/
noise.jl
2152 lines (1992 loc) · 77.7 KB
/
noise.jl
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# noise, using OpenSimplex algorithm (patent free)
using Random
"""
noise(x) ; detail = 1, persistence = 1.0) # 1D
noise(x, y) ; detail = 1, persistence = 1.0) # 2D
noise(x, y, z) ; detail = 1, persistence = 1.0) # 3D
noise(x, y, z, w) ; detail = 1, persistence = 1.0) # 4D
Generate a noise value between 0.0 and 1.0 corresponding to the `x`, `y`,
`z`, and `w` values. An `x` value on its own produces 1D noise, `x` and `y`
make 2D noise, and so on.
The `detail` value is an integer (>= 1) specifying how many octaves of noise
you want.
The `persistence` value, typically between 0.0 and 1.0, controls how quickly the
amplitude diminishes for each successive octave for values of `detail` greater
than 1.
"""
noise(x; detail::T = 1, persistence = 1.0) where T <: Integer =
_octaves([x], octaves=detail, persistence=persistence)
noise(x, y; detail::T = 1, persistence = 1.0) where T <: Integer =
_octaves([x, y], octaves=detail, persistence=persistence)
noise(x, y, z; detail::T = 1, persistence = 1.0) where T <: Integer =
_octaves([x, y, z], octaves=detail, persistence=persistence)
noise(x, y, z, w; detail::T = 1, persistence = 1.0) where T <: Integer =
_octaves([x, y, z, w], octaves=detail, persistence=persistence)
# call simplexnoise on values in array
# coords is [x] or [x, y] or [x, y, z] or [x, y, z, w]
function _octaves(coords::Array{T, 1} where T <: Real;
octaves::Int = 1,
persistence=1.0)
total = 0.0
frequency = 1.0
amplitude = 1.0
maxval = 0.0
l = length(coords)
for i in 1:octaves
if l == 1
total += simplexnoise(coords[1] * frequency) * amplitude
elseif l == 2
total += simplexnoise(coords[1] * frequency, coords[2] * frequency) * amplitude
elseif l == 3
total += simplexnoise(coords[1] * frequency, coords[2] * frequency, coords[3] * frequency) * amplitude
elseif l == 4
total += simplexnoise(coords[1] * frequency, coords[2] * frequency, coords[3] * frequency, coords[4] * frequency) * amplitude
end
maxval += amplitude
amplitude *= persistence
frequency *= 2
end
return total / maxval
end
# Most of this code is the original OpenSimplexNoise code.
# I converted it to Julia but I don't understand it all... [cormullion]
# OpenSimplex Noise
# by Kurt Spencer
#
# v1.1 (October 5, 2014)
# - Added 2D and 4D implementations.
# - Proper gradient sets for all dimensions, from a
# dimensionally-generalizable scheme with an actual
# rhyme and reason behind it.
# - Removed default permutation array in favor of
# default seed.
# - Changed seed-based constructor to be independent
# of any particular randomization library, so results
# will be the same when ported to other languages.
const STRETCH_CONSTANT_2D = -0.211324865405187 # (1/sqrt(2+1)-1)/2
const SQUISH_CONSTANT_2D = 0.366025403784439 # (sqrt(2+1)-1)/2
const STRETCH_CONSTANT_3D = -0.16666 # (1/sqrt(3+1)-1)/3
const SQUISH_CONSTANT_3D = 0.333333 # (sqrt(3+1)-1)/3
const STRETCH_CONSTANT_4D = -0.138196601125011 # (1/sqrt(4+1)-1)/4
const SQUISH_CONSTANT_4D = 0.309016994374947 # (sqrt(4+1)-1)/4
const NORM_CONSTANT_2D = 47
const NORM_CONSTANT_3D = 103
const NORM_CONSTANT_4D = 30
const DEFAULT_SEED = 0
# Gradients for 2D. They approximate the directions to the
# vertices of an octagon from the center.
const gradients2D = Int8[
5, 2, 2, 5,
-5, 2, -2, 5,
5, -2, 2, -5,
-5, -2, -2, -5]
# Gradients for 3D. They approximate the directions to the
# vertices of a rhombicuboctahedron from the center, skewed so
# that the triangular and square facets can be inscribed inside
# circles of the same radius.
const gradients3D = Int8[
-11, 4, 4, -4, 11, 4, -4, 4, 11,
11, 4, 4, 4, 11, 4, 4, 4, 11,
-11, -4, 4, -4, -11, 4, -4, -4, 11,
11, -4, 4, 4, -11, 4, 4, -4, 11,
-11, 4, -4, -4, 11, -4, -4, 4, -11,
11, 4, -4, 4, 11, -4, 4, 4, -11,
-11, -4, -4, -4, -11, -4, -4, -4, -11,
11, -4, -4, 4, -11, -4, 4, -4, -11]
