Support arbitrary expressions in perlin noise rendering script.

scripts/devel/test-perlin.lua

@@ -4,61 +4,117 @@ local args = {...}
 local rng = dfhack.random.new(3)
 
 if #args < 3 then
-    qerror('Usage: devel/test-perlin <fname.pgm> <density> <coeff|expr...x[...y[...z]]>...')
+    qerror('Usage: devel/test-perlin <fname.pgm> <density> <expr> [-xy <xyscale>] [-z <zscale>]')
 end
 
 local fname = table.remove(args,1)
 local goal = tonumber(table.remove(args,1)) or qerror('Invalid density')
+local expr = table.remove(args,1) or qerror('No expression')
+local zscale = 2
+local xyscale = 1
 
-local zscale = 6
+for i = 1,#args,2 do
-
+    if args[i] == '-xy' then
-local coeffs = {}
+        xyscale = tonumber(args[i+1]) or qerror('Invalid xyscale')
-local fns = {}
+    end
+    if args[i] == '-z' then
+        zscale = tonumber(args[i+1]) or qerror('Invalid zscale')
+    end
+end
 
-local env = copyall(math)
+local fn_env = copyall(math)
-env.apow = function(x,y) return math.pow(math.abs(x),y) end
+
+fn_env.rng = rng
+fn_env.apow = function(x,y) return math.pow(math.abs(x),y) end
+fn_env.spow = function(x,y) return x*math.pow(math.abs(x),y-1) end
+
+-- Noise functions are referenced from expressions
+-- as variables of form like "x3a", where:
+-- 1) x is one of x/y/z/w independent functions in each octave
+-- 2) 3 is the octave number; 0 corresponds to the whole range
+-- 3) a is the subtype
+
+-- Independent noise functions: support 4
+local ids = { 'x', 'y', 'z', 'w' }
+-- Subtype: provides an offset to the coordinates
+local subs = {
+    [''] = { 0,   0,   0   },
+    a =    { 0.5, 0,   0   },
+    b =    { 0,   0.5, 0   },
+    c =    { 0.5, 0.5, 0   },
+    d =    { 0,   0,   0.5 },
+    e =    { 0.5, 0,   0.5 },
+    f =    { 0,   0.5, 0.5 },
+    g =    { 0.5, 0.5, 0.5 },
+}
+
+function mkdelta(v)
+    if v == 0 then
+        return ''
+    else
+        return '+'..v
+    end
+end
 
-for i = 1,#args do
+function mkexpr(expr)
-    local fn = rng:perlin(3);
+    -- Collect referenced variables
-    local fn2 = rng:perlin(3);
+    local max_octave = -1
-    local fn3 = rng:perlin(3);
+    local vars = {}
-    local fn4 = rng:perlin(3);
 
-    fns[i] = fn;
+    for var,id,octave,subtype in string.gmatch(expr,'%f[%w](([xyzw])(%d+)(%a*))%f[^%w]') do
+        if not vars[var] then
+            octave = tonumber(octave)
 
-    local val = string.match(args[i],'^([+-]?[%d.]+)$')
+            if octave > max_octave then
-    if val then
+                max_octave = octave
-        coeffs[i] = function(x) return x * val end
-    else
-        local argstr = 'x'
-        if string.match(args[i], '%f[%w]w%f[^%w]') then
-            argstr = 'x,y,z,w'
-            fns[i] = function(x,y,z)
-                return fn(x,y,z), fn2(x,y,z), fn3(x+0.5,y+0.5,z+0.5), fn4(x+0.5,y+0.5,z+0.5)
-            end
-        elseif string.match(args[i], '%f[%w]z%f[^%w]') then
-            argstr = 'x,y,z'
-            fns[i] = function(x,y,z)
-                return fn(x,y,z), fn2(x,y,z), fn3(x+0.5,y+0.5,z+0.5)
-            end
-        elseif string.match(args[i], '%f[%w]y%f[^%w]') then
-            argstr = 'x,y'
-            fns[i] = function(x,y,z)
-                return fn(x,y,z), fn2(x,y,z)
             end
+
+            local sub = subs[subtype] or qerror('Invalid subtype: '..subtype)
+
+            vars[var] = { id = id, octave = octave, subtype = subtype, sub = sub }
         end
+    end
+
+    if max_octave < 0 then
+        qerror('No noise function references in expression.')
+    end
 
