implicit-0.3.0.0: Graphics/Implicit/ExtOpenScad/Primitives.hs
-- Implicit CAD. Copyright (C) 2011, Christopher Olah (chris@colah.ca)
-- Copyright 2016, Julia Longtin (julial@turinglace.com)
-- Released under the GNU AGPLV3+, see LICENSE
-- Idealy, we'd like to parse a superset of openscad code, with some improvements.
-- This file provides primitive objects for the openscad parser.
-- Allow us to use type signatures in patterns.
{-# LANGUAGE ScopedTypeVariables #-}
-- Export one set containing all of the primitive modules.
module Graphics.Implicit.ExtOpenScad.Primitives (primitiveModules) where
import Prelude(String, Either(Left, Right), Bool(True, False), Maybe(Just, Nothing), ($), pure, either, id, (-), (==), (&&), (<), (*), cos, sin, pi, (/), (>), const, uncurry, fromInteger, round, (/=), (||), not, null, fmap, (<>), otherwise)
import Graphics.Implicit.Definitions (ℝ, ℝ2, ℝ3, ℕ, SymbolicObj2, SymbolicObj3, fromℕtoℝ)
import Graphics.Implicit.ExtOpenScad.Definitions (OVal (OObj2, OObj3, ONModule), ArgParser, Symbol(Symbol), StateC, SourcePosition)
import Graphics.Implicit.ExtOpenScad.Util.ArgParser (doc, defaultTo, example, test, eulerCharacteristic)
import qualified Graphics.Implicit.ExtOpenScad.Util.ArgParser as GIEUA (argument)
import Graphics.Implicit.ExtOpenScad.Util.OVal (OTypeMirror, caseOType, divideObjs, (<||>))
import Graphics.Implicit.ExtOpenScad.Util.StateC (errorC)
-- Note the use of a qualified import, so we don't have the functions in this file conflict with what we're importing.
import qualified Graphics.Implicit.Primitives as Prim (sphere, rect3R, rectR, translate, circle, polygonR, extrudeR, cylinder2, union, unionR, intersect, intersectR, difference, differenceR, rotate, rotate3V, rotate3, scale, extrudeR, extrudeRM, rotateExtrude, shell, pack3, pack2)
import Control.Monad (mplus)
import Data.AffineSpace (distanceSq)
default (ℝ)
-- | Use the old syntax when defining arguments.
argument :: OTypeMirror desiredType => String -> ArgParser desiredType
argument a = GIEUA.argument (Symbol a)
-- | The only thing exported here. basically, a list of modules.
primitiveModules :: [(Symbol, OVal)]
primitiveModules =
[
onModIze sphere [([("r", noDefault)], noSuite), ([("d", noDefault)], noSuite)]
, onModIze cube [([("x", noDefault), ("y", noDefault), ("z", noDefault), ("center", hasDefault), ("r", hasDefault)], noSuite),([("size", noDefault), ("center", hasDefault), ("r", hasDefault)], noSuite)]
, onModIze square [([("x", noDefault), ("y", noDefault), ("center", hasDefault), ("r", hasDefault)], noSuite), ([("size", noDefault), ("center", hasDefault), ("r", hasDefault)], noSuite)]
, onModIze cylinder [([("r", hasDefault), ("h", hasDefault), ("r1", hasDefault), ("r2", hasDefault), ("$fn", hasDefault), ("center", hasDefault)], noSuite),
([("d", hasDefault), ("h", hasDefault), ("d1", hasDefault), ("d2", hasDefault), ("$fn", hasDefault), ("center", hasDefault)], noSuite)]
, onModIze circle [([("r", noDefault), ("$fn", hasDefault)], noSuite), ([("d", noDefault), ("$fn", hasDefault)], noSuite)]
, onModIze polygon [([("points", noDefault)], noSuite)]
