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catmull_rom.go
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/
catmull_rom.go
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package colorgrad
import (
"math"
)
// Adapted from https://qroph.github.io/2018/07/30/smooth-paths-using-catmull-rom-splines.html
func toCatmullRomSegments(values []float64) [][4]float64 {
alpha := 0.5
tension := 0.0
n := len(values)
vals := make([]float64, n+2)
vals[0] = 2*values[0] - values[1]
for i, v := range values {
vals[i+1] = v
}
vals[n+1] = 2*values[n-1] - values[n-2]
segments := [][4]float64{}
for i := 1; i < len(vals)-2; i++ {
v0 := vals[i-1]
v1 := vals[i]
v2 := vals[i+1]
v3 := vals[i+2]
t0 := 0.0
t1 := t0 + math.Pow(math.Abs(v0-v1), alpha)
t2 := t1 + math.Pow(math.Abs(v1-v2), alpha)
t3 := t2 + math.Pow(math.Abs(v2-v3), alpha)
m1 := (1. - tension) * (t2 - t1) * ((v0-v1)/(t0-t1) - (v0-v2)/(t0-t2) + (v1-v2)/(t1-t2))
m2 := (1. - tension) * (t2 - t1) * ((v1-v2)/(t1-t2) - (v1-v3)/(t1-t3) + (v2-v3)/(t2-t3))
if math.IsNaN(m1) {
m1 = 0
}
if math.IsNaN(m2) {
m2 = 0
}
a := 2*v1 - 2*v2 + m1 + m2
b := -3*v1 + 3*v2 - 2*m1 - m2
c := m1
d := v1
segments = append(segments, [4]float64{a, b, c, d})
}
return segments
}
type catmullRomGradient struct {
segments [][4][4]float64
positions []float64
min float64
max float64
mode BlendMode
first Color
last Color
}
func newCatmullRomGradient(colors []Color, positions []float64, space BlendMode) Gradient {
n := len(colors)
a := make([]float64, n)
b := make([]float64, n)
c := make([]float64, n)
d := make([]float64, n)
for i, col := range colors {
var arr [4]float64
switch space {
case BlendRgb:
arr = [4]float64{col.R, col.G, col.B, col.A}
case BlendLinearRgb:
arr = col2linearRgb(col)
case BlendOklab:
arr = col2oklab(col)
}
a[i] = arr[0]
b[i] = arr[1]
c[i] = arr[2]
d[i] = arr[3]
}
s1 := toCatmullRomSegments(a)
s2 := toCatmullRomSegments(b)
s3 := toCatmullRomSegments(c)
s4 := toCatmullRomSegments(d)
segments := make([][4][4]float64, len(s1))
for i, v1 := range s1 {
segments[i] = [4][4]float64{
v1,
s2[i],
s3[i],
s4[i],
}
}
min := positions[0]
max := positions[n-1]
gradbase := catmullRomGradient{
segments: segments,
positions: positions,
min: min,
max: max,
mode: space,
first: colors[0],
last: colors[len(colors)-1],
}
return Gradient{
grad: gradbase,
dmin: min,
dmax: max,
}
}
func (g catmullRomGradient) At(t float64) Color {
if math.IsNaN(t) {
return Color{A: 1}
}
if t <= g.min {
return g.first
}
if t >= g.max {
return g.last
}
low := 0
high := len(g.positions)
for low < high {
mid := (low + high) / 2
if g.positions[mid] < t {
low = mid + 1
} else {
high = mid
}
}
if low == 0 {
low = 1
}
pos0 := g.positions[low-1]
pos1 := g.positions[low]
seg_a := g.segments[low-1][0]
seg_b := g.segments[low-1][1]
seg_c := g.segments[low-1][2]
seg_d := g.segments[low-1][3]
t1 := (t - pos0) / (pos1 - pos0)
t2 := t1 * t1
t3 := t2 * t1
a := seg_a[0]*t3 + seg_a[1]*t2 + seg_a[2]*t1 + seg_a[3]
b := seg_b[0]*t3 + seg_b[1]*t2 + seg_b[2]*t1 + seg_b[3]
c := seg_c[0]*t3 + seg_c[1]*t2 + seg_c[2]*t1 + seg_c[3]
d := seg_d[0]*t3 + seg_d[1]*t2 + seg_d[2]*t1 + seg_d[3]
switch g.mode {
case BlendRgb:
return Color{R: a, G: b, B: c, A: d}
case BlendLinearRgb:
return LinearRgb(a, b, c, d)
case BlendOklab:
return Oklab(a, b, c, d).Clamp()
}
return Color{}
}