N*1.5*offset)]
            << [Graphics..stroke arc0.end.p--(+arc0.end.rN*~2*offset)]
            << [putlabelBelow [Graphics..TeX `$l$´] [Layout..mspoint arc 0.8] 0]
    }
    {
      offset: ~5bp
      arc0: [shift z][]e
      arc: [Geometry..sidepath2 [Geometry..upsample_bends 20° arc0] offset]
      IO..•page << [Graphics..stroke arc head:angleHead tail:angleHead]
            << [Graphics..stroke arc0.begin.p--(+arc0.begin.N*1.5*offset)]
            << [Graphics..stroke arc0.end.p--(+arc0.end.rN*~2*offset)]
            << [putlabelAbove [Graphics..TeX `$h$´] [Layout..mspoint arc 0.7] 0]
    }

  }

}


Traits..@width:1cm
|
{
  pth: (~5cm,~10cm)--(3cm,(+0cm))

  /** First we set up variables that mirror the formal parameters of ShapesArrow.
   **/
  p: [Geometry..reverse pth]
  width:3
  frontAngle:40°
  rearAngle:150°

  /** Show the arrowhead.
   **/
  IO..•page << Traits..@stroking:[Traits..gray 0.7] | [Graphics..stroke pth head:[Graphics..ShapesArrow width:width frontAngle:frontAngle rearAngle:rearAngle ...]]

  /** Then we paste the implementation of ShapesArrow...
   **/
  z: p.begin.p
    lMax: 0.99*[Numeric..Math..abs p]
    w: 0.5*[if [typeof width]=Data..Type..§Float Traits..@width*width width]
    el: [Numeric..Math..min w/[Numeric..Math..sin 0.5*frontAngle] lMax]
    l: [Numeric..Math..min w * ( [Numeric..Math..cot 0.5*frontAngle] - [Numeric..Math..cot 0.5*rearAngle] ) lMax]
    e: [p 0]--[p el] >> [shift ~z]
    sl: [p l]
    pr: sl.p
    dr: e.end.p
    dra: [angle dr]
    drl: (|dr|)
    r: w / [Numeric..Math..sin 0.5*rearAngle]
  d1: sl.p + [[rotate 0.5*rearAngle] (r*sl.T)] - z
  d2: sl.p + [[rotate ~0.5*rearAngle] (r*sl.T)] - z

  /** The following paths are not bound to variables in the implementation, but we need them here.
   **/
  e1: [[shift z]*[rotate [angle d1]-dra]*[scale (|d1|)/drl] e]
  e2: [[shift z]*[rotate [angle d2]-dra]*[scale (|d2|)/drl] e]

  /** ... so that we can annotate the result!
   **/

  IO..•page << Traits..@width:3bp & Traits..@stroking:[Traits..gray 0.8] | [Graphics..stroke pth]

  Traits..@width:1.5bp & Traits..@stroking:Traits..RGB..BLUE
  |
  {
    IO..•page << [Graphics..stroke [shift z][]e]
          << [Graphics..stroke e1]
          << [Graphics..stroke e2]
  }

  Traits..@width:5bp & Traits..@stroking:Traits..RGB..RED
  |
  {
    IO..•page << [Graphics..spot pr] << [Graphics..spot z] << [Graphics..spot e1.end.p] << [Graphics..spot e2.end.p]
  }

  hStyle: Traits..@width:0.5bp & Traits..@stroking:[Traits..gray 0.2]
  angleHead: [Graphics..ShapesArrow width:2bp ...]

  hStyle
  |
  {
    {
      rLbl: 2cm
      arc1: [Geometry..ccw_arc z pr e1.end.p rLbl]
      arc2: [Geometry..cw_arc z pr e2.end.p rLbl]
      IO..•page << [Graphics..stroke arc1 head:angleHead tail:angleHead]
            << [putlabelLeft [Graphics..TeX `$\alpha$´] [Layout..mspoint arc1 0.5] 0]
            << [Graphics..stroke arc2 head:angleHead tail:angleHead]
            << [putlabelLeft [Graphics..TeX `$\alpha$´] [Layout..mspoint arc2 0.5] ~0.5]
    }
    {
      p: e1.end.p--pr
      IO..•page << [Graphics..stroke p]
            << [putlabelRight [Graphics..TeX `$r$´] [Layout..mspoint p 0.5] 0]
    }
    {
      p: pr--e2.end.p
      IO..•page << [Graphics..stroke p]
            << [putlabelRight [Graphics..TeX `$r$´] [Layout..mspoint p 0.5] 0]
    }
    {
      pw: pr + [Numeric..Math..cos 0.5*rearAngle]*r*sl.T
      p1: pw--e1.end.p
      p2: pw--e2.end.p
      IO..•page << [Graphics..stroke p1 head:angleHead tail:angleHead]
            << [putlabelLeft [Graphics..TeX `$w$´] [Layout..mspoint p1 0.5] 1]
            << [Graphics..stroke p2 head:angleHead tail:angleHead]
            << [putlabelLeft [Graphics..TeX `$w$´] [Layout..mspoint p2 0.5] ~1]
    }
    {
      hLine: pr--(+(1.2*r*sl.T))
      arc1: [Geometry..ccw_arc pr hLine.end.p e1.end.p 0.9*r]
      arc2: [Geometry..cw_arc pr hLine.end.p e2.end.p 0.9*r]
      IO..•page << [Graphics..stroke hLine]
            << [Graphics..stroke arc1 head:angleHead tail:angleHead]
            << [putlabelLeft [Graphics..TeX `$\beta$´] [Layout..mspoint arc1 0.5] 1]
            << [Graphics..stroke arc2 head:angleHead tail:angleHead]
            << [putlabelLeft [Graphics..TeX `$\beta$´] [Layout..mspoint arc2 0.5] ~1]
    }

    {
      offset: 5bp
      arc0: p.begin--[p l]
      arc: [Geometry..sidepath [Geometry..upsample_bends 20° arc0] offset]
      IO..•page << [Graphics..stroke arc head:angleHead tail:angleHead]
            << [Graphics..stroke arc0.begin.p--(+arc0.begin.N*1.5*offset)]
            << [Graphics..stroke arc0.end.p--(+arc0.end.rN*~2*offset)]
            << [putlabelBelow [Graphics..TeX `$l$´] [Layout..mspoint arc 0.8] 0]
    }
    {
      offset: ~5bp
      arc0: [shift z][]e
      arc: [Geometry..sidepath [Geometry..upsample_bends 20° arc0] offset]
      IO..•page << [Graphics..stroke arc head:angleHead tail:angleHead]
            << [Graphics..stroke arc0.begin.p--(+arc0.begin.N*1.5*offset)]
            << [Graphics..stroke arc0.end.p--(+arc0.end.rN*~2*offset)]
            << [putlabelAbove [Graphics..TeX `$h$´] [Layout..mspoint arc 0.7] 0]
            << [putlabelBelow [Graphics..TeX `$h$´] [Layout..mspoint e1 0.7] 0]
            << [putlabelAbove [Graphics..TeX `$h$´] [Layout..mspoint e2 0.7] 0]
    }

  }

}