# Gradients for 4D. They approximate the directions to the
# vertices of a disprismatotesseractihexadecachoron from the center,
# skewed so that the tetrahedral and cubic facets can be inscribed inside
# spheres of the same radius.
# [yes, a disprismatotesseractihexadecachoron !]
const gradients4D = Int8[
3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3,
-3, 1, 1, 1, -1, 3, 1, 1, -1, 1, 3, 1, -1, 1, 1, 3,
3, -1, 1, 1, 1, -3, 1, 1, 1, -1, 3, 1, 1, -1, 1, 3,
-3, -1, 1, 1, -1, -3, 1, 1, -1, -1, 3, 1, -1, -1, 1, 3,
3, 1, -1, 1, 1, 3, -1, 1, 1, 1, -3, 1, 1, 1, -1, 3,
-3, 1, -1, 1, -1, 3, -1, 1, -1, 1, -3, 1, -1, 1, -1, 3,
3, -1, -1, 1, 1, -3, -1, 1, 1, -1, -3, 1, 1, -1, -1, 3,
-3, -1, -1, 1, -1, -3, -1, 1, -1, -1, -3, 1, -1, -1, -1, 3,
3, 1, 1, -1, 1, 3, 1, -1, 1, 1, 3, -1, 1, 1, 1, -3,
-3, 1, 1, -1, -1, 3, 1, -1, -1, 1, 3, -1, -1, 1, 1, -3,
3, -1, 1, -1, 1, -3, 1, -1, 1, -1, 3, -1, 1, -1, 1, -3,
-3, -1, 1, -1, -1, -3, 1, -1, -1, -1, 3, -1, -1, -1, 1, -3,
3, 1, -1, -1, 1, 3, -1, -1, 1, 1, -3, -1, 1, 1, -1, -3,
-3, 1, -1, -1, -1, 3, -1, -1, -1, 1, -3, -1, -1, 1, -1, -3,
3, -1, -1, -1, 1, -3, -1, -1, 1, -1, -3, -1, 1, -1, -1, -3,
-3, -1, -1, -1, -1, -3, -1, -1, -1, -1, -3, -1, -1, -1, -1, -3]
function extrapolate(xsb::Int, ysb::Int, dx::Float64, dy::Float64)
index::Int = perm[1 + (perm[1 + xsb & 0xFF] + ysb) & 0xFF] & 0x0E
return gradients2D[mod1(1 + index, end)] * dx +
gradients2D[mod1(1 + index + 1, end)] * dy
end
function extrapolate(xsb::Int, ysb::Int, zsb::Int, dx, dy, dz)
index::Int = permGradIndex3D[1 + (perm[1 + (perm[1 + xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF]
return gradients3D[mod1(index, end)] * dx +
gradients3D[mod1(1 + index + 1, end)] * dy +
gradients3D[mod1(1 + index + 2, end)] * dz
end
function extrapolate(xsb::Int, ysb::Int, zsb::Int, wsb::Int, dx, dy, dz, dw)
index::Int = perm[1 + (perm[1 + (perm[1 + (perm[1 + xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF] + wsb) & 0xFF] & 0xFC
return gradients4D[mod1(index, end)] * dx +
gradients4D[mod1(1 + index + 1, end)] * dy +
gradients4D[mod1(1 + index + 2, end)] * dz +
gradients4D[mod1(1 + index + 3, end)] * dw
end
###############################################################################
# Initializing the random stuff
# I couldn't get the original's wacky bit twiddling and overflow random code to
# produce nice results. So I'm just using Julia's standard random number
# generation here...
# TODO Investigate the original Linear Congruential Generators approach to sowing
# seeds...
# Initialize the two main arrays that are used by all noise functions
const perm = Array{Int8}(undef, 256)
const permGradIndex3D = Array{Int8}(undef, 256)
"""
initnoise(seed::Int)
initnoise()
Initialize the noise generation code.
```
julia> initnoise(); noise(1)
0.7453148982810598
julia> initnoise(); noise(1)
0.7027617067916981
```
If you provide an integer seed, it will be used
to seed `Random.seed!()`` when the noise code is initialized:
```
julia> initnoise(41); noise(1) # yesterday
0.7134000046640385
julia> initnoise(41); noise(1) # today
0.7134000046640385
```
If you need to control which type of random number generator is used, you can provide
your own and it will be used instead of the default Julia implementation.
```
julia> rng = MersenneTwister(1234) # any AbstractRNG
julia> initnoise(rng)
```
"""
function initnoise(seed)
Random.seed!(seed)
for i in 1:256
perm[i] = rand(Int8)
permGradIndex3D[i] = rand(Int8)
end
end
function initnoise()
for i in 1:256
perm[i] = rand(Int8)
permGradIndex3D[i] = rand(Int8)
end
end
function initnoise(rng::AbstractRNG)
for i in 1:256
perm[i] = rand(rng, Int8)
permGradIndex3D[i] = rand(rng, Int8)
end
end
initnoise()
###############################################################################
#
# 1D OpenSimplex Noise is really 2D noise
simplexnoise(x) = simplexnoise(x, 0)
#
###############################################################################
###############################################################################
#
# 2D OpenSimplex Noise
#
# comments from original Java source
# TODO convert to Julia properly
###############################################################################
function simplexnoise(x, y)
# Place input coordinates onto grid.
stretchOffset = (x + y) * STRETCH_CONSTANT_2D
xs = x + stretchOffset
ys = y + stretchOffset
# Floor to get grid coordinates of rhombus (stretched square) super-cell origin.
xsb = convert(Int, floor(xs))
ysb = convert(Int, floor(ys))
# Skew out to get actual coordinates of rhombus origin. We'll need these later.
squishOffset = (xsb + ysb) * SQUISH_CONSTANT_2D
xb = xsb + squishOffset
yb = ysb + squishOffset
# Compute grid coordinates relative to rhombus origin.
xins = xs - xsb
yins = ys - ysb
# Sum those together to get a value that determines which region we're in.
inSum = xins + yins
# Positions relative to origin point.
dx0 = x - xb
dy0 = y - yb
# We'll be defining these inside the next block and using them afterwards.
# dx_ext, dy_ext, xsv_ext, ysv_ext
value = 0.0
# Contribution (1,0)
dx1 = dx0 - 1 - SQUISH_CONSTANT_2D
dy1 = dy0 - 0 - SQUISH_CONSTANT_2D
attn1 = 2 - dx1 * dx1 - dy1 * dy1
if attn1 > 0
attn1 *= attn1
value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, dx1, dy1)
end
# Contribution (0,1)
dx2 = dx0 - 0 - SQUISH_CONSTANT_2D
dy2 = dy0 - 1 - SQUISH_CONSTANT_2D
attn2 = 2 - dx2 * dx2 - dy2 * dy2
if attn2 > 0
attn2 *= attn2
value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, dx2, dy2)
end
if inSum <= 1 # We're inside the triangle (2-Simplex) at (0,0)
zins = 1 - inSum
if (zins > xins) || (zins > yins) # (0,0) is one of the closest two triangular vertices
if xins > yins
xsv_ext = xsb + 1
ysv_ext = ysb - 1
dx_ext = dx0 - 1
dy_ext = dy0 + 1
else
xsv_ext = xsb - 1
ysv_ext = ysb + 1
dx_ext = dx0 + 1
dy_ext = dy0 - 1
end
else # (1,0) and (0,1) are the closest two vertices.
xsv_ext = xsb + 1
ysv_ext = ysb + 1
dx_ext = dx0 - 1 - 2 * SQUISH_CONSTANT_2D
dy_ext = dy0 - 1 - 2 * SQUISH_CONSTANT_2D
end
else # We're inside the triangle (2-Simplex) at (1,1)
zins = 2 - inSum
if (zins < xins) || (zins < yins) # (0,0) is one of the closest two triangular vertices
if xins > yins
xsv_ext = xsb + 2
ysv_ext = ysb + 0
dx_ext = dx0 - 2 - 2 * SQUISH_CONSTANT_2D
dy_ext = dy0 + 0 - 2 * SQUISH_CONSTANT_2D
else
xsv_ext = xsb + 0
ysv_ext = ysb + 2
dx_ext = dx0 + 0 - 2 * SQUISH_CONSTANT_2D
dy_ext = dy0 - 2 - 2 * SQUISH_CONSTANT_2D
end
else # (1,0) and (0,1) are the closest two vertices.