, onModIze union [([("r", hasDefault)], requiredSuite)]
, onModIze intersect [([("r", hasDefault)], requiredSuite)]
, onModIze difference [([("r", hasDefault)], requiredSuite)]
, onModIze translate [([("x", noDefault), ("y", noDefault), ("z", noDefault)], requiredSuite), ([("v", noDefault)], requiredSuite)]
, onModIze rotate [([("a", noDefault), ("v", hasDefault)], requiredSuite)]
, onModIze scale [([("v", noDefault)], requiredSuite)]
, onModIze extrude [([("height", hasDefault), ("center", hasDefault), ("twist", hasDefault), ("scale", hasDefault), ("translate", hasDefault), ("r", hasDefault)], requiredSuite)]
, onModIze rotateExtrude [([("a", hasDefault), ("r", hasDefault), ("translate", hasDefault), ("rotate", hasDefault)], requiredSuite)]
, onModIze shell [([("w", noDefault)], requiredSuite)]
, onModIze pack [([("size", noDefault), ("sep", noDefault)], requiredSuite)]
, onModIze unit [([("unit", noDefault)], requiredSuite)]
]
where
hasDefault = True
noDefault = False
noSuite :: Maybe Bool
noSuite = Nothing
requiredSuite = Just True
onModIze func rawInstances = (name, ONModule name implementation instances)
where
(name, implementation) = func
instances = fmap fixup rawInstances
fixup :: ([(String, Bool)], Maybe Bool) -> ([(Symbol, Bool)], Maybe Bool)
fixup (args, suiteInfo) = (fmap fixupArgs args, suiteInfo)
where
fixupArgs :: (String, Bool) -> (Symbol, Bool)
fixupArgs (symbol, maybeDefault) = (Symbol symbol, maybeDefault)
-- | sphere is a module without a suite.
-- this means that the parser will look for this like
-- sphere(args...);
sphere :: (Symbol, SourcePosition -> [OVal] -> ArgParser (StateC [OVal]))
sphere = moduleWithoutSuite "sphere" $ \_ _ -> do
example "sphere(3);"
example "sphere(r=5);"
-- arguments:
-- The radius, r, which is a (real) number.
-- Because we don't provide a default, this ends right
-- here if it doesn't get a suitable argument!
r <-
do
radius :: ℝ <- argument "r" `doc` "radius of the sphere"
pure radius
<|> do
diameter :: ℝ <- argument "d" `doc` "diameter of the sphere"
pure $ diameter/2
-- This module adds a 3D object, a sphere of radius r,
-- using the sphere implementation in Prim
-- (Graphics.Implicit.Primitives)
addObj3 $ Prim.sphere r
-- | FIXME: square1, square2 like cylinder has?
-- | FIXME: translate for square2?
cube :: (Symbol, SourcePosition -> [OVal] -> ArgParser (StateC [OVal]))
cube = moduleWithoutSuite "cube" $ \_ _ -> do
-- examples
example "cube(size = [2,3,4], center = true, r = 0.5);"
example "cube(4);"
-- arguments (two forms)
((x1,x2), (y1,y2), (z1,z2)) <-
do
x :: Either ℝ ℝ2 <- argument "x"
`doc` "x or x-interval"
y :: Either ℝ ℝ2 <- argument "y"
`doc` "y or y-interval"
z :: Either ℝ ℝ2 <- argument "z"
`doc` "z or z-interval"
center :: Bool <- argument "center"
`doc` "should center? (non-intervals)"
`defaultTo` False
let
toInterval' :: ℝ -> ℝ2
toInterval' = toInterval center
pure (either toInterval' id x,
either toInterval' id y,
either toInterval' id z)
<|> do
size :: Either ℝ ℝ3 <- argument "size"
`doc` "cube size"
center :: Bool <- argument "center"
`doc` "should center?"
