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YogeshPateliOS/Potrace_MACOS

Created June 9, 2021 07:23
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Potrace_MACOS
import Foundation
import Cocoa
final class Potrace {
class Point<T> {
var x: T
var y: T
init(x: T, y: T) {
self.x = x
self.y = y
}
func copy() -> Point<T> {
return Point<T>(x: self.x, y: self.y)
}
static func toPointF(point: PointI) -> PointF {
return PointF(x: Double(point.x), y: Double(point.y))
}
}
typealias PointF = Point<Double>
typealias PointI = Point<Int>
struct Bitmap {
var w: Int
var h: Int
var size: Int
var data: [UInt8]
init(width: Int, height: Int) {
self.w = width
self.h = height
self.size = width * height
self.data = [UInt8](repeating: 0, count: self.size)
}
func at(x: Int, y: Int) -> Bool {
return (x >= 0 && x < self.w && y >= 0 && y < self.h) &&
data[self.w * y + x] == 1
}
func index(i: Int) -> PointI {
let point = PointI(x: 0, y: 0)
point.y = Int(floor(Double(i / self.w)))
point.x = i - point.y * self.w
return point
}
mutating func flip(x: Int, y: Int) {
if self.at(x: x, y: y) {
data[self.w * y + x] = 0
} else {
data[self.w * y + x] = 1
}
}
func copy() -> Bitmap {
var bm = Bitmap(width: w, height: h)
for (index, value) in data.enumerated() {
bm.data[index] = value
}
return bm
}
}
class Curve {
var n: Int
var tag: [String]
var c: BoxedArray<PointF>
var alphacurve: Int
var vertex: BoxedArray<PointF>
var alpha: [Double]
var alpha0: [Double]
var beta: [Double]
init(n: Int) {
self.n = n
self.tag = [String](repeating: "", count: n)
self.c = BoxedArray(repeating: Point(x: 0.0, y: 0.0), count: n * 3)
self.alphacurve = 0
self.vertex = BoxedArray(repeating: Point(x: 0.0, y: 0.0), count: n)
self.alpha = [Double](repeating: 0.0, count: n)
self.alpha0 = [Double](repeating: 0.0, count: n)
self.beta = [Double](repeating: 0.0, count: n)
}
}
struct Sum {
var x: Int
var y: Int
var xy: Int
var x2: Int
var y2: Int
}
class Path {
var area: Int
var len: Int
var curve: Curve
var pt: BoxedArray<PointI>
var minX: Int
var minY: Int
var maxX: Int
var maxY: Int
var sign: String
var sums: BoxedArray<Sum>
var lon: [Int]
var po: [Int]
var m: Int
var x0: Int
var y0: Int
init() {
self.area = 0
self.len = 0
self.curve = Curve(n: 0)
self.pt = BoxedArray()
self.minX = 100000
self.minY = 100000
self.maxX = -1
self.maxY = -1
self.sign = ""
self.sums = BoxedArray()
self.lon = []
self.po = []
self.m = 0
self.x0 = 0
self.y0 = 0
}
}
/*
* Potrace.Settings
*
* turnpolicy ("black" / "white" / "left" / "right" / "minority" / "majority")
* how to resolve ambiguities in path decomposition. (default: "minority")
*
* turdsize
* suppress speckles of up to this size (default: 2)
*
* optcurve (true / false)
* turn on/off curve optimization (default: true)
*
* alphamax
* corner threshold parameter (default: 1)
*
* opttolerance
* curve optimization tolerance (default: 0.2)
*/
public struct Settings {
var turnpolicy: String
var turdsize: Int
var optcurve: Bool
var alphamax: Double
var opttolerance: Double
init(turnPolicy: String = "minority",
turdSize: Int = 2,
optCurve: Bool = true,
alphaMax: Double = 1.0,
optTolerance: Double = 0.2) {
self.turnpolicy = turnPolicy
self.turdsize = turdSize
self.optcurve = optCurve
self.alphamax = alphaMax
self.opttolerance = optTolerance
}
}
fileprivate var bm: Bitmap!
fileprivate var info: Settings!
