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h.clj
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(ns fastmath.fields.h
(:require [fastmath.core :as m]
[fastmath.random :as r]
[fastmath.vector :as v]
[fastmath.fields.utils :as u])
(:import [fastmath.vector Vec2 Vec3 Vec4]))
(set! *unchecked-math* :warn-on-boxed)
(m/use-primitive-operators)
(defn hadamard
([] {:type :random})
([^double amount _]
(fn [^Vec2 v]
(-> (cond
(< (r/drand) m/THIRD) (v/mult v 0.5)
(< (r/drand) m/TWO_THIRD) (Vec2. (* 0.5 (.y v)) (- (* -0.5 (.x v)) 0.5))
:else (Vec2. (- (* -0.5 (.y v)) 0.5) (* 0.5 (.x v))))
(v/mult amount)))))
(defn- hamid-pline
^Vec2 [^Vec4 xy] ;; x1:x y1:y x2:z y2:w
(let [ydiff (- (.w xy) (.y xy))
xdiff (- (.z xy) (.x xy))
m (if (zero? xdiff) 10000.0 (/ ydiff xdiff))
line-length (m/hypot-sqrt xdiff ydiff)
d (r/drand line-length)
xoffset (/ d (m/sqrt (inc (* m m))))
xoffset (if (< (.z xy) (.x xy)) (- xoffset) xoffset)
yoffset (m/abs (* m xoffset))
yoffset (if (< (.w xy) (.y xy)) (- yoffset) xoffset)]
(Vec2. (+ (.x xy) xoffset)
(+ (.y xy) yoffset))))
(defn- hamid-pcircle
^Vec2 [^Vec3 xy filled]
(let [radius (if (and filled (> (r/drand) 0.05)) (r/drand (.z xy)) (.z xy))
a (r/drand m/TWO_PI)]
(Vec2. (+ (.x xy) (* radius (m/cos a)))
(+ (.y xy) (* radius (m/sin a))))))
(defn- hamid-A
^Vec2 [^long n]
(let [n (rem n 400.0)]
(cond
(< n 100) (Vec2. (/ n 100.0) 0.0)
(< n 200) (Vec2. 1.0 (/ (- n 100.0) 100.0))
(< n 300) (Vec2. (/ (- 300.0 n) 100.0) 1.0)
:else (Vec2. 0.0 (/ (- 400.0 n) 100.0)))))
(defn hamid
([] {:type :pattern
:config (fn [] {:presetid (r/irand 20)
:npoints (r/irand 100 5000)
:filled (r/brand)
:a (r/randval (u/sirand 1 3) (u/sdrand 0.125 2.0))
:b (r/randval (u/sirand 1 3) (u/sdrand 0.125 2.0))
:c (r/randval (u/sirand 1 3) (u/sdrand 0.125 2.0))
:d (r/randval (u/sirand 1 3) (u/sdrand 0.125 2.0))
:e (r/randval (u/sirand 1 3) (u/sdrand 0.125 2.0))
:f (r/randval (u/sirand 1 3) (u/sdrand 0.125 2.0))
:g (r/randval (u/sirand 1 3) (u/sdrand 0.125 2.0))
:h (r/randval (u/sirand 1 3) (u/sdrand 0.125 2.0))
:i (r/randval (u/sirand 1 3) (u/sdrand 0.125 2.0))
:j (r/randval (u/sirand 1 3) (u/sdrand 0.125 2.0))
:k (r/randval (u/sirand 1 3) (u/sdrand 0.125 2.0))
:l (r/randval (u/sirand 1 3) (u/sdrand 0.125 2.0))
:m (r/randval (u/sirand 1 3) (u/sdrand 0.125 2.0))
:n (r/randval (u/sirand 1 3) (u/sdrand 0.125 2.0))
:o (r/randval (u/sirand 1 3) (u/sdrand 0.125 2.0))
:p (r/randval (u/sirand 1 3) (u/sdrand 0.125 2.0))})})
([^double amount {:keys [^long presetid ^long npoints filled