`defaultTo` False
let (x,y, z) = either (\w -> (w,w,w)) id size
pure (toInterval center x, toInterval center y, toInterval center z)
-- arguments shared between forms
r :: ℝ <- argument "r"
`doc` "radius of rounding"
`defaultTo` 0
-- Tests
test "cube(4);"
`eulerCharacteristic` 2
test "cube(size=[2,3,4]);"
`eulerCharacteristic` 2
test "cube([2,3,4]);" -- openscad syntax
`eulerCharacteristic` 2
-- Implementation
addObj3 $ Prim.rect3R r (x1, y1, z1) (x2, y2, z2)
square :: (Symbol, SourcePosition -> [OVal] -> ArgParser (StateC [OVal]))
square = moduleWithoutSuite "square" $ \_ _ -> do
-- examples
example "square(x=[-2,2], y=[-1,5]);"
example "square(size = [3,4], center = true, r = 0.5);"
example "square(4);"
-- arguments (two forms)
((x1,x2), (y1,y2)) <-
do
x :: Either ℝ ℝ2 <- argument "x"
`doc` "x or x-interval"
y :: Either ℝ ℝ2 <- argument "y"
`doc` "y or y-interval"
center :: Bool <- argument "center"
`doc` "should center? (non-intervals)"
`defaultTo` False
let
toInterval' :: ℝ -> ℝ2
toInterval' = toInterval center
pure (either toInterval' id x,
either toInterval' id y)
<|> do
size :: Either ℝ ℝ2 <- argument "size"
`doc` "square size"
center :: Bool <- argument "center"
`doc` "should center?"
`defaultTo` False
let (x,y) = either (\w -> (w,w)) id size
pure (toInterval center x, toInterval center y)
-- arguments shared between forms
r :: ℝ <- argument "r"
`doc` "radius of rounding"
`defaultTo` 0
-- Tests
test "square(2);"
`eulerCharacteristic` 0
test "square(size=[2,3]);"
`eulerCharacteristic` 0
-- Implementation
addObj2 $ Prim.rectR r (x1, y1) (x2, y2)
cylinder :: (Symbol, SourcePosition -> [OVal] -> ArgParser (StateC [OVal]))
cylinder = moduleWithoutSuite "cylinder" $ \_ _ -> do
example "cylinder(r=10, h=30, center=true);"
example "cylinder(r1=4, r2=6, h=10);"
example "cylinder(r=5, h=10, $fn = 6);"
-- arguments
(r,r1,r2) <-
do
radius :: ℝ <- argument "r"
`defaultTo` 1
`doc` "radius of cylinder"
radius1 :: ℝ <- argument "r1"
`defaultTo` 1
`doc` "bottom radius; overrides r"
radius2 :: ℝ <- argument "r2"
`defaultTo` 1
`doc` "top radius; overrides r"
pure (radius, radius1, radius2)
<|> do
diameter :: ℝ <- argument "d"
`defaultTo` 2
`doc` "diameter of cylinder"
diameter1 :: ℝ <- argument "d1"
`defaultTo` 2
`doc` "bottom diameter; overrides d"
diameter2 :: ℝ <- argument "d2"
`defaultTo` 2
`doc` "top diameter; overrides d"
pure (diameter/2, diameter1/2, diameter2/2)
h :: Either ℝ ℝ2 <- argument "h"
`defaultTo` Left 1
`doc` "height of cylinder"
sides :: ℕ <- argument "$fn"
`defaultTo` (-1)
`doc` "number of sides, for making prisms"
center :: Bool <- argument "center"
`defaultTo` False
`doc` "center cylinder with respect to z?"
-- Tests
test "cylinder(r=10, h=30, center=true);"
`eulerCharacteristic` 0
test "cylinder(r=5, h=10, $fn = 6);"
`eulerCharacteristic` 0
let
(h1, h2) = either (toInterval center) id h
dh = h2 - h1
shift :: SymbolicObj3 -> SymbolicObj3
shift =
if h1 == 0
then id
else Prim.translate (0,0,h1)
-- The result is a computation state modifier that adds a 3D object,
-- based on the args.