fileprivate var pathlist = [Path]()
init(data: UnsafeMutableRawPointer, width: Int, height: Int) {
let pixelData = data.assumingMemoryBound(to: UInt8.self)
bm = Bitmap(width: width, height: height)
var j = 0, i = 0
for _ in 0..<bm.data.count {
let val = 0.2126 * Double(pixelData[i]) + 0.7153 * Double(pixelData[i + 1]) +
0.0721 * Double(pixelData[i + 2])
bm.data[j] = val < 128 ? 1 : 0
i += 4
j += 1
}
}
func process(settings: Settings = Settings()) {
self.info = settings
bmToPathList()
processPath()
}
func bmToPathList() {
var bm1 = bm.copy()
var currentPoint = Point(x: 0, y: 0)
var path: Path
func findNext(point: PointI) -> PointI? {
var i = bm1.w * point.y + point.x
while i < bm1.size && bm1.data[i] != 1 {
i += 1
}
if i < bm1.size {
return bm1.index(i: i)
} else {
return nil
}
}
func majority(x: Int, y: Int) -> Int {
for i in 2..<5 {
var ct = 0
for a in (-i + 1)...(i - 1) {
ct += bm1.at(x: x + a, y: y + i - 1) ? 1 : -1
ct += bm1.at(x: x + i - 1, y: y + a - 1) ? 1 : -1
ct += bm1.at(x: x + a - 1, y: y - i) ? 1 : -1
ct += bm1.at(x: x - i, y: y + a) ? 1 : -1
}
return ct > 0 ? 1 : 0
}
return 0
}
func findPath(point: PointI) -> Path {
var path = Path(),
x = point.x, y = point.y,
dirx = 0, diry = 1, tmp: Int
path.sign = bm.at(x: point.x, y: point.y) ? "+" : "-"
while true {
path.pt.append(Point(x: x, y: y))
if x > path.maxX {
path.maxX = x
}
if x < path.minX {
path.minX = x
}
if y > path.maxY {
path.maxY = y
}
if y < path.minY {
path.minY = y
}
path.len += 1
x += dirx
y += diry
path.area -= x * diry
if x == point.x && y == point.y {
break
}
let l = bm1.at(x: x + (dirx + diry - 1 ) / 2, y: y + (diry - dirx - 1) / 2)
let r = bm1.at(x: x + (dirx - diry - 1) / 2, y: y + (diry + dirx - 1) / 2)
if r && !l {
if info.turnpolicy == "right" ||
(info.turnpolicy == "black" && path.sign == "+") ||
(info.turnpolicy == "white" && path.sign == "-") ||
(info.turnpolicy == "majority" && majority(x: x, y: y) != 0) ||
(info.turnpolicy == "minority" && majority(x: x, y: y) == 0) {
tmp = dirx
dirx = -diry
diry = tmp
} else {
tmp = dirx
dirx = diry
diry = -tmp
}
} else if r {
tmp = dirx
dirx = -diry
diry = tmp
} else if !l {
tmp = dirx
dirx = diry
diry = -tmp
}
}
return path
}
func xorPath(path: Path) {
var y1 = path.pt[0].y,
len = path.len,
x: Int, y: Int, maxX: Int, minY: Int
for i in 1..<len {
x = path.pt[i].x
y = path.pt[i].y
if y != y1 {
minY = y1 < y ? y1 : y
maxX = path.maxX
for j in x..<maxX {
bm1.flip(x: j, y: minY)
}
y1 = y
}
}
}
while let currentPoint = findNext(point: currentPoint) {
path = findPath(point: currentPoint)
xorPath(path: path)
if path.area > info.turdsize {
pathlist.append(path)
}
}
}
//
// processPath
//
func processPath() {
struct Quad {
var data: [Double]
init() {
self.data = [Double](repeating: 0.0, count: 9)
}
func at(x: Int, y: Int) -> Double {
return self.data[x * 3 + y]
}
}
func mod(a: Int, n: Int) -> Int {
return a >= n ? a % n : a>=0 ? a : n-1-(-1-a) % n
}
func xprod(p1: PointI, p2: PointI) -> Int {
return p1.x * p2.y - p1.y * p2.x
}
func cyclic(a: Int, b: Int, c: Int) -> Bool {
if a <= c {
return (a <= b && b < c)
} else {
return (a <= b || b < c)
}
}
func sign(i: Int) -> Int {
return i > 0 ? 1 : i < 0 ? -1 : 0
}
func quadform(Q: Quad, w: PointF) -> Double {
var v = [Double](repeating: 0.0, count: 3)
var sum: Double = 0.0
v[0] = w.x
v[1] = w.y
v[2] = 1
for i in 0..<3 {
for j in 0..<3 {
sum += Double(v[i]) * Q.at(x: i, y: j) * Double(v[j])
}
}
return sum
}
func interval(lambda: Double, a: PointF, b: PointF) -> PointF {
let res = PointF(x: 0, y: 0)
res.x = a.x + lambda * (b.x - a.x)
res.y = a.y + lambda * (b.y - a.y)
return res
}
func dorth_infty(p0: PointF, p2: PointF) -> PointI {
