+++ /dev/null
-module EEOver
-
-open System
-
-let private EPS = 1.0e-5
-
-let inline private ellipse2tr (x: float) (y: float) (aa: float) (bb: float) (cc: float) (dd: float) (ee: float) (ff: float) : float =
- aa * x * x + bb * x * y + cc * y * y + dd * x + ee * y + ff
-
-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) =
- let a1b1 = a1 * b1
- let a2b2 = a2 * b2
- let area_1 = Math.PI * a1b1
- let area_2 = Math.PI * a2b2
- let relsize = a1b1 - a2b2
-
- if relsize > 0.0
- then
- if (h2_tr * h2_tr) / (a1 * a1) + (k2_tr * k2_tr) / (b1 * b1) < 1.0
- then area_2
- else 0.0
-
- elif relsize < 0.0
- then
- if ff < 0.0
- then area_1
- else 0.0
-
- else
- if abs (h1 - h2) < EPS && abs (k1 - k2) < EPS && abs (area_1 - area_2) < EPS
- then area_1
- else 0.0
-
-type private PointType = TANGENT_POINT | INTERSECTION_POINT
-
-let private istanpt (x: float) (y: float) (a1: float) (b1: float) (aa: float) (bb: float) (cc: float) (dd: float) (ee: float) (ff: float) : PointType =
- let x =
- if abs x > a1
- then
- if x < 0.0 then -a1 else a1
- else x
-
- let theta =
- if y < 0.0
- then 2.0 * Math.PI - acos (x / a1)
- else acos (x / a1)
-
- let eps_radian = 0.1
-
- let x1 = a1 * cos (theta + eps_radian)
- let y1 = b1 * sin (theta + eps_radian)
- let x2 = a1 * cos (theta - eps_radian)
- let y2 = b1 * sin (theta - eps_radian)
-
- let test1 = ellipse2tr x1 y1 aa bb cc dd ee ff
- let test2 = ellipse2tr x2 y2 aa bb cc dd ee ff
-
-#if DEBUG_LOG
- printf "\t\t--- debug istanpt with (x,y)=(%f, %f), A1=%f, B1=%f\n" x y a1 b1
- printf "theta=%f\n" theta
- printf "eps_Radian=%f\n" eps_radian
- printf "(x1, y1)=(%f, %f)\n" x1 y1
- printf "(x2, y2)=(%f, %f)\n" x2 y2
- printf "test1=%f\n" test1
- printf "test2=%f\n" test2
-#endif
-
- if test1 * test2 > 0.0
- then TANGENT_POINT
- else INTERSECTION_POINT
-
-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) =
- if abs x.[0] > a1
- then x.[0] <- if x.[0] < 0.0 then -a1 else a1
-
- let mutable theta1 =
- if y.[0] < 0.0
- then 2.0 * Math.PI - acos (x.[0] / a1)
- else acos (x.[0] / a1)
-
- if abs x.[1] > a1
- then x.[1] <- if x.[1] < 0.0 then -a1 else a1
-
- let mutable theta2 =
- if y.[1] < 0.0
- then 2.0 * Math.PI - acos (x.[1] / a1)
- else acos (x.[1] / a1)
-
- if theta1 > theta2
- then
- let tmp = theta1
- theta1 <- theta2
- theta2 <- tmp
-
- let xmid = a1 * cos ((theta1 + theta2) / 2.0)
- let ymid = b1 * sin ((theta1 + theta2) / 2.0)
-
- if ellipse2tr xmid ymid aa bb cc dd ee ff > 0.0
- then
- let tmp = theta1
- theta1 <- theta2
- theta2 <- tmp
-
- if theta1 > theta2
- then
- theta1 <- theta1 - 2.0 * Math.PI
