pure-noise-0.2.2.0: src/Numeric/Noise/Cellular.hs
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE OverloadedLists #-}
{-# LANGUAGE RecordWildCards #-}
{-# LANGUAGE StrictData #-}
-- |
-- Maintainer: Jeremy Nuttall <jeremy@jeremy-nuttall.com>
-- Stability : experimental
module Numeric.Noise.Cellular (
-- * Configuration
CellularConfig (..),
defaultCellularConfig,
CellularDistanceFn (..),
CellularResult (..),
-- * 2D Noise
noise2,
-- * 3D Noise
noise3,
) where
import Data.Bits
import Data.Foldable (foldl') -- redundant since GHC 9.10.1, here for compat
import Data.Primitive.PrimArray
import GHC.Generics (Generic)
import Numeric.Noise.Internal
import Numeric.Noise.Internal.Math
-- | Configuration for cellular (Worley) noise generation.
--
-- Cellular noise is based on distances to randomly distributed cell points,
-- creating a distinctive cellular or organic pattern.
data CellularConfig a = CellularConfig
{ cellularDistanceFn :: CellularDistanceFn
-- ^ Distance metric to use when computing distance to cell points.
, cellularJitter :: a
-- ^ Amount of randomness in cell point positions.
-- \( 0 \) creates a regular grid, \( 1 \) creates fully random positions.
-- Values outside \( [0, 1] \) may produce unusual results.
, cellularResult :: CellularResult
-- ^ What value to return from the noise function.
}
deriving (Generic, Show)
-- | Default configuration for cellular noise generation.
defaultCellularConfig :: (RealFrac a) => CellularConfig a
defaultCellularConfig =
CellularConfig
{ cellularDistanceFn = DistEuclidean
, cellularJitter = 1
, cellularResult = CellValue
}
{-# INLINEABLE defaultCellularConfig #-}
-- | Distance function for cellular noise calculations.
--
-- Different distance metrics produce different visual characteristics
-- in the cellular pattern.
data CellularDistanceFn
= -- | \( \sqrt{dx^2 + dy^2} \) - Creates circular cells with smooth edges.
DistEuclidean
| -- | \( dx^2 + dy^2 \) - Faster than 'DistEuclidean' with similar appearance.
DistEuclideanSq
| -- | \( |dx| + |dy| \) - Creates diamond-shaped cells with sharp edges.
DistManhattan
| -- | Hybrid of Euclidean and Manhattan distances.
DistHybrid
deriving (Generic, Read, Show, Eq, Ord, Enum, Bounded)
-- | What value to return from cellular noise evaluation.
--
-- These options allow for different visual effects by returning different
-- properties of the cell structure.
--
-- Distance-based results are not confined to @[-1, 1]@ under every metric —
-- 'DistManhattan' and 'DistHybrid' can exceed 1, matching FastNoiseLite.
data CellularResult
= -- | Return the hash value of the nearest cell point.
-- Creates discrete regions with constant values.
CellValue
| -- | Return the distance to the nearest cell point.
-- Creates a classic Worley noise pattern with cell boundaries.
Distance
| -- | Return the distance to the second-nearest cell point.
-- Creates larger, more organic-looking cells.
Distance2
| -- | Return the sum of distances to the two nearest cell points.
-- Creates smooth, rounded cells.
Distance2Add
| -- | Return the difference between distances to the two nearest cell points.
-- Emphasizes cell boundaries and creates sharp edges.
Distance2Sub
| -- | Return the product of distances to the two nearest cell points.
-- Creates cells with varying contrast.
Distance2Mul
| -- | Return the ratio of nearest to second-nearest distance.
-- Creates normalized cell patterns.
Distance2Div
deriving (Generic, Read, Show, Eq, Ord, Enum, Bounded)
distance :: (RealFrac a) => CellularDistanceFn -> a -> a -> a
distance = \case
DistEuclidean -> \ !x !y -> x * x + y * y
DistEuclideanSq -> \ !x !y -> x * x + y * y
DistManhattan -> \ !x !y -> abs x + abs y
DistHybrid -> \ !x !y -> abs x + abs y + (x * x + y * y)
{-# INLINE distance #-}
normDist :: (Floating a) => CellularDistanceFn -> a -> a
normDist = \case
DistEuclidean -> sqrt
_ -> id
{-# INLINE normDist #-}
distance3 :: (RealFrac a) => CellularDistanceFn -> a -> a -> a -> a
distance3 = \case
DistEuclidean -> \ !x !y !z -> x * x + y * y + z * z
DistEuclideanSq -> \ !x !y !z -> x * x + y * y + z * z
DistManhattan -> \ !x !y !z -> abs x + abs y + abs z
DistHybrid -> \ !x !y !z -> abs x + abs y + abs z + (x * x + y * y + z * z)
{-# INLINE distance3 #-}
-- | Fold the candidate cell points with the selector 'cellularResult' needs.