let r = PointI(x: 0, y: 0)
r.y = sign(i: Int(p2.x - p0.x))
r.x = -sign(i: Int(p2.y - p0.y))
return r
}
func ddenom(p0: PointF, p2: PointF) -> Double {
let r = dorth_infty(p0: p0, p2: p2)
return Double(r.y) * (p2.x - p0.x) - Double(r.x) * (p2.y - p0.y)
}
func dpara(p0: PointF, p1: PointF, p2: PointF) -> Double {
let x1 = p1.x - p0.x
let y1 = p1.y - p0.y
let x2 = p2.x - p0.x
let y2 = p2.y - p0.y
return x1 * y2 - x2 * y1
}
func cprod(p0: PointF, p1: PointF, p2: PointF, p3: PointF) -> Double {
let x1 = p1.x - p0.x
let y1 = p1.y - p0.y
let x2 = p3.x - p2.x
let y2 = p3.y - p2.y
return x1 * y2 - x2 * y1
}
func iprod(p0: PointF, p1: PointF, p2: PointF) -> Double {
let x1 = p1.x - p0.x
let y1 = p1.y - p0.y
let x2 = p2.x - p0.x
let y2 = p2.y - p0.y
return x1*x2 + y1*y2
}
func iprod1(p0: PointF, p1: PointF, p2: PointF, p3: PointF) -> Double {
let x1 = p1.x - p0.x
let y1 = p1.y - p0.y
let x2 = p3.x - p2.x
let y2 = p3.y - p2.y
return x1 * x2 + y1 * y2
}
func ddist(p: PointF, q: PointF) -> Double {
let part1 = (p.x - q.x) * (p.x - q.x)
let part2 = (p.y - q.y) * (p.y - q.y)
return sqrt(part1 + part2)
}
func bezier(t: Double, p0: PointF, p1: PointF, p2: PointF, p3: PointF) -> PointF {
let s = 1.0 - t
let res = PointF(x: 0, y: 0)
let part1 = s*s*s*p0.x
let part11 = 3*(s*s*t)*p1.x
let part2 = 3*(t*t*s)*p2.x
let part22 = t*t*t*p3.x
let part3 = s*s*s*p0.y
let part33 = 3*(s*s*t)*p1.y
let part4 = 3*(t*t*s)*p2.y
let part44 = t*t*t*p3.y
res.x = part1 + part11 + part2 + part22
res.y = part3 + part33 + part4 + part44
return res
}
func tangent(p0: PointF, p1: PointF, p2: PointF, p3: PointF, q0: PointF, q1: PointF) -> Double {
var s: Double, r1: Double, r2: Double
let A = cprod(p0: p0, p1: p1, p2: q0, p3: q1)
let B = cprod(p0: p1, p1: p2, p2: q0, p3: q1)
let C = cprod(p0: p2, p1: p3, p2: q0, p3: q1)
let a = A - 2 * B + C
let b = -2 * A + 2 * B
let c = A
let d = b * b - 4 * a * c
if a == 0 || d < 0 {
return -1.0
}
s = sqrt(d)
r1 = (-b + s) / (2 * a)
r2 = (-b - s) / (2 * a)
if r1 >= 0 && r1 <= 1 {
return r1
} else if r2 >= 0 && r2 <= 1 {
return r2
} else {
return -1.0
}
}
func calcSums(path: Path) {
var x: Int, y: Int
path.x0 = path.pt[0].x
path.y0 = path.pt[0].y
path.sums = BoxedArray()
let s = path.sums
s.append(Sum(x: 0, y: 0, xy: 0, x2: 0, y2: 0))
for i in 0 ..< path.len {
x = path.pt[i].x - path.x0
y = path.pt[i].y - path.y0
s.append(Sum(x: s[i].x + x, y: s[i].y + y, xy: s[i].xy + x * y,
x2: s[i].x2 + x * x, y2: s[i].y2 + y * y))
}
}
func calcLon(path: Path) {
var n = path.len, pt = path.pt, dir: Int,
pivk = [Int](repeating: 0, count: n),
nc = [Int](repeating: 0, count: n),
ct = [Int](repeating: 0, count: 4)
path.lon = [Int](repeating: 0, count: n)
var constraint = [PointI(x: 0, y: 0), PointI(x: 0, y: 0)],
cur = PointI(x: 0, y: 0),
off = PointI(x: 0, y: 0),
dk = PointI(x: 0, y: 0),
foundk: Int = 0
var i: Int, j: Int, k1: Int, a: Int, b: Int, c: Int, d: Int, k: Int = 0
for i in (0...n-1).reversed() {
if pt[i].x != pt[k].x && pt[i].y != pt[k].y {
k = i + 1
}
nc[i] = k
}
for i in (0...n-1).reversed() {
ct[0] = 0
ct[1] = 0
ct[2] = 0
ct[3] = 0
dir = (3 + 3 * (pt[mod(a: i + 1, n: n)].x - pt[i].x) +
(pt[mod(a: i + 1, n: n)].y - pt[i].y)) / 2
ct[dir] += 1
constraint[0].x = 0
constraint[0].y = 0
constraint[1].x = 0
constraint[1].y = 0
k = nc[i]
k1 = i
while true {
foundk = 0
dir = (3 + 3 * sign(i: pt[k].x - pt[k1].x) +
sign(i: pt[k].y - pt[k1].y)) / 2
ct[dir] += 1
if ct[0] != 0 && ct[1] != 0 && ct[2] != 0 && ct[3] != 0 {
pivk[i] = k1
foundk = 1
break
}
cur.x = pt[k].x - pt[i].x
cur.y = pt[k].y - pt[i].y
if xprod(p1: constraint[0], p2: cur) < 0 || xprod(p1: constraint[1], p2: cur) > 0 {
break
}
if abs(cur.x) <= 1 && abs(cur.y) <= 1 {
