1
// Translation from https://github.com/chraibi/EEOver.
2 module ParasitemiaCore.EEOver
6 let private EPS = 1.0e-7
8 let inline private ellipse2tr (x
: float) (y
: float) (aa
: float) (bb
: float) (cc
: float) (dd
: float) (ee
: float) (ff
: float) : float =
9 aa
* x
* x
+ bb
* x
* y
+ cc
* y
* y
+ dd
* x
+ ee
* y
+ ff
11 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) =
14 let area_1 = Math.PI * a1b1
15 let area_2 = Math.PI * a2b2
16 let relsize = a1b1 - a2b2
20 if (h2_tr
* h2_tr
) / (a1
* a1
) + (k2_tr
* k2_tr
) / (b1
* b1
) < 1.0
31 if abs
(h1
- h2
) < EPS && abs
(k1
- k2
) < EPS && abs
(area_1 - area_2) < EPS
35 type private PointType = TANGENT_POINT | INTERSECTION_POINT
37 let private istanpt
(x
: float) (y
: float) (a1
: float) (b1
: float) (aa
: float) (bb
: float) (cc
: float) (dd
: float) (ee
: float) (ff
: float) : PointType =
41 if x < 0.0 then -a1
else a1
46 then 2.0 * Math.PI - acos
(x / a1)
51 let x1 = a1 * cos
(theta + eps_radian)
52 let y1 = b1
* sin
(theta + eps_radian)
53 let x2 = a1 * cos
(theta - eps_radian)
54 let y2 = b1
* sin
(theta - eps_radian)
56 let test1 = ellipse2tr x1 y1 aa bb cc dd ee
ff
57 let test2 = ellipse2tr x2 y2 aa bb cc dd ee
ff
60 printf
"\t\t--- debug istanpt with (x,y)=(%f, %f), A1=%f, B1=%f\n" x y
a1 b1
61 printf
"theta=%f\n" theta
62 printf
"eps_Radian=%f\n" eps_radian
63 printf
"(x1, y1)=(%f, %f)\n" x1 y1
64 printf
"(x2, y2)=(%f, %f)\n" x2 y2
65 printf
"test1=%f\n" test1
66 printf
"test2=%f\n" test2
69 if test1 * test2 > 0.0
71 else INTERSECTION_POINT
73 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) =
75 then x.[0] <- if x.[0] < 0.0 then -a1 else a1
79 then 2.0 * Math.PI - acos (x.[0] / a1)
80 else acos (x.[0] / a1)
83 then x.[1] <- if x.[1] < 0.0 then -a1 else a1
87 then 2.0 * Math.PI - acos (x.[1] / a1)
88 else acos (x.[1] / a1)
96 let xmid = a1 * cos
((theta1 + theta2) / 2.0)
97 let ymid = b1
* sin
((theta1 + theta2) / 2.0)
99 if ellipse2tr xmid ymid aa bb cc dd ee
ff > 0.0
107 theta1 <- theta1 - 2.0 * Math.PI
109 let trsign = if (theta2 - theta1) > Math.PI then 1.0 else -1.0
111 let mutable area1 = 0.5 * (a1 * b1
* (theta2 - theta1) + trsign * abs
(x.[0] * y
.[1] - x.[1] * y
.[0]))
116 printf
"TWO area1=%f\n" area1
118 area1 <- area1 + a1 * b1
120 let cosphi = cos
(phi_1
- phi_2
)
121 let sinphi = sin
(phi_1
- phi_2
)
123 let mutable x1_tr = (x.[0] - h2_tr
) * cosphi + (y
.[0] - k2_tr
) * -sinphi
124 let mutable y1_tr = (x.[0] - h2_tr
) * sinphi + (y
.[0] - k2_tr
) * cosphi
125 let mutable x2_tr = (x.[1] - h2_tr
) * cosphi + (y
.[1] - k2_tr
) * -sinphi
126 let mutable y2_tr = (x.[1] - h2_tr
) * sinphi + (y
.[1] - k2_tr
) * cosphi
130 x1_tr <- if x1_tr < 0.0 then -a2
else a2
134 theta1 <- 2.0 * Math.PI - acos (x1_tr / a2)
136 theta1 <- acos (x1_tr / a2)
140 x2_tr <- if x2_tr < 0.0 then -a2 else a2
144 theta2 <- 2.0 * Math.PI - acos (x2_tr / a2)