-
- let trsign = if (theta2 - theta1) > Math.PI then 1.0 else -1.0
-
- let mutable area1 = 0.5 * (a1 * b1 * (theta2 - theta1) + trsign * abs (x.[0] * y.[1] - x.[1] * y.[0]))
-
- if area1 < 0.0
- then
-#if DEBUG_LOG
- printf "TWO area1=%f\n" area1
-#endif
- area1 <- area1 + a1 * b1
-
- let cosphi = cos (phi_1 - phi_2)
- let sinphi = sin (phi_1 - phi_2)
-
- let mutable x1_tr = (x.[0] - h2_tr) * cosphi + (y.[0] - k2_tr) * -sinphi
- let mutable y1_tr = (x.[0] - h2_tr) * sinphi + (y.[0] - k2_tr) * cosphi
- let mutable x2_tr = (x.[1] - h2_tr) * cosphi + (y.[1] - k2_tr) * -sinphi
- let mutable y2_tr = (x.[1] - h2_tr) * sinphi + (y.[1] - k2_tr) * cosphi
-
- if abs x1_tr > a2
- then
- x1_tr <- if x1_tr < 0.0 then -a2 else a2
-
- if y1_tr < 0.0
- then
- theta1 <- 2.0 * Math.PI - acos (x1_tr / a2)
- else
- theta1 <- acos (x1_tr / a2)
-
- if abs x2_tr > a2
- then
- x2_tr <- if x2_tr < 0.0 then -a2 else a2
-
- if y2_tr < 0.0
- then
- theta2 <- 2.0 * Math.PI - acos (x2_tr / a2)
- else
- theta2 <- acos (x2_tr / a2)
-
- if theta1 > theta2
- then
- let tmp = theta1
- theta1 <- theta2
- theta2 <- tmp
-
- let xmid = a2 * cos ((theta1 + theta2) / 2.0)
- let ymid = b2 * sin ((theta1 + theta2) / 2.0)
-
- let cosphi = cos (phi_2 - phi_1)
- let sinphi = sin (phi_2 - phi_1)
- let xmid_rt = xmid * cosphi + ymid * -sinphi + h2_tr
- let ymid_rt = xmid * sinphi + ymid * cosphi + k2_tr
-
- if (xmid_rt * xmid_rt) / (a1 * a1) + (ymid_rt * ymid_rt) / (b1 * b1) > 1.0
- then
- let tmp = theta1
- theta1 <- theta2
- theta2 <- tmp
-
- if theta1 > theta2
- then
- theta1 <- theta1 - 2.0 * Math.PI
-
- let trsign = if theta2 - theta1 > Math.PI then 1.0 else -1.0
-
- let mutable area2 = 0.5 * (a2 * b2 * (theta2 - theta1) + trsign * abs (x1_tr * y2_tr - x2_tr * y1_tr))
- if area2 < 0.0
- then
-#if DEBUG_LOG
- printf "TWO area2=%f\n" area2
-#endif
- area2 <- area2 + a2 * b2
-
- area1 + area2
-
-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 =
- let mutable tanpts = 0
- let mutable tanindex = 0
- for i in 0..2 do
- if istanpt xint.[i] yint.[i] a1 b2 aa bb cc dd ee ff = TANGENT_POINT
- then
- tanpts <- tanpts + 1
- tanindex <- i
-#if DEBUG_LOG
- printf "tanindex=%d\n" tanindex
-#endif
-
- if tanpts <> 1
- then
- -1.0
- else
- match tanindex with
- | 0 ->
- xint.[0] <- xint.[2]
- yint.[0] <- yint.[2]
- | 1 ->
- xint.[1] <- xint.[2]
- yint.[1] <- yint.[2]
- | _ ->
- ()
- twointpts xint yint a1 b1 phi_1 a2 b2 h2_tr k2_tr phi_2 aa bb cc dd ee ff
-
-
-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 =
- let a1b1 = a1 * b1
- let a2b2 = a2 * b2