// NOOP
} else {
off.x = cur.x + ((cur.y >= 0 && (cur.y > 0 || cur.x < 0)) ? 1 : -1)
off.y = cur.y + ((cur.x <= 0 && (cur.x < 0 || cur.y < 0)) ? 1 : -1)
if xprod(p1: constraint[0], p2: off) >= 0 {
constraint[0].x = off.x
constraint[0].y = off.y
}
off.x = cur.x + ((cur.y <= 0 && (cur.y < 0 || cur.x < 0)) ? 1 : -1)
off.y = cur.y + ((cur.x >= 0 && (cur.x > 0 || cur.y < 0)) ? 1 : -1)
if xprod(p1: constraint[1], p2: off) <= 0 {
constraint[1].x = off.x
constraint[1].y = off.y
}
}
k1 = k
k = nc[k1]
if (!cyclic(a: k, b: i, c: k1)) {
break
}
}
if foundk == 0 {
dk.x = sign(i: pt[k].x-pt[k1].x)
dk.y = sign(i: pt[k].y-pt[k1].y)
cur.x = pt[k1].x - pt[i].x
cur.y = pt[k1].y - pt[i].y
a = xprod(p1: constraint[0], p2: cur)
b = xprod(p1: constraint[0], p2: dk)
c = xprod(p1: constraint[1], p2: cur)
d = xprod(p1: constraint[1], p2: dk)
j = 10000000
if b < 0 {
j = Int(floor(Double(a / -b)))
}
if d > 0 {
j = min(j, Int(floor(Double(-c / d))))
}
pivk[i] = mod(a: k1+j, n: n)
}
}
j=pivk[n-1]
path.lon[n-1]=j
for i in (0...n-2).reversed() {
if cyclic(a: i+1, b: pivk[i], c: j) {
j=pivk[i]
}
path.lon[i]=j
}
i = n - 1
while cyclic(a: mod(a: i+1, n: n), b: j, c: path.lon[i]) {
i -= 1
}
}
func bestPolygon(path: Path) {
func penalty3(path: Path, i: Int, jj: Int) -> Double {
let n = path.len, pt = path.pt
let sums = path.sums
var x: Int, y: Int, xy: Int, x2: Int, y2: Int,
k: Int, a: Double, b: Double, c: Double, s: Double,
px: Double, py: Double, ex: Int, ey: Int,
r: Int = 0
var j = jj
if j >= n {
j -= n
r = 1
}
if r == 0 {
x = sums[j+1].x - sums[i].x
y = sums[j+1].y - sums[i].y
x2 = sums[j+1].x2 - sums[i].x2
xy = sums[j+1].xy - sums[i].xy
y2 = sums[j+1].y2 - sums[i].y2
k = j+1 - i
} else {
x = sums[j+1].x - sums[i].x + sums[n].x
y = sums[j+1].y - sums[i].y + sums[n].y
x2 = sums[j+1].x2 - sums[i].x2 + sums[n].x2
xy = sums[j+1].xy - sums[i].xy + sums[n].xy
y2 = sums[j+1].y2 - sums[i].y2 + sums[n].y2
k = j+1 - i + n
}
px = (Double(pt[i].x + pt[j].x) / 2.0) - Double(pt[0].x)
py = (Double(pt[i].y + pt[j].y) / 2.0) - Double(pt[0].y)
ey = (pt[j].x - pt[i].x)
ex = -(pt[j].y - pt[i].y)
let a1 = (Double(x2) - Double(2*x)*px)
let a2 = Double(k) + px*px
a = a1 / a2
let b1 = (Double(xy) - Double(x)*py - Double(y)*px)
let b2 = Double(k) + px*py
b = b1 / b2
let c1 = (Double(y2) - Double(2*y)*py)
let c2 = Double(k) + py*py
c = c1 / c2
let s1 = Double(ex * ex) * a
let s2 = Double(2 * ex * ey) * b
let s3 = Double(ey * ey) * c
s = s1 + s2 + s3
return sqrt(s)
}
var i: Int, j: Int, m: Int,
n = path.len,
pen = [Double](repeating: 0.0, count: n + 1),
prev = [Int](repeating: 0, count: n + 1),
clip0 = [Int](repeating: 0, count: n),
clip1 = [Int](repeating: 0, count: n + 1),
seg0 = [Int](repeating: 0, count: n + 1),
seg1 = [Int](repeating: 0, count: n + 1),
thispen: Double, best: Double, c: Int
for i in 0..<n {
c = mod(a: path.lon[mod(a: i-1, n: n)]-1, n: n)
if c == i {
c = mod(a: i+1, n: n)
}
if c < i {
clip0[i] = n
} else {
clip0[i] = c
}
}
j = 1
for i in 0..<n {
while j <= clip0[i] {
clip1[j] = i
j += 1
}
}
i = 0
j = 0
while i < n {
seg0[j] = i
i = clip0[i]
j += 1
}
seg0[j] = n
m = j
i = n
j = m
while j > 0 {
seg1[j] = i
i = clip1[i]
j -= 1
}
seg1[0] = 0
pen[0]=0
j = 1
while j <= m {
for i in seg1[j]...seg0[j] {
best = -1
for k in (clip1[i]...seg0[j-1]).reversed() {
thispen = penalty3(path: path, i: k, jj: i) + pen[k]
if best < 0 || thispen < best {
prev[i] = k
best = thispen
}
}
pen[i] = best
}
j += 1
}
path.m = m
path.po = [Int](repeating: 0, count: m)
i = n
j = m - 1
while i > 0 {
i = prev[i]
path.po[j] = i
j -= 1
}
}
func adjustVertices(path: Path) {
func pointslope(path: Path, ii: Int, jj: Int, ctr: PointF, dir: PointF) {
