feat: new arguments for perpendicular method of point

This should complete all of Joyce's options for constructing
   a point by being perpendicular to something. Also fixes coloring
   of the sphere and adds the planeSlider method for constructing a
   point.

src/adapptlet.civet

@@ -312,7 +312,7 @@ function jToG(
          // we can adjust components after setting overall color, etc.
 
          // Color the "Faces"; they default to 'brighter':
-         if invisible colors[3]
+         if invisible(colors[3]) and (klass !== 'sphere' or invisible colors[2])
             for each face of parts[2]
                if face is name
                   console.log 'Fading out interior of', face if traceC
@@ -322,13 +322,16 @@ function jToG(
                   console.log 'Hiding face', face if traceC
                   api.setVisible face, false
          else
-            faceRGB := joyce2rgb(colors[3] or 'brighter', cdata.bg)
+            surface .= colors[3]
+            if klass is 'sphere' and invisible surface
+               surface = colors[2] // for Joyce, spheres had one circular "edge"
+            faceRGB := joyce2rgb(surface or 'brighter', cdata.bg)
             deep := ['circle', 'polygon', 'sector']
             filling := deep.includes(klass) ? 0.7 : 0.2
             for each face of parts[2]
                if traceC
                   console.log 'Coloring face', face, 'to',
-                     colors[3], '=', faceRGB
+                     surface, '=', faceRGB
                api.setVisible face, true
                api.setFilling face, filling
                api.setColor face, ...faceRGB
@@ -683,12 +686,36 @@ classHandler: Record<JoyceClass, ClassHandler> :=
             unless pt then return
             commands.push `${name} = ${pt[0]} + ${pt[2]} - ${pt[1]}`
          'perpendicular'
-            // Note only the two-point option implemented so far
+            pt := args.subpoints
-            unless args.subpoints return
+            unless pt return
             inPlane := args.plane ? `,${args.plane[0]}` : defaultPlane
-            [center, direction] := args.subpoints
+            center := pt[0]
+            switch pt.length
+               when 2
                   commands.push
-               `${name} = Rotate(${direction}, pi/2, ${center}${inPlane})`
+                     `${name} = Rotate(${pt[1]}, pi/2, ${center}${inPlane})`
+               when 3 // perpendicular **to** the plane
+                  // Uses lots of auxiliaries
+                  commands.push
+                     `${aux}1 = Circle(${center}, Distance(${pt[1]}, ${pt[2]})${inPlane})`
+                     `${aux}2 = PointIn(${aux}1)`
+                     `${aux}3 = PerpendicularLine(${center}${inPlane})`
+                     `${aux}4 = Plane(${aux}2, ${aux}3)`
+                     `${name} = Rotate(${aux}2, pi/2, ${center}, ${aux}4)`
+                  auxiliaries.push aux+n for n of [1..4]
+               when 4
+                  commands.push
+                     `${aux}1 = Ray(${center}, Rotate(${pt[1]}, pi/2, ${center}${inPlane}))`
+                     `${aux}2 = Circle(${center}, Distance(${pt[2]},${pt[3]})${inPlane})`
+                     `${name} = Intersect(${aux}1, ${aux}2)`
+                  auxiliaries.push aux+1, aux+2
+         'planeSlider'
+            pln := args.plane?[0]
+            unless pln then return
+            commands.push `${name} = PointIn(${pln})`
+            if args.scalar and args.scalar.length
+               callbacks.push (api: AppletObject) =>
+                  api.setCoords name, ...vertFlipped(args.scalar or [], cdata)
          /proportion|similar/
             [source, displacement] :=
                proportionSimilar method, args, cdata, aux, commands, auxiliaries
@@ -741,7 +768,7 @@ classHandler: Record<JoyceClass, ClassHandler> :=
               `${aux}4 = If(${condition}, ${aux}2, ${aux}1)`
             ends[0] = aux + 3
             ends[1] = aux + 4
-            auxiliaries.push ...[1..4].map (n) => aux + n
+            auxiliaries.push aux+n for n of [1..4]
          'chord'
             // To match Joyce, we need to get the ordering here correct.
             // The complicated condition about distances is modeled after
@@ -765,7 +792,7 @@ classHandler: Record<JoyceClass, ClassHandler> :=
               `${aux}4 = If(${condition}, ${aux}1, ${aux}2)`
             ends[0] = aux + 3
             ends[1] = aux + 4
-            auxiliaries.push ...[1..4].map (n) => aux + n
+            auxiliaries.push aux+n for n of [1..4]
          'connect'
             unless args.subpoints and args.subpoints.length is 2 then return
             ends[0] = args.subpoints[0]
@@ -946,7 +973,7 @@ classHandler: Record<JoyceClass, ClassHandler> :=
                   `${aux}1 = Angle(${pt[3]},${pt[2]},${pt[4]}${inSourcePlane})`
                   `${aux}2 = Rotate(${pt[1]},${aux}1,${pt[0]}${inDestPlane})`
                   `${aux}3 = ${pt[0]} + (${aux}2 - ${pt[0]})*${factor}`
-               auxiliaries.push ...[1..3].map (n) => aux + n
+               auxiliaries.push aux+n for n of [1..3]
                pt = [pt[0], pt[1], aux+3]
             else
                commands.push ''
@@ -1041,8 +1068,7 @@ classHandler: Record<JoyceClass, ClassHandler> :=
                `${aux}5 = ${pt[3]} + ${pt[1]} - ${pt[0]}`
                `${aux}6 = ${pt[3]} + ${pt[2]} - ${pt[0]}`
                `${aux}7 = ${pt[3]} + ${pt[2]} + ${pt[1]} - 2*${pt[0]}`
-            for i of [4..7]
+            auxiliaries.push aux+i for i of [4..7]
-               auxiliaries.push aux+i
             pt = [...pt, ...auxiliaries]
             parts[0].push ...pt
             generalRecipe :=
@@ -1134,7 +1160,7 @@ function makeAngDiv(
       `${aux}2 = Angle(${start}, ${center}, ${end}${inPlane})`
       `${aux}3 = If(${aux}2 > pi, ${aux}2 - 2*pi, ${aux}2)`
       `${aux}4 = Rotate(${start}, ${aux}3/${n}, ${center}${inPlane})`
-   auxiliaries.push ...[2..4].map (i) => `${aux}${i}`
+   auxiliaries.push aux+i for i of [2..4]
    return {center, foot: `Intersect(${destination}, Ray(${center}, ${aux}4))`}
 
 // helper for separating color of perimeter and interior: