/
opensimplex_base.go
2178 lines (2007 loc) · 55.8 KB
/
opensimplex_base.go
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package opensimplex
import "math"
// Vanilla opensimplex implementation, matching Kurt Spencer's Java
// reference implementation as exactly as possible.
// A seeded Noise instance. Reusing a Noise instance (rather than recreating it
// from a known seed) will save some calculation time.
type noise struct {
perm []int16
permGradIndex3D []int16
}
// Returns a random noise value in two dimensions. Repeated calls with the same
// x/y inputs will have the same output.
func (s *noise) Eval2(x, y float64) float64 {
// Place input coordinates onto grid.
stretchOffset := (x + y) * stretchConstant2D
xs := float64(x + stretchOffset)
ys := float64(y + stretchOffset)
// Floor to get grid coordinates of rhombus (stretched square) super-cell origin.
xsb := int32(math.Floor(xs))
ysb := int32(math.Floor(ys))
// Skew out to get actual coordinates of rhombus origin. We'll need these later.
squishOffset := float64(xsb+ysb) * squishConstant2D
xb := float64(xsb) + squishOffset
yb := float64(ysb) + squishOffset
// Compute grid coordinates relative to rhombus origin.
xins := xs - float64(xsb)
yins := ys - float64(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.
var dx_ext, dy_ext float64
var xsv_ext, ysv_ext int32
value := float64(0)
// Contribution (1,0)
dx1 := dx0 - 1 - squishConstant2D
dy1 := dy0 - 0 - squishConstant2D
attn1 := 2 - dx1*dx1 - dy1*dy1
if attn1 > 0 {
attn1 *= attn1
value += attn1 * attn1 * s.extrapolate2(xsb+1, ysb+0, dx1, dy1)
}
// Contribution (0,1)
dx2 := dx0 - 0 - squishConstant2D
dy2 := dy0 - 1 - squishConstant2D
attn2 := 2 - dx2*dx2 - dy2*dy2
if attn2 > 0 {
attn2 *= attn2
value += attn2 * attn2 * s.extrapolate2(xsb+0, ysb+1, dx2, dy2)
}
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
}
} else { // (1,0) and (0,1) are the closest two vertices.
xsv_ext = xsb + 1
ysv_ext = ysb + 1
dx_ext = dx0 - 1 - 2*squishConstant2D
dy_ext = dy0 - 1 - 2*squishConstant2D
}
} 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*squishConstant2D
dy_ext = dy0 + 0 - 2*squishConstant2D
} else {
xsv_ext = xsb + 0
ysv_ext = ysb + 2
dx_ext = dx0 + 0 - 2*squishConstant2D
dy_ext = dy0 - 2 - 2*squishConstant2D
}
} else { // (1,0) and (0,1) are the closest two vertices.
dx_ext = dx0
dy_ext = dy0
xsv_ext = xsb
ysv_ext = ysb
}
xsb += 1
ysb += 1
dx0 = dx0 - 1 - 2*squishConstant2D
dy0 = dy0 - 1 - 2*squishConstant2D
}
// Contribution (0,0) or (1,1)
attn0 := 2 - dx0*dx0 - dy0*dy0
if attn0 > 0 {
attn0 *= attn0
value += attn0 * attn0 * s.extrapolate2(xsb, ysb, dx0, dy0)
}
// 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 * s.extrapolate2(xsv_ext, ysv_ext, dx_ext, dy_ext)
}
return value / normConstant2D
}
// Returns a random noise value in three dimensions.
func (s *noise) Eval3(x, y, z float64) float64 {
// Place input coordinates on simplectic honeycomb.
stretchOffset := (x + y + z) * stretchConstant3D
xs := float64(x + stretchOffset)
ys := float64(y + stretchOffset)
zs := float64(z + stretchOffset)
// Floor to get simplectic honeycomb coordinates of rhombohedron (stretched cube) super-cell origin.