-- Shared by 'noise2' and 'noise3'; INLINE so the folds fuse with the callers'
-- point comprehensions (see the note on @points@ in 'noise2').
selectResult :: (RealFrac a, Floating a) => CellularResult -> CellularDistanceFn -> [(Hash, a)] -> a
selectResult res distFn points =
let norm = normDist distFn
coeff = 1 / (maxHash + 1)
{-# INLINE selectMinHash #-}
selectMinHash =
let minHash (!hMin, !dMin) (!h, !d)
| d < dMin = (h, d)
| otherwise = (hMin, dMin)
in foldl' minHash (0, infinity) points
{-# INLINE selectMinDist #-}
selectMinDist =
let minDist !dMin (_, !d)
| d < dMin = d
| otherwise = dMin
in foldl' minDist infinity points
{-# INLINE selectSmallestTwo #-}
selectSmallestTwo =
let smallestTwo (!c, !d0, !d1) (!h, !d)
| d < d0 = (h, d, d0)
| d < d1 = (c, d0, d)
| otherwise = (c, d0, d1)
in foldl' smallestTwo (0, infinity, infinity) points
in case res of
CellValue ->
let (!hash, !_) = selectMinHash
in fromIntegral hash * coeff
Distance ->
let !d0 = selectMinDist
in norm d0 - 1
Distance2 ->
let (!_, !_, !d1) = selectSmallestTwo
in norm d1 - 1
Distance2Add ->
let (!_, !d0, !d1) = selectSmallestTwo
in (norm d1 + norm d0) * 0.5 - 1
Distance2Sub ->
let (!_, !d0, !d1) = selectSmallestTwo
in norm d1 - norm d0 - 1
Distance2Mul ->
let (!_, !d0, !d1) = selectSmallestTwo
in norm d1 * norm d0 * 0.5 - 1
Distance2Div ->
let (!_, !d0, !d1) = selectSmallestTwo
in norm d0 / norm d1 - 1
{-# INLINE selectResult #-}
noise2 :: (RealFrac a, Floating a) => CellularConfig a -> Noise2 a
noise2 CellularConfig{..} = mkNoise2 $ \ !seed !x !y ->
let !jitter = cellularJitter * 0.43701595
!rx = fastRound x
!ry = fastRound y
dist = distance cellularDistanceFn
{-# INLINE pointDist #-}
pointDist !xi !yi =
let !px = fromIntegral xi - x
!py = fromIntegral yi - y
!h = hash2 seed (primeX * xi) (primeY * yi)
!i = h .&. 0x1FE
!rvx = lookupRandVec2d i
!rvy = lookupRandVec2d (i .|. 1)
!d = dist (px + rvx * jitter) (py + rvy * jitter)
in (h, d)
-- The [-1 .. 1] comprehension is load-bearing: enumFromTo takes part in
-- foldr/build fusion with the folds below, so no list is ever built.
-- OverloadedLists literals here would desugar to fromListN (no fusion),
-- and hand-unrolled cons-chains defeat the fold's fusion entirely
-- (measured ~5x slower). Same applies to the 3D comprehension.
{-# INLINE points #-}
points = [pointDist (rx + xi) (ry + yi) | !xi <- [-1 .. 1], !yi <- [-1 .. 1]]
in selectResult cellularResult cellularDistanceFn points
{-# INLINE [2] noise2 #-}
noise3 :: (RealFrac a, Floating a) => CellularConfig a -> Noise3 a
noise3 CellularConfig{..} = mkNoise3 $ \ !seed !x !y !z ->
let !jitter = cellularJitter * 0.39614353
!rx = fastRound x
!ry = fastRound y
!rz = fastRound z
dist = distance3 cellularDistanceFn
{-# INLINE pointDist #-}
pointDist !xi !yi !zi =
let !px = fromIntegral xi - x
!py = fromIntegral yi - y
!pz = fromIntegral zi - z
!h = hash3 seed (primeX * xi) (primeY * yi) (primeZ * zi)
!i = h .&. 0x3FC
!rvx = lookupRandVec3d i
!rvy = lookupRandVec3d (i .|. 1)
!rvz = lookupRandVec3d (i .|. 2)
!d = dist (px + rvx * jitter) (py + rvy * jitter) (pz + rvz * jitter)
in (h, d)
{-# INLINE points #-}
points =
[ pointDist (rx + xi) (ry + yi) (rz + zi)
| !xi <- [-1 .. 1]
, !yi <- [-1 .. 1]
, !zi <- [-1 .. 1]
]
in selectResult cellularResult cellularDistanceFn points
{-# INLINE [2] noise3 #-}
lookupRandVec2d :: (RealFrac a) => Hash -> a
lookupRandVec2d = realToFrac . indexPrimArray randVecs2dd . fromIntegral
{-# NOINLINE [1] lookupRandVec2d #-}
{-# RULES
"lookupRandVec2d/Float" forall h.
lookupRandVec2d h =
indexPrimArray randVecs2df (fromIntegral h)
"lookupRandVec2d/Double" forall h.
lookupRandVec2d h =
indexPrimArray randVecs2dd (fromIntegral h)
#-}
randVecs2df :: PrimArray Float
randVecs2df = mapPrimArray realToFrac randVecs2dd
-- >>> sizeofPrimArray randVecs2dd == 512
-- True
{- ORMOLU_DISABLE -}
randVecs2dd :: PrimArray Double
randVecs2dd =
[-0.2700222198,-0.9628540911,0.3863092627,-0.9223693152,0.04444859006,-0.999011673,-0.5992523158,-0.8005602176
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]
lookupRandVec3d :: (RealFrac a) => Hash -> a
lookupRandVec3d = realToFrac . indexPrimArray randVecs3dd . fromIntegral
{-# NOINLINE [1] lookupRandVec3d #-}
{-# RULES
"lookupRandVec3d/Float" forall h.
lookupRandVec3d h =
indexPrimArray randVecs3df (fromIntegral h)
"lookupRandVec3d/Double" forall h.
lookupRandVec3d h =
indexPrimArray randVecs3dd (fromIntegral h)
#-}
randVecs3df :: PrimArray Float
randVecs3df = mapPrimArray realToFrac randVecs3dd
-- >>> sizeofPrimArray randVecs3dd == 1024
-- True
{- ORMOLU_DISABLE -}
randVecs3dd :: PrimArray Double
randVecs3dd =
[-0.7292736885,-0.6618439697,0.1735581948,0,0.790292081,-0.5480887466,-0.2739291014,0
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]
{- ORMOLU_ENABLE -}