let n = path.len
let sums = path.sums
var x: Int, y: Int, xy: Int, x2: Int, y2: Int,
k: Int, a: Double, b: Double, c: Double, lambda2: Double,
l: Double,
r: Int = 0
var i = ii
var j = jj
while j>=n {
j-=n
r+=1
}
while i>=n {
i-=n
r-=1
}
while j<0 {
j+=n
r-=1
}
while i<0 {
i+=n
r+=1
}
x = sums[j+1].x-sums[i].x+r*sums[n].x
y = sums[j+1].y-sums[i].y+r*sums[n].y
x2 = sums[j+1].x2-sums[i].x2+r*sums[n].x2
xy = sums[j+1].xy-sums[i].xy+r*sums[n].xy
y2 = sums[j+1].y2-sums[i].y2+r*sums[n].y2
k = j+1-i+r*n
ctr.x = Double(x/k)
ctr.y = Double(y/k)
a = Double((x2-x*x/k)/k)
b = Double((xy-x*y/k)/k)
c = Double((y2-y*y/k)/k)
lambda2 = (a+c+sqrt((a-c)*(a-c)+4*b*b))/2
a -= lambda2
c -= lambda2
if abs(a) >= abs(c) {
l = sqrt(a*a+b*b)
if l != 0 {
dir.x = -b/l
dir.y = a/l
}
} else {
l = sqrt(c*c+b*b)
if l != 0 {
dir.x = -c/l
dir.y = b/l
}
}
if l == 0 {
dir.x = 0.0
dir.y = 0.0
}
}
var m = path.m, po = path.po, n = path.len, pt = path.pt,
x0 = path.x0, y0 = path.y0,
ctr = [PointF](repeating: PointF(x: 0, y: 0), count: m),
dir = [PointF](repeating: PointF(x: 0, y: 0), count: m),
q = [Quad](repeating: Quad(), count: m),
v = [Double](repeating: 0.0, count: m), d: Double, j: Int,
s = PointI(x: 0, y: 0)
path.curve = Curve(n: m)
for i in 0..<m {
j = po[mod(a: i+1, n: m)]
j = mod(a: j-po[i], n: n)+po[i]
ctr[i] = PointF(x: 0, y: 0)
dir[i] = PointF(x: 0, y: 0)
pointslope(path: path, ii: po[i], jj: j, ctr: ctr[i], dir: dir[i])
}
for i in 0..<m {
q[i] = Quad()
d = dir[i].x * dir[i].x + dir[i].y * dir[i].y
if d == 0.0 {
for j in 0..<3 {
for k in 0..<3 {
q[i].data[j * 3 + k] = 0
}
}
} else {
v[0] = dir[i].y
v[1] = -dir[i].x
v[2] = -v[1] * ctr[i].y - v[0] * ctr[i].x
for l in 0..<3 {
for k in 0..<3 {
q[i].data[l * 3 + k] = v[l] * v[k] / d
}
}
}
}
var Q: Quad, w: PointF, dx: Double, dy: Double,
det: Double, min: Double, cand: Double, xmin: Double, ymin: Double
for i in 0..<m {
Q = Quad()
w = PointF(x: 0, y: 0)
s.x = pt[po[i]].x-x0
s.y = pt[po[i]].y-y0
j = mod(a: i-1, n: m)
for l in 0..<3 {
for k in 0..<3 {
Q.data[l * 3 + k] = q[j].at(x: l, y: k) + q[i].at(x: l, y: k)
}
}
while true {
det = Q.at(x: 0, y: 0)*Q.at(x: 1, y: 1) - Q.at(x: 0, y: 1)*Q.at(x: 1, y: 0)
if det != 0.0 {
w.x = (-Q.at(x: 0, y: 2)*Q.at(x: 1, y: 1) + Q.at(x: 1, y: 2)*Q.at(x: 0, y: 1)) / det
w.y = ( Q.at(x: 0, y: 2)*Q.at(x: 1, y: 0) - Q.at(x: 1, y: 2)*Q.at(x: 0, y: 0)) / det
break
}
if (Q.at(x: 0, y: 0) > Q.at(x: 1, y: 1)) {
v[0] = -Q.at(x: 0, y: 1)
v[1] = Q.at(x: 0, y: 0)
} else if (Q.at(x: 1, y: 1) != 0) {
v[0] = -Q.at(x: 1, y: 1)
v[1] = Q.at(x: 1, y: 0)
} else {
v[0] = 1
v[1] = 0
}
d = v[0] * v[0] + v[1] * v[1]
v[2] = -v[1] * Double(s.y) - v[0] * Double(s.x)
for l in 0..<3 {
for k in 0..<3 {
Q.data[l * 3 + k] += v[l] * v[k] / d
}
}
}
dx = abs(w.x-Double(s.x))
dy = abs(w.y-Double(s.y))
if dx <= 0.5 && dy <= 0.5 {
path.curve.vertex[i] = PointF(x: w.x+Double(x0), y: w.y+Double(y0))
continue
}
min = quadform(Q: Q, w: PointI.toPointF(point: s))
xmin = Double(s.x)
ymin = Double(s.y)
if (Q.at(x: 0, y: 0) != 0.0) {
for z in 0..<2 {
w.y = Double(s.y)-0.5+Double(z)
w.x = -(Q.at(x: 0, y: 1) * w.y + Q.at(x: 0, y: 2)) / Q.at(x: 0, y: 0)
dx = abs(w.x-Double(s.x))
cand = quadform(Q: Q, w: w)
if dx <= 0.5 && cand < min {
min = cand
xmin = w.x
ymin = w.y
}
}
}
if (Q.at(x: 1, y: 1) != 0.0) {
for z in 0..<2 {
w.x = Double(s.x)-0.5+Double(z)
w.y = -(Q.at(x: 1, y: 0) * w.x + Q.at(x: 1, y: 2)) / Q.at(x: 1, y: 1)
dy = abs(w.y-Double(s.y))
cand = quadform(Q: Q, w: w)
if dy <= 0.5 && cand < min {
min = cand
xmin = w.x
ymin = w.y
}
}
}
for l in 0..<3 {
for k in 0..<3 {
w.x = Double(s.x)-0.5+Double(l)
w.y = Double(s.y)-0.5+Double(k)
cand = quadform(Q: Q, w: w)
if cand < min {
