Parasitemia/ParasitemiaCore/EEOver.fs

   1 module ParasitemiaCore.EEOver
   2
   3 open System
   4
   5 let private EPS = 1.0e-7
   6
   7 let inline private ellipse2tr (x: float) (y: float) (aa: float) (bb: float) (cc: float) (dd: float) (ee: float) (ff: float) : float =
   8     aa * x * x + bb * x * y + cc * y * y + dd * x + ee * y + ff
   9
  10 let private nointpts (a1: float) (b1: float) (a2: float) (b2: float) (h1: float) (k1: float) (h2: float) (k2: float) (phi_1: float) (phi_2: float) (h2_tr: float) (k2_tr: float) (aa: float) (bb: float) (cc: float) (dd: float) (ee: float) (ff: float) =
  11     let a1b1 = a1 * b1
  12     let a2b2 = a2 * b2
  13     let area_1 = Math.PI * a1b1
  14     let area_2 = Math.PI * a2b2
  15     let relsize = a1b1 - a2b2
  16
  17     if relsize > 0.0
  18     then
  19         if (h2_tr * h2_tr) / (a1 * a1) + (k2_tr * k2_tr) / (b1 * b1) < 1.0
  20         then area_2
  21         else 0.0
  22
  23     elif relsize < 0.0
  24     then
  25         if ff < 0.0
  26         then area_1
  27         else 0.0
  28
  29     else
  30         if abs (h1 - h2) < EPS && abs (k1 - k2) < EPS && abs (area_1 - area_2) < EPS
  31         then area_1
  32         else 0.0
  33
  34 type private PointType = TANGENT_POINT | INTERSECTION_POINT
  35
  36 let private istanpt (x: float) (y: float) (a1: float) (b1: float) (aa: float) (bb: float) (cc: float) (dd: float) (ee: float) (ff: float) : PointType =
  37     let x =
  38         if abs x > a1
  39         then
  40             if x < 0.0 then -a1 else a1
  41         else x
  42
  43     let theta =
  44         if y < 0.0
  45         then 2.0 * Math.PI - acos (x / a1)
  46         else acos (x / a1)
  47
  48     let eps_radian = 0.1
  49
  50     let x1 = a1 * cos (theta + eps_radian)
  51     let y1 = b1 * sin (theta + eps_radian)
  52     let x2 = a1 * cos (theta - eps_radian)
  53     let y2 = b1 * sin (theta - eps_radian)
  54
  55     let test1 = ellipse2tr x1 y1 aa bb cc dd ee ff
  56     let test2 = ellipse2tr x2 y2 aa bb cc dd ee ff
  57
  58 #if DEBUG_LOG
  59     printf "\t\t--- debug istanpt with (x,y)=(%f, %f), A1=%f, B1=%f\n" x y a1 b1
  60     printf "theta=%f\n" theta
  61     printf "eps_Radian=%f\n" eps_radian
  62     printf "(x1, y1)=(%f, %f)\n" x1 y1
  63     printf "(x2, y2)=(%f, %f)\n" x2 y2
  64     printf "test1=%f\n" test1
  65     printf "test2=%f\n" test2
  66 #endif
  67
  68     if test1 * test2 > 0.0
  69     then TANGENT_POINT
  70     else INTERSECTION_POINT
  71
  72 let private twointpts (x: float[]) (y: float[]) (a1: float) (b1: float) (phi_1: float) (a2: float) (b2: float) (h2_tr: float) (k2_tr: float) (phi_2: float) (aa: float) (bb: float) (cc: float) (dd: float) (ee: float) (ff: float) =
  73     if abs x.[0] > a1
  74     then x.[0] <- if x.[0] < 0.0 then -a1 else a1
  75
  76     let mutable theta1 =
  77         if y.[0] < 0.0
  78         then 2.0 * Math.PI - acos (x.[0] / a1)
  79         else acos (x.[0] / a1)
  80
  81     if abs x.[1] > a1
  82     then x.[1] <- if x.[1] < 0.0 then -a1 else a1
  83
  84     let mutable theta2 =
  85         if y.[1] < 0.0
  86         then 2.0 * Math.PI - acos (x.[1] / a1)
  87         else acos (x.[1] / a1)
  88
  89     if theta1 > theta2
  90     then