- let area_1 = Math.PI * a1b1
- let area_2 = Math.PI * a2b2
-
- let theta = Array.zeroCreate 4
-
- for i in 0 .. 3 do
- if abs xint.[i] > a1
- then
- xint.[i] <- if xint.[i] < 0.0 then -a1 else a1
- theta.[i] <- if yint.[i] < 0.0 then 2.0 * Math.PI - acos (xint.[i] / a1) else acos (xint.[i] / a1)
-
-#if DEBUG_LOG
- for k in 0..3 do
- printf "k=%d: Theta = %f, xint=%f, yint=%f\n" k theta.[k] xint.[k] yint.[k]
-#endif
-
- for j in 1 .. 3 do
- let tmp0 = theta.[j]
- let tmp1 = xint.[j]
- let tmp2 = yint.[j]
-
- let mutable k = j - 1
- let mutable k2 = 0
- while k >= 0 do
- if theta.[k] <= tmp0
- then
- k2 <- k + 1
- k <- -1
- else
- theta.[k+1] <- theta.[k]
- xint.[k+1] <- xint.[k]
- yint.[k+1] <- yint.[k]
- k <- k - 1
- k2 <- k + 1
-
- theta.[k2] <- tmp0
- xint.[k2] <- tmp1
- yint.[k2] <- tmp2
-
-
-#if DEBUG_LOG
- printf "AFTER sorting\n"
- for k in 0..3 do
- printf "k=%d: Theta = %f, xint=%f, yint=%f\n" k theta.[k] xint.[k] yint.[k]
-#endif
-
- let area1 = 0.5 * abs ((xint.[2] - xint.[0]) * (yint.[3] - yint.[1]) - (xint.[3] - xint.[1]) * (yint.[2] - yint.[0]))
-
- let cosphi = cos (phi_1 - phi_2)
- let sinphi = sin (phi_1 - phi_2)
-
- let theta_tr = Array.zeroCreate 4
- let xint_tr = Array.zeroCreate 4
- let yint_tr = Array.zeroCreate 4
-
- for i in 0..3 do
- xint_tr.[i] <- (xint.[i] - h2_tr) * cosphi + (yint.[i] - k2_tr) * -sinphi
- yint_tr.[i] <- (xint.[i] - h2_tr) * sinphi + (yint.[i] - k2_tr) * cosphi
-
- if abs xint_tr.[i] > a2
- then
- xint_tr.[i] <- if xint_tr.[i] < 0.0 then -a2 else a2
-
- 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)
-
- let xmid = a1 * cos ((theta.[0] + theta.[1]) / 2.0)
- let ymid = b1 * sin ((theta.[0] + theta.[1]) / 2.0)
-
- let mutable area2, area3, area4, area5 = 0.0, 0.0, 0.0, 0.0
-
- if ellipse2tr xmid ymid aa bb cc dd ee ff < 0.0
- then
- area2 <- 0.5 * (a1b1 * (theta.[1] - theta.[0]) - abs (xint.[0] * yint.[1] - xint.[1] * yint.[0]))
- area3 <- 0.5 * (a1b1 * (theta.[3] - theta.[2]) - abs (xint.[2] * yint.[3] - xint.[3] * yint.[2]))
- area4 <- 0.5 * (a2b2 * (theta_tr.[2] - theta_tr.[1]) - abs (xint_tr.[1] * yint_tr.[2] - xint_tr.[2] * yint_tr.[1]))
-
- if theta_tr.[3] > theta_tr.[0]
- then
- 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]))
- else
- area5 <- 0.5 * (a2b2 * (theta_tr.[0] - theta_tr.[3]) - abs (xint_tr.[3] * yint_tr.[0] - xint_tr.[0] * yint_tr.[3]))
- else
- area2 <- 0.5 * (a1b1 * (theta.[2] - theta.[1]) - abs (xint.[1] * yint.[2] - xint.[2] * yint.[1]))
- area3 <- 0.5 * (a1b1 * (theta.[0] - (theta.[3] - 2.0 * Math.PI)) - abs (xint.[3] * yint.[0] - xint.[0] * yint.[3]))
