%% physketch.mechanics.sty
%% Mechanics part of physketch: bodies, pistons, springs, rods, pulleys,
%% fulcrums, weights and nuts.
%%
%% Copyright (C) 2024-2026 Azamat Gimaev
%% This work may be distributed and/or modified under the conditions of
%% the LaTeX Project Public License, either version 1.3c of this license
%% or (at your option) any later version.
\NeedsTeXFormat{LaTeX2e}[2020/10/01]
\ProvidesPackage{physketch.mechanics}
  [2026/10/20 v0.1.0 physketch: mechanics]

\RequirePackage{physketch.general}

% ---------------------------------------------------------------------
% Bodies
% ---------------------------------------------------------------------
\tikzset{
  body/.style       = {draw, fill=body},
  light body/.style = {draw, fill=lightbody},
  dark body/.style  = {draw, fill=darkbody},
  piston/.style     = {draw, fill=body},
  lifted/.style     = {shift={(#1:\pgfkeysvalueof{/physketch/gap})}},
  lifted/.default   = 90,
}

% ---------------------------------------------------------------------
% Springs
% ---------------------------------------------------------------------
% \draw[spring] (A) -- (B);  \draw[spring={coils=8, amplitude=3mm}] ...
\pgfqkeys{/physketch/spring}{
  segment length/.initial = 2mm,
  coils/.initial          = {},
  amplitude/.initial      = 2mm,
  ends/.initial           = 1mm,
  shape/.is choice,
  shape/snake/.code       = \def\physketch@spring@shape{snake},
  shape/zigzag/.code      = \def\physketch@spring@shape{zigzag},
  snake/.style            = {shape=snake},
  zigzag/.style           = {shape=zigzag},
}
\def\physketch@spring@shape{snake}

% one half of a period, up (#1 = 1) or down (#1 = -1)
\pgfdeclaredecoration{physketch spring}{initial}{
  \state{initial}[width=0pt, next state=up,
      persistent precomputation=\physketch@spring@setup]{}
  \state{up}[width=.5\pgfdecorationsegmentlength, next state=down,
      switch if less than=.5\pgfdecorationsegmentlength-0.01pt to final]
    {\physketch@spring@half{1}}
  \state{down}[width=.5\pgfdecorationsegmentlength, next state=up,
      switch if less than=.5\pgfdecorationsegmentlength-0.01pt to final]
    {\physketch@spring@half{-1}}
  \state{final}{\pgfpathlineto{\pgfpointdecoratedpathlast}}
}
\def\physketch@spring@setup{%
  \edef\physketch@coils{\pgfkeysvalueof{/physketch/spring/coils}}%
  \ifx\physketch@coils\@empty
    \pgfmathsetlength\pgfdecorationsegmentlength
      {\pgfkeysvalueof{/physketch/spring/segment length}}%
  \else
    \pgfmathsetlength\pgfdecorationsegmentlength
      {\pgfdecoratedremainingdistance/(\physketch@coils)}%
  \fi
  \pgfmathsetlength\pgfdecorationsegmentamplitude
    {\pgfkeysvalueof{/physketch/spring/amplitude}}%
}
\def\physketch@spring@half#1{%
  \csname physketch@spring@\physketch@spring@shape\endcsname{#1}%
}
\def\physketch@spring@snake#1{%
  \pgfpathsine{\pgfqpoint{.25\pgfdecorationsegmentlength}%
    {#1\pgfdecorationsegmentamplitude}}%
  \pgfpathcosine{\pgfqpoint{.25\pgfdecorationsegmentlength}%
    {-#1\pgfdecorationsegmentamplitude}}%
}
\def\physketch@spring@zigzag#1{%
  \pgfpathlineto{\pgfqpoint{.25\pgfdecorationsegmentlength}%
    {#1\pgfdecorationsegmentamplitude}}%
  \pgfpathlineto{\pgfqpoint{.5\pgfdecorationsegmentlength}{0pt}}%
}

% circuitikz also has a `spring' key (a bipole); physketch.circuits
% keeps it as `circuit spring' and calls this macro again
\def\physketch@definespring{%
  \tikzset{
    spring/.code = {%
      \pgfqkeys{/physketch/spring}{##1}%
      \tikzset{decorate, decoration={physketch spring,
        pre length=\pgfkeysvalueof{/physketch/spring/ends},
        post length=\pgfkeysvalueof{/physketch/spring/ends}}}%
    },
    spring/.default = {},
  }%
}
\physketch@definespring

