2017-11-07 11:43:00

1 files changed, 171 insertions, 6 deletions

diff --git a/doc/context/sources/general/manuals/nodes/nodes.tex b/doc/context/sources/general/manuals/nodes/nodes.tex
index 190e654fc..7bf88302c 100644
--- a/doc/context/sources/general/manuals/nodes/nodes.tex
+++ b/doc/context/sources/general/manuals/nodes/nodes.tex
@@ -20,7 +20,7 @@
 % comment   : This manual orginates in an article by Alan so anything wrong in here is Hans
 %             fault as he converted it.
 %
-% comment   : The conver images are form the NASA website.
+% comment   : The conver images are from the NASA website.
 
 \definemeasure [layout:margin] [\paperheight/20]
 
@@ -179,6 +179,14 @@
   [offset=1pt,
    foregroundcolor=white]
 
+\startMPdefinitions
+  ahlength  := 12pt ;
+  ahangle   := 30 ;
+  ahvariant := 1 ; % dimpled
+\stopMPdefinitions
+
+% Only here do we use the special nodes:: instance
+
 \startreusableMPgraphic{nodes::krebs}
 
    % The Bethe cycle for energy production in stars (1939), following
@@ -236,7 +244,7 @@
         % Alan wanted a sun in the background combined somehow with the energy
         % harvesting molecule so here we go. The images that are used come from
         % the NASA website and I used them as screen saver for a while. The
-        % version that I generate use another variant than the one on the users
+        % version that I generate uses a variant from the one on the user's
         % machine.
 
         draw textext("\externalfigure[\framedparameter{imagename}]")
@@ -292,10 +300,6 @@ figure} [fig:AB].
 
 \startplacefigure [reference=fig:AB]
     \startMPcode
-        ahlength  := 12pt ;
-        ahangle   := 30 ;
-        ahvariant := 1 ; % dimpled
-
         u := 1cm ;
         save nodepath ; path nodepath ;
         nodepath := (left -- right) scaled u ;
@@ -673,6 +677,8 @@ located on the same path.
          \cite[authoryears] [Krebs1946] representation of a catalytic process.}]
 \startMPcode
 
+  % differs slightly from \reuseMPgraphic{nodes::krebs}
+
   % The Bethe cycle for energy production in stars (1939), following Krebs (1946)
 
   save p ; path p[] ;
@@ -1141,6 +1147,165 @@ the tree structure.
 
