feat: Complete operation through Book Twelve

The only actual new command is the construction of a polygon
   as a face of a previously defined polyhedron.
   Aside from that, just adds some hacky "bugfixes" to Joyce's
   underlying Geometry Applet code to convert drawings that
   Joyce left in 2D when they should be in 3D.

src/adapptlet.civet

@@ -30,6 +30,7 @@ type Description
    usesCaptions: JoyceName[]
    klass: JoyceClass
    ends?: [GeoName, GeoName]
+   parts?: string[][]
 
 // We put both JoyceNames and GeoNames in here, pointing to each other
 // with the otherName property:
@@ -188,7 +189,8 @@ type ClassHandler = (
    args: JoyceArguments,
    index: number,
    cdata: ConstructionData,
-   colors: string[]) => Commander
+   colors: string[],
+   jname: string) => Commander
 type RGB = [number, number, number]
 type XYZ = RGB
 
@@ -274,7 +276,7 @@ function jToG(
          (args.subpoints ?= []).push depGeo
       else if depKlass is 'line'
          (args.subpoints ?= []).push ...ends ?? []
-   cmdr = classHandler[klass] name, method, args, index, cdata, colors
+   cmdr = classHandler[klass] name, method, args, index, cdata, colors, jname
    unless name is jname then cmdr.callbacks.push (api: AppletObject) =>
       api.setCaption name, jname
       api.setLabelStyle name, 3  // style CAPTION = 3
@@ -428,8 +430,10 @@ function jToG(
             console.log 'Setting label vis of', name, 'to', show if traceC
             api.setLabelVisible name, show
 
-   cdata.elements[jname] = {otherName: name, usesCaptions, klass, cmdr.ends}
+   cdata.elements[jname] =
-   cdata.elements[name] = {otherName: jname, usesCaptions, klass, cmdr.ends}
+      {otherName: name, usesCaptions, klass, cmdr.ends, cmdr.parts}
+   cdata.elements[name] =
+      {otherName: jname, usesCaptions, klass, cmdr.ends, cmdr.parts}
    cmdr
 
 function pivotListener(slider: string)
@@ -574,7 +578,7 @@ function proportionSimilar(
 // All of the detailed semantics of each available command lies in this
 // function.
 classHandler: Record<JoyceClass, ClassHandler> :=
-   point: (name, method, args, index, cdata, colors): Commander =>
+   point: (name, method, args, index, cdata, colors, jname): Commander =>
       return := freshCommander()
       {commands, callbacks, parts, auxiliaries} := return.value
       zeroVector := cdata.is3d ? 'Vector((0,0,0))' : 'Vector((0,0))'
@@ -582,7 +586,7 @@ classHandler: Record<JoyceClass, ClassHandler> :=
       aux := name + 'aUx'
       pivotable := cdata.pivot and name !== pivotData[cdata.pivot].pivot
       parts[0].push name
-      // HACK: Special-case corrections for Joyce Elements Bk XI
+      // HACK: Special-case corrections for Joyce Elements Bk XI & XII
       if cdata.title is 'XI.4'
          if name is 'Z' and method is 'fixed' and args.scalar?.length is 3
             method = 'perpendicular'
@@ -598,6 +602,18 @@ classHandler: Record<JoyceClass, ClassHandler> :=
             args.subpoints = ['B','P1','P3']
             args.plane = ['xOyPlane']
             commands.push 'B=(80,140)'
+      if cdata.title is 'XII.7'
+         if (name is 'E' and method is 'lineSlider'
+             and args.subpoints?[1] is cdata.elements['1Y'].otherName)
+            args.subpoints[1] = cdata.elements['1Z'].otherName
+      if cdata.title is 'XII.8'
+         if (name is 'M' and method is 'lineSlider'
+             and args.subpoints?[1] is cdata.elements['1Y'].otherName)
+            args.subpoints[1] = cdata.elements['1Z'].otherName
+      if cdata.title is 'XII.9'
+         if (jname is 'a' and method is 'lineSlider'
+             and args.subpoints?[1] is cdata.elements['1Y'].otherName)
+            args.subpoints[1] = cdata.elements['1Z'].otherName
       switch method
          /angle(?:Bisector|Divider)/
             {center, foot} :=
@@ -976,6 +992,11 @@ classHandler: Record<JoyceClass, ClassHandler> :=
                      'point'
                         moreParts[0].push newObj
                         api.setVisible newObj, false
+         'face'
+            unless args.polyhedron?.length is 1 then return
+            unless args.scalar?.length is 1 then return
+            element := cdata.elements[args.polyhedron[0]]
+            commands.push `${name} = ${element.parts?[2][args.scalar[0]-1]}`
          ///triangle|similar|parallelogram|application|quadrilateral
                |octagon|pentagon|hexagon///
             unless args.subpoints then return
@@ -1058,7 +1079,7 @@ classHandler: Record<JoyceClass, ClassHandler> :=
             auxiliaries.push aux + 1
             makeLinesInvisible callbacks, name
 
-   plane: (name, method, args) =>
+   plane: (name, method, args, index, cdata) =>
       return := freshCommander()
       {commands, callbacks, parts, auxiliaries} := return.value
       parts[2].push name
@@ -1166,7 +1187,7 @@ classHandler: Record<JoyceClass, ClassHandler> :=
                      'segment'
                         moreParts[1].push newObj
                      else
-                        moreParts[2].push newObj
+                        moreParts[2].splice 1,0,newObj
          /pyramid|tetrahedron/
             base .= args.polygon?[0]
             ends[0] = base or aux + 1