146 theta2 <- acos (x2_tr / a2)
154 let xmid = a2 * cos
((theta1 + theta2) / 2.0)
155 let ymid = b2
* sin
((theta1 + theta2) / 2.0)
157 let cosphi = cos
(phi_2
- phi_1
)
158 let sinphi = sin
(phi_2
- phi_1
)
159 let xmid_rt = xmid * cosphi + ymid * -sinphi + h2_tr
160 let ymid_rt = xmid * sinphi + ymid * cosphi + k2_tr
162 if (xmid_rt * xmid_rt) / (a1 * a1) + (ymid_rt * ymid_rt) / (b1
* b1
) > 1.0
170 theta1 <- theta1 - 2.0 * Math.PI
172 let trsign = if theta2 - theta1 > Math.PI then 1.0 else -1.0
174 let mutable area2 = 0.5 * (a2 * b2
* (theta2 - theta1) + trsign * abs
(x1_tr * y2_tr - x2_tr * y1_tr))
178 printf
"TWO area2=%f\n" area2
180 area2 <- area2 + a2 * b2
184 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 =
185 let mutable tanpts = 0
186 let mutable tanindex = 0
188 if istanpt
xint.[i
] yint
.[i
] a1 b2 aa bb cc dd ee
ff = TANGENT_POINT
193 printf
"tanindex=%d\n" tanindex
209 twointpts
xint yint
a1 b1 phi_1
a2 b2 h2_tr k2_tr phi_2 aa bb cc dd ee
ff
211 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 =
214 let area_1 = Math.PI * a1b1
215 let area_2 = Math.PI * a2b2
217 let theta = Array.zeroCreate
4
222 xint.[i
] <- if xint.[i
] < 0.0 then -a1 else a1
223 theta.[i
] <- if yint
.[i
] < 0.0 then 2.0 * Math.PI - acos (xint.[i
] / a1) else acos (xint.[i
] / a1)
227 printf
"k=%d: Theta = %f, xint=%f, yint=%f\n" k
theta.[k
] xint.[k
] yint
.[k
]
235 let mutable k = j
- 1
243 theta.[k+1] <- theta.[k]
244 xint.[k+1] <- xint.[k]
245 yint
.[k+1] <- yint
.[k]
255 printf
"AFTER sorting\n"
257 printf
"k=%d: Theta = %f, xint=%f, yint=%f\n" k theta.[k] xint.[k] yint
.[k]
260 let area1 = 0.5 * abs
((xint.[2] - xint.[0]) * (yint
.[3] - yint
.[1]) - (xint.[3] - xint.[1]) * (yint
.[2] - yint
.[0]))
262 let cosphi = cos
(phi_1
- phi_2
)
263 let sinphi = sin
(phi_1
- phi_2
)
265 let theta_tr = Array.zeroCreate
4
266 let xint_tr = Array.zeroCreate
4
267 let yint_tr = Array.zeroCreate
4
270 xint_tr.[i
] <- (xint.[i
] - h2_tr
) * cosphi + (yint
.[i
] - k2_tr
) * -sinphi
271 yint_tr.[i
] <- (xint.[i
] - h2_tr
) * sinphi + (yint
.[i
] - k2_tr
) * cosphi
273 if abs
xint_tr.[i
] > a2
275 xint_tr.[i
] <- if xint_tr.[i
] < 0.0 then -a2 else a2
277 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)
279 let xmid = a1 * cos
((theta.[0] + theta.[1]) / 2.0)
280 let ymid = b1
* sin
((theta.[0] + theta.[1]) / 2.0)
282 let mutable area2, area3
, area4
, area5
= 0.0, 0.0, 0.0, 0.0
284 if ellipse2tr xmid ymid aa bb cc dd ee
ff < 0.0
286 area2 <- 0.5 * (a1b1 * (theta.[1] - theta.[0]) - abs
(xint.[0] * yint
.[1] - xint.[1] * yint
.[0]))
287 area3
<- 0.5 * (a1b1 * (theta.[3] - theta.[2]) - abs
(xint.[2] * yint
.[3] - xint.[3] * yint
.[2]))
288 area4
<- 0.5 * (a2b2 * (theta_tr.[2] - theta_tr.[1]) - abs
(xint_tr.[1] * yint_tr.[2] - xint_tr.[2] * yint_tr.[1]))
290 if theta_tr.[3] > theta_tr.[0]