xsb := int32(math.Floor(xs))
ysb := int32(math.Floor(ys))
zsb := int32(math.Floor(zs))
// Skew out to get actual coordinates of rhombohedron origin. We'll need these later.
squishOffset := float64(xsb+ysb+zsb) * squishConstant3D
xb := float64(xsb) + squishOffset
yb := float64(ysb) + squishOffset
zb := float64(zsb) + squishOffset
// Compute simplectic honeycomb coordinates relative to rhombohedral origin.
xins := xs - float64(xsb)
yins := ys - float64(ysb)
zins := zs - float64(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.
var dx_ext0, dy_ext0, dz_ext0 float64
var dx_ext1, dy_ext1, dz_ext1 float64
var xsv_ext0, ysv_ext0, zsv_ext0 int32
var xsv_ext1, ysv_ext1, zsv_ext1 int32
value := float64(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 := byte(0x01)
bPoint := byte(0x02)
aScore := xins
bScore := yins
if aScore >= bScore && zins > bScore {
bScore = zins
bPoint = 0x04
} else if aScore < bScore && zins > aScore {
aScore = zins
aPoint = 0x04
}
// 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.
var c byte // Our other closest vertex is the closest out of a and b.
if bScore > aScore {
c = bPoint
} else {
c = aPoint
}
if (c & 0x01) == 0 {
xsv_ext0 = xsb - 1
xsv_ext1 = xsb
dx_ext0 = dx0 + 1
dx_ext1 = dx0
} else {
xsv_ext1 = xsb + 1
xsv_ext0 = xsv_ext1
dx_ext1 = dx0 - 1
dx_ext0 = dx_ext1
}
if (c & 0x02) == 0 {
ysv_ext1 = ysb
ysv_ext0 = ysv_ext1
dy_ext1 = dy0
dy_ext0 = dy_ext1
if (c & 0x01) == 0 {
ysv_ext1 -= 1
dy_ext1 += 1
} else {
ysv_ext0 -= 1
dy_ext0 += 1
}
} else {
ysv_ext1 = ysb + 1
ysv_ext0 = ysv_ext1
dy_ext1 = dy0 - 1
dy_ext0 = dy_ext1
}
if (c & 0x04) == 0 {
zsv_ext0 = zsb
zsv_ext1 = zsb - 1
dz_ext0 = dz0
dz_ext1 = dz0 + 1
} else {
zsv_ext1 = zsb + 1
zsv_ext0 = zsv_ext1
dz_ext1 = dz0 - 1
dz_ext0 = dz_ext1
}
} 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*squishConstant3D
dx_ext1 = dx0 + 1 - squishConstant3D
} else {
xsv_ext1 = xsb + 1
xsv_ext0 = xsv_ext1
dx_ext0 = dx0 - 1 - 2*squishConstant3D
dx_ext1 = dx0 - 1 - squishConstant3D
}
if (c & 0x02) == 0 {
ysv_ext0 = ysb
ysv_ext1 = ysb - 1
dy_ext0 = dy0 - 2*squishConstant3D
dy_ext1 = dy0 + 1 - squishConstant3D
} else {
ysv_ext1 = ysb + 1
ysv_ext0 = ysv_ext1
dy_ext0 = dy0 - 1 - 2*squishConstant3D
dy_ext1 = dy0 - 1 - squishConstant3D
}
if (c & 0x04) == 0 {
zsv_ext0 = zsb
zsv_ext1 = zsb - 1
dz_ext0 = dz0 - 2*squishConstant3D
dz_ext1 = dz0 + 1 - squishConstant3D
} else {
zsv_ext1 = zsb + 1
zsv_ext0 = zsv_ext1
dz_ext0 = dz0 - 1 - 2*squishConstant3D
dz_ext1 = dz0 - 1 - squishConstant3D
}
}
// Contribution (0,0,0)
attn0 := 2 - dx0*dx0 - dy0*dy0 - dz0*dz0
if attn0 > 0 {
attn0 *= attn0
value += attn0 * attn0 * s.extrapolate3(xsb+0, ysb+0, zsb+0, dx0, dy0, dz0)
}
// Contribution (1,0,0)
dx1 := dx0 - 1 - squishConstant3D
dy1 := dy0 - 0 - squishConstant3D
dz1 := dz0 - 0 - squishConstant3D
attn1 := 2 - dx1*dx1 - dy1*dy1 - dz1*dz1
if attn1 > 0 {
attn1 *= attn1
value += attn1 * attn1 * s.extrapolate3(xsb+1, ysb+0, zsb+0, dx1, dy1, dz1)
}
// Contribution (0,1,0)
dx2 := dx0 - 0 - squishConstant3D
dy2 := dy0 - 1 - squishConstant3D
dz2 := dz1
attn2 := 2 - dx2*dx2 - dy2*dy2 - dz2*dz2
if attn2 > 0 {
attn2 *= attn2
value += attn2 * attn2 * s.extrapolate3(xsb+0, ysb+1, zsb+0, dx2, dy2, dz2)
}
// Contribution (0,0,1)
dx3 := dx2
dy3 := dy1
dz3 := dz0 - 1 - squishConstant3D
attn3 := 2 - dx3*dx3 - dy3*dy3 - dz3*dz3
if attn3 > 0 {
attn3 *= attn3
value += attn3 * attn3 * s.extrapolate3(xsb+0, ysb+0, zsb+1, dx3, dy3, dz3)
}
} else if 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 := byte(0x06)
aScore := xins
bPoint := byte(0x05)
bScore := yins
if aScore <= bScore && zins < bScore {
bScore = zins
bPoint = 0x03
} else if aScore > bScore && zins < aScore {
aScore = zins
aPoint = 0x03
}
// 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.
var c byte // Our other closest vertex is the closest out of a and b.
if bScore < aScore {
c = bPoint
} else {
c = aPoint
}
if (c & 0x01) != 0 {
xsv_ext0 = xsb + 2
xsv_ext1 = xsb + 1
dx_ext0 = dx0 - 2 - 3*squishConstant3D
dx_ext1 = dx0 - 1 - 3*squishConstant3D
} else {
xsv_ext1 = xsb
xsv_ext0 = xsv_ext1
dx_ext1 = dx0 - 3*squishConstant3D
dx_ext0 = dx_ext1
}
if (c & 0x02) != 0 {
ysv_ext1 = ysb + 1
ysv_ext0 = ysv_ext1
dy_ext1 = dy0 - 1 - 3*squishConstant3D
dy_ext0 = dy_ext1
if (c & 0x01) != 0 {
ysv_ext1 += 1
dy_ext1 -= 1
} else {
ysv_ext0 += 1
dy_ext0 -= 1
}
} else {
ysv_ext1 = ysb
ysv_ext0 = ysv_ext1
dy_ext1 = dy0 - 3*squishConstant3D
dy_ext0 = dy_ext1
}
if (c & 0x04) != 0 {
zsv_ext0 = zsb + 1
zsv_ext1 = zsb + 2
dz_ext0 = dz0 - 1 - 3*squishConstant3D
dz_ext1 = dz0 - 2 - 3*squishConstant3D
} else {
zsv_ext1 = zsb
zsv_ext0 = zsv_ext1
dz_ext1 = dz0 - 3*squishConstant3D
dz_ext0 = dz_ext1
}
} 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 - squishConstant3D
dx_ext1 = dx0 - 2 - 2*squishConstant3D
} else {
xsv_ext1 = xsb
xsv_ext0 = xsv_ext1
dx_ext0 = dx0 - squishConstant3D
dx_ext1 = dx0 - 2*squishConstant3D
}
if (c & 0x02) != 0 {
ysv_ext0 = ysb + 1
ysv_ext1 = ysb + 2
dy_ext0 = dy0 - 1 - squishConstant3D
dy_ext1 = dy0 - 2 - 2*squishConstant3D
} else {
ysv_ext1 = ysb
ysv_ext0 = ysv_ext1
dy_ext0 = dy0 - squishConstant3D
dy_ext1 = dy0 - 2*squishConstant3D
}
if (c & 0x04) != 0 {
zsv_ext0 = zsb + 1
zsv_ext1 = zsb + 2
dz_ext0 = dz0 - 1 - squishConstant3D
dz_ext1 = dz0 - 2 - 2*squishConstant3D
} else {
zsv_ext1 = zsb
zsv_ext0 = zsv_ext1
dz_ext0 = dz0 - squishConstant3D
dz_ext1 = dz0 - 2*squishConstant3D
}
}
// Contribution (1,1,0)
dx3 := dx0 - 1 - 2*squishConstant3D
dy3 := dy0 - 1 - 2*squishConstant3D
dz3 := dz0 - 0 - 2*squishConstant3D
attn3 := 2 - dx3*dx3 - dy3*dy3 - dz3*dz3
if attn3 > 0 {
attn3 *= attn3
value += attn3 * attn3 * s.extrapolate3(xsb+1, ysb+1, zsb+0, dx3, dy3, dz3)
}
// Contribution (1,0,1)
dx2 := dx3
dy2 := dy0 - 0 - 2*squishConstant3D
dz2 := dz0 - 1 - 2*squishConstant3D
attn2 := 2 - dx2*dx2 - dy2*dy2 - dz2*dz2
if attn2 > 0 {
attn2 *= attn2
value += attn2 * attn2 * s.extrapolate3(xsb+1, ysb+0, zsb+1, dx2, dy2, dz2)
}
// Contribution (0,1,1)
dx1 := dx0 - 0 - 2*squishConstant3D
dy1 := dy3
dz1 := dz2
attn1 := 2 - dx1*dx1 - dy1*dy1 - dz1*dz1
if attn1 > 0 {
attn1 *= attn1
value += attn1 * attn1 * s.extrapolate3(xsb+0, ysb+1, zsb+1, dx1, dy1, dz1)
}
// Contribution (1,1,1)
dx0 = dx0 - 1 - 3*squishConstant3D
dy0 = dy0 - 1 - 3*squishConstant3D
dz0 = dz0 - 1 - 3*squishConstant3D
attn0 := 2 - dx0*dx0 - dy0*dy0 - dz0*dz0
if attn0 > 0 {
attn0 *= attn0
value += attn0 * attn0 * s.extrapolate3(xsb+1, ysb+1, zsb+1, dx0, dy0, dz0)
}
} else { // We're inside the octahedron (Rectified 3-Simplex) in between.
var aScore, bScore float64
var aPoint, bPoint byte
var aIsFurtherSide, bIsFurtherSide bool
// 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
}
// 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
}
// 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
} else if aScore > bScore && bScore < score {
bScore = score
bPoint = 0x06
bIsFurtherSide = true
}
} else {
score := 1 - p3
if aScore <= bScore && aScore < score {
aScore = score
aPoint = 0x01
aIsFurtherSide = false
} else if aScore > bScore && bScore < score {
bScore = score
bPoint = 0x01
bIsFurtherSide = false
}
}
// 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*squishConstant3D
dy_ext0 = dy0 - 1 - 3*squishConstant3D
dz_ext0 = dz0 - 1 - 3*squishConstant3D
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*squishConstant3D
dy_ext1 = dy0 - 2*squishConstant3D
dz_ext1 = dz0 - 2*squishConstant3D
xsv_ext1 = xsb + 2
ysv_ext1 = ysb
zsv_ext1 = zsb
} else if (c & 0x02) != 0 {
dx_ext1 = dx0 - 2*squishConstant3D
dy_ext1 = dy0 - 2 - 2*squishConstant3D
dz_ext1 = dz0 - 2*squishConstant3D
xsv_ext1 = xsb
ysv_ext1 = ysb + 2
zsv_ext1 = zsb
} else {
dx_ext1 = dx0 - 2*squishConstant3D
dy_ext1 = dy0 - 2*squishConstant3D
dz_ext1 = dz0 - 2 - 2*squishConstant3D
xsv_ext1 = xsb
ysv_ext1 = ysb
zsv_ext1 = zsb + 2
}
} 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 {
dx_ext1 = dx0 + 1 - squishConstant3D
dy_ext1 = dy0 - 1 - squishConstant3D
dz_ext1 = dz0 - 1 - squishConstant3D
xsv_ext1 = xsb - 1
ysv_ext1 = ysb + 1
zsv_ext1 = zsb + 1
} else if (c & 0x02) == 0 {
dx_ext1 = dx0 - 1 - squishConstant3D
dy_ext1 = dy0 + 1 - squishConstant3D
dz_ext1 = dz0 - 1 - squishConstant3D
xsv_ext1 = xsb + 1
ysv_ext1 = ysb - 1
zsv_ext1 = zsb + 1
} else {
dx_ext1 = dx0 - 1 - squishConstant3D
dy_ext1 = dy0 - 1 - squishConstant3D
dz_ext1 = dz0 + 1 - squishConstant3D
xsv_ext1 = xsb + 1
ysv_ext1 = ysb + 1
zsv_ext1 = zsb - 1
}
}
} else { // One point on (0,0,0) side, one point on (1,1,1) side
var c1, c2 byte
if aIsFurtherSide {
c1 = aPoint
c2 = bPoint
} else {
c1 = bPoint
c2 = aPoint
}
// One contribution is a permutation of (1,1,-1)
if (c1 & 0x01) == 0 {
dx_ext0 = dx0 + 1 - squishConstant3D
dy_ext0 = dy0 - 1 - squishConstant3D
dz_ext0 = dz0 - 1 - squishConstant3D
xsv_ext0 = xsb - 1
ysv_ext0 = ysb + 1
zsv_ext0 = zsb + 1
} else if (c1 & 0x02) == 0 {
dx_ext0 = dx0 - 1 - squishConstant3D
dy_ext0 = dy0 + 1 - squishConstant3D
dz_ext0 = dz0 - 1 - squishConstant3D
xsv_ext0 = xsb + 1
ysv_ext0 = ysb - 1
zsv_ext0 = zsb + 1
} else {
dx_ext0 = dx0 - 1 - squishConstant3D
dy_ext0 = dy0 - 1 - squishConstant3D
dz_ext0 = dz0 + 1 - squishConstant3D
xsv_ext0 = xsb + 1
ysv_ext0 = ysb + 1
zsv_ext0 = zsb - 1
}
// One contribution is a permutation of (0,0,2)
dx_ext1 = dx0 - 2*squishConstant3D
dy_ext1 = dy0 - 2*squishConstant3D
dz_ext1 = dz0 - 2*squishConstant3D
xsv_ext1 = xsb
ysv_ext1 = ysb
zsv_ext1 = zsb
if (c2 & 0x01) != 0 {
dx_ext1 -= 2
xsv_ext1 += 2
} else if (c2 & 0x02) != 0 {
dy_ext1 -= 2
ysv_ext1 += 2
} else {
dz_ext1 -= 2
zsv_ext1 += 2
}
}
// Contribution (1,0,0)
dx1 := dx0 - 1 - squishConstant3D
dy1 := dy0 - 0 - squishConstant3D
dz1 := dz0 - 0 - squishConstant3D
attn1 := 2 - dx1*dx1 - dy1*dy1 - dz1*dz1
if attn1 > 0 {
attn1 *= attn1
value += attn1 * attn1 * s.extrapolate3(xsb+1, ysb+0, zsb+0, dx1, dy1, dz1)
}
// Contribution (0,1,0)
dx2 := dx0 - 0 - squishConstant3D
dy2 := dy0 - 1 - squishConstant3D
dz2 := dz1
attn2 := 2 - dx2*dx2 - dy2*dy2 - dz2*dz2
if attn2 > 0 {
attn2 *= attn2
value += attn2 * attn2 * s.extrapolate3(xsb+0, ysb+1, zsb+0, dx2, dy2, dz2)
}
// Contribution (0,0,1)
dx3 := dx2
dy3 := dy1
dz3 := dz0 - 1 - squishConstant3D
attn3 := 2 - dx3*dx3 - dy3*dy3 - dz3*dz3
if attn3 > 0 {
attn3 *= attn3