  91         let tmp = theta1
  92         theta1 <- theta2
  93         theta2 <- tmp
  94
  95     let xmid = a1 * cos ((theta1 + theta2) / 2.0)
  96     let ymid = b1 * sin ((theta1 + theta2) / 2.0)
  97
  98     if ellipse2tr xmid ymid aa bb cc dd ee ff > 0.0
  99     then
 100         let tmp = theta1
 101         theta1 <- theta2
 102         theta2 <- tmp
 103
 104     if theta1 > theta2
 105     then
 106         theta1 <- theta1 - 2.0 * Math.PI
 107
 108     let trsign = if (theta2 - theta1) > Math.PI then 1.0 else -1.0
 109
 110     let mutable area1 = 0.5 * (a1 * b1 * (theta2 - theta1) + trsign * abs (x.[0] * y.[1] - x.[1] * y.[0]))
 111
 112     if area1 < 0.0
 113     then
 114 #if DEBUG_LOG
 115         printf "TWO area1=%f\n" area1
 116 #endif
 117         area1 <- area1 + a1 * b1
 118
 119     let cosphi = cos (phi_1 - phi_2)
 120     let sinphi = sin (phi_1 - phi_2)
 121
 122     let mutable x1_tr = (x.[0] - h2_tr) * cosphi + (y.[0] - k2_tr) * -sinphi
 123     let mutable y1_tr = (x.[0] - h2_tr) * sinphi + (y.[0] - k2_tr) * cosphi
 124     let mutable x2_tr = (x.[1] - h2_tr) * cosphi + (y.[1] - k2_tr) * -sinphi
 125     let mutable y2_tr = (x.[1] - h2_tr) * sinphi + (y.[1] - k2_tr) * cosphi
 126
 127     if abs x1_tr > a2
 128     then
 129         x1_tr <- if x1_tr < 0.0 then -a2 else a2
 130
 131     if y1_tr < 0.0
 132     then
 133         theta1 <- 2.0 * Math.PI - acos (x1_tr / a2)
 134     else
 135         theta1 <- acos (x1_tr / a2)
 136
 137     if abs x2_tr > a2
 138     then
 139         x2_tr <- if x2_tr < 0.0 then -a2 else a2
 140
 141     if y2_tr < 0.0
 142     then
 143         theta2 <- 2.0 * Math.PI - acos (x2_tr / a2)
 144     else
 145         theta2 <- acos (x2_tr / a2)
 146
 147     if theta1 > theta2
 148     then
 149         let tmp = theta1
 150         theta1 <- theta2
 151         theta2 <- tmp
 152
 153     let xmid = a2 * cos ((theta1 + theta2) / 2.0)
 154     let ymid = b2 * sin ((theta1 + theta2) / 2.0)
 155
 156     let cosphi = cos (phi_2 - phi_1)
 157     let sinphi = sin (phi_2 - phi_1)
 158     let xmid_rt = xmid * cosphi + ymid * -sinphi + h2_tr
 159     let ymid_rt = xmid * sinphi + ymid * cosphi + k2_tr
 160
 161     if (xmid_rt * xmid_rt) / (a1 * a1) + (ymid_rt * ymid_rt) / (b1 * b1) > 1.0
 162     then
 163         let tmp = theta1
 164         theta1 <- theta2
 165         theta2 <- tmp
 166
 167     if theta1 > theta2
 168     then
 169         theta1 <- theta1 - 2.0 * Math.PI
 170
 171     let trsign = if theta2 - theta1 > Math.PI then 1.0 else -1.0
 172
 173     let mutable area2 = 0.5 * (a2 * b2 * (theta2 - theta1) + trsign * abs (x1_tr * y2_tr - x2_tr * y1_tr))
 174     if area2 < 0.0
 175     then
 176 #if DEBUG_LOG
 177         printf "TWO area2=%f\n" area2
 178 #endif
 179         area2 <- area2 + a2 * b2
 180
 181     area1 + area2
 182
 183 let private threeintpts (xint: float[]) (yint: float[]) (a1: float) (b1: float) (phi_1: float) (a2: float) (b2: float) (h2_tr: float) (k2_tr: float) (phi_2: float) (aa: float) (bb: float) (cc: float) (dd: float) (ee: float) (ff: float) : float =
 184     let mutable tanpts = 0
 185     let mutable tanindex = 0
 186     for i in 0..2 do
 187         if istanpt xint.[i] yint.[i] a1 b2 aa bb cc dd ee ff = TANGENT_POINT