^double a ^double b ^double c ^double d ^double e
^double f ^double g ^double h ^double i ^double j
^double k ^double l ^double m ^double n ^double o ^double p]}]
(let [npointsd (/ (double npoints))
presetid (int (rem presetid 20))
hamid-line-1 (let [fa (* a 4.0 m/PI) fb (* b 2.0 m/PI)
fc (* c 8.0 m/PI) fd (* d 4.0 m/PI)
fe (* e -0.5) ff (* f -0.5)]
(fn [^double in]
(Vec4. (- (m/sin (* fa in))) (- (m/cos (* fb in)))
(* fe (m/sin (* fc in))) (* ff (m/cos (* fd in))))))
hamid-line-2 (let [fa (* a 2.0 m/PI) fb (* b 2.0 m/PI)
fc (* c 8.0 m/PI) fd (* d 12.0 m/PI)
fe (* e -0.5) ff (* f -0.5)]
(fn [^double in]
(Vec4. (- (m/sin (* fa in))) (- (m/cos (* fb in)))
(* fe (m/sin (* fc in))) (* ff (m/cos (* fd in))))))
hamid-line-3 (let [fa (* a 8.0 m/PI) fb (* b 2.0 m/PI)
fc (* c 6.0 m/PI) fd (* d 2.0 m/PI)
fe (* e -0.5) ff (* f -0.5)]
(fn [^double in]
(Vec4. (- (m/sin (* fa in))) (- (m/cos (* fb in)))
(* fe (m/sin (* fc in))) (* ff (m/cos (* fd in))))))
hamid-line-4 (let [fa (* a 10.0 m/PI) fb (* b 2.0 m/PI)
fc (* c 12.0 m/PI) fd (* d 2.0 m/PI)
fe (* e -0.5) ff (* f -0.5)]
(fn [^double in]
(Vec4. (- (m/sin (* fa in))) (- (m/cos (* fb in)))
(* fe (m/sin (* fc in))) (* ff (m/cos (* fd in))))))
hamid-line-5 (let [fa (* a 10.0 m/PI) fb (* b 8.0 m/PI)
fc (* c 12.0 m/PI) fd (* d 10.0 m/PI)
s (/ 699.0 npoints)]
(fn [^double in]
(let [in (+ in s)]
(Vec4. (m/sin (* fa in)) (m/cos (* fb in))
(m/sin (* fc in)) (m/cos (* fd in))))))
hamid-line-6 (let [fa (* a -2.0) fb (* b 4.0 m/PI) f1 (/ npoints 1000.0)
fc (* c 0.5) fd (* d 6.0 m/PI) fi (* i 3.0)
fej (/ (* e j -2.0) 15.0) ff (* f 6.0 m/PI)
fgk (/ (* g k 4.0) 15.0) fh (* h 2.0 m/PI)]
(fn [^double in]
(Vec4. (* fa (m/cos (* fb in f1))) (* fc (u/spow (m/cos (* fd in)) fi))
(* fej (m/sin (* ff in))) (* fgk (m/sin (* fh in))))))
hamid-line-7 (let [fa (* a 3.0) fb (* b 2.0 m/PI) fh (* h 3.0)
fc (* c 8.0 m/PI) fd (* d 1.5) fe (* e 2.0 m/PI)
fi (* i 3.0) ff (* f -0.5) fg (* g 6.0 m/PI)]
(fn [^double in]
(Vec4. (* fa (u/spow (m/sin (* fb in)) fh)) (- (m/cos (* fc in)))
(* fd (u/spow (m/sin (* fe in)) fi)) (* ff (m/sin (* fg in))))))
hamid-line-8 (let [fa (* a 6.0 m/PI) fb (* 8.0 m/PI)
fc (* c 1.5) ff (* 3.0 f)
fd (* d -0.5) fe (* e 6.0 m/PI)]
(fn [^double in]
(Vec4. (m/cos (* fa in)) (- (m/cos (* fb in)))
(* fc (u/spow (m/sin (* m/TWO_PI in)) ff))
(* fd (m/cos (* fe in))))))
hamid-line-9 (let [fa (* a 20.0 m/PI) fb (* b 18.0 m/PI)
fe (* e 3.0) fc (* c 16.0 m/PI)
fd (* d 14.0 m/PI) ff (* f 3.0)]
(fn [^double in]
(Vec4. (m/cb (m/sin (* fa in))) (u/spow (m/cos (* fb in)) fe)