- area4 <- 0.5 * (a2b2 * (theta_tr.[1] - theta_tr.[0]) - abs (xint_tr.[0] * yint_tr.[1] - xint_tr.[1] * yint_tr.[0]))
- area5 <- 0.5 * (a2b2 * (theta_tr.[3] - theta_tr.[2]) - abs (xint_tr.[2] * yint_tr.[3] - xint_tr.[3] * yint_tr.[2]))
-
- if area5 < 0.0
- then
-#if DEBUG_LOG
- printf "\n\t\t-------------> area5 is negativ (%f). Add: pi*A2*B2=%f <------------\n" area5 area_2
-#endif
- area5 <- area5 + area_2
-
- if area4 < 0.0
- then
-#if DEBUG_LOG
- printf "\n\t\t-------------> area4 is negativ (%f). Add: pi*A2*B2=%f <------------\n" area4 area_2
-#endif
- area4 <- area4 + area_2
-
- if area3 < 0.0
- then
-#if DEBUG_LOG
- printf "\n\t\t-------------> area3 is negativ (%f). Add: pi*A2*B2=%f <------------\n" area3 area_1
-#endif
- area3 <- area3 + area_1
-
- if area2 < 0.0
- then
-#if DEBUG_LOG
- printf "\n\t\t-------------> area2 is negativ (%f). Add: pi*A2*B2=%f <------------\n" area2 area_1
-#endif
- area2 <- area2 + area_1
-
-#if DEBUG_LOG
- printf "\narea1=%f, area2=%f area3=%f, area4=%f, area5=%f\n\n" area1 area2 area3 area4 area5
-#endif
-
- area1 + area2 + area3 + area4 + area5
-
-let private quadroots (p: float[]) (r: float[,]) =
- let mutable b = -p.[1] / (2.0 * p.[0])
- let c = p.[2] / p.[0]
- let mutable d = b * b - c
-
- if d >= 0.0
- then
- if b > 0.0
- then
- b <- sqrt d + b
- r.[1, 2] <- b
- else
- b <- -sqrt d + b
- r.[1, 2] <- b
- r.[1, 1] <- c / b
- r.[2, 1] <- 0.0
- r.[2, 2] <- 0.0
- else
- d <- sqrt -d
- r.[2, 1] <- d
- r.[2, 2] <- -d
- r.[1, 1] <- b
- r.[1, 2] <- b
-
-let private cubicroots (p: float[]) (r: float[,]) =
- if p.[0] <> 1.0 then
- for k in 1..3 do
- p.[k] <- p.[k] / p.[0]
- p.[0] <- 1.0
- let s = p.[1] / 3.0
- let mutable t = s * p.[1]
- let mutable b = 0.5 * (s * (t / 1.5 - p.[2]) + p.[3])
- t <- (t - p.[2]) / 3.0
- let mutable c = t * t * t
- let mutable d = b * b - c
-
- if d >= 0.0
- then
- d <- ((sqrt d) + (abs b)) ** (1.0 / 3.0)
- if d <> 0.0
- then
- if b > 0.0
- then b <- -d
- else b <- d
- c <- t / b
- d <- sqrt(0.75) * (b - c)
- r.[2, 2] <- d
- b <- b + c
- c <- -0.5 * b - s
- r.[1, 2] <- c
- if b > 0.0 && s <= 0.0 || b < 0.0 && s > 0.0
- then
- r.[1, 1] <- c
- r.[2, 1] <- -d
- r.[1, 3] <- b - s
- r.[2, 3] <- 0.0
- else
- r.[1, 1] <- b - s
- r.[2, 1] <- 0.0
- r.[1, 3] <- c
- r.[2, 3] <- -d
- else
- if b = 0.0
- then d <- (atan 1.0) / 1.5
- else d <- atan ((sqrt -d) / (abs b)) / 3.0
-
- if b < 0.0
- then b <- 2.0 * (sqrt t)
- else b <- -2.0 * (sqrt t)
-
- c <- (cos d) * b
- t <- -(sqrt 0.75) * (sin d) * b - 0.5 * c
- d <- -t - c - s
- c <- c - s
- t <- t - s