min = cand
xmin = w.x
ymin = w.y
}
}
}
path.curve.vertex[i] = PointF(x: xmin + Double(x0), y: ymin + Double(y0))
}
}
func reverse(path: Path) {
var curve = path.curve, m = curve.n, v = curve.vertex,
i: Int, j: Int, tmp: PointF
i = 0
j = m - 1
while i < j {
tmp = v[i]
v[i] = v[j]
v[j] = tmp
i += 1
j -= 1
}
}
func smooth(path: Path) {
let m = path.curve.n, curve = path.curve
var j: Int, k: Int, dd: Double, denom: Double, alpha: Double,
p2: PointF, p3: PointF, p4: PointF
for i in 0..<m {
j = mod(a: i+1, n: m)
k = mod(a: i+2, n: m)
p4 = interval(lambda: 1/2.0, a: curve.vertex[k], b: curve.vertex[j])
denom = ddenom(p0: curve.vertex[i], p2: curve.vertex[k])
if denom != 0.0 {
dd = dpara(p0: curve.vertex[i], p1: curve.vertex[j], p2: curve.vertex[k]) / denom
dd = abs(dd)
alpha = dd>1 ? (1 - 1.0/dd) : 0
alpha /= 0.75
} else {
alpha = 4/3.0
}
curve.alpha0[j] = alpha
if alpha >= info.alphamax {
curve.tag[j] = "CORNER"
curve.c[3 * j + 1] = curve.vertex[j]
curve.c[3 * j + 2] = p4
} else {
if alpha < 0.55 {
alpha = 0.55
} else if alpha > 1 {
alpha = 1
}
p2 = interval(lambda: 0.5+0.5*alpha, a: curve.vertex[i], b: curve.vertex[j])
p3 = interval(lambda: 0.5+0.5*alpha, a: curve.vertex[k], b: curve.vertex[j])
curve.tag[j] = "CURVE"
curve.c[3 * j + 0] = p2
curve.c[3 * j + 1] = p3
curve.c[3 * j + 2] = p4
}
curve.alpha[j] = alpha
curve.beta[j] = 0.5
}
curve.alphacurve = 1
}
func optiCurve(path: Path) {
class Opti {
var pen: Double
var c: BoxedArray<PointF>
var t: Double
var s: Double
var alpha: Double
init() {
self.pen = 0
self.c = BoxedArray(repeating: PointF(x: 0, y: 0), count: 2)
self.t = 0
self.s = 0
self.alpha = 0
}
}
func opti_penalty(path: Path, i: Int, j: Int, res: Opti,
opttolerance: Double, convc: Array<Int>, areac: Array<Double>) -> Int {
var m = path.curve.n, curve = path.curve, vertex = curve.vertex,
k: Int, k1: Int, k2: Int, conv: Int, i1: Int,
area: Double, alpha: Double, d: Double, d1: Double, d2: Double,
p0: PointF, p1: PointF, p2: PointF, p3: PointF, pt: PointF,
A: Double, R: Double, A1: Double, A2: Double, A3: Double, A4: Double,
s: Double, t: Double
if i == j {
return 1
}
k = i
i1 = mod(a: i+1, n: m)
k1 = mod(a: k+1, n: m)
conv = convc[k1]
if (conv == 0) {
return 1
}
d = ddist(p: vertex[i], q: vertex[i1])
k = k1
while k != j {
k1 = mod(a: k+1, n: m)
k2 = mod(a: k+2, n: m)
if (convc[k1] != conv) {
return 1
}
if (sign(i: Int(cprod(p0: vertex[i], p1: vertex[i1], p2: vertex[k1], p3: vertex[k2]))) !=
conv) {
return 1
}
if (iprod1(p0: vertex[i], p1: vertex[i1], p2: vertex[k1], p3: vertex[k2]) <
d * ddist(p: vertex[k1], q: vertex[k2]) * -0.999847695156) {
return 1
}
k = k1
}
p0 = curve.c[mod(a: i,n: m) * 3 + 2].copy()
p1 = vertex[mod(a: i+1,n: m)].copy()
p2 = vertex[mod(a: j,n: m)].copy()
p3 = curve.c[mod(a: j,n: m) * 3 + 2].copy()
area = areac[j] - areac[i]
area -= dpara(p0: vertex[0], p1: curve.c[i * 3 + 2], p2: curve.c[j * 3 + 2])/2
if (i>=j) {
area += areac[m]
}
A1 = dpara(p0: p0, p1: p1, p2: p2)
A2 = dpara(p0: p0, p1: p1, p2: p3)
A3 = dpara(p0: p0, p1: p2, p2: p3)
A4 = A1+A3-A2
if (A2 == A1) {
return 1
}
t = A3/(A3-A4)
s = A2/(A2-A1)
A = A2 * t / 2.0
if (A == 0.0) {
return 1
}
R = area / A
alpha = 2 - sqrt(4 - R / 0.3)
res.c[0] = interval(lambda: t * alpha, a: p0, b: p1)
res.c[1] = interval(lambda: s * alpha, a: p3, b: p2)
res.alpha = alpha
res.t = t
res.s = s
p1 = res.c[0].copy()
p2 = res.c[1].copy()
res.pen = 0
k = mod(a: i+1,n: m)
while k != j {
k1 = mod(a: k+1,n: m)
t = tangent(p0: p0, p1: p1, p2: p2, p3: p3, q0: vertex[k], q1: vertex[k1])
if (t < -0.5) {
return 1
}
pt = bezier(t: t, p0: p0, p1: p1, p2: p2, p3: p3)
d = ddist(p: vertex[k], q: vertex[k1])
if (d == 0.0) {
return 1
}