(m/cb (m/sin (* fc in))) (u/spow (m/cos (* fd in)) ff))))
hamid-line-10 (fn [^long in]
(let [^Vec2 out1 (hamid-A in)
^Vec2 out2 (hamid-A (+ in 199))]
(Vec4. (.x out1) (.y out1) (.x out2) (.y out2))))
hamid-circle-10 (let [fa (* a m/TWO_THIRD) fb (* b 2.0 m/PI) fc (* c 36.0 m/PI)
fd (* d 30.0 m/PI) fk (/ k 3.0)
fl (* l 3.0) fm (/ m 3.0)
fen (* e n m/TWO_THIRD) ff (* f 2.0 m/PI) fg (* g 36.0 m/PI)
fh (* h 30.0 m/PI) fo (/ o 3.0) fi (* i 14.0 m/PI) fp (/ p 5.0)
fj (* j 36.0 m/PI)]
(fn [^double in]
(Vec3. (+ (* fa (m/sin (* fb in)))
(* fk (m/sin (* fc in)) (m/cos (* fd in)))
(* fm (u/spow (m/sin (* 43.982297150257104 in)) fl)))
(+ (* fen (m/cos (* ff in)))
(* fo (m/cos (* fg in)) (m/cos (* fh in)))
(* fp (m/cb (m/cos (* fi in)))))
(+ 0.006666666666666667 (/ (m/sq (m/sq (m/sin (* fj in)))) 9.0)))))
hamid-circle-11 (let [fa (* a 14.0 m/PI) fb (* b 32.0 m/PI)
fc (* c 20.0 m/PI) fd (/ d 3.0)]
(fn [^double in]
(Vec3. (m/sin (* fa in)) (m/cos (* fb in))
(* fd (m/sq (m/sin (* fc in)))))))
hamid-circle-12 (let [fa (* a m/TWO_THIRD) fb (* b 6.0 m/PI) fc (* c 36.0 m/PI)
fd (* d 30.0 m/PI) fk (* k 3.0)
fe (* e 14.0) fl (/ l 4.0) fm (* m 3.0)
ff (* f m/TWO_THIRD) fg (* g 6.0 m/PI)
fh (* h 28.0 m/PI) fi (* i 30.0 m/PI) fp (/ p 20.0)
ffn (/ n 5.0) fj (* j 36.0 m/PI) fo (* o 4.0)]
(fn [^double in]
(Vec3. (+ (* fa (m/sin (* fb in)))
(* 0.25 (m/sin (* fc in)) (m/cos (* fd in)))
(* fl (u/spow (m/sin (* fe in)) fk)))
(+ (* ff (m/cos (* fg in)))
(* m/THIRD (m/cos (* fh in)) (m/cos (* fi in)))
(* ffn (u/spow (m/cos (* 43.982297150257104 in)) fm)))
(+ 0.006666666666666667
(* fp (u/spow (m/sq (m/sin (* fj in))) fo))))))
hamid-circle-13 (let [fa (* a 10.0 m/PI) fb (* b 28.0 m/PI) fe (* e 3.0)
fc (* c 18.0 m/PI) fd (/ d 3.0)]
(fn [^double in]
(Vec3. (m/sin (* fa in)) (u/spow (m/cos (* fb in)) fe)
(* fd (m/sq (m/sin (* fc in)))))))
hamid-circle-14 (let [fa (* a m/TWO_THIRD) fb (* b 18.0 m/PI) fc (* c 40.0 m/PI)
fd (* d 30.0 m/PI) fe (* e 34.0 m/PI) fk (* k 3.0) fl (/ l 4.0)
ff (* f m/TWO_THIRD) fg (* g 18.0 m/PI) fh (* h 28.0 m/PI)
f1 125.66370614359172 fi (* i 34.0 m/PI) fm (* m 3.0) ffn (/ n 3.0)
fj (* j 56.0 m/PI) fp (/ p 8.0) fo (* o 4.0)]
(fn [^double in]
(Vec3. (+ (* fa (m/sin (* fb in)))
(* m/THIRD (m/cb (m/sin (* fc in)))
(* (m/cos (* fd in))))
(* fl (u/spow (m/sin (* fe in)) fk)))
(+ (* ff (m/cos (* fg in)))
(* m/THIRD (m/cb (m/cos (* fh in)))
(m/cos (* f1 in)))
(* ffn (u/spow (m/cos (* fi in)) fm)))
(+ 0.006666666666666667 (* fp (u/spow (m/sin (* fj in)) fo))))))
hamid-circle-15 (let [fa (* a m/TWO_THIRD) fb (* b 14.0 m/PI) fc (* c 10.0 m/PI)