 188         then
 189             tanpts <- tanpts + 1
 190             tanindex <- i
 191 #if DEBUG_LOG
 192     printf "tanindex=%d\n" tanindex
 193 #endif
 194
 195     if tanpts <> 1
 196     then
 197         -1.0
 198     else
 199         match tanindex with
 200         | 0 ->
 201             xint.[0] <- xint.[2]
 202             yint.[0] <- yint.[2]
 203         | 1 ->
 204             xint.[1] <- xint.[2]
 205             yint.[1] <- yint.[2]
 206         | _ ->
 207             ()
 208         twointpts xint yint a1 b1 phi_1 a2 b2 h2_tr k2_tr phi_2 aa bb cc dd ee ff
 209
 210 let private fourintpts (xint: float[]) (yint: float[]) (a1: float) (b1: float) (phi_1: float) (a2: float) (b2: float) (h2_tr: float) (k2_tr: float) (phi_2: float) (aa: float) (bb: float) (cc: float) (dd: float) (ee: float) (ff: float) : float =
 211     let a1b1 = a1 * b1
 212     let a2b2 = a2 * b2
 213     let area_1 = Math.PI * a1b1
 214     let area_2 = Math.PI * a2b2
 215
 216     let theta = Array.zeroCreate 4
 217
 218     for i in 0 .. 3 do
 219         if abs xint.[i] > a1
 220         then
 221             xint.[i] <- if xint.[i] < 0.0 then -a1 else a1
 222         theta.[i] <- if yint.[i] < 0.0 then 2.0 * Math.PI - acos (xint.[i] / a1) else acos (xint.[i] / a1)
 223
 224 #if DEBUG_LOG
 225     for k in 0..3 do
 226         printf "k=%d:  Theta = %f, xint=%f, yint=%f\n" k theta.[k] xint.[k] yint.[k]
 227 #endif
 228
 229     for j in 1 .. 3 do
 230         let tmp0 = theta.[j]
 231         let tmp1 = xint.[j]
 232         let tmp2 = yint.[j]
 233
 234         let mutable k = j - 1
 235         let mutable k2 = 0
 236         while k >= 0 do
 237             if theta.[k] <= tmp0
 238             then
 239                 k2 <- k + 1
 240                 k <- -1
 241             else
 242                 theta.[k+1] <- theta.[k]
 243                 xint.[k+1] <- xint.[k]
 244                 yint.[k+1] <- yint.[k]
 245                 k <- k - 1
 246                 k2 <- k + 1
 247
 248         theta.[k2] <- tmp0
 249         xint.[k2] <- tmp1
 250         yint.[k2] <- tmp2
 251
 252
 253 #if DEBUG_LOG
 254     printf "AFTER sorting\n"
 255     for k in 0..3 do
 256         printf "k=%d:  Theta = %f, xint=%f, yint=%f\n" k theta.[k] xint.[k] yint.[k]
 257 #endif
 258
 259     let area1 = 0.5 * abs ((xint.[2] - xint.[0]) * (yint.[3] - yint.[1]) - (xint.[3] - xint.[1]) * (yint.[2] - yint.[0]))
 260
 261     let cosphi = cos (phi_1 - phi_2)
 262     let sinphi = sin (phi_1 - phi_2)
 263
 264     let theta_tr = Array.zeroCreate 4
 265     let xint_tr = Array.zeroCreate 4
 266     let yint_tr = Array.zeroCreate 4
 267
 268     for i in 0..3 do
 269         xint_tr.[i] <- (xint.[i] - h2_tr) * cosphi + (yint.[i] - k2_tr) * -sinphi
 270         yint_tr.[i] <- (xint.[i] - h2_tr) * sinphi + (yint.[i] - k2_tr) * cosphi
 271
 272         if abs xint_tr.[i] > a2
 273         then
 274             xint_tr.[i] <- if xint_tr.[i] < 0.0 then -a2 else a2
 275
 276         theta_tr.[i] <- if yint_tr.[i] < 0.0 then 2.0 * Math.PI - acos (xint_tr.[i] / a2) else acos (xint_tr.[i] / a2)
 277
 278     let xmid = a1 * cos ((theta.[0] + theta.[1]) / 2.0)
 279     let ymid = b1 * sin ((theta.[0] + theta.[1]) / 2.0)
 280
 281     let mutable area2, area3, area4, area5 = 0.0, 0.0, 0.0, 0.0