292 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]))
294 area5
<- 0.5 * (a2b2 * (theta_tr.[0] - theta_tr.[3]) - abs
(xint_tr.[3] * yint_tr.[0] - xint_tr.[0] * yint_tr.[3]))
296 area2 <- 0.5 * (a1b1 * (theta.[2] - theta.[1]) - abs
(xint.[1] * yint
.[2] - xint.[2] * yint
.[1]))
297 area3
<- 0.5 * (a1b1 * (theta.[0] - (theta.[3] - 2.0 * Math.PI)) - abs
(xint.[3] * yint
.[0] - xint.[0] * yint
.[3]))
298 area4
<- 0.5 * (a2b2 * (theta_tr.[1] - theta_tr.[0]) - abs
(xint_tr.[0] * yint_tr.[1] - xint_tr.[1] * yint_tr.[0]))
299 area5
<- 0.5 * (a2b2 * (theta_tr.[3] - theta_tr.[2]) - abs
(xint_tr.[2] * yint_tr.[3] - xint_tr.[3] * yint_tr.[2]))
304 printf
"\n\t\t-------------> area5 is negative (%f). Add: pi*A2*B2=%f <------------\n" area5
area_2
306 area5
<- area5
+ area_2
311 printf
"\n\t\t-------------> area4 is negative (%f). Add: pi*A2*B2=%f <------------\n" area4
area_2
313 area4
<- area4
+ area_2
318 printf
"\n\t\t-------------> area3 is negative (%f). Add: pi*A2*B2=%f <------------\n" area3
area_1
320 area3
<- area3
+ area_1
325 printf
"\n\t\t-------------> area2 is negative (%f). Add: pi*A2*B2=%f <------------\n" area2 area_1
327 area2 <- area2 + area_1
330 printf
"\narea1=%f, area2=%f area3=%f, area4=%f, area5=%f\n\n" area1 area2 area3 area4 area5
333 area1 + area2 + area3
+ area4
+ area5
335 let private quadroots
(p
: float[]) (r
: float[,]) =
336 let mutable b = -p
.[1] / (2.0 * p
.[0])
337 let c = p
.[2] / p
.[0]
338 let mutable d = b * b - c
359 let private cubicroots
(p
: float[]) (r
: float[,]) =
362 p
.[k] <- p
.[k] / p
.[0]
365 let mutable t = s * p
.[1]
366 let mutable b = 0.5 * (s * (t / 1.5 - p
.[2]) + p
.[3])
367 t <- (t - p
.[2]) / 3.0
368 let mutable c = t * t * t
369 let mutable d = b * b - c
373 d <- ((sqrt
d) + (abs
b)) ** (1.0 / 3.0)
380 d <- sqrt
(0.75) * (b - c)
385 if b > 0.0 && s <= 0.0 || b < 0.0 && s > 0.0
398 then d <- (atan
1.0) / 1.5
399 else d <- atan
((sqrt
-d) / (abs
b)) / 3.0
402 then b <- 2.0 * (sqrt
t)
403 else b <- -2.0 * (sqrt
t)
406 t <- -(sqrt
0.75
) * (sin
d) * b - 0.5 * c
429 let private biquadroots
(p
: float[]) (r
: float[,]) =
433 p
.[k] <- p
.[k] / p
.[0]
436 let mutable b = 2.0 * e
437 let mutable c = b ** 2.0
438 let mutable d = 0.75 * c
439 b <- p
.[3] + b *(c - p
.[2])
440 let mutable a = p
.[2] - d
441 c <- p
.[4] + e * (e * a - p
.[3])
444 let mutable quadExecuted = false
452 r
.[j
, k+2] <- r
.[j
, k]
457 r
.[1,k] <- r
.[1,k] - e
461 p.[2] <- (p.[1] * p.[1] - c) * 0.25
462 p.[3] <- b * b / -64.0
468 if r
.[2, k] = 0.0 && r
.[1, k] > 0.0
472 if a >= 0.0 && b >= 0.0
475 elif
a <= 0.0 && b <= 0.0
480 b <- 0.5 * (a + b / p.[1])
485 if not
quadExecuted && p.[2] < 0.0
493 elif not
quadExecuted
497 b <- (sqrt
p.[2]) * 2.0 + p.[1]
499 b <- -(sqrt
p.[2]) * 2.0 + p.[1]
513 /// Return a tuple (area, x intersections, y intersections).