addObj3 $ if r1 == 1 && r2 == 1
then let
obj2 = if sides < 0 then Prim.circle r else Prim.polygonR 0
[(r*cos θ, r*sin θ) | θ <- [2*pi*fromℕtoℝ n/fromℕtoℝ sides | n <- [0 .. sides - 1]]]
obj3 = Prim.extrudeR 0 obj2 dh
in shift obj3
else shift $ Prim.cylinder2 r1 r2 dh
circle :: (Symbol, SourcePosition -> [OVal] -> ArgParser (StateC [OVal]))
circle = moduleWithoutSuite "circle" $ \_ _ -> do
example "circle(r=10); // circle"
example "circle(r=5, $fn=6); //hexagon"
-- Arguments
r <-
do
radius :: ℝ <- argument "r"
`doc` "radius of the circle"
pure radius
<|> do
diameter :: ℝ <- argument "d"
`doc` "diameter of the circle"
pure $ diameter/2
sides :: ℕ <- argument "$fn"
`doc` "if defined, makes a regular polygon with n sides instead of a circle"
`defaultTo` (-1)
test "circle(r=10);"
`eulerCharacteristic` 0
test "circle(d=20);"
`eulerCharacteristic` 0
addObj2 $ if sides < 3
then Prim.circle r
else Prim.polygonR 0
[(r*cos θ, r*sin θ) | θ <- [2*pi*fromℕtoℝ n/fromℕtoℝ sides | n <- [0 .. sides - 1]]]
-- | FIXME: 3D Polygons?
-- | FIXME: handle rectangles that are not grid alligned.
-- | FIXME: allow for rounding of polygon corners, specification of vertex ordering.
-- | FIXME: polygons have to have more than two points, or do not generate geometry, and generate an error.
polygon :: (Symbol, SourcePosition -> [OVal] -> ArgParser (StateC [OVal]))
polygon = moduleWithoutSuite "polygon" $ \_ _ -> do
example "polygon ([(0,0), (0,10), (10,0)]);"
points :: [ℝ2] <- argument "points"
`doc` "vertices of the polygon"
{- r :: ℝ <- argument "r"
`doc` "rounding of the polygon corners"
paths :: [ℕ] <- argument "paths"
`doc` "order to go through vertices"
`defaultTo` []
case paths of
[] -> addObj2 $ Prim.polygonR r points
_ -> pure $ pure []
`defaultTo` 0
-}
let
addPolyOrSquare pts
| [p1,p2,p3,p4] <- pts =
let
d1d2 = distanceSq p1 p2
d3d4 = distanceSq p3 p4
d1d3 = distanceSq p1 p3
d2d4 = distanceSq p2 p4
d1d4 = distanceSq p1 p4
d2d3 = distanceSq p2 p3
isGridAligned :: ℝ2 -> ℝ2 -> Bool
isGridAligned (x1, y1) (x2, y2) = x1 == x2 || y1 == y2
-- | Rectangles have no overlapping points,
-- the distance on each side is equal to it's opposing side,
-- and the distance between the pairs of opposing corners are equal.