dx_ext = dx0
dy_ext = dy0
xsv_ext = xsb
ysv_ext = ysb
end
xsb += 1
ysb += 1
dx0 = dx0 - 1 - 2 * SQUISH_CONSTANT_2D
dy0 = dy0 - 1 - 2 * SQUISH_CONSTANT_2D
end
# Contribution (0,0) or (1,1)
attn0 = 2 - dx0 * dx0 - dy0 * dy0
if attn0 > 0
attn0 *= attn0
value += attn0 * attn0 * extrapolate(xsb, ysb, dx0, dy0)
end
# Extra Vertex
attn_ext = 2 - dx_ext * dx_ext - dy_ext * dy_ext
if attn_ext > 0
attn_ext *= attn_ext
value += attn_ext * attn_ext * extrapolate(xsv_ext, ysv_ext, dx_ext, dy_ext)
end
# convert to [0, 1]
res = value / NORM_CONSTANT_2D
return clamp((res + 1) / 2, 0.0, 1.0)
end
# 3D OpenSimplex Noise.
# TODO convert to Julia properly
function simplexnoise(x, y, z)
# Place input coordinates on simplectic honeycomb.
stretchOffset = (x + y + z) * STRETCH_CONSTANT_3D
xs = x + stretchOffset
ys = y + stretchOffset
zs = z + stretchOffset
# Floor to get simplectic honeycomb coordinates of rhombohedron (stretched cube) super-cell origin.
xsb = convert(Int, floor(xs))
ysb = convert(Int, floor(ys))
zsb = convert(Int, floor(zs))
# Skew out to get actual coordinates of rhombohedron origin. We'll need these later.
squishOffset = (xsb + ysb + zsb) * SQUISH_CONSTANT_3D
xb = xsb + squishOffset
yb = ysb + squishOffset
zb = zsb + squishOffset
# Compute simplectic honeycomb coordinates relative to rhombohedral origin.
xins = xs - xsb
yins = ys - ysb
zins = zs - zsb
# Sum those together to get a value that determines which region we're in.
inSum = xins + yins + zins
# Positions relative to origin point.
dx0 = x - xb
dy0 = y - yb
dz0 = z - zb
# We'll be defining these inside the next block and using them afterwards.
# dx_ext0, dy_ext0, dz_ext0
# dx_ext1, dy_ext1, dz_ext1
# int xsv_ext0, ysv_ext0, zsv_ext0
# int xsv_ext1, ysv_ext1, zsv_ext1
value = 0.0
if inSum <= 1 # We're inside the tetrahedron (3-Simplex) at (0,0,0)
# Determine which two of (0,0,1), (0,1,0), (1,0,0) are closest.
aPoint = 0x01
aScore = xins
bPoint = 0x02
bScore = yins
if (aScore >= bScore) && (zins > bScore)
bScore = zins
bPoint = 0x04
elseif (aScore < bScore) && (zins > aScore)
aScore = zins
aPoint = 0x04
end
# Now we determine the two lattice points not part of the tetrahedron that may contribute.
# This depends on the closest two tetrahedral vertices, including (0,0,0)
wins = 1 - inSum
if (wins > aScore) || (wins > bScore) # (0,0,0) is one of the closest two tetrahedral vertices.
c = (bScore > aScore) ? bPoint : aPoint # Our other closest vertex is the closest out of a and b.
if (c & 0x01) == 0
xsv_ext0 = xsb - 1
xsv_ext1 = xsb
dx_ext0 = dx0 + 1
dx_ext1 = dx0
else
xsv_ext0 = xsv_ext1 = xsb + 1
dx_ext0 = dx_ext1 = dx0 - 1
end
if (c & 0x02) == 0
ysv_ext0 = ysv_ext1 = ysb
dy_ext0 = dy_ext1 = dy0
if (c & 0x01) == 0
ysv_ext1 -= 1
dy_ext1 += 1
else
ysv_ext0 -= 1
dy_ext0 += 1
end
else
ysv_ext0 = ysv_ext1 = ysb + 1
dy_ext0 = dy_ext1 = dy0 - 1
end
if (c & 0x04) == 0
zsv_ext0 = zsb
zsv_ext1 = zsb - 1
dz_ext0 = dz0
dz_ext1 = dz0 + 1
else
zsv_ext0 = zsv_ext1 = zsb + 1
dz_ext0 = dz_ext1 = dz0 - 1
end
else # (0,0,0) is not one of the closest two tetrahedral vertices.
c = (aPoint | bPoint) # Our two extra vertices are determined by the closest two.