value += attn3 * attn3 * s.extrapolate3(xsb+0, ysb+0, zsb+1, dx3, dy3, dz3)
}
// Contribution (1,1,0)
dx4 := dx0 - 1 - 2*squishConstant3D
dy4 := dy0 - 1 - 2*squishConstant3D
dz4 := dz0 - 0 - 2*squishConstant3D
attn4 := 2 - dx4*dx4 - dy4*dy4 - dz4*dz4
if attn4 > 0 {
attn4 *= attn4
value += attn4 * attn4 * s.extrapolate3(xsb+1, ysb+1, zsb+0, dx4, dy4, dz4)
}
// Contribution (1,0,1)
dx5 := dx4
dy5 := dy0 - 0 - 2*squishConstant3D
dz5 := dz0 - 1 - 2*squishConstant3D
attn5 := 2 - dx5*dx5 - dy5*dy5 - dz5*dz5
if attn5 > 0 {
attn5 *= attn5
value += attn5 * attn5 * s.extrapolate3(xsb+1, ysb+0, zsb+1, dx5, dy5, dz5)
}
// Contribution (0,1,1)
dx6 := dx0 - 0 - 2*squishConstant3D
dy6 := dy4
dz6 := dz5
attn6 := 2 - dx6*dx6 - dy6*dy6 - dz6*dz6
if attn6 > 0 {
attn6 *= attn6
value += attn6 * attn6 * s.extrapolate3(xsb+0, ysb+1, zsb+1, dx6, dy6, dz6)
}
}
// 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 * s.extrapolate3(xsv_ext0, ysv_ext0, zsv_ext0, dx_ext0, dy_ext0, dz_ext0)
}
// 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 * s.extrapolate3(xsv_ext1, ysv_ext1, zsv_ext1, dx_ext1, dy_ext1, dz_ext1)
}
return value / normConstant3D
}
// Returns a random noise value in four dimensions.
func (s *noise) Eval4(x, y, z, w float64) float64 {
// Place input coordinates on simplectic honeycomb.
stretchOffset := (x + y + z + w) * stretchConstant4D
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 := int32(math.Floor(xs))
ysb := int32(math.Floor(ys))
zsb := int32(math.Floor(zs))
wsb := int32(math.Floor(ws))
// Skew out to get actual coordinates of stretched rhombo-hypercube origin. We'll need these later.
squishOffset := float64(xsb+ysb+zsb+wsb) * squishConstant4D
xb := float64(xsb) + squishOffset
yb := float64(ysb) + squishOffset
zb := float64(zsb) + squishOffset
wb := float64(wsb) + squishOffset
// Compute simplectic honeycomb coordinates relative to rhombo-hypercube origin.
xins := xs - float64(xsb)
yins := ys - float64(ysb)
zins := zs - float64(zsb)
wins := ws - float64(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
// We'll be defining these inside the next block and using them afterwards.
var dx_ext0, dy_ext0, dz_ext0, dw_ext0 float64
var dx_ext1, dy_ext1, dz_ext1, dw_ext1 float64
var dx_ext2, dy_ext2, dz_ext2, dw_ext2 float64
var xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0 int32
var xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1 int32
var xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2 int32
var value float64 = 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.