in if (p1 /= p2 && p2 /= p3 && p3 /= p4 && p4 /= p1)
&& (d1d2==d3d4 && d1d3==d2d4)
&& (d1d4==d2d3) && isGridAligned p1 p2
then Prim.rectR 0 p1 p3
else Prim.polygonR 0 pts
| otherwise = Prim.polygonR 0 points
addObj2 $ addPolyOrSquare points
union :: (Symbol, SourcePosition -> [OVal] -> ArgParser (StateC [OVal]))
union = moduleWithSuite "union" $ \_ children -> do
r :: ℝ <- argument "r"
`defaultTo` 0
`doc` "Radius of rounding for the union interface"
pure $ pure $ if r > 0
then objReduce (Prim.unionR r) (Prim.unionR r) children
else objReduce Prim.union Prim.union children
intersect :: (Symbol, SourcePosition -> [OVal] -> ArgParser (StateC [OVal]))
intersect = moduleWithSuite "intersection" $ \_ children -> do
r :: ℝ <- argument "r"
`defaultTo` 0
`doc` "Radius of rounding for the intersection interface"
pure $ pure $ if r > 0
then objReduce (Prim.intersectR r) (Prim.intersectR r) children
else objReduce Prim.intersect Prim.intersect children
difference :: (Symbol, SourcePosition -> [OVal] -> ArgParser (StateC [OVal]))
difference = moduleWithSuite "difference" $ \_ children -> do
r :: ℝ <- argument "r"
`defaultTo` 0
`doc` "Radius of rounding for the difference interface"
pure $ pure $ if r > 0
then objReduce (Prim.differenceR r) (Prim.differenceR r) children
else objReduce Prim.difference Prim.difference children
translate :: (Symbol, SourcePosition -> [OVal] -> ArgParser (StateC [OVal]))
translate = moduleWithSuite "translate" $ \_ children -> do
example "translate ([2,3]) circle (4);"
example "translate ([5,6,7]) sphere(5);"
(x,y,z) <-
do
x :: ℝ <- argument "x"
`doc` "x amount to translate";
y :: ℝ <- argument "y"
`doc` "y amount to translate";
z :: ℝ <- argument "z"
`doc` "z amount to translate"
`defaultTo` 0;
pure (x,y,z);
<|> do
v :: Either ℝ (Either ℝ2 ℝ3) <- argument "v"
`doc` "vector to translate by"
pure $ case v of
Left x -> (x,0,0)
Right (Left (x,y) ) -> (x,y,0)
Right (Right (x,y,z)) -> (x,y,z)
pure $ pure $
objMap (Prim.translate (x,y)) (Prim.translate (x,y,z)) children
-- | FIXME: rotating a module that is not found pures no geometry, instead of an error.
-- | FIXME: error reporting on fallthrough.
-- + FIXME: rotate(y=90) would be nice.
rotate :: (Symbol, SourcePosition -> [OVal] -> ArgParser (StateC [OVal]))
rotate = moduleWithSuite "rotate" $ \_ children -> do
a <- argument "a"
`doc` "value to rotate by; angle or list of angles"
v <- argument "v"
`defaultTo` (0, 0, 1)
`doc` "Vector to rotate around if a is a single angle"
-- caseOType matches depending on whether size can be coerced into
-- the right object. See Graphics.Implicit.ExtOpenScad.Util
-- Entries must be joined with the operator <||>
-- Final entry must be fall through.
pure $ pure $ caseOType a $
( \θ ->
objMap (Prim.rotate $ deg2rad θ) (Prim.rotate3V (deg2rad θ) v) children
) <||> ( \(yz,zx,xy) ->
objMap (Prim.rotate $ deg2rad xy ) (Prim.rotate3 (deg2rad yz, deg2rad zx, deg2rad xy) ) children
) <||> ( \(yz,zx) ->
objMap id (Prim.rotate3 (deg2rad yz, deg2rad zx, 0)) children
) <||> const []
where
deg2rad :: ℝ -> ℝ
deg2rad x = x / 180 * pi
scale :: (Symbol, SourcePosition -> [OVal] -> ArgParser (StateC [OVal]))
scale = moduleWithSuite "scale" $ \_ children -> do
example "scale(2) square(5);"
example "scale([2,3]) square(5);"
example "scale([2,3,4]) cube(5);"
v <- argument "v"
`doc` "vector or scalar to scale by"
let
scaleObjs stretch2 stretch3 =
objMap (Prim.scale stretch2) (Prim.scale stretch3) children
pure $ pure $ case v of
Left x -> scaleObjs (x,1) (x,1,1)
Right (Left (x,y)) -> scaleObjs (x,y) (x,y,1)
Right (Right (x,y,z)) -> scaleObjs (x,y) (x,y,z)
-- | FIXME: avoid the approximation in getBox3. better definition of function()?
extrude :: (Symbol, SourcePosition -> [OVal] -> ArgParser (StateC [OVal]))
extrude = moduleWithSuite "linear_extrude" $ \_ children -> do
example "linear_extrude(10) square(5);"
height :: Either ℝ (ℝ -> ℝ -> ℝ) <- argument "height" `defaultTo` Left 1
`doc` "height to extrude to..."