fd (* d 28.0 m/PI) fe (* e 46.0 m/PI) fm (* m 3.0) ffn (/ n 3.0)
ff (* f 14.0 m/PI) fg (* g 10.0 m/PI) fh (* h 28.0 m/PI)
fj (* j 34.0 m/PI) fo (* o 3.0)
fk (* k 72.0 m/PI) fl (* l 12.0) fp (/ p 20.0)]
(fn [^double in]
(Vec3. (+ (* fa (m/sin (* fb in)))
(* m/THIRD (m/cb (m/sin (* fc in)))
(* (m/cos (* fd in))))
(* ffn (u/spow (m/sin (* fe in)) fm)))
(+ (* m/TWO_THIRD (m/cos (* ff in)))
(* m/THIRD (m/cb (m/cos (* fg in)))
(m/cos (* fh in)))
(* m/THIRD (u/spow (m/cos (* fj in)) fo)))
(+ 0.006666666666666667
(* 0.1111111111111111 (m/sq (m/cb (m/sin (* fk in)))))
(* fp (m/sq (m/sq (m/sin (* fl in)))))))))
hamid-circle-16 (let [fa (* a 38.0 m/PI) fb (* b 26.0 m/PI) fc (* c 18.0 m/PI)
fl (* l 3.0) fm (/ m 2.0) fd (* d 18.0 m/PI) fe (* e 38.0 m/PI)
ff (* f 36.0 m/PI) fg (* g 18.0 m/PI) ffn (* n 3.0) fo (/ o 4.0)
fh (* h 18.0 m/PI) fi (* i 100.0 m/PI)
fj (* j 72.0 m/PI) fk (* k 18.0 m/PI) fp (/ p 20.0)]
(fn [^double in]
(Vec3. (+ (* 0.5 (m/sin (* fa in)) (m/cos (* fb in)))
(* fm (u/spow (m/sin (* fc in)) fl)))
(+ (* m/TWO_THIRD (m/cos (* fd in)))
(* m/THIRD (m/cos (* fe in)) (m/cos (* ff in)))
(* fo (u/spow (m/cos (* fg in)) ffn)))
(+ 0.006666666666666667
(* 0.01 (u/spow (m/sin (* fh in)) 10.0)
(m/cb (m/sq (m/sin (* fi in)))))
(* fp (m/sq (m/sq (m/sq (m/sin (* fj in)))))
(m/cb (m/sq (m/cos (* fk in)))))))))
hamid-circle-17 (let [fa (* a 2.0) fb (* b 10.0 m/PI) fc (* c 6.0 m/PI)
fd (* d 28.0 m/PI) fe (* e 126.0 m/PI) fl (/ m 10.0)
ff (* f 6.0 m/PI) fg (* g 18.0 m/PI) fh (* h 36.0 m/PI)
fi (* i 126.0 m/PI) fm (/ m 10.0)
fj (* j 48.0 m/PI) fk (* k 12.0 m/PI) ffn (* 2.0 n)
fo (/ o 18.0)]
(fn [^double in]
(Vec3. (+ (* fa (m/sin (* fb in)))
(* m/THIRD (m/cb (m/sin (* fc in))) (m/cos (* fd in)))
(* fl (m/sin (* fe in))))
(+ (* m/TWO_THIRD (m/cos (* ff in)))
(* m/THIRD (m/cb (m/cos (* fg in))) (m/cos (* fh in)))
(* fm (m/cos (* fi in))))
(+ 0.006666666666666667
(* fo (m/sq (m/sq (m/sin (* fj in))))
(inc (u/spow (m/sin (* fk in)) ffn)))))))
hamid-circle-18 (let [fa (* a 0.4) fb (* b 18.0 m/PI) fc (* c 34.0 m/PI)
fj (* j 3.0) fk (/ k 3.0) fd (* d 50.0 m/PI) fl (* l 3.0)
fm (* m 3.0) fe (* e 18.0 m/PI) ff (* f 34.0 m/PI) ffn (* n 3.0)
fg (* g 50.0 m/PI) fo (/ o 10.0) fi (* i 58.0 m/PI) fp (/ p 10.0)]
(fn [^double in]
(Vec3. (+ (* fa (m/sin (* fb in)))
(* fk (u/spow (m/sin (* fc in)) fj))
(* fm (u/spow (m/sin (* fd in)) fl)))
(+ (* m/TWO_THIRD (m/cos (* fe in)))
(* m/THIRD (m/cb (m/cos (* ff in))))
(* fo (u/spow (m/cos (* fg in)) ffn)))
(+ 0.006666666666666667