 282
 283     if ellipse2tr xmid ymid aa bb cc dd ee ff < 0.0
 284     then
 285         area2 <- 0.5 * (a1b1 * (theta.[1] - theta.[0]) - abs (xint.[0] * yint.[1] - xint.[1] * yint.[0]))
 286         area3 <- 0.5 * (a1b1 * (theta.[3] - theta.[2]) - abs (xint.[2] * yint.[3] - xint.[3] * yint.[2]))
 287         area4 <- 0.5 * (a2b2 * (theta_tr.[2] - theta_tr.[1]) - abs (xint_tr.[1] * yint_tr.[2] - xint_tr.[2] * yint_tr.[1]))
 288
 289         if theta_tr.[3] > theta_tr.[0]
 290         then
 291             area5 <- 0.5 * (a2b2 * (theta_tr.[0] - (theta_tr.[3] - 2.0 * Math.PI)) - abs (xint_tr.[3] * yint_tr.[0] - xint_tr.[0] * yint_tr.[3]))
 292         else
 293             area5 <- 0.5 * (a2b2 * (theta_tr.[0] - theta_tr.[3]) - abs (xint_tr.[3] * yint_tr.[0] - xint_tr.[0] * yint_tr.[3]))
 294     else
 295         area2 <- 0.5 * (a1b1 * (theta.[2] - theta.[1]) - abs (xint.[1] * yint.[2] - xint.[2] * yint.[1]))
 296         area3 <- 0.5 * (a1b1 * (theta.[0] - (theta.[3] - 2.0 * Math.PI)) - abs (xint.[3] * yint.[0] - xint.[0] * yint.[3]))
 297         area4 <- 0.5 * (a2b2 * (theta_tr.[1] - theta_tr.[0]) - abs (xint_tr.[0] * yint_tr.[1] - xint_tr.[1] * yint_tr.[0]))
 298         area5 <- 0.5 * (a2b2 * (theta_tr.[3] - theta_tr.[2]) - abs (xint_tr.[2] * yint_tr.[3] - xint_tr.[3] * yint_tr.[2]))
 299
 300     if area5 < 0.0
 301     then
 302 #if DEBUG_LOG
 303         printf "\n\t\t-------------> area5 is negative (%f). Add: pi*A2*B2=%f <------------\n" area5 area_2
 304 #endif
 305         area5 <- area5 + area_2
 306
 307     if area4 < 0.0
 308     then
 309 #if DEBUG_LOG
 310         printf "\n\t\t-------------> area4 is negative (%f). Add: pi*A2*B2=%f <------------\n" area4 area_2
 311 #endif
 312         area4 <- area4 + area_2
 313
 314     if area3 < 0.0
 315     then
 316 #if DEBUG_LOG
 317         printf "\n\t\t-------------> area3 is negative (%f). Add: pi*A2*B2=%f <------------\n" area3 area_1
 318 #endif
 319         area3 <- area3 + area_1
 320
 321     if area2 < 0.0
 322     then
 323 #if DEBUG_LOG
 324         printf "\n\t\t-------------> area2 is negative (%f). Add: pi*A2*B2=%f <------------\n" area2 area_1
 325 #endif
 326         area2 <- area2 + area_1
 327
 328 #if DEBUG_LOG
 329     printf "\narea1=%f, area2=%f area3=%f, area4=%f, area5=%f\n\n" area1 area2 area3 area4 area5
 330 #endif
 331
 332     area1 + area2 + area3 + area4 + area5
 333
 334 let private quadroots (p: float[]) (r: float[,]) =
 335     let mutable b = -p.[1] / (2.0 * p.[0])
 336     let c = p.[2] / p.[0]
 337     let mutable d = b * b - c
 338
 339     if d >= 0.0
 340     then
 341         if b > 0.0
 342         then
 343             b <- sqrt d + b
 344             r.[1, 2] <- b
 345         else
 346             b <- -sqrt d + b
 347             r.[1, 2] <- b
 348         r.[1, 1] <- c / b
 349         r.[2, 1] <- 0.0
 350         r.[2, 2] <- 0.0
 351     else
 352         d <- sqrt -d
 353         r.[2, 1] <- d
 354         r.[2, 2] <- -d
 355         r.[1, 1] <- b
 356         r.[1, 2] <- b
 357
 358 let private cubicroots (p: float[]) (r: float[,]) =
 359     if p.[0] <> 1.0 then
 360         for k in 1..3 do
 361             p.[k] <- p.[k] / p.[0]
 362         p.[0] <- 1.0
 363     let s = p.[1] / 3.0