-
- if abs c > abs t
- then
- r.[1, 3] <- c
- else
- r.[1, 3] <- t
- t <- c
-
- if abs d > abs t
- then
- r.[1, 2] <- d
- else
- r.[1, 2] <- t
- t <- d
-
- r.[1, 1] <- t
- for k in 1..3 do
- r.[2, k] <- 0.0
-
-let private biquadroots (p: float[]) (r: float[,]) =
- if p.[0] <> 1.0
- then
- for k in 1..4 do
- p.[k] <- p.[k] / p.[0]
- p.[0] <- 1.0
- let e = 0.25 * p.[1]
- let mutable b = 2.0 * e
- let mutable c = b ** 2.0
- let mutable d = 0.75 * c
- b <- p.[3] + b *(c - p.[2])
- let mutable a = p.[2] - d
- c <- p.[4] + e * (e * a - p.[3])
- a <- a - d
-
- let mutable quadExecuted = false
- let inline quad () =
- if not quadExecuted
- then
- p.[2] <- c / b
- quadroots p r
- for k in 1..2 do
- for j in 1..2 do
- r.[j, k+2] <- r.[j, k]
- p.[1] <- -p.[1]
- p.[2] <- b
- quadroots p r
- for k in 1..4 do
- r.[1,k] <- r.[1,k] - e
- quadExecuted <- true
-
- p.[1] <- 0.5 * a
- p.[2] <- (p.[1] * p.[1] - c) * 0.25
- p.[3] <- b * b / -64.0
- if p.[3] < 0.0
- then
- cubicroots p r
- let mutable k = 1
- while k < 4 do
- if r.[2, k] = 0.0 && r.[1, k] > 0.0
- then
- d <- r.[1, k] * 4.0
- a <- a + d
- if a >= 0.0 && b >= 0.0
- then
- p.[1] <- sqrt d
- elif a <= 0.0 && b <= 0.0
- then
- p.[1] <- sqrt d
- else
- p.[1] <- -(sqrt d)
- b <- 0.5 * (a + b / p.[1])
- quad ()
- k <- 4
- k <- k + 1
-
- if not quadExecuted && p.[2] < 0.0
- then
- b <- sqrt c
- d <- b + b - a
- p.[1] <- 0.0
- if d > 0.0
- then
- p.[1] <- sqrt d
- elif not quadExecuted
- then
- if p.[1] > 0.0
- then
- b <- (sqrt p.[2]) * 2.0 + p.[1]
- else
- b <- -(sqrt p.[2]) * 2.0 + p.[1]
-
- if b <> 0.0
- then
- p.[1] <- 0.0
- else
- for k in 1..4 do
- r.[1, k] <- -e
- r.[2, k] <- 0.0
- quadExecuted <- true
-
- quad ()
-
-// Return a tuple (area, x intersections, y intersections)
-let EEOverlapArea (e1: Types.Ellipse) (e2: Types.Ellipse) : (float32 * float32[] * float32[]) option =
- let h1, k1, a1, b1, phi_1 = float e1.Cx, float e1.Cy, float e1.A, float e1.B, float e1.Alpha
- let h2, k2, a2, b2, phi_2 = float e2.Cx, float e2.Cy, float e2.A, float e2.B, float e2.Alpha
-
- if a1 <= EPS || b1 <= EPS || a2 <= EPS || b2 <= EPS
- then
- None
- else
- let phi_1 = phi_1 % Math.PI //(if phi_1 > Math.PI / 2.0 then phi_1 - Math.PI else phi_1) % Math.PI
- let phi_2 = phi_2 % Math.PI //(if phi_2 > Math.PI / 2.0 then phi_2 - Math.PI else phi_2) % Math.PI
- let h2_tr, k2_tr, phi_2r =
- let cosphi = cos phi_1
- let sinphi = sin phi_1
- (h2 - h1) * cosphi + (k2 - k1) * sinphi, (h1 - h2) * sinphi + (k2 - k1) * cosphi, (phi_2 - phi_1) % (2.0 * Math.PI)
-
-#if DEBUG_LOG