if (c & 0x01) == 0
xsv_ext0 = xsb
xsv_ext1 = xsb - 1
dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_3D
dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_3D
else
xsv_ext0 = xsv_ext1 = xsb + 1
dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D
dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D
end
if (c & 0x02) == 0
ysv_ext0 = ysb
ysv_ext1 = ysb - 1
dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_3D
dy_ext1 = dy0 + 1 - SQUISH_CONSTANT_3D
else
ysv_ext0 = ysv_ext1 = ysb + 1
dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D
dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D
end
if (c & 0x04) == 0
zsv_ext0 = zsb
zsv_ext1 = zsb - 1
dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_3D
dz_ext1 = dz0 + 1 - SQUISH_CONSTANT_3D
else
zsv_ext0 = zsv_ext1 = zsb + 1
dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D
dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D
end
end
# Contribution (0,0,0)
attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0
if attn0 > 0
attn0 *= attn0
value += attn0 * attn0 * extrapolate(xsb + 0, ysb + 0, zsb + 0, dx0, dy0, dz0)
end
# Contribution (1,0,0)
dx1 = dx0 - 1 - SQUISH_CONSTANT_3D
dy1 = dy0 - 0 - SQUISH_CONSTANT_3D
dz1 = dz0 - 0 - SQUISH_CONSTANT_3D
attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1
if attn1 > 0
attn1 *= attn1
value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1)
end
# Contribution (0,1,0)
dx2 = dx0 - 0 - SQUISH_CONSTANT_3D
dy2 = dy0 - 1 - SQUISH_CONSTANT_3D
dz2 = dz1
attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2
if attn2 > 0
attn2 *= attn2
value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2)
end
# Contribution (0,0,1)
dx3 = dx2
dy3 = dy1
dz3 = dz0 - 1 - SQUISH_CONSTANT_3D
attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3
if attn3 > 0
attn3 *= attn3
value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, dx3, dy3, dz3)
end
elseif inSum >= 2 # We're inside the tetrahedron (3-Simplex) at (1,1,1)
# Determine which two tetrahedral vertices are the closest, out of (1,1,0), (1,0,1), (0,1,1) but not (1,1,1).
aPoint = 0x06
aScore = xins
bPoint = 0x05
bScore = yins
if (aScore <= bScore) && (zins < bScore)
bScore = zins
bPoint = 0x03
elseif (aScore > bScore) && (zins < aScore)
aScore = zins
aPoint = 0x03
end
# Now we determine the two lattice points not part of the tetrahedron that may contribute.
# This depends on the closest two tetrahedral vertices, including (1,1,1)
wins = 3 - inSum
if wins < aScore || wins < bScore # (1,1,1) is one of the closest two tetrahedral vertices.
c = (bScore < aScore ? bPoint : aPoint) # Our other closest vertex is the closest out of a and b.
if (c & 0x01) != 0
xsv_ext0 = xsb + 2
xsv_ext1 = xsb + 1
dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_3D
dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D
else
xsv_ext0 = xsv_ext1 = xsb
dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_3D
end
if (c & 0x02) != 0
ysv_ext0 = ysv_ext1 = ysb + 1
dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D
if (c & 0x01) != 0
ysv_ext1 += 1
dy_ext1 -= 1
else
ysv_ext0 += 1
dy_ext0 -= 1
end
else
ysv_ext0 = ysv_ext1 = ysb
dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_3D
end
if (c & 0x04) != 0
zsv_ext0 = zsb + 1
zsv_ext1 = zsb + 2
dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D
dz_ext1 = dz0 - 2 - 3 * SQUISH_CONSTANT_3D
else
zsv_ext0 = zsv_ext1 = zsb
dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_3D
end
else # (1,1,1) is not one of the closest two tetrahedral vertices.
c = (aPoint & bPoint) # Our two extra vertices are determined by the closest two.