 364     let mutable t = s * p.[1]
 365     let mutable b = 0.5 * (s * (t / 1.5 - p.[2]) + p.[3])
 366     t <- (t - p.[2]) / 3.0
 367     let mutable c = t * t * t
 368     let mutable d = b * b - c
 369
 370     if d >= 0.0
 371     then
 372         d <- ((sqrt d) + (abs b)) ** (1.0 / 3.0)
 373         if d <> 0.0
 374         then
 375             if b > 0.0
 376             then b <- -d
 377             else b <- d
 378             c <- t / b
 379         d <- sqrt(0.75) * (b - c)
 380         r.[2, 2] <- d
 381         b <- b + c
 382         c <- -0.5 * b - s
 383         r.[1, 2] <- c
 384         if b > 0.0 && s <= 0.0 || b < 0.0 && s > 0.0
 385         then
 386             r.[1, 1] <- c
 387             r.[2, 1] <- -d
 388             r.[1, 3] <- b - s
 389             r.[2, 3] <- 0.0
 390         else
 391             r.[1, 1] <- b - s
 392             r.[2, 1] <- 0.0
 393             r.[1, 3] <- c
 394             r.[2, 3] <- -d
 395     else
 396         if b = 0.0
 397         then d <- (atan 1.0) / 1.5
 398         else d <- atan ((sqrt -d) / (abs b)) / 3.0
 399
 400         if b < 0.0
 401         then b <- 2.0 * (sqrt t)
 402         else b <- -2.0 * (sqrt t)
 403
 404         c <- (cos d) * b
 405         t <- -(sqrt 0.75) * (sin d) * b - 0.5 * c
 406         d <- -t - c - s
 407         c <- c - s
 408         t <- t - s
 409
 410         if abs c > abs t
 411         then
 412             r.[1, 3] <- c
 413         else
 414             r.[1, 3] <- t
 415             t <- c
 416
 417         if abs d > abs t
 418         then
 419             r.[1, 2] <- d
 420         else
 421             r.[1, 2] <- t
 422             t <- d
 423
 424         r.[1, 1] <- t
 425         for k in 1..3 do
 426             r.[2, k] <- 0.0
 427
 428 let private biquadroots (p: float[]) (r: float[,]) =
 429     if p.[0] <> 1.0
 430     then
 431         for k in 1..4 do
 432             p.[k] <- p.[k] / p.[0]
 433         p.[0] <- 1.0
 434     let e = 0.25 * p.[1]
 435     let mutable b = 2.0 * e
 436     let mutable c = b ** 2.0
 437     let mutable d = 0.75 * c
 438     b <- p.[3] + b *(c - p.[2])
 439     let mutable a = p.[2] - d
 440     c <- p.[4] + e * (e * a - p.[3])
 441     a <- a - d
 442
 443     let mutable quadExecuted = false
 444     let inline quad () =
 445         if not quadExecuted
 446         then
 447             p.[2] <- c / b
 448             quadroots p r
 449             for k in 1..2 do
 450                 for j in 1..2 do
 451                     r.[j, k+2] <- r.[j, k]
 452             p.[1] <- -p.[1]
 453             p.[2] <- b
 454             quadroots p r
 455             for k in 1..4 do
 456                 r.[1,k] <- r.[1,k] - e
 457             quadExecuted <- true
 458
 459     p.[1] <- 0.5 * a
 460     p.[2] <- (p.[1] * p.[1] - c) * 0.25
 461     p.[3] <- b * b / -64.0
 462     if p.[3] < 0.0
 463     then
 464         cubicroots p r
 465         let mutable k = 1
 466         while k < 4 do
 467             if r.[2, k] = 0.0 && r.[1, k] > 0.0
 468             then
 469                 d <- r.[1, k] * 4.0
 470                 a <- a + d
 471                 if a >= 0.0 && b >= 0.0
 472                 then
 473                     p.[1] <- sqrt d
 474                 elif a <= 0.0 && b <= 0.0