515 let EEOverlapArea (e1
: Types.Ellipse) (e2
: Types.Ellipse) : (float32
* float32
[] * float32
[]) option =
516 let h1, k1
, a1, b1
, phi_1
= float e1.Cx, float e1.Cy, float e1.A, float e1.B, float e1.Alpha
517 let h2, k2, a2, b2
, phi_2
= float e2.Cx, float e2.Cy, float e2.A, float e2.B, float e2.Alpha
519 if a1 <= EPS || b1 <= EPS || a2 <= EPS || b2 <= EPS
523 let phi_1 = phi_1 % Math.PI
524 let phi_2 = phi_2 % Math.PI
525 let h2_tr, k2_tr
, phi_2r
=
526 let cosphi = cos
phi_1
527 let sinphi = sin
phi_1
528 (h2 - h1) * cosphi + (k2 - k1
) * sinphi, (h1 - h2) * sinphi + (k2 - k1
) * cosphi, (phi_2 - phi_1) % (2.0 * Math.PI)
531 printf
"H2_TR=%f, K2_TR=%f, PHI_2R=%f\n" h2_tr k2_tr phi_2r
534 let cosphi = cos
phi_2r
535 let cosphi2 = cosphi ** 2.0
536 let sinphi = sin
phi_2r
537 let sinphi2 = sinphi ** 2.0
538 let cosphisinphi = 2.0 * cosphi * sinphi
541 let tmp0 = (cosphi * h2_tr + sinphi * k2_tr
) / a22
542 let tmp1 = (sinphi * h2_tr - cosphi * k2_tr
) / b22
543 let tmp2 = cosphi * h2_tr + sinphi * k2_tr
544 let tmp3 = sinphi * h2_tr - cosphi * k2_tr
546 let aa = cosphi2 / a22 + sinphi2 / b22
547 let bb = cosphisinphi / a22 - cosphisinphi / b22
548 let cc = sinphi2 / a22 + cosphi2 / b22
549 let dd = -2.0 * cosphi * tmp0 - 2.0 * sinphi * tmp1
550 let ee = -2.0 * sinphi * tmp0 + 2.0 * cosphi * tmp1
551 let ff = tmp2 * tmp2 / a22 + tmp3 * tmp3 / b22 - 1.0
554 (a1 * (a1 * aa - dd) + ff) * (a1 * (a1 * aa + dd) + ff)
555 2.0 * b1 * (a1 * a1 * (aa * ee - bb * dd) + ee * ff)
556 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)
557 2.0 * b1 * (b1 * b1 * cc * ee + a1 * a1 * (bb * dd - aa * ee))
558 a1 * a1 * a1 * a1 * aa * aa + b1 * b1 * (a1 * a1 * (bb * bb - 2.0 * aa * cc) + b1 * b1 * cc * cc)
563 printf
"cy[%d]=%f\n" i
cy.[i
]
566 let py = Array.zeroCreate
<float> 5
567 let r = Array2D.zeroCreate
<float> 3 5
573 py.[4-i
] <- cy.[i
] / cy.[4]
577 printf
"py[%d]=%f\n" i
py.[i
]
582 elif abs
cy.[3] > EPS
585 py.[3 - i
] <- cy.[i
] / cy.[3]
590 elif abs
cy.[2] > EPS
593 py.[2-i
] <- cy.[i
] / cy.[2]
598 elif abs
cy.[1] > EPS
600 r.[1, 1] <- -cy.[0] / cy.[1]
608 printf
"nroots = %d\n" nroots
611 let ychk = Array.init
nroots (fun _ -> Double.MaxValue)
612 let mutable nychk = 0
613 for i
= 1 to nroots do
614 if abs
r.[2, i
] < EPS
616 ychk.[nychk] <- r.[1, i
] * b1
619 printf
"ROOT is Real, i=%d --> %f (B1=%f)\n" i
r.[1, i
] b1
621 Array.sortInPlace
ychk