center :: Bool <- argument "center" `defaultTo` False
`doc` "center? (the z component)"
twistArg :: Either ℝ (ℝ -> ℝ) <- argument "twist" `defaultTo` Left 0
`doc` "twist as we extrude, either a total amount to twist or a function..."
scaleArg :: Either ℝ (ℝ -> ℝ) <- argument "scale" `defaultTo` Left 1
`doc` "scale according to this funciton as we extrude..."
translateArg :: Either ℝ2 (ℝ -> ℝ2) <- argument "translate" `defaultTo` Left (0,0)
`doc` "translate according to this funciton as we extrude..."
r :: ℝ <- argument "r" `defaultTo` 0
`doc` "round the top/bottom."
let
heightn = case height of
Left h -> h
Right f -> f 0 0
height' = case height of
Left a -> Left a
Right f -> Right $ uncurry f
shiftAsNeeded :: SymbolicObj3 -> SymbolicObj3
shiftAsNeeded =
if center
then Prim.translate (0,0,-heightn/2.0)
else id
isTwistID = case twistArg of
Left constant -> constant == 0
Right _ -> False
isScaleID = case scaleArg of
Left constant -> constant == 1
Right _ -> False
isTransID = case translateArg of
Left constant -> constant == (0,0)
Right _ -> False
pure $ pure $ obj2UpMap (
\obj -> case height of
Left constHeight | isTwistID && isScaleID && isTransID ->
shiftAsNeeded $ Prim.extrudeR r obj constHeight
_ ->
shiftAsNeeded $ Prim.extrudeRM r twistArg scaleArg translateArg obj height'
) children
rotateExtrude :: (Symbol, SourcePosition -> [OVal] -> ArgParser (StateC [OVal]))
rotateExtrude = moduleWithSuite "rotate_extrude" $ \_ children -> do
example "rotate_extrude() translate(20) circle(10);"
totalRot :: ℝ <- argument "a" `defaultTo` 360
`doc` "angle to sweep"
r :: ℝ <- argument "r" `defaultTo` 0
translateArg :: Either ℝ2 (ℝ -> ℝ2) <- argument "translate" `defaultTo` Left (0,0)
rotateArg :: Either ℝ (ℝ -> ℝ ) <- argument "rotate" `defaultTo` Left 0
let
is360m :: ℝ -> Bool
is360m n = 360 * fromInteger (round $ n / 360) /= n
cap = is360m totalRot
|| either ( /= (0,0)) (\f -> f 0 /= f totalRot) translateArg
|| either is360m (\f -> is360m (f 0 - f totalRot)) rotateArg
capM = if cap then Just r else Nothing
pure $ pure $ obj2UpMap (Prim.rotateExtrude totalRot capM translateArg rotateArg) children
shell :: (Symbol, SourcePosition -> [OVal] -> ArgParser (StateC [OVal]))
shell = moduleWithSuite "shell" $ \_ children -> do
w :: ℝ <- argument "w"
`doc` "width of the shell..."
pure $ pure $ objMap (Prim.shell w) (Prim.shell w) children
-- Not a permanent solution! Breaks if can't pack.
pack :: (Symbol, SourcePosition -> [OVal] -> ArgParser (StateC [OVal]))
pack = moduleWithSuite "pack" $ \sourcePosition children -> do
example "pack ([45,45], sep=2) { circle(10); circle(10); circle(10); circle(10); }"
-- arguments
size :: ℝ2 <- argument "size"
`doc` "size of 2D box to pack objects within"
sep :: ℝ <- argument "sep"
`doc` "mandetory space between objects"
-- The actual work...
pure $
let (obj2s, obj3s, others) = divideObjs children
in if not $ null obj3s
then case Prim.pack3 size sep obj3s of
Just solution -> pure $ OObj3 solution : (fmap OObj2 obj2s <> others)
Nothing -> do
errorC sourcePosition "Can't pack given objects in given box with the present algorithm."