 475                 then
 476                     p.[1] <- sqrt d
 477                 else
 478                     p.[1] <- -(sqrt d)
 479                 b <- 0.5 * (a + b / p.[1])
 480                 quad ()
 481                 k <- 4
 482             k <- k + 1
 483
 484     if not quadExecuted && p.[2] < 0.0
 485     then
 486         b <- sqrt c
 487         d <- b + b - a
 488         p.[1] <- 0.0
 489         if d > 0.0
 490         then
 491             p.[1] <- sqrt d
 492     elif not quadExecuted
 493     then
 494         if p.[1] > 0.0
 495         then
 496             b <- (sqrt p.[2]) * 2.0 + p.[1]
 497         else
 498             b <- -(sqrt p.[2]) * 2.0 + p.[1]
 499
 500         if b <> 0.0
 501         then
 502             p.[1] <- 0.0
 503         else
 504             for k in 1..4 do
 505                 r.[1, k] <- -e
 506                 r.[2, k] <- 0.0
 507             quadExecuted <- true
 508
 509     quad ()
 510
 511 // Return a tuple (area, x intersections, y intersections)
 512 let EEOverlapArea (e1: Types.Ellipse) (e2: Types.Ellipse) : (float32 * float32[] * float32[]) option =
 513     let h1, k1, a1, b1, phi_1 = float e1.Cx, float e1.Cy, float e1.A, float e1.B, float e1.Alpha
 514     let h2, k2, a2, b2, phi_2 = float e2.Cx, float e2.Cy, float e2.A, float e2.B, float e2.Alpha
 515
 516     if a1 <= EPS || b1 <= EPS || a2 <= EPS || b2 <= EPS
 517     then
 518         None
 519     else
 520         let phi_1 = phi_1 % Math.PI
 521         let phi_2 = phi_2 % Math.PI
 522         let h2_tr, k2_tr, phi_2r =
 523             let cosphi = cos phi_1
 524             let sinphi = sin phi_1
 525             (h2 - h1) * cosphi + (k2 - k1) * sinphi, (h1 - h2) * sinphi + (k2 - k1) * cosphi, (phi_2 - phi_1) % (2.0 * Math.PI)
 526
 527 #if DEBUG_LOG
 528         printf "H2_TR=%f, K2_TR=%f, PHI_2R=%f\n" h2_tr k2_tr phi_2r
 529 #endif
 530
 531         let cosphi = cos phi_2r
 532         let cosphi2 = cosphi ** 2.0
 533         let sinphi = sin phi_2r
 534         let sinphi2 = sinphi ** 2.0
 535         let cosphisinphi = 2.0 * cosphi * sinphi
 536         let a22 = a2 ** 2.0
 537         let b22 = b2 ** 2.0
 538         let tmp0 = (cosphi * h2_tr + sinphi * k2_tr) / a22
 539         let tmp1 = (sinphi * h2_tr - cosphi * k2_tr) / b22
 540         let tmp2 = cosphi * h2_tr + sinphi * k2_tr
 541         let tmp3 = sinphi * h2_tr - cosphi * k2_tr
 542
 543         let aa = cosphi2 / a22 + sinphi2 / b22
 544         let bb = cosphisinphi / a22 - cosphisinphi / b22
 545         let cc = sinphi2 / a22 + cosphi2 / b22
 546         let dd = -2.0 * cosphi * tmp0 - 2.0 * sinphi * tmp1
 547         let ee = -2.0 * sinphi * tmp0 + 2.0 * cosphi * tmp1
 548         let ff = tmp2 * tmp2 / a22 + tmp3 * tmp3 / b22 - 1.0
 549
 550         let cy = [|
 551             (a1 * (a1 * aa - dd) + ff) * (a1 * (a1 * aa + dd) + ff)
 552             2.0 * b1 * (a1 * a1 * (aa * ee - bb * dd) + ee * ff)
 553             a1 * a1 * ((b1 * b1 * (2.0 * aa * cc - bb * bb) + dd * dd - 2.0 * aa * ff) - 2.0 * a1 * a1 * aa * aa) + b1 * b1 * (2.0 * cc * ff + ee * ee)
 554             2.0 * b1 * (b1 * b1 * cc * ee + a1 * a1 * (bb * dd - aa * ee))
 555             a1 * a1 * a1 * a1 * aa * aa + b1 * b1 * (a1 * a1 * (bb * bb - 2.0 * aa * cc) + b1 * b1 * cc * cc)