var aPoint byte = 0x01
aScore := xins
var bPoint byte = 0x02
bScore := yins
if aScore >= bScore && zins > bScore {
bScore = zins
bPoint = 0x04
} else if aScore < bScore && zins > aScore {
aScore = zins
aPoint = 0x04
}
if aScore >= bScore && wins > bScore {
bScore = wins
bPoint = 0x08
} else if aScore < bScore && wins > aScore {
aScore = wins
aPoint = 0x08
}
// 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.
var c byte
// Our other closest vertex is the closest out of a and b.
if bScore > aScore {
c = bPoint
} else {
c = aPoint
}
if (c & 0x01) == 0 {
xsv_ext0 = xsb - 1
xsv_ext2 = xsb
xsv_ext1 = xsv_ext2
dx_ext0 = dx0 + 1
dx_ext2 = dx0
dx_ext1 = dx_ext2
} else {
xsv_ext2 = xsb + 1
xsv_ext1 = xsv_ext2
xsv_ext0 = xsv_ext1
dx_ext2 = dx0 - 1
dx_ext1 = dx_ext2
dx_ext0 = dx_ext1
}
if (c & 0x02) == 0 {
ysv_ext2 = ysb
ysv_ext1 = ysv_ext2
ysv_ext0 = ysv_ext1
dy_ext2 = dy0
dy_ext1 = dy_ext2
dy_ext0 = dy_ext1
if (c & 0x01) == 0x01 {
ysv_ext0 -= 1
dy_ext0 += 1
} else {
ysv_ext1 -= 1
dy_ext1 += 1
}
} else {
ysv_ext2 = ysb + 1
ysv_ext1 = ysv_ext2
ysv_ext0 = ysv_ext1
dy_ext2 = dy0 - 1
dy_ext1 = dy_ext2
dy_ext0 = dy_ext1
}
if (c & 0x04) == 0 {
zsv_ext2 = zsb
zsv_ext1 = zsv_ext2
zsv_ext0 = zsv_ext1
dz_ext2 = dz0
dz_ext1 = dz_ext2
dz_ext0 = dz_ext1
if (c & 0x03) != 0 {
if (c & 0x03) == 0x03 {
zsv_ext0 -= 1
dz_ext0 += 1
} else {
zsv_ext1 -= 1
dz_ext1 += 1
}
} else {
zsv_ext2 -= 1
dz_ext2 += 1
}
} else {
zsv_ext2 = zsb + 1
zsv_ext1 = zsv_ext2
zsv_ext0 = zsv_ext1
dz_ext2 = dz0 - 1
dz_ext1 = dz_ext2
dz_ext0 = dz_ext1
}
if (c & 0x08) == 0 {
wsv_ext1 = wsb
wsv_ext0 = wsv_ext1
wsv_ext2 = wsb - 1
dw_ext1 = dw0
dw_ext0 = dw_ext1
dw_ext2 = dw0 + 1
} else {
wsv_ext2 = wsb + 1
wsv_ext1 = wsv_ext2
wsv_ext0 = wsv_ext1
dw_ext2 = dw0 - 1
dw_ext1 = dw_ext2
dw_ext0 = dw_ext1
}
} 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_ext2 = xsb
xsv_ext0 = xsv_ext2
xsv_ext1 = xsb - 1
dx_ext0 = dx0 - 2*squishConstant4D
dx_ext1 = dx0 + 1 - squishConstant4D
dx_ext2 = dx0 - squishConstant4D
} else {
xsv_ext2 = xsb + 1
xsv_ext1 = xsv_ext2
xsv_ext0 = xsv_ext1
dx_ext0 = dx0 - 1 - 2*squishConstant4D
dx_ext2 = dx0 - 1 - squishConstant4D
dx_ext1 = dx_ext2
}
if (c & 0x02) == 0 {
ysv_ext2 = ysb
ysv_ext1 = ysv_ext2
ysv_ext0 = ysv_ext1
