In the last two tutorials, we saw a useful feature and trick which allows us to model arbitrary connectivity patterns between relations. However, these mechanisms require programmers to use an unintuitive interface: L.Where(...) loops. In earlier tutorials, we saw a much more intuitive loop syntax for triangle meshes: v.edges. The missing ingredient is a macro. In this tutorial, we explain how geometric domain authors can encapsulate and hide relational details behind more intuitive syntax.

Besides macros, we’ll also introduce field-functions. These two tools allow simulation and geometric domain authors to abstract functionality and retrofit old code.

Unlike previous tutorials, this file will not compute much, though it can still be safely executed.

import 'ebb'
local L = require 'ebblib'

local ioOff = require ''
local PN    = require 'ebb.lib.pathname'
local mesh  = ioOff.LoadTrimesh( PN.scriptdir() .. '' )

local vdb   = require('ebb.lib.vdb')

local v_triples       = mesh.triangles.v:Dump({})
local tri_ids, v_ids  = {}, {}
for k=0,mesh.triangles:Size()-1 do
  tri_ids[ 3*k + 1 ] = k
  tri_ids[ 3*k + 2 ] = k
  tri_ids[ 3*k + 3 ] = k
  local triple = v_triples[k+1]
  v_ids[ 3*k + 1 ] = triple[1]
  v_ids[ 3*k + 2 ] = triple[2]
  v_ids[ 3*k + 3 ] = triple[3]

local triangles_of_vertex = L.NewRelation {
  name = "triangles_of_vertex",
  size = #tri_ids,
triangles_of_vertex:NewField('tri', mesh.triangles):Load(tri_ids)
triangles_of_vertex:NewField('v', mesh.vertices):Load(v_ids)


The program starts the same way as in the last tutorial; by defining a join-table.

local swap_macro = L.Macro(function(a, b)
  return ebb quote
    var tmp = a
    a = b
    b = tmp
  in 0 end
local ebb use_swap( v : mesh.vertices )
  var a : = 1
  var b : = 2
  swap_macro(a, b)
  L.assert(b == 1)

To start, we define a macro that swaps two values. This macro is defined by a Lua function that runs at compile time, returning a quoted piece of Ebb code. This quoted bit of code gets spliced into the ebb function below where swap_macro is called. That is, the macro gets substituted, rather than executed like a function. The design here is very similar to Terra, though less fully developed. (Note that the in 0 is needed in case an Ebb quote is used somewhere where an expression is expected.)

Why not just define swap with another Ebb function? If we did that, then the two arguments to swap would be passed by value. Swapping them would accomplish nothing in the calling context. However, because a macro is substituted, the parameters are really just other bits of code containing the variable symbols/names. In general, macros are needed in some weird cases like these where we want to break the rules of normal function calls.

local triangle_macro = L.Macro(function(v)
  return ebb `L.Where(triangles_of_vertex.v, v).tri
mesh.vertices:NewFieldMacro('triangles', triangle_macro)

One of the special features of Ebb is the ability to install macros on relations as if they were fields. Now that we’ve installed this macro, we can clean up the code for computing the dual-area of a vertex.

mesh.vertices:NewField('dual_area', L.double):Load(0.0)
mesh.triangles:NewField('area', L.double):Load(0.0)

local ebb compute_area ( t : mesh.triangles )
  var e01 = t.v[1].pos - t.v[0].pos
  var e02 = t.v[2].pos - t.v[0].pos

  t.area = L.length( L.cross(e01, e02) )

local ebb compute_dual_area ( v : mesh.vertices )
  for t in v.triangles do
    v.dual_area += t.area
  v.dual_area = v.dual_area / 3.0

Notice that the query loop in compute_dual_area() now reads for t in v.triangles do rather than for t in L.Where(...).tri do. Even though L.Where(...) is not a value that could be returned from a function, we can use a macro to abstract the snippet of code. By further using the NewFieldMacro() feature, we can make the user-syntax clean and uniform. This is how v.edges is defined in the standard triangle library.

mesh.vertices:NewField('density', L.double):Load(1.0)
mesh.vertices:NewFieldReadFunction('mass', ebb ( v )
  return v.dual_area * v.density

Besides Field Macros, we can also install functions as if they were fields. This gives us a way to define derived quantities without having to compute and store a new field. For instance, here mass can be defined in terms of area and density. If the area changes, then so does the mass. Field-functions convert to function calls unlike field-macros, which get replaced by a macro-substitution.

When possible, try to use a field function before you resort to a macro. You will generally have an easier time debugging your code and avoiding gotchas.

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a part of the Liszt project and PSAAP II center at Stanford University