pure children
else case Prim.pack2 size sep obj2s of
Just solution -> pure $ OObj2 solution : others
Nothing -> do
errorC sourcePosition "Can't pack given objects in given box with the present algorithm."
pure children
unit :: (Symbol, SourcePosition -> [OVal] -> ArgParser (StateC [OVal]))
unit = moduleWithSuite "unit" $ \sourcePosition children -> do
example "unit(\"inch\") {..}"
-- arguments
name :: String <- argument "unit"
`doc` "the unit you wish to work in"
let
mmRatio :: String -> Maybe ℝ
mmRatio "inch" = Just 25.4
mmRatio "in" = mmRatio "inch"
mmRatio "foot" = Just 304.8
mmRatio "ft" = mmRatio "foot"
mmRatio "yard" = Just 914.4
mmRatio "yd" = mmRatio "yard"
mmRatio "mm" = Just 1
mmRatio "cm" = Just 10
mmRatio "dm" = Just 100
mmRatio "m" = Just 1000
mmRatio "km" = Just 1000000
mmRatio "µm" = Just 0.001
mmRatio "um" = mmRatio "µm"
mmRatio "nm" = Just 0.0000001
mmRatio _ = Nothing
-- The actual work...
pure $ case mmRatio name of
Nothing -> do
errorC sourcePosition $ "unrecognized unit " <> name
pure children
Just r ->
pure $ objMap (Prim.scale (r,r)) (Prim.scale (r,r,r)) children
---------------
(<|>) :: ArgParser a -> ArgParser a -> ArgParser a
(<|>) = mplus
moduleWithSuite :: String -> (SourcePosition -> [OVal] -> ArgParser (StateC [OVal])) -> (Symbol, SourcePosition -> [OVal] -> ArgParser (StateC [OVal]))
moduleWithSuite name modArgMapper = (Symbol name, modArgMapper)
moduleWithoutSuite :: String -> (SourcePosition -> [OVal] -> ArgParser (StateC [OVal])) -> (Symbol, SourcePosition -> [OVal] -> ArgParser (StateC [OVal]))
moduleWithoutSuite name modArgMapper = (Symbol name, modArgMapper)
addObj2 :: SymbolicObj2 -> ArgParser (StateC [OVal])
addObj2 x = pure $ pure [OObj2 x]
addObj3 :: SymbolicObj3 -> ArgParser (StateC [OVal])
addObj3 x = pure $ pure [OObj3 x]
objMap :: (SymbolicObj2 -> SymbolicObj2) -> (SymbolicObj3 -> SymbolicObj3) -> [OVal] -> [OVal]
objMap obj2mod obj3mod (x:xs) = case x of
OObj2 obj2 -> OObj2 (obj2mod obj2) : objMap obj2mod obj3mod xs
OObj3 obj3 -> OObj3 (obj3mod obj3) : objMap obj2mod obj3mod xs
a -> a : objMap obj2mod obj3mod xs
objMap _ _ [] = []
objReduce :: ([SymbolicObj2] -> SymbolicObj2) -> ([SymbolicObj3] -> SymbolicObj3) -> [OVal] -> [OVal]
objReduce obj2reduce obj3reduce l = case divideObjs l of
( [], [], others) -> others
( [], obj3s, others) -> OObj3 (obj3reduce obj3s) : others
(obj2s, [], others) -> OObj2 (obj2reduce obj2s) : others
(obj2s, obj3s, others) -> OObj2 (obj2reduce obj2s) : OObj3 (obj3reduce obj3s) : others
obj2UpMap :: (SymbolicObj2 -> SymbolicObj3) -> [OVal] -> [OVal]
obj2UpMap obj2upmod (x:xs) = case x of
OObj2 obj2 -> OObj3 (obj2upmod obj2) : obj2UpMap obj2upmod xs
a -> a : obj2UpMap obj2upmod xs
obj2UpMap _ [] = []
toInterval :: Bool -> ℝ -> ℝ2
toInterval center h =
if center
then (-h/2, h/2)
else (0, h)