Add relations to center and orient the construction

engine-proto/Engine.jl

@@ -72,21 +72,21 @@ const coordnames = IdDict{Symbol, Vector{Union{Symbol, Nothing}}}(
   nameof(Sphere) => [:rₛ, :sₛ, :xₛ, :yₛ, :zₛ]
 )
 
-coordname(elem::Element, index) = coordnames[nameof(typeof(elem))][index]
+coordname(elt::Element, index) = coordnames[nameof(typeof(elt))][index]
 
-function pushcoordname!(coordnamelist, indexed_elem::Tuple{Any, Element}, coordindex)
-  elemindex, elem = indexed_elem
-  name = coordname(elem, coordindex)
+function pushcoordname!(coordnamelist, indexed_elt::Tuple{Any, Element}, coordindex)
+  eltindex, elt = indexed_elt
+  name = coordname(elt, coordindex)
   if !isnothing(name)
-    subscript = Subscripts.sub(string(elemindex))
+    subscript = Subscripts.sub(string(eltindex))
     push!(coordnamelist, Symbol(name, subscript))
   end
 end
 
-function takecoord!(coordlist, indexed_elem::Tuple{Any, Element}, coordindex)
-  elem = indexed_elem[2]
-  if !isnothing(coordname(elem, coordindex))
-    push!(elem.coords, popfirst!(coordlist))
+function takecoord!(coordlist, indexed_elt::Tuple{Any, Element}, coordindex)
+  elt = indexed_elt[2]
+  if !isnothing(coordname(elt, coordindex))
+    push!(elt.coords, popfirst!(coordlist))
   end
 end
 
@@ -132,12 +132,12 @@ mutable struct Construction{T}
   end
 end
 
-function Base.push!(ctx::Construction{T}, elem::Point{T}) where T
-  push!(ctx.points, elem)
+function Base.push!(ctx::Construction{T}, elt::Point{T}) where T
+  push!(ctx.points, elt)
 end
 
-function Base.push!(ctx::Construction{T}, elem::Sphere{T}) where T
-  push!(ctx.spheres, elem)
+function Base.push!(ctx::Construction{T}, elt::Sphere{T}) where T
+  push!(ctx.spheres, elt)
 end
 
 function Base.push!(ctx::Construction{T}, rel::Relation{T}) where T
@@ -150,10 +150,10 @@ end
 function realize(ctx::Construction{T}) where T
   # collect coordinate names
   coordnamelist = Symbol[]
-  elemenum = enumerate(Iterators.flatten((ctx.spheres, ctx.points)))
+  eltenum = enumerate(Iterators.flatten((ctx.spheres, ctx.points)))
   for coordindex in 1:5
-    for indexed_elem in elemenum
-      pushcoordname!(coordnamelist, indexed_elem, coordindex)
+    for indexed_elt in eltenum
+      pushcoordname!(coordnamelist, indexed_elt, coordindex)
     end
   end
   
@@ -161,25 +161,34 @@ function realize(ctx::Construction{T}) where T
   coordring, coordqueue = polynomial_ring(parent_type(T)(), coordnamelist, ordering = :degrevlex)
   
   # retrieve coordinates
-  for (_, elem) in elemenum
-    empty!(elem.coords)
+  for (_, elt) in eltenum
+    empty!(elt.coords)
   end
   for coordindex in 1:5
-    for indexed_elem in elemenum
-      takecoord!(coordqueue, indexed_elem, coordindex)
+    for indexed_elt in eltenum
+      takecoord!(coordqueue, indexed_elt, coordindex)
     end
   end
   
   # construct coordinate vectors
-  for (_, elem) in elemenum
-    buildvec!(elem)
+  for (_, elt) in eltenum
+    buildvec!(elt)
   end
   
   # turn relations into equations
   eqns = vcat(
     equation.(ctx.relations),
-    [elem.rel for (_, elem) in elemenum if !isnothing(elem.rel)]
+    [elt.rel for (_, elt) in eltenum if !isnothing(elt.rel)]
   )
+  
+  # add relations to center and orient the construction
+  if !isempty(ctx.points)
+    append!(eqns, [sum(pt.coords[k] for pt in ctx.points) for k in 1:3])
+  end
+  if !isempty(ctx.spheres)
+    append!(eqns, [sum(sph.coords[k] for sph in ctx.spheres) for k in 3:4])
+  end
+  
   Generic.Ideal(coordring, eqns)
 end