% ---------------------------------------------------------------------
% Rods divided into equal parts
% ---------------------------------------------------------------------
% \draw[rod={segments=10, width=1.5mm, name=R}] (A) -- (B);
% A straight bar from A to B made of alternating light and dark parts.
% With a name it provides the coordinates R-<i> (i = 0..segments) on the
% axis of the bar at the borders of the parts, and R-<i>-top, R-<i>-bottom
% on its sides (top is on the left of the direction from A to B).
\newif\ifphysketch@rod@dark
\pgfqkeys{/physketch/rod}{
  segments/.initial = 10,
  width/.initial    = 1.5mm,
  name/.initial     = {},
  light/.initial    = white,
  dark/.initial     = darkbody,
  start dark/.code  = \physketch@rod@darktrue,
  start light/.code = \physketch@rod@darkfalse,
}
\pgfdeclaredecoration{physketch rod}{segment}{
  \state{segment}[width=\pgfdecoratedinputsegmentremainingdistance,
                  next state=segment]{%
    \pgfinterruptpath
      \pgfscope
        \physketch@rod@draw
      \endpgfscope
    \endpgfinterruptpath
  }
  \state{final}{}
}
\def\physketch@rodkey#1{\pgfkeysvalueof{/physketch/rod/#1}}
\def\physketch@rod@draw{%
  \pgfmathsetlengthmacro\physketch@L{\pgfdecoratedinputsegmentlength}%
  \pgfmathsetlengthmacro\physketch@ww{\physketch@rodkey{width}}%
  \pgfmathsetlengthmacro\physketch@w{\physketch@ww/2}%
  \pgfmathtruncatemacro\physketch@n{\physketch@rodkey{segments}}%
  \pgfmathsetlengthmacro\physketch@seg{\physketch@L/\physketch@n}%
  \edef\physketch@name{\physketch@rodkey{name}}%
  \ifphysketch@rod@dark\def\physketch@parity{0}\else\def\physketch@parity{1}\fi
  % the parts
  \foreach \physketch@i in {1,...,\physketch@n}{%
    \pgfmathsetlengthmacro\physketch@x{(\physketch@i-1)*\physketch@seg}%
    \pgfmathparse{mod(\physketch@i+\physketch@parity,2)==0}%
    \ifnum\pgfmathresult=1
      \pgfsetfillcolor{\physketch@rodkey{dark}}%
    \else
      \pgfsetfillcolor{\physketch@rodkey{light}}%
    \fi
    \pgfpathrectangle{\pgfqpoint{\physketch@x}{-\physketch@w}}%
      {\pgfqpoint{\physketch@seg}{\physketch@ww}}%
    \pgfusepath{fill}%
  }%
  % the outline
  \pgfpathrectangle{\pgfqpoint{0pt}{-\physketch@w}}%
    {\pgfqpoint{\physketch@L}{\physketch@ww}}%
  \pgfusepath{stroke}%
  % the coordinates
  \ifx\physketch@name\@empty\else
    \foreach \physketch@i in {0,...,\physketch@n}{%
      \pgfmathsetlengthmacro\physketch@x{\physketch@i*\physketch@seg}%
      \pgfcoordinate{\physketch@name-\physketch@i}%
        {\pgfqpoint{\physketch@x}{0pt}}%
      \pgfcoordinate{\physketch@name-\physketch@i-top}%
        {\pgfqpoint{\physketch@x}{\physketch@w}}%
      \pgfcoordinate{\physketch@name-\physketch@i-bottom}%
        {\pgfqpoint{\physketch@x}{-\physketch@w}}%
    }%
  \fi
}
\tikzset{
  rod/.code = {%
    \physketch@rod@darkfalse
    \pgfqkeys{/physketch/rod}{#1}%
    \tikzset{decorate, decoration={physketch rod}}%
  },
  rod/.default = {},
}