d1 = dpara(p0: vertex[k], p1: vertex[k1], p2: pt) / d
if (abs(d1) > opttolerance) {
return 1
}
if (iprod(p0: vertex[k], p1: vertex[k1], p2: pt) < 0 ||
iprod(p0: vertex[k1], p1: vertex[k], p2: pt) < 0) {
return 1
}
res.pen += d1 * d1
k=k1
}
k = i
while k == j {
k1 = mod(a: k+1,n: m)
t = tangent(p0: p0, p1: p1, p2: p2, p3: p3, q0: curve.c[k * 3 + 2], q1: curve.c[k1 * 3 + 2])
if (t < -0.5) {
return 1
}
pt = bezier(t: t, p0: p0, p1: p1, p2: p2, p3: p3)
d = ddist(p: curve.c[k * 3 + 2], q: curve.c[k1 * 3 + 2])
if (d == 0.0) {
return 1
}
d1 = dpara(p0: curve.c[k * 3 + 2], p1: curve.c[k1 * 3 + 2], p2: pt) / d
d2 = dpara(p0: curve.c[k * 3 + 2], p1: curve.c[k1 * 3 + 2], p2: vertex[k1]) / d
d2 *= 0.75 * curve.alpha[k1]
if (d2 < 0) {
d1 = -d1
d2 = -d2
}
if (d1 < d2 - opttolerance) {
return 1
}
if (d1 < d2) {
res.pen += (d1 - d2) * (d1 - d2)
}
k=k1
}
return 0
}
var curve = path.curve, m = curve.n, vert = curve.vertex,
pt = Array<Int>(repeating: 0, count: m + 1),
pen = Array<Double>(repeating: 0, count: m + 1),
len = Array<Int>(repeating: 0, count: m + 1),
opt = Array<Opti>(repeating: Opti(), count: m + 1),
om: Int, i: Int,j: Int,r: Int,
o = Opti(), p0: PointF,
i1: Int, area: Double, alpha: Double, ocurve: Curve,
s: Array<Double>, t: Array<Double>
var convc = Array<Int>(repeating: 0, count: m),
areac = Array<Double>(repeating: 0, count: m+1)
for i in 0..<m {
if (curve.tag[i] == "CURVE") {
let val = dpara(p0: vert[mod(a: i-1,n: m)], p1: vert[i], p2: vert[mod(a: i+1,n: m)])
convc[i] = sign(i: Int(val))
} else {
convc[i] = 0
}
}
area = 0.0
areac[0] = 0.0
p0 = curve.vertex[0]
for i in 0..<m {
i1 = mod(a: i+1, n: m)
if (curve.tag[i1] == "CURVE") {
alpha = curve.alpha[i1]
area += 0.3 * alpha * (4-alpha) *
dpara(p0: curve.c[i * 3 + 2], p1: vert[i1], p2: curve.c[i1 * 3 + 2])/2
area += dpara(p0: p0, p1: curve.c[i * 3 + 2], p2: curve.c[i1 * 3 + 2])/2
}
areac[i+1] = area
}
pt[0] = -1
pen[0] = 0
len[0] = 0
for j in 1...m {
pt[j] = j-1
pen[j] = pen[j-1]
len[j] = len[j-1]+1
i = j - 2
while i>=0 {
r = opti_penalty(path: path, i: i, j: mod(a: j,n: m), res: o, opttolerance: info.opttolerance, convc: convc,
areac: areac)
if r == 1 {
break
}
if (len[j] > len[i]+1 ||
(len[j] == len[i]+1 && pen[j] > pen[i] + o.pen)) {
pt[j] = i
pen[j] = pen[i] + o.pen
len[j] = len[i] + 1
opt[j] = o
o = Opti()
}
i -= 1
}
}
om = len[m]
ocurve = Curve(n: om)
s = Array<Double>(repeating: 0, count: om)
t = Array<Double>(repeating: 0, count: om)
j = m
for i in (0...om-1).reversed() {
if (pt[j]==j-1) {
ocurve.tag[i] = curve.tag[mod(a: j,n: m)]
ocurve.c[i * 3 + 0] = curve.c[mod(a: j,n: m) * 3 + 0]
ocurve.c[i * 3 + 1] = curve.c[mod(a: j,n: m) * 3 + 1]
ocurve.c[i * 3 + 2] = curve.c[mod(a: j,n: m) * 3 + 2]
ocurve.vertex[i] = curve.vertex[mod(a: j,n: m)]
ocurve.alpha[i] = curve.alpha[mod(a: j,n: m)]
ocurve.alpha0[i] = curve.alpha0[mod(a: j,n: m)]
ocurve.beta[i] = curve.beta[mod(a: j,n: m)]
s[i] = 1.0
t[i] = 1.0
} else {
ocurve.tag[i] = "CURVE"
ocurve.c[i * 3 + 0] = opt[j].c[0]
ocurve.c[i * 3 + 1] = opt[j].c[1]
ocurve.c[i * 3 + 2] = curve.c[mod(a: j,n: m) * 3 + 2]
ocurve.vertex[i] = interval(lambda: opt[j].s, a: curve.c[mod(a: j,n: m) * 3 + 2],
b: vert[mod(a: j,n: m)])
ocurve.alpha[i] = opt[j].alpha
ocurve.alpha0[i] = opt[j].alpha
s[i] = opt[j].s
t[i] = opt[j].t
}
j = pt[j]
}
for i in 0..<om {
i1 = mod(a: i+1,n: om)
ocurve.beta[i] = s[i] / (s[i] + t[i1])
}
ocurve.alphacurve = 1
path.curve = ocurve
}
for i in 0..<pathlist.count {
let path = pathlist[i]
calcSums(path: path)
calcLon(path: path)
bestPolygon(path: path)
adjustVertices(path: path)
if (path.sign == "-") {
reverse(path: path)
}
smooth(path: path)
if (info.optcurve) {
optiCurve(path: path)
}
}
}