if (c & 0x01) != 0
xsv_ext0 = xsb + 1
xsv_ext1 = xsb + 2
dx_ext0 = dx0 - 1 - SQUISH_CONSTANT_3D
dx_ext1 = dx0 - 2 - 2 * SQUISH_CONSTANT_3D
else
xsv_ext0 = xsv_ext1 = xsb
dx_ext0 = dx0 - SQUISH_CONSTANT_3D
dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D
end
if (c & 0x02) != 0
ysv_ext0 = ysb + 1
ysv_ext1 = ysb + 2
dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D
dy_ext1 = dy0 - 2 - 2 * SQUISH_CONSTANT_3D
else
ysv_ext0 = ysv_ext1 = ysb
dy_ext0 = dy0 - SQUISH_CONSTANT_3D
dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D
end
if (c & 0x04) != 0
zsv_ext0 = zsb + 1
zsv_ext1 = zsb + 2
dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D
dz_ext1 = dz0 - 2 - 2 * SQUISH_CONSTANT_3D
else
zsv_ext0 = zsv_ext1 = zsb
dz_ext0 = dz0 - SQUISH_CONSTANT_3D
dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D
end
end
# Contribution (1,1,0)
dx3 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D
dy3 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D
dz3 = dz0 - 0 - 2 * SQUISH_CONSTANT_3D
attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3
if attn3 > 0
attn3 *= attn3
value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, dx3, dy3, dz3)
end
# Contribution (1,0,1)
dx2 = dx3
dy2 = dy0 - 0 - 2 * SQUISH_CONSTANT_3D
dz2 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D
attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2
if attn2 > 0
attn2 *= attn2
value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, dx2, dy2, dz2)
end
# Contribution (0,1,1)
dx1 = dx0 - 0 - 2 * SQUISH_CONSTANT_3D
dy1 = dy3
dz1 = dz2
attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1
if attn1 > 0
attn1 *= attn1
value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, dx1, dy1, dz1)
end
# Contribution (1,1,1)
dx0 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D
dy0 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D
dz0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D
attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0
if attn0 > 0
attn0 *= attn0
value += attn0 * attn0 * extrapolate(xsb + 1, ysb + 1, zsb + 1, dx0, dy0, dz0)
end
else # We're inside the octahedron (Rectified 3-Simplex) in between.
# Decide between point (0,0,1) and (1,1,0) as closest
p1 = xins + yins
if p1 > 1
aScore = p1 - 1
aPoint = 0x03
aIsFurtherSide = true
else
aScore = 1 - p1
aPoint = 0x04
aIsFurtherSide = false
end
# Decide between point (0,1,0) and (1,0,1) as closest
p2 = xins + zins
if p2 > 1
bScore = p2 - 1
bPoint = 0x05
bIsFurtherSide = true
else
bScore = 1 - p2
bPoint = 0x02
bIsFurtherSide = false
end
# The closest out of the two (1,0,0) and (0,1,1) will replace the furthest out of the two decided above, if closer.
p3 = yins + zins
if p3 > 1
score = p3 - 1
if (aScore <= bScore) && (aScore < score)
aScore = score
aPoint = 0x06
aIsFurtherSide = true
elseif (aScore > bScore) && (bScore < score)
bScore = score
bPoint = 0x06
bIsFurtherSide = true
end
else
score = 1 - p3
if (aScore <= bScore) && (aScore < score)
aScore = score
aPoint = 0x01
aIsFurtherSide = false
elseif (aScore > bScore) && (bScore < score)