- printf "H2_TR=%f, K2_TR=%f, PHI_2R=%f\n" h2_tr k2_tr phi_2r
-#endif
-
- let cosphi = cos phi_2r
- let cosphi2 = cosphi ** 2.0
- let sinphi = sin phi_2r
- let sinphi2 = sinphi ** 2.0
- let cosphisinphi = 2.0 * cosphi * sinphi
- let a22 = a2 ** 2.0
- let b22 = b2 ** 2.0
- let tmp0 = (cosphi * h2_tr + sinphi * k2_tr) / a22
- let tmp1 = (sinphi * h2_tr - cosphi * k2_tr) / b22
- let tmp2 = cosphi * h2_tr + sinphi * k2_tr
- let tmp3 = sinphi * h2_tr - cosphi * k2_tr
-
- let aa = cosphi2 / a22 + sinphi2 / b22
- let bb = cosphisinphi / a22 - cosphisinphi / b22
- let cc = sinphi2 / a22 + cosphi2 / b22
- let dd = -2.0 * cosphi * tmp0 - 2.0 * sinphi * tmp1
- let ee = -2.0 * sinphi * tmp0 + 2.0 * cosphi * tmp1
- let ff = tmp2 * tmp2 / a22 + tmp3 * tmp3 / b22 - 1.0
-
- let cy = [|
- (a1 * (a1 * aa - dd) + ff) * (a1 * (a1 * aa + dd) + ff)
- 2.0 * b1 * (a1 * a1 * (aa * ee - bb * dd) + ee * ff)
- 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)
- 2.0 * b1 * (b1 * b1 * cc * ee + a1 * a1 * (bb * dd - aa * ee))
- a1 * a1 * a1 * a1 * aa * aa + b1 * b1 * (a1 * a1 * (bb * bb - 2.0 * aa * cc) + b1 * b1 * cc * cc)
- |]
-
-#if DEBUG_LOG
- for i in 0..4 do
- printf "cy[%d]=%f\n" i cy.[i]
-#endif
-
- let py = Array.zeroCreate<float> 5
- let r = Array2D.zeroCreate<float> 3 5
-
- let nroots =
- if abs cy.[4] > EPS
- then
- for i in 0 .. 3 do
- py.[4-i] <- cy.[i] / cy.[4]
- py.[0] <- 1.0
-#if DEBUG_LOG
- for i in 0..4 do
- printf "py[%d]=%f\n" i py.[i]
-#endif
- biquadroots py r
- 4
-
- elif abs cy.[3] > EPS
- then
- for i in 0..2 do
- py.[3 - i] <- cy.[i] / cy.[3]
- py.[0] <- 1.0
- cubicroots py r
- 3
-
- elif abs cy.[2] > EPS
- then
- for i in 0..1 do
- py.[2-i] <- cy.[i] / cy.[2]
- py.[0] <- 1.0
- quadroots py r
- 2
-
- elif abs cy.[1] > EPS
- then
- r.[1, 1] <- -cy.[0] / cy.[1]
- r.[2, 1] <- 0.0
- 1
-
- else
- 0
-
-#if DEBUG_LOG
- printf "nroots = %d\n" nroots
-#endif
-
- let ychk = Array.init nroots (fun _ -> Double.MaxValue)
- let mutable nychk = 0
- for i in 1 .. nroots do
- if abs r.[2, i] < EPS
- then
- ychk.[nychk] <- r.[1, i] * b1
- nychk <- nychk + 1
-#if DEBUG_LOG
- printf "ROOT is Real, i=%d --> %f (B1=%f)\n" i r.[1, i] b1
-#endif
- Array.sortInPlace ychk
-
-#if DEBUG_LOG
- printf "nychk=%d\n" ychk.Length
- for j in 0 .. ychk.Length - 1 do
- printf "\t j=%d, ychk=%f\n" j ychk.[j]
-#endif
-
- let mutable nintpts = 0
-
- let xint = Array.zeroCreate 4
- let yint = Array.zeroCreate 4
-
- let mutable returnValue = 0.0
-
- let mutable i = 0
- while returnValue = 0.0 && i < nychk do
-#if DEBUG_LOG
- printf "------------->i=%d (nychk=%d)\n" i nychk
-#endif
-