(* fp (m/sq (m/sq (m/sin (* fi in)))))))))
hamid-circle-19 (let [fa (* a 10.0 m/PI) fb (* b 16.0 m/PI) fi (/ i 2.0)
fd (* d 10.0 m/PI) fe (* e 34.0 m/PI) fk (/ k 2.0)
fh (* h 2.0) fj (* j 2.0) fg (* g 52.0 m/PI)
fl (* l 4.0) fm (/ m 10.0)]
(fn [^double in]
(Vec3. (* (m/cos (* fa in)) (- c (* fi (u/spow (m/sin (* fb in)) fh))))
(* (m/sin (* fd in)) (- f (* fk (u/spow (m/cos (* fe in)) fj))))
(+ 0.005 (* fm (u/spow (m/sin (* fg in)) fl))))))]
(fn [_]
(-> (let [iin (inc (r/lrand npoints))
in (* iin npointsd)]
(case presetid
0 (hamid-pline (hamid-line-1 in))
1 (hamid-pline (hamid-line-2 in))
2 (hamid-pline (hamid-line-3 in))
3 (hamid-pline (hamid-line-4 in))
4 (hamid-pline (hamid-line-5 in))
5 (hamid-pline (hamid-line-6 in))
6 (hamid-pline (hamid-line-7 in))
7 (hamid-pline (hamid-line-8 in))
8 (hamid-pline (hamid-line-9 in))
9 (hamid-pline (hamid-line-10 iin))
10 (hamid-pcircle (hamid-circle-10 in) filled)
11 (hamid-pcircle (hamid-circle-11 in) filled)
12 (hamid-pcircle (hamid-circle-12 in) filled)
13 (hamid-pcircle (hamid-circle-13 in) filled)
14 (hamid-pcircle (hamid-circle-14 in) filled)
15 (hamid-pcircle (hamid-circle-15 in) filled)
16 (hamid-pcircle (hamid-circle-16 in) filled)
17 (hamid-pcircle (hamid-circle-17 in) filled)
18 (hamid-pcircle (hamid-circle-18 in) filled)
19 (hamid-pcircle (hamid-circle-19 in) filled)
(hamid-pline (hamid-line-3 in))))
(v/mult amount))))))
(defn handkerchief
"Handkerchief"
([] {:type :regular})
([^double amount _]
(fn [^Vec2 v]
(let [angle (v/heading v)
r (v/mag v)]
(Vec2. (* amount (* r (m/sin (+ angle r))))
(* amount (* r (m/cos (- angle r)))))))))
(defn heart
"Heart"
([] {:type :regular})
([^double amount _]
(fn [^Vec2 v]
(let [r (v/mag v)
theta (v/heading v)
rt (* r theta)
sr (m/sin rt)
cr (m/cos rt)]
(Vec2. (* amount r sr) (- (* amount r cr)))))))
(defn heartwf
([] {:type :regular
:config (fn [] (let [scale-r-left (r/drand 0.5 2.0)]
{:scale-x (u/sdrand 0.5 2.0)
:shift-t (r/drand)
:scale-r-left scale-r-left
:scale-r-right (r/randval scale-r-left (r/drand 0.5 2.0))}))})
([^double amount {:keys [^double scale-x ^double shift-t
^double scale-r-left ^double scale-r-right]}]
(fn [^Vec2 v]
(let [a (m/atan2 (.x v) (.y v))
r (v/mag v)
t (if (neg? a)
(min 60.0 (- (* -19.098593171027442 a scale-r-left) shift-t))
(min 60.0 (- (* 19.098593171027442 a scale-r-right) shift-t)))
tt (- (* 40.0 t) (* t t))
tr (m/radians t)
nx (* 0.001 (+ tt 1200.0) (m/sin tr) r)
nx (* amount scale-x (if (neg? a) (- nx) nx))
ny (* amount -0.001 (+ tt 400.0) (m/cos tr) r)]