% ---------------------------------------------------------------------
% Pulleys
% ---------------------------------------------------------------------
% \pulley[name=p, outer=1cm, inner=0.05cm]{(x,y)}
% The pulley is a circular node `p' (anchors p.west, p.-45, ...) with an
% axle node `p-center'; lines drawn from (p-center) start at the axle.
\pgfqkeys{/physketch/pulley}{
  name/.initial  = {},
  outer/.initial = 0.5cm,
  inner/.initial = 0.05cm,
  .unknown/.code = \physketch@unknown{#1},
}
\NewDocumentCommand\pulley{O{}m}{%
  \begingroup
    \def\physketch@opts{}%
    \pgfqkeys{/physketch/pulley}{#1}%
    \physketch@getname{pulley}%
    \pgfmathsetlengthmacro\physketch@outer{2*(\pgfkeysvalueof{/physketch/pulley/outer})}%
    \pgfmathsetlengthmacro\physketch@inner{2*(\pgfkeysvalueof{/physketch/pulley/inner})}%
    \edef\physketch@do{\noexpand\node[transform shape, circle, draw, thick, inner sep=0pt,
      outer sep=0pt, minimum size=\physketch@outer,
      \unexpanded\expandafter{\physketch@opts}] (\physketch@name) at
      \unexpanded{#2} {};}%
    \physketch@do
    \node[transform shape, circle, draw, fill=white, inner sep=0pt, outer sep=0pt,
      minimum size=\physketch@inner] (\physketch@name-center) at #2 {};
  \endgroup
}

% ---------------------------------------------------------------------
% Pistons
% ---------------------------------------------------------------------
% \piston[name=P, width=2cm, thickness=1mm, rod=1cm, rod side=north]{(x,y)}
% The plate is a rectangular node `P' centred at (x,y); the rod starts at
% P.<rod side> and ends at the coordinate `P-rod'.
\pgfqkeys{/physketch/piston}{
  name/.initial      = {},
  width/.initial     = 2cm,
  thickness/.initial = 1mm,
  rod/.initial       = 1cm,
  rod side/.initial  = north,
  .unknown/.code     = \physketch@unknown{#1},
}
\NewDocumentCommand\piston{O{}m}{%
  \begingroup
    \def\physketch@opts{}%
    \pgfqkeys{/physketch/piston}{#1}%
    \physketch@getname{piston}%
    \pgfmathsetlengthmacro\physketch@w{\pgfkeysvalueof{/physketch/piston/width}}%
    \pgfmathsetlengthmacro\physketch@h{\pgfkeysvalueof{/physketch/piston/thickness}}%
    \pgfmathsetlengthmacro\physketch@rod{\pgfkeysvalueof{/physketch/piston/rod}}%
    \edef\physketch@side{\pgfkeysvalueof{/physketch/piston/rod side}}%
    \edef\physketch@do{\noexpand\node[transform shape, rectangle, draw, fill=body,
      inner sep=0pt, outer sep=0pt, minimum width=\physketch@w,
      minimum height=\physketch@h, \unexpanded\expandafter{\physketch@opts}]
      (\physketch@name) at \unexpanded{#2} {};}%
    \physketch@do
    \coordinate (\physketch@name-rod) at
      ($(\physketch@name.\physketch@side)!-\physketch@rod!(\physketch@name.center)$);
    \ifdim\physketch@rod>0pt
      \draw[thick] (\physketch@name.\physketch@side) -- (\physketch@name-rod);
    \fi
  \endgroup
}

% ---------------------------------------------------------------------
% Pictures
% ---------------------------------------------------------------------
\tikzset{
  % a fulcrum (point of support): the apex is at the origin, the base with
  % its hatching below; rotate=180 gives a point of suspension
  pics/fulcrum/.style = {code={
    \draw (0,0) -- (0.1,-0.173) -- (-0.1,-0.173) -- cycle;
    \draw[surface] (-0.2,-0.173) -- (0.2,-0.173);
    \coordinate (-center) at (0,0);
    \coordinate (-base) at (0,-0.173);
  }},
  pics/weight/.style = {code={
    \draw[fill=body] (-.2,0) -- (-.2,.3)
      .. controls (0,.4) and (-.1,.4) .. (-.1,.5) arc[start angle=180,
      end angle=0, radius=.1] .. controls (.1,.4) and (0,.4) .. (.2,.3)
      -- (.2,0) -- cycle;
    \coordinate (-center) at (0,.2);
    \coordinate (-top) at (0,.6);
  }},
  pics/nut/.style = {code={
    \begin{scope}[scale=0.4]
      \draw[fill=body, even odd rule]
        (0:1) -- (60:1) -- (120:1) -- (180:1) -- (240:1) -- (300:1) -- cycle
        (0,0) circle[radius=0.45];
    \end{scope}
    \coordinate (-center) at (0,0);
  }},
}

\endinput