func getBezierPath(scale size: Double = 1.0) -> NSBezierPath {
func path(curve: Curve, bezierPath: NSBezierPath) {
func bezier(i: Int) {
bezierPath.addCurve(to: CGPoint(x: (curve.c[i * 3 + 2].x * size), y: (curve.c[i * 3 + 2].y * size)),
controlPoint1: CGPoint(x: (curve.c[i * 3 + 0].x * size), y: (curve.c[i * 3 + 0].y * size)),
controlPoint2: CGPoint(x: (curve.c[i * 3 + 1].x * size), y: (curve.c[i * 3 + 1].y * size)))
}
func segment(i: Int) {
bezierPath.addLine(to: CGPoint(x: (curve.c[i * 3 + 1].x * size), y: (curve.c[i * 3 + 1].y * size)))
bezierPath.addLine(to: CGPoint(x: (curve.c[i * 3 + 2].x * size), y: (curve.c[i * 3 + 2].y * size)))
}
let n = curve.n
let x = (curve.c[(n - 1) * 3 + 2].x * size)
let y = (curve.c[(n - 1) * 3 + 2].y * size)
bezierPath.move(to: CGPoint(x: x, y: y))
for i in 0..<n {
if (curve.tag[i] == "CURVE") {
bezier(i: i)
} else if (curve.tag[i] == "CORNER") {
segment(i: i)
}
}
}
let len = pathlist.count
var c: Curve
let bezierPath = NSBezierPath()
for i in 0 ..< len {
c = pathlist[i].curve
path(curve: c, bezierPath: bezierPath)
}
bezierPath.usesEvenOddFillRule = true
return bezierPath
}
func getSVG(scale size: Double = 1.0, opt_type: String? = nil) -> String {
func path(curve: Curve) -> String {
func bezier(i: Int) -> String {
var b = "C " + String(format: "%f", (curve.c[i * 3 + 0].x * size).toFixed(3)) + " " +
String(format: "%f",(curve.c[i * 3 + 0].y * size).toFixed(3)) + ","
b += String(format: "%f", (curve.c[i * 3 + 1].x * size).toFixed(3)) + " " +
String(format: "%f", (curve.c[i * 3 + 1].y * size).toFixed(3)) + ","
b += String(format: "%f", (curve.c[i * 3 + 2].x * size).toFixed(3)) + " " +
String(format: "%f", (curve.c[i * 3 + 2].y * size).toFixed(3)) + " "
return b
}
func segment(i: Int) -> String {
var s = "L " + String(format: "%f", (curve.c[i * 3 + 1].x * size).toFixed(3)) + " " +
String(format: "%f", (curve.c[i * 3 + 1].y * size).toFixed(3)) + " "
s += String(format: "%f", (curve.c[i * 3 + 2].x * size).toFixed(3)) + " " +
String(format: "%f", (curve.c[i * 3 + 2].y * size).toFixed(3)) + " "
return s
}
let n = curve.n
var p = "M" + String(format: "%f", (curve.c[(n - 1) * 3 + 2].x * size).toFixed(3)) +
" " + String(format: "%f", (curve.c[(n - 1) * 3 + 2].y * size).toFixed(3)) + " "
for i in 0..<n {
if (curve.tag[i] == "CURVE") {
p += bezier(i: i)
} else if (curve.tag[i] == "CORNER") {
p += segment(i: i)
}
}
return p
}
var w = Double(bm.w) * size, h = Double(bm.h) * size,
len = pathlist.count, c: Curve, strokec: String, fillc: String, fillrule: String
var svg = "<svg id=\"svg\" version=\"1.1\" width=\"\(w)\" height=\"\(h)\" xmlns=\"http://www.w3.org/2000/svg\">"
svg += "<path d=\""
for i in 0 ..< len {
c = pathlist[i].curve
svg += path(curve: c)
}
if (opt_type == "curve") {
strokec = "black"
fillc = "none"
fillrule = ""
} else {
strokec = "none"
fillc = "black"
fillrule = " fill-rule=\"evenodd\""
}
svg += "\" stroke=\"\(strokec)\" fill=\"\(fillc)\" \(fillrule)/></svg>"
return svg
}
}
extension Double {
func toFixed(_ places: Int) -> Double {
let divisor = pow(10.0, Double(places))
return (self * divisor).rounded() / divisor
}
}
class BoxedArray<T> : MutableCollection {
var array: [T]
init() {
self.array = [T]()
}
init(repeating: T, count: Int) {
self.array = [T](repeating: repeating, count: count)
}
func index(after i: (Int)) -> (Int) {
return array.index(after: i)
}
var endIndex: (Int) {
return array.endIndex
}
var startIndex: (Int) {
return array.startIndex
}
func append(_ item: T) {
array.append(item)
}
subscript (index: Int) -> T {
get { return array[index] }
set(newValue) { array[index] = newValue }
}
}
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