(Vec2. nx ny)))))
(defn hemisphere
"Hemisphere"
([] {:type :regular})
([^double amount _]
(fn [^Vec2 v]
(let [r (/ amount (m/sqrt (inc (v/magsq v))))]
(Vec2. (* r (.x v))
(* r (.y v)))))))
(defn hexmodulus
([] {:type :regular
:config (fn [] {:size (u/sdrand 0.5 2.0)})})
([^double amount {:keys [^double size]}]
(let [hsize (/ m/SQRT3_2 size)
weight (/ amount m/SQRT3_2)]
(fn [^Vec2 v]
(let [^Vec2 XY (v/mult v hsize)
x (- (* m/SQRT3_3 (.x XY))
(* m/THIRD (.y XY)))
z (* m/TWO_THIRD (.y XY))
y (- (- x) z)
rx (m/round x)
ry (m/round y)
rz (m/round z)
x-diff (m/abs (- rx x))
y-diff (m/abs (- ry y))
z-diff (m/abs (- rz z))
^Vec2 r (cond
(and (> x-diff y-diff)
(> x-diff z-diff)) (Vec2. (- (- ry) rz) rz)
(> y-diff z-diff) (Vec2. rx rz)
:else (Vec2. rx (- (- rx) ry)))
fx-h (+ (* m/SQRT3 (.x r)) (* m/SQRT3_2 (.y r)))
fy-h (* 1.5 (.y r))
fx (- (.x XY) fx-h)
fy (- (.y XY) fy-h)]
(Vec2. (* fx weight) (* fy weight)))))))
(defn- hexes-cell-centre
^Vec2 [^Vec2 in ^double s]
(Vec2. (* s (+ (* 1.5 (.x in)) (* -1.5 (.y in))))
(* s m/SQRT3_2 (+ (.x in) (.y in)))))
(defn hexes
([] {:type :regular
:config (fn [] {:cellsize (u/sdrand 0.5 2.0)
:power (r/drand -2.0 2.0)
:rotate (r/drand -1.0 1.0)
:scale (u/sdrand 0.5 2.0)})})
([^double amount {:keys [^double cellsize ^double power ^double rotate ^double scale]}]
(let [a (* rotate m/TWO_PI)
sr (/ cellsize)]
(fn [^Vec2 U]
(let [x (* m/THIRD (.x U))
y (* m/SQRT3_3 (.y U))
H (Vec2. (m/floor (* sr (+ x y))) (m/floor (* sr (- y x))))
P (mapv #(hexes-cell-centre (v/add H %) cellsize) u/offsets)
q (u/closest P 9 U)
H (v/add H (u/offsets q))
P (mapv #(hexes-cell-centre (v/add H (u/offsets %)) cellsize) [4 5 8 7 3 0 1])
P0 (P 0)
L1 (u/voronoi P 7 0 U)
Do (v/sub U P0)
trgL (* scale (m/pow (+ L1 m/EPSILON) power))
V (v/rotate Do a)
L2 (u/voronoi P 7 0 (v/add V P0))
L (max L1 L2)
R (if (< L 0.5)
(/ trgL L1)
(if (> L 0.8)
(/ trgL L2)
(/ (+ (* (/ trgL L1) (- 0.8 L))
(* (/ trgL L2) (- L 0.5))) 0.3)))]
(v/mult (v/add (v/mult V R) P0) amount))))))
(defn hole2
"Hole2"
([] {:type :regular
:config (fn [] {:a (r/drand -2.0 2.0)
:b (r/drand -2.0 2.0)
:c (r/drand 3.0)
:d (r/drand -2.0 2.0)
:inside (r/brand)
:shape (r/irand 10)})})
([^double amount {:keys [^double a ^double b ^double c ^double d inside shape]}]
(fn [v]
(let [rhosq (v/magsq v)
theta (* d (v/heading v))
delta (* c (m/pow (inc (/ theta m/PI)) a))
r (case (unchecked-int shape)
1 (m/sqrt (+ rhosq delta))
2 (m/sqrt (+ rhosq (m/sin (* b theta)) delta))
3 (m/sqrt (+ rhosq (m/sin theta) delta))
4 (m/sqrt (- (inc (+ rhosq (m/sin theta))) delta))