 \stopsubject
 
+\startsubject [title=A 3D projection]
+
+% This special instance could become part of the base distribution...
+
+\defineMPinstance [three] [format=metafun,extensions=yes,initializations=yes,method=double]
+
+\startMPdefinitions{three}
+% Simple 3D->2D projection
+% Adapted from Urs Oswald, Dr.sc.math. ETH
+% http://www.ursoswald.ch/metapost/tutorial.html
+% and extended!
+
+transform t, Txy, Pxy ;
+pair P[] ;
+path p[] ;
+
+P0=origin ;                             % origin in MetaPost coordinates (bp)
+P1=(left rotated 60) scaled (cosd 60) ; % x axis (in mathematical coordinates)
+
+% t: maps mathematical 2D coordinates onto MetaPost coordinates.
+
+t:=identity shifted P0 ;
+
+% Pxy is the projection of the 3D plane z=0 onto the mathematical 2D coordinates.
+% Pxy is determined by  3  e q u a t i o n s  describing
+% how (1,0), (0,1), and (0,0) are mapped
+
+   P1=(1,0)transformed Pxy ;   % Pxy: (1,0) --> P1
+(1,0)=(0,1)transformed Pxy ;   %      (0,1) --> (1,0)
+(0,0)=(0,0)transformed Pxy ;   %      (0,0) --> (0,0)
+
+% mathematical 2D coordinates --> MetaPost coordinates
+
+Txy:=Pxy transformed t ;
+
+let triplet=color ;
+let Xpart=redpart ;
+let Ypart=greenpart ;
+let Zpart=bluepart ;
+triplet Origin, Xunitvector, Yunitvector, Zunitvector ;
+Origin      = (0,0,0) ;
+Xunitvector = (1,0,0) ;
+Yunitvector = (0,1,0) ;
+Zunitvector = (0,0,1) ;
+
+% overloads let abs=length ; from plain.mp
+
+vardef abs primary p =
+  if triplet p : sqrt((Xpart p)**2+(Ypart p)**2+(Zpart p)**2) else : length p fi
+enddef ;
+
+vardef projection expr t  =      % returns MetaPost coordinates (bp)
+   if triplet t :
+     (Xpart t, Ypart t) transformed Txy shifted (0,Zpart t)
+   elseif pair t :
+     t transformed Txy
+   else :
+     origin transformed Txy
+   fi
+enddef ;
+
+primarydef p dotproduct q =
+  ((Xpart p)*(Xpart q) + (Ypart p)*(Ypart q) + (Zpart p)*(Zpart q))
+enddef ;
+
+primarydef p crossproduct q =
+  ((Ypart p)*(Zpart q) - (Zpart p)*(Ypart q),
+   (Zpart p)*(Xpart q) - (Xpart p)*(Zpart q),
+   (Xpart p)*(Ypart q) - (Ypart p)*(Xpart q))
+enddef ;
+
+primarydef p rotatedaboutX q =
+  hide(
+    pair yz ;
+    yz:=(Ypart p, Zpart p) ;
+    yz:=yz rotated q ;)
+  (Xpart p, xpart yz, ypart yz)
+enddef ;
+
+primarydef p rotatedaboutY q =
+  hide(
+    pair zx ;
+    zx:=(Zpart p, Xpart p) ;
+    zx:=zx rotated q ;)
+  (ypart zx, Ypart p, xpart zx)
+enddef ;
+
+primarydef p rotatedaboutZ q =
+  hide(
+    pair xy ;
+    xy:=(Xpart p, Ypart p) ;
+    xy:=xy rotated q ;)
+  (xpart xy, ypart xy, Zpart p)
+enddef ;
+
+vardef draw_vector@# (expr v, s) text t =
+    if triplet v :
+      drawarrow projection(Origin)--projection(v) t ;
+      if string s :
+        label@#(s, projection(v)) t ;
+      fi
+    fi
+enddef ;
+
+\stopMPdefinitions
+
+\startMPcalculation{three}
+    ahlength  := 12pt ;
+    ahangle   := 30 ;
+    ahvariant := 1 ; % dimpled
+\stopMPcalculation
+
+\startplacefigure [location=left]
+    \startMPcode{three}
+
+        nodepath := (
+            projection Origin --
+            projection (1,0,0) --
+            projection (1,1,0) --
+            projection (0,1,0) --
+            projection (0,1,1) --
+            projection (1,1,1) --
+            projection (1,0,1) --
+            projection (0,0,1) --
+            cycle
+        ) scaled 5cm ;
+
+        draw node(0,"\node{${\cal C}_{i\cal P}^{\mathrm{nt}}$}") ;
+        draw node(1,"\node{${\cal C}_{i\cal G}^{\mathrm{nt}}$}") ;
+        draw node(2,"\node{${\cal C}_{j\cal P}^{\mathrm{nt}}$}") ;
+        draw node(3,"\node{${\cal C}_{j\cal G}^{\mathrm{nt}}$}") ;
+        draw node(4,"\node{${\cal C}_{j\cal G}$}") ;
+        draw node(5,"\node{${\cal C}_{j\cal P}$}") ;
+        draw node(6,"\node{${\cal C}_{i\cal G}$}") ;
+        draw node(7,"\node{${\cal C}_{i\cal P}$}") ;
+
+        interim crossingscale := 30 ;
+
+        drawdoublearrows fromto(0,0,1) ;
+        drawdoublearrows fromto(0,1,2) ;
+        drawdoublearrows fromto(0,2,3) ;
+        drawdoublearrows fromto(0,3,0) crossingunder fromto(0,2,5) ;
+
+        drawdoublearrows fromto(0,7,6) ;
+        drawdoublearrows fromto(0,6,5) ;
+        drawdoublearrows fromto(0,5,4) ; label.lft("\node{$τ_j$~}", center fromto(0,5,4)) ;
+        drawdoublearrows fromto(0,7,4) ; label.top("\node{$σ$}",    center fromto(0,7,4)) ;
+
+        drawdoublearrows fromto(0,0,7) crossingunder fromto(0,6,5) ;
+                            label.lrt("\node{$Ψ^{\mathrm{nt}}$}", center fromto(0,0,7)) ;
+        drawdoublearrows fromto(0,1,6) ;
+        drawdoublearrows fromto(0,2,5) ;
+        drawdoublearrows fromto(0,3,4) ;
+
+    \stopMPcode
+\stopplacefigure
+
+\stopsubject
+
 \startsubject [title=Two final examples]
 
 \defineframed