dy_ext0 = dy0 - 2*squishConstant4D
dy_ext2 = dy0 - squishConstant4D
dy_ext1 = dy_ext2
if (c & 0x01) == 0x01 {
ysv_ext1 -= 1
dy_ext1 += 1
} else {
ysv_ext2 -= 1
dy_ext2 += 1
}
} else {
ysv_ext2 = ysb + 1
ysv_ext1 = ysv_ext2
ysv_ext0 = ysv_ext1
dy_ext0 = dy0 - 1 - 2*squishConstant4D
dy_ext2 = dy0 - 1 - squishConstant4D
dy_ext1 = dy_ext2
}
if (c & 0x04) == 0 {
zsv_ext2 = zsb
zsv_ext1 = zsv_ext2
zsv_ext0 = zsv_ext1
dz_ext0 = dz0 - 2*squishConstant4D
dz_ext2 = dz0 - squishConstant4D
dz_ext1 = dz_ext2
if (c & 0x03) == 0x03 {
zsv_ext1 -= 1
dz_ext1 += 1
} else {
zsv_ext2 -= 1
dz_ext2 += 1
}
} else {
zsv_ext2 = zsb + 1
zsv_ext1 = zsv_ext2
zsv_ext0 = zsv_ext1
dz_ext0 = dz0 - 1 - 2*squishConstant4D
dz_ext2 = dz0 - 1 - squishConstant4D
dz_ext1 = dz_ext2
}
if (c & 0x08) == 0 {
wsv_ext1 = wsb
wsv_ext0 = wsv_ext1
wsv_ext2 = wsb - 1
dw_ext0 = dw0 - 2*squishConstant4D
dw_ext1 = dw0 - squishConstant4D
dw_ext2 = dw0 + 1 - squishConstant4D
} else {
wsv_ext2 = wsb + 1
wsv_ext1 = wsv_ext2
wsv_ext0 = wsv_ext1
dw_ext0 = dw0 - 1 - 2*squishConstant4D
dw_ext2 = dw0 - 1 - squishConstant4D
dw_ext1 = dw_ext2
}
}
// Contribution (0,0,0,0)
attn0 := 2 - dx0*dx0 - dy0*dy0 - dz0*dz0 - dw0*dw0
if attn0 > 0 {
attn0 *= attn0
value += attn0 * attn0 * s.extrapolate4(xsb+0, ysb+0, zsb+0, wsb+0, dx0, dy0, dz0, dw0)
}
// Contribution (1,0,0,0)
dx1 := dx0 - 1 - squishConstant4D
dy1 := dy0 - 0 - squishConstant4D
dz1 := dz0 - 0 - squishConstant4D
dw1 := dw0 - 0 - squishConstant4D
attn1 := 2 - dx1*dx1 - dy1*dy1 - dz1*dz1 - dw1*dw1
if attn1 > 0 {
attn1 *= attn1
value += attn1 * attn1 * s.extrapolate4(xsb+1, ysb+0, zsb+0, wsb+0, dx1, dy1, dz1, dw1)
}
// Contribution (0,1,0,0)
dx2 := dx0 - 0 - squishConstant4D
dy2 := dy0 - 1 - squishConstant4D
dz2 := dz1
dw2 := dw1
attn2 := 2 - dx2*dx2 - dy2*dy2 - dz2*dz2 - dw2*dw2
if attn2 > 0 {
attn2 *= attn2
value += attn2 * attn2 * s.extrapolate4(xsb+0, ysb+1, zsb+0, wsb+0, dx2, dy2, dz2, dw2)
}
// Contribution (0,0,1,0)
dx3 := dx2
dy3 := dy1
dz3 := dz0 - 1 - squishConstant4D
dw3 := dw1
attn3 := 2 - dx3*dx3 - dy3*dy3 - dz3*dz3 - dw3*dw3
if attn3 > 0 {
attn3 *= attn3
value += attn3 * attn3 * s.extrapolate4(xsb+0, ysb+0, zsb+1, wsb+0, dx3, dy3, dz3, dw3)
}
// Contribution (0,0,0,1)
dx4 := dx2