bScore = score
bPoint = 0x01
bIsFurtherSide = false
end
end
# Where each of the two closest points are determines how the extra two vertices are calculated.
if aIsFurtherSide == bIsFurtherSide
if aIsFurtherSide # Both closest points on (1,1,1) side
# One of the two extra points is (1,1,1)
dx_ext0 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D
dy_ext0 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D
dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D
xsv_ext0 = xsb + 1
ysv_ext0 = ysb + 1
zsv_ext0 = zsb + 1
# Other extra point is based on the shared axis.
c = aPoint & bPoint
if (c & 0x01) != 0
dx_ext1 = dx0 - 2 - 2 * SQUISH_CONSTANT_3D
dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D
dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D
xsv_ext1 = xsb + 2
ysv_ext1 = ysb
zsv_ext1 = zsb
elseif (c & 0x02) != 0
dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D
dy_ext1 = dy0 - 2 - 2 * SQUISH_CONSTANT_3D
dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D
xsv_ext1 = xsb
ysv_ext1 = ysb + 2
zsv_ext1 = zsb
else
dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D
dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D
dz_ext1 = dz0 - 2 - 2 * SQUISH_CONSTANT_3D
xsv_ext1 = xsb
ysv_ext1 = ysb
zsv_ext1 = zsb + 2
end
else # Both closest points on (0,0,0) side
# One of the two extra points is (0,0,0)
dx_ext0 = dx0
dy_ext0 = dy0
dz_ext0 = dz0
xsv_ext0 = xsb
ysv_ext0 = ysb
zsv_ext0 = zsb
# Other extra point is based on the omitted axis.
c = aPoint | bPoint
if (c & 0x01) == 0 # other extra omitted axis
dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_3D
dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D
dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D
xsv_ext1 = xsb - 1
ysv_ext1 = ysb + 1
zsv_ext1 = zsb + 1
elseif (c & 0x02) == 0
dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D
dy_ext1 = dy0 + 1 - SQUISH_CONSTANT_3D
dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D
xsv_ext1 = xsb + 1
ysv_ext1 = ysb - 1
zsv_ext1 = zsb + 1
else
dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D
dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D
dz_ext1 = dz0 + 1 - SQUISH_CONSTANT_3D
xsv_ext1 = xsb + 1
ysv_ext1 = ysb + 1
zsv_ext1 = zsb - 1
end
end
else # One point on (0,0,0) side, one point on (1,1,1) side
if aIsFurtherSide
c1 = aPoint
c2 = bPoint
else
c1 = bPoint
c2 = aPoint
end
# One contribution is a permutation of (1,1,-1)
if c1 & 0x01 == 0
dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_3D
dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D
dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D
xsv_ext0 = xsb - 1
ysv_ext0 = ysb + 1
zsv_ext0 = zsb + 1
elseif c1 & 0x02 == 0
dx_ext0 = dx0 - 1 - SQUISH_CONSTANT_3D
dy_ext0 = dy0 + 1 - SQUISH_CONSTANT_3D
dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D
xsv_ext0 = xsb + 1
ysv_ext0 = ysb - 1
zsv_ext0 = zsb + 1
else
dx_ext0 = dx0 - 1 - SQUISH_CONSTANT_3D
dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D
dz_ext0 = dz0 + 1 - SQUISH_CONSTANT_3D
xsv_ext0 = xsb + 1
ysv_ext0 = ysb + 1
zsv_ext0 = zsb - 1
end
# One contribution is a permutation of (0,0,2)
dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D
dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D
dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D
xsv_ext1 = xsb
ysv_ext1 = ysb
zsv_ext1 = zsb
if (c2 & 0x01) != 0
dx_ext1 -= 2
xsv_ext1 += 2
elseif (c2 & 0x02) != 0
dy_ext1 -= 2
ysv_ext1 += 2
else
dz_ext1 -= 2
zsv_ext1 += 2
end
end
# Contribution (1,0,0)
dx1 = dx0 - 1 - SQUISH_CONSTANT_3D
dy1 = dy0 - 0 - SQUISH_CONSTANT_3D
dz1 = dz0 - 0 - SQUISH_CONSTANT_3D
attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1
if attn1 > 0
attn1 *= attn1
value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1)
end
# Contribution (0,1,0)
dx2 = dx0 - 0 - SQUISH_CONSTANT_3D
dy2 = dy0 - 1 - SQUISH_CONSTANT_3D
dz2 = dz1
attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2
if attn2 > 0
attn2 *= attn2
value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2)
end
# Contribution (0,0,1)
dx3 = dx2
dy3 = dy1
dz3 = dz0 - 1 - SQUISH_CONSTANT_3D
attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3
if attn3 > 0
attn3 *= attn3
value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, dx3, dy3, dz3)
end
# Contribution (1,1,0)
dx4 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D
dy4 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D
dz4 = dz0 - 0 - 2 * SQUISH_CONSTANT_3D
attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4
if attn4 > 0
attn4 *= attn4
value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 0, dx4, dy4, dz4)
end
# Contribution (1,0,1)
dx5 = dx4
dy5 = dy0 - 0 - 2 * SQUISH_CONSTANT_3D
dz5 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D
attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5
if attn5 > 0
attn5 *= attn5
value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 0, zsb + 1, dx5, dy5, dz5)
end
# Contribution (0,1,1)
dx6 = dx0 - 0 - 2 * SQUISH_CONSTANT_3D
dy6 = dy4
dz6 = dz5
attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6
if attn6 > 0
attn6 *= attn6
value += attn6 * attn6 * extrapolate(xsb + 0, ysb + 1, zsb + 1, dx6, dy6, dz6)
end
end
# First extra vertex
attn_ext0 = 2 - dx_ext0 * dx_ext0 - dy_ext0 * dy_ext0 - dz_ext0 * dz_ext0
if attn_ext0 > 0
attn_ext0 *= attn_ext0
value += attn_ext0 * attn_ext0 * extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, dx_ext0, dy_ext0, dz_ext0)
end
# Second extra vertex
attn_ext1 = 2 - dx_ext1 * dx_ext1 - dy_ext1 * dy_ext1 - dz_ext1 * dz_ext1
if attn_ext1 > 0
attn_ext1 *= attn_ext1
value += attn_ext1 * attn_ext1 * extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, dx_ext1, dy_ext1, dz_ext1)
end
res = value / NORM_CONSTANT_3D
# convert to [0, 1]
return clamp((res + 1) / 2, 0.0, 1.0)