5 (m/sqrt (+ rhosq (m/abs (m/tan theta)) delta))
6 (m/sqrt (+ rhosq (inc (m/sin (* b theta))) delta))
7 (m/sqrt (+ rhosq (m/abs (m/sin (* 0.5 b theta))) delta))
8 (m/sqrt (+ rhosq (m/sin (* m/PI (m/sin (* b theta)))) delta))
9 (m/sqrt (+ rhosq (* 0.5 (+ (m/sin (* b theta))
(m/sin (+ m/M_PI_2 (* 2.0 b theta))))) delta))
(+ delta (m/sqrt rhosq)))
r1 (if inside
(/ amount r)
(* amount r))]
(Vec2. (* r1 (m/cos theta))
(* r1 (m/sin theta)))))))
(defn hole
([] {:type :regular
:config (fn [] {:inside (r/brand)
:a (r/drand -3.0 3.0)})})
([^double amount {:keys [inside ^double a]}]
(fn [^Vec2 v]
(let [alpha (v/heading v)
delta (m/pow (inc (/ alpha m/PI)) a)
r (if inside
(* amount (/ delta (+ (v/magsq v) delta)))
(* amount (m/sqrt (+ (v/magsq v) delta))))]
(Vec2. (* r (m/cos alpha)) (* r (m/sin alpha)))))))
(defn holesq
([] {:type :regular})
([^double amount _]
(fn [^Vec2 v]
(let [^Vec2 v (v/mult v amount)
fax (m/abs (.x v))
fay (m/abs (.y v))]
(if (> (+ fax fay) 1.0)
v
(if (> fax fay)
(let [t (if (neg? (.x v))
(* 0.5 (dec (+ (.x v) fay)))
(* 0.5 (inc (- (.x v) fay))))]
(Vec2. (+ (.x v) t) (+ (.y v) (.y v))))
(let [t (if (neg? (.y v))
(* 0.5 (dec (+ (.y v) fax)))
(* 0.5 (inc (- (.y v) fax))))]
(Vec2. (+ (.x v) (.x v)) (+ (.y v) t)))))))))
(defn horseshoe
"Horseshoe"
([] {:type :regular})
([^double amount _]
(fn [^Vec2 v]
(let [r (+ m/EPSILON (v/mag v))
sina (/ (.x v) r)
cosa (/ (.y v) r)]
(Vec2. (* amount (- (* sina (.x v)) (* cosa (.y v))))
(* amount (+ (* cosa (.x v)) (* sina (.y v)))))))))
(defn hyperbolicellipse
([] {:type :regular
:config (fn [] {:a (u/sdrand 0.05 2.0)})})
([^double amount {:keys [^double a]}]
(fn [^Vec2 v]
(let [ay (* a (.y v))
ex+ (m/exp (.x v))
ex- (m/exp (- (.x v)))]
(Vec2. (* amount 0.5 (- ex+ ex-) (m/cos ay))
(* amount 0.5 (+ ex+ ex-) (m/sin ay)))))))
(defn hyperbolic
"Hyperbolic"
([] {:type :regular})
([^double amount _]
(fn [^Vec2 v]
(let [r (+ m/EPSILON (v/mag v))
theta (v/heading v)]
(Vec2. (* amount (/ (m/sin theta) r))
(* amount (m/cos theta) r))))))
(defn hypershift2
([] {:type :random
:config (fn [] {:p (r/randval (u/sirand 4 15) (u/sdrand 4.0 15.0))
:q (r/randval (u/sirand 4 15) (u/sdrand 4.0 15.0))})})
([^double amount {:keys [^double p ^double q]}]
(let [pq (/ m/PI q)
pp (/ m/PI p)
spq (m/sin pq)
spp (m/sin pp)
shift (/ (m/sin (- m/HALF_PI pq pp))
(m/sqrt (- 1.0 (* spq spq) (* spp spp))))
scale2 (* (/ (m/sqrt (dec (/ (m/sq (m/sin (+ m/HALF_PI pp))) (m/sq spq)))))
(dec (/ (m/sin (+ m/HALF_PI pp)) spq)))
scale (- 1.0 (* shift shift))]
(fn [^Vec2 v]