- if not (i < nychk - 1 && abs (ychk.[i] - ychk.[i+1]) < EPS / 2.0)
- then
-#if DEBUG_LOG
- printf "check intersecting points. nintps is %d" nintpts
-#endif
-
- let x1 = if abs ychk.[i] > b1 then 0.0 else a1 * sqrt (1.0 - (ychk.[i] * ychk.[i]) / (b1 * b1))
- let x2 = -x1
-
-#if DEBUG_LOG
- printf "\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)
- 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)
-#endif
-
- if abs (ellipse2tr x1 ychk.[i] aa bb cc dd ee ff) < EPS
- then
- nintpts <- nintpts + 1
-#if DEBUG_LOG
- printf "first if x1. acc nintps=%d\n" nintpts
-#endif
- if nintpts > 4
- then
- returnValue <- -1.0
- else
- xint.[nintpts-1] <- x1
- yint.[nintpts-1] <- ychk.[i]
-#if DEBUG_LOG
- printf "nintpts=%d, xint=%f, x2=%f, i=%d, yint=%f\n" nintpts x1 x2 i ychk.[i]
-#endif
-
- if returnValue <> -1.0 && abs (ellipse2tr x2 ychk.[i] aa bb cc dd ee ff) < EPS && abs (x2 - x1) > EPS
- then
- nintpts <- nintpts + 1
-#if DEBUG_LOG
- printf "first if x2. nintps=%d, Dx=%f (eps2=%f) \n" nintpts (abs (x2 - x1)) EPS
-#endif
- if nintpts > 4
- then
- returnValue <- -1.0
- else
- xint.[nintpts-1] <- x2
- yint.[nintpts-1] <- ychk.[i]
-
-#if DEBUG_LOG
- printf "nintpts=%d, x1=%f, xint=%f, i=%d, yint=%f\n" nintpts x1 x2 i ychk.[i]
-#endif
-
-#if DEBUG_LOG
- else
- printf "i=%d, multiple roots: %f <--------> %f. continue\n" i ychk.[i] ychk.[i-1]
-#endif
- i <- i + 1
-
-
- if returnValue = -1.0
- then
- None
- else
- let area =
- match nintpts with
- | 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
- | 2 -> match istanpt xint.[0] yint.[0] a1 b1 aa bb cc dd ee ff with
- | TANGENT_POINT ->
-#if DEBUG_LOG
- printf "one point is tangent\n"
-#endif
- nointpts a1 b1 a2 b2 h1 k1 h2 k2 phi_1 phi_2 h2_tr k2_tr aa bb cc dd ee ff
-
- | INTERSECTION_POINT ->
-#if DEBUG_LOG
- printf "check twointpts\n"
-#endif
- twointpts xint yint a1 b1 phi_1 a2 b2 h2_tr k2_tr phi_2 aa bb cc dd ee ff
- | 3 -> threeintpts xint yint a1 b1 phi_1 a2 b2 h2_tr k2_tr phi_2 aa bb cc dd ee ff
- | 4 -> fourintpts xint yint a1 b1 phi_1 a2 b2 h2_tr k2_tr phi_2 aa bb cc dd ee ff
- | _ -> -1.0
- if nintpts = 0
- then Some (float32 area, [||], [||])
- else
- let xTransform : float32[] = Array.zeroCreate nintpts
- let yTransform : float32[] = Array.zeroCreate nintpts
- for i in 0 .. (nintpts - 1) do
- xTransform.[i] <- float32 <| cos phi_1 * xint.[i] - sin phi_1 * yint.[i] + h1
- yTransform.[i] <- float32 <| sin phi_1 * xint.[i] + cos phi_1 * yint.[i] + k1
- Some (float32 area, xTransform, yTransform)
\ No newline at end of file
projects / master-thesis.git / blobdiff