 556             |]
 557
 558 #if DEBUG_LOG
 559         for i in 0..4 do
 560             printf "cy[%d]=%f\n" i cy.[i]
 561 #endif
 562
 563         let py = Array.zeroCreate<float> 5
 564         let r = Array2D.zeroCreate<float> 3 5
 565
 566         let nroots =
 567             if abs cy.[4] > EPS
 568             then
 569                 for i in 0 .. 3 do
 570                     py.[4-i] <- cy.[i] / cy.[4]
 571                 py.[0] <- 1.0
 572 #if DEBUG_LOG
 573                 for i in 0..4 do
 574                     printf "py[%d]=%f\n" i py.[i]
 575 #endif
 576                 biquadroots py r
 577                 4
 578
 579             elif abs cy.[3] > EPS
 580             then
 581                 for i in 0..2 do
 582                     py.[3 - i] <- cy.[i] / cy.[3]
 583                 py.[0] <- 1.0
 584                 cubicroots py r
 585                 3
 586
 587             elif abs cy.[2] > EPS
 588             then
 589                 for i in 0..1 do
 590                     py.[2-i] <- cy.[i] / cy.[2]
 591                 py.[0] <- 1.0
 592                 quadroots py r
 593                 2
 594
 595             elif abs cy.[1] > EPS
 596             then
 597                 r.[1, 1] <- -cy.[0] / cy.[1]
 598                 r.[2, 1] <- 0.0
 599                 1
 600
 601             else
 602                 0
 603
 604 #if DEBUG_LOG
 605         printf "nroots = %d\n" nroots
 606 #endif
 607
 608         let ychk = Array.init nroots (fun _ -> Double.MaxValue)
 609         let mutable nychk = 0
 610         for i in 1 .. nroots do
 611             if abs r.[2, i] < EPS
 612             then
 613                 ychk.[nychk] <- r.[1, i] * b1
 614                 nychk <- nychk + 1
 615 #if DEBUG_LOG
 616                 printf "ROOT is Real,  i=%d --> %f (B1=%f)\n" i r.[1, i] b1
 617 #endif
 618         Array.sortInPlace ychk
 619
 620 #if DEBUG_LOG
 621         printf "nychk=%d\n" ychk.Length
 622         for j in 0 .. ychk.Length - 1 do
 623             printf "\t j=%d, ychk=%f\n" j ychk.[j]
 624 #endif
 625
 626         let mutable nintpts = 0
 627
 628         let xint = Array.zeroCreate 4
 629         let yint = Array.zeroCreate 4
 630
 631         let mutable returnValue = 0.0
 632
 633         let mutable i = 0
 634         while returnValue = 0.0 && i < nychk do
 635 #if DEBUG_LOG
 636             printf "------------->i=%d (nychk=%d)\n" i nychk
 637 #endif
 638
 639             if not (i < nychk - 1 && abs (ychk.[i] - ychk.[i+1]) < EPS / 2.0)
 640             then
 641 #if DEBUG_LOG
 642                 printf "check intersecting points. nintps is %d"  nintpts
 643 #endif
 644
 645                 let x1 = if abs ychk.[i] > b1 then 0.0 else a1 * sqrt (1.0 - (ychk.[i] * ychk.[i]) / (b1 * b1))
 646                 let x2 = -x1
 647
 648 #if DEBUG_LOG
 649                 printf "\n\tx1=%f, y1=%f, A=%f. B=%f ---> ellipse2tr(x1)= %f\n" x1 ychk.[i] a1 b1 (ellipse2tr x1 ychk.[i] aa bb cc dd ee ff)
 650                 printf "\tx2=%f, y1=%f, A=%f. B=%f ---> ellipse2tr(x2)= %f\n" x2 ychk.[i] a1 b1 (ellipse2tr x2 ychk.[i] aa bb cc dd ee ff)
 651 #endif
 652
 653                 if abs (ellipse2tr x1 ychk.[i] aa bb cc dd ee ff) < EPS