-        local f,err = load(
+    -- Allocate the noise functions
-            'return function('..argstr..') return ('..args[i]..') end',
+    local code = ''
-            '=(expr)', 't', env
+
-        )
+    for i = 0,max_octave do
-        if not f then
+        for j,id in ipairs(ids) do
-            qerror(err)
+            code = code .. 'local _fn_'..i..'_'..id..' = rng:perlin(3)\n';
         end
-        coeffs[i] = f()
     end
+
+    -- Evaluate variables
+    code = code .. 'return function(x,y,z)\n'
+
+    for var,info in pairs(vars) do
+        local fn = '_fn_'..info.octave..'_'..info.id
+        local mul = math.pow(2,info.octave)
+        mul = math.min(48*4, mul)
+        code = code .. '    local '..var
+                    .. ' = _fn_'..info.octave..'_'..info.id
+                    .. '(x*'..mul..mkdelta(info.sub[1])
+                    .. ',y*'..mul..mkdelta(info.sub[2])
+                    .. ',z*'..mul..mkdelta(info.sub[3])
+                    .. ')\n'
+    end
+
+    -- Complete and compile the function
+    code = code .. '    return ('..expr..')\nend\n'
+
+    local f,err = load(code, '=(expr)', 't', fn_env)
+    if not f then
+        qerror(err)
+    end
+    return f()
 end
 
+local field_fn = mkexpr(expr)
+
 function render(thresh,file)
     local area = 0
     local line, arr = '', {}
@@ -68,16 +124,10 @@ function render(thresh,file)
             line = ''
             for zx = 0,1 do
                 for x = 0,48*4-1 do
-                    local tx = (0.5+x)/(48*2)
+                    local tx = (0.5+x)/(48*4/xyscale)
-                    local ty = (0.5+y)/(48*2)
+                    local ty = (0.5+y)/(48*4/xyscale)
-                    local tz = 0.5+(zx+zy*2)/(48*2/zscale)
+                    local tz = 0.3+(zx+zy*2)/(48*4/zscale)
-                    local v1 = 0
+                    local v1 = field_fn(tx, ty, tz)
-                    for i = 1,#coeffs do
-                        v1 = v1 + coeffs[i](fns[i](tx,ty,tz))
-                        tx = tx*2
-                        ty = ty*2
-                        tz = tz*2
-                    end
                     local v = -1
                     if v1 > thresh then
                         v = v1;
@@ -103,12 +153,13 @@ function render(thresh,file)
 end
 
 function search(fn,min,max,goal,eps)
-    while true do
+    local center
-        local center = (max+min)/2
+    for i = 1,32 do
+        center = (max+min)/2
         local cval = fn(center)
         print('At '..center..': '..cval)
         if math.abs(cval-goal) < eps then
-            return center
+            break
         end
         if cval > goal then
             min = center
@@ -116,16 +167,19 @@ function search(fn,min,max,goal,eps)
             max = center
         end
     end
+    return center
 end
 
-local thresh = search(render, -1, 1, goal, 0.001)
+local thresh = search(render, -2, 2, goal, math.min(0.001,goal/20))
 
 local file,err = io.open(fname, 'wb')
 if not file then
     print('error: ',err)
     return
 end
-file:write('P5\n768 768\n255\n')
+file:write('P5\n')
+file:write('# '..goal..' '..expr..' '..xyscale..' '..zscale..'\n')
+file:write('768 768\n255\n')
 local area = render(thresh, file)
 file:close()