end
# 4D OpenSimplex Noise.
function simplexnoise(x, y, z, w)
# TODO convert to Julia properly
# Place input coordinates on simplectic honeycomb.
stretchOffset = (x + y + z + w) * STRETCH_CONSTANT_4D
xs = x + stretchOffset
ys = y + stretchOffset
zs = z + stretchOffset
ws = w + stretchOffset
# Floor to get simplectic honeycomb coordinates of rhombo-hypercube super-cell origin.
xsb = convert(Int, floor(xs))
ysb = convert(Int, floor(ys))
zsb = convert(Int, floor(zs))
wsb = convert(Int, floor(ws))
# Skew out to get actual coordinates of stretched rhombo-hypercube origin. We'll need these later.
squishOffset = (xsb + ysb + zsb + wsb) * SQUISH_CONSTANT_4D
xb = xsb + squishOffset
yb = ysb + squishOffset
zb = zsb + squishOffset
wb = wsb + squishOffset
# Compute simplectic honeycomb coordinates relative to rhombo-hypercube origin.
xins = xs - xsb
yins = ys - ysb
zins = zs - zsb
wins = ws - wsb
# Sum those together to get a value that determines which region we're in.
inSum = xins + yins + zins + wins
# Positions relative to origin point.
dx0 = x - xb
dy0 = y - yb
dz0 = z - zb
dw0 = w - wb
value = 0.0
if inSum <= 1 # We're inside the pentachoron (4-Simplex) at (0,0,0,0)
# Determine which two of (0,0,0,1), (0,0,1,0), (0,1,0,0), (1,0,0,0) are closest.
aPoint = 0x01
aScore = xins
bPoint = 0x02
bScore = yins
if (aScore >= bScore) && (zins > bScore)
bScore = zins
bPoint = 0x04
elseif (aScore < bScore) && (zins > aScore)
aScore = zins
aPoint = 0x04
end
if (aScore >= bScore) && (wins > bScore)
bScore = wins
bPoint = 0x08
elseif (aScore < bScore) && (wins > aScore)
aScore = wins
aPoint = 0x08
end
# Now we determine the three lattice points not part of the pentachoron that may contribute.
# This depends on the closest two pentachoron vertices, including (0,0,0,0)
uins = 1 - inSum
if (uins > aScore) || (uins > bScore) # (0,0,0,0) is one of the closest two pentachoron vertices.
c = (bScore > aScore ? bPoint : aPoint) # Our other closest vertex is the closest out of a and b.
if (c & 0x01) == 0
xsv_ext0 = xsb - 1
xsv_ext1 = xsv_ext2 = xsb
dx_ext0 = dx0 + 1
dx_ext1 = dx_ext2 = dx0
else
xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1
dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 1
end
if (c & 0x02) == 0
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb
dy_ext0 = dy_ext1 = dy_ext2 = dy0
if (c & 0x01) == 0x01
ysv_ext0 -= 1
dy_ext0 += 1
else
ysv_ext1 -= 1
dy_ext1 += 1
end
else
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1
dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1
end
if (c & 0x04) == 0
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb
dz_ext0 = dz_ext1 = dz_ext2 = dz0
if (c & 0x03) != 0
if (c & 0x03) == 0x03
zsv_ext0 -= 1
dz_ext0 += 1
else
zsv_ext1 -= 1
dz_ext1 += 1
end
else
zsv_ext2 -= 1
dz_ext2 += 1
end
else
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1
dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1
end
if (c & 0x08) == 0
wsv_ext0 = wsv_ext1 = wsb
wsv_ext2 = wsb - 1
dw_ext0 = dw_ext1 = dw0
dw_ext2 = dw0 + 1
else
wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1
dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 1
end
else # (0,0,0,0) is not one of the closest two pentachoron vertices.
c = aPoint | bPoint # Our three extra vertices are determined by the closest two.
if (c & 0x01) == 0
xsv_ext0 = xsv_ext2 = xsb
xsv_ext1 = xsb - 1
dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_4D
dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_4D