 654                 then
 655                     nintpts <- nintpts + 1
 656 #if DEBUG_LOG
 657                     printf "first if x1. acc nintps=%d\n" nintpts
 658 #endif
 659                     if nintpts > 4
 660                     then
 661                         returnValue <- -1.0
 662                     else
 663                         xint.[nintpts-1] <- x1
 664                         yint.[nintpts-1] <- ychk.[i]
 665 #if DEBUG_LOG
 666                     printf "nintpts=%d, xint=%f, x2=%f, i=%d, yint=%f\n" nintpts x1 x2 i ychk.[i]
 667 #endif
 668
 669                 if returnValue <> -1.0 && abs (ellipse2tr x2 ychk.[i] aa bb cc dd ee ff) < EPS && abs (x2 - x1) > EPS
 670                 then
 671                     nintpts <- nintpts + 1
 672 #if DEBUG_LOG
 673                     printf "first if x2. nintps=%d, Dx=%f (eps2=%f) \n" nintpts (abs (x2 - x1)) EPS
 674 #endif
 675                     if nintpts > 4
 676                     then
 677                         returnValue <- -1.0
 678                     else
 679                         xint.[nintpts-1] <- x2
 680                         yint.[nintpts-1] <- ychk.[i]
 681
 682 #if DEBUG_LOG
 683                     printf "nintpts=%d, x1=%f, xint=%f, i=%d, yint=%f\n" nintpts x1 x2 i ychk.[i]
 684 #endif
 685
 686 #if DEBUG_LOG
 687             else
 688                 printf "i=%d, multiple roots: %f  <--------> %f. continue\n" i ychk.[i] ychk.[i-1]
 689 #endif
 690             i <- i + 1
 691
 692         if returnValue = -1.0
 693         then
 694             None
 695         else
 696             let area =
 697                 match nintpts with
 698                 | 0 | 1 -> nointpts a1 b1 a2 b2 h1 k1 h2 k2 phi_1 phi_2 h2_tr k2_tr aa bb cc dd ee ff
 699                 | 2 -> match istanpt xint.[0] yint.[0] a1 b1 aa bb cc dd ee ff with
 700                        | TANGENT_POINT ->
 701 #if DEBUG_LOG
 702                             printf "one point is tangent\n"
 703 #endif
 704                             nointpts a1 b1 a2 b2 h1 k1 h2 k2 phi_1 phi_2 h2_tr k2_tr aa bb cc dd ee ff
 705
 706                        | INTERSECTION_POINT ->
 707 #if DEBUG_LOG
 708                             printf "check twointpts\n"
 709 #endif
 710                             twointpts xint yint a1 b1 phi_1 a2 b2 h2_tr k2_tr phi_2 aa bb cc dd ee ff
 711                 | 3 -> threeintpts xint yint a1 b1 phi_1 a2 b2 h2_tr k2_tr phi_2 aa bb cc dd ee ff
 712                 | 4 -> fourintpts xint yint a1 b1 phi_1 a2 b2 h2_tr k2_tr phi_2 aa bb cc dd ee ff
 713                 | _ -> -1.0
 714
 715             if area = -1.0
 716             then
 717                 None
 718             elif nintpts = 0
 719             then
 720                 Some (float32 area, [||], [||])
 721             else
 722                 let xTransform : float32[] = Array.zeroCreate nintpts
 723                 let yTransform : float32[] = Array.zeroCreate nintpts
 724                 for i in 0 .. (nintpts - 1) do
 725                     xTransform.[i] <- float32 <| cos phi_1 * xint.[i] - sin phi_1 * yint.[i] + h1
 726                     yTransform.[i] <- float32 <| sin phi_1 * xint.[i] + cos phi_1 * yint.[i] + k1
 727                 Some (float32 area, xTransform, yTransform)