624 printf
"nychk=%d\n" ychk.Length
625 for j
= 0 to ychk.Length - 1 do
626 printf
"\t j=%d, ychk=%f\n" j ychk.[j]
629 let mutable nintpts = 0
631 let xint = Array.zeroCreate
4
632 let yint = Array.zeroCreate
4
634 let mutable returnValue = 0.0
637 while returnValue = 0.0 && i < nychk do
639 printf
"------------->i=%d (nychk=%d)\n" i nychk
642 if not
(i < nychk - 1 && abs
(ychk.[i] - ychk.[i+1]) < EPS / 2.0)
645 printf
"check intersecting points. nintps is %d" nintpts
648 let x1 = if abs
ychk.[i] > b1 then 0.0 else a1 * sqrt
(1.0 - (ychk.[i] * ychk.[i]) / (b1 * b1))
652 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)
653 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)
656 if abs
(ellipse2tr x1 ychk.[i] aa bb cc dd ee ff) < EPS
658 nintpts <- nintpts + 1
660 printf
"first if x1. acc nintps=%d\n" nintpts
666 xint.[nintpts-1] <- x1
667 yint.[nintpts-1] <- ychk.[i]
669 printf
"nintpts=%d, xint=%f, x2=%f, i=%d, yint=%f\n" nintpts x1 x2 i ychk.[i]
672 if returnValue <> -1.0 && abs
(ellipse2tr x2 ychk.[i] aa bb cc dd ee ff) < EPS && abs
(x2 - x1) > EPS
674 nintpts <- nintpts + 1
676 printf
"first if x2. nintps=%d, Dx=%f (eps2=%f) \n" nintpts (abs
(x2 - x1)) EPS
682 xint.[nintpts-1] <- x2
683 yint.[nintpts-1] <- ychk.[i]
686 printf
"nintpts=%d, x1=%f, xint=%f, i=%d, yint=%f\n" nintpts x1 x2 i ychk.[i]
691 printf
"i=%d, multiple roots: %f <--------> %f. continue\n" i ychk.[i] ychk.[i-1]
695 if returnValue = -1.0
701 | 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
702 | 2 -> match istanpt
xint.[0] yint.[0] a1 b1 aa bb cc dd ee ff with
705 printf
"one point is tangent\n"
707 nointpts
a1 b1 a2 b2 h1 k1
h2 k2 phi_1 phi_2 h2_tr k2_tr
aa bb cc dd ee ff
709 | INTERSECTION_POINT ->
711 printf
"check twointpts\n"
713 twointpts
xint yint a1 b1 phi_1 a2 b2 h2_tr k2_tr
phi_2 aa bb cc dd ee ff
714 | 3 -> threeintpts
xint yint a1 b1 phi_1 a2 b2 h2_tr k2_tr
phi_2 aa bb cc dd ee ff
715 | 4 -> fourintpts
xint yint a1 b1 phi_1 a2 b2 h2_tr k2_tr
phi_2 aa bb cc dd ee ff
723 Some (float32
area, [||], [||])
725 let xTransform : float32
[] = Array.zeroCreate
nintpts
726 let yTransform : float32
[] = Array.zeroCreate
nintpts
727 for i in 0 .. (nintpts - 1) do
728 xTransform.[i] <- float32
<| cos phi_1 * xint.[i] - sin
phi_1 * yint.[i] + h1
729 yTransform.[i] <- float32
<| sin phi_1 * xint.[i] + cos phi_1 * yint.[i] + k1
730 Some (float32
area, xTransform, yTransform)