(let [^Vec2 F (v/mult v scale2)
rad (/ (v/magsq F))
x (+ (* rad (.x v)) shift)
y (* rad (.y v))
rad (* amount (/ scale (+ (* x x) (* y y))))
angle (* pp (inc (* 2.0 (mod (r/lrand) p))))
X (+ (* rad x) shift)
Y (* rad y)
cosa (m/cos angle)
sina (m/sin angle)]
(Vec2. (- (* cosa X) (* sina Y))
(+ (* sina X) (* cosa Y))))))))
(defn hypershift
"Hypershift"
([] {:type :regular
:config (fn [] {:shift (r/drand -2.0 2.0)
:stretch (r/drand -2.0 2.0)})})
([^double amount {:keys [^double shift ^double stretch]}]
(let [scale (- 1.0 (* shift shift))]
(fn [^Vec2 v]
(let [rad (/ (v/magsq v))
x (+ shift (* rad (.x v)))
y (* rad (.y v))
r (/ (* amount scale) (+ (* x x) (* y y)))]
(Vec2. (+ shift (* r x))
(* r y stretch)))))))
(defn hypertile1
([] {:type :random
:config (fn [] {:p (r/randval 0.9 (u/sirand 4 15) (u/sdrand 4.0 15.0))
:q (r/randval (u/sirand 4 15) (u/sdrand 4.0 15.0))})})
([^double amount {:keys [^double p ^double q]}]
(let [pa (/ m/TWO_PI p)
pq (/ m/TWO_PI q)
r2 (- 1.0 (/ (dec (m/cos pa))
(+ (m/cos pa) (m/cos pq))))
r (if (pos? r2) (/ (m/sqrt r2)) 1.0)]
(fn [^Vec2 v]
(let [rpa (* pa (r/lrand))
sina (m/sin rpa)
cosa (m/cos rpa)
re (* r cosa)
im (* r sina)
a (+ (.x v) re)
b (- (.y v) im)
c (inc (- (* re (.x v)) (* im (.y v))))
d (+ (* re (.y v)) (* im (.x v)))
vr (/ amount (+ (* c c) (* d d)))]
(Vec2. (* vr (+ (* a c) (* b d)))
(* vr (- (* b c) (* a d)))))))))
(defn hypertile2
([] {:type :random
:config (fn [] {:p (r/randval 0.9 (u/sirand 4 15) (u/sdrand 4.0 15.0))
:q (r/randval (u/sirand 4 15) (u/sdrand 4.0 15.0))})})
([^double amount {:keys [^double p ^double q]}]
(let [pa (/ m/TWO_PI p)
pq (/ m/TWO_PI q)
r2 (- 1.0 (/ (dec (m/cos pa))
(+ (m/cos pa) (m/cos pq))))
r (if (pos? r2) (/ (m/sqrt r2)) 1.0)]
(fn [^Vec2 v]
(let [a (+ (.x v) r)
b (.y v)
c (inc (* r (.x v)))
d (* r (.y v))
x (+ (* a c) (* b d))
y (- (* b c) (* a d))
vr (/ amount (+ (* c c) (* d d)))
rpa (* pa (r/lrand))
sina (m/sin rpa)
cosa (m/cos rpa)]
(Vec2. (* vr (+ (* x cosa) (* y sina)))
(* vr (- (* y cosa) (* x sina)))))))))
(defn hypertile
([] {:type :random
:config (fn [] {:p (r/randval 0.9 (u/sirand 4 8) (u/sdrand 4.0 8.0))
:q (r/randval (u/sirand 4 8) (u/sdrand 4.0 8.0))
:n (r/randval (r/irand -10 10) (r/drand -10.0 10.0))})})
([^double amount {:keys [^double p ^double q ^double n]}]
(let [pa (/ m/TWO_PI p)
pq (/ m/TWO_PI q)
r2 (inc (/ (- 1.0 (m/cos pa))
(+ (m/cos pa) (m/cos pq))))
r (if (pos? r2) (/ (m/sqrt r2)) 1.0)
a (* n pa)
re (* r (m/cos a))
im (* r (m/sin a))]
(fn [^Vec2 v]
(let [a (+ (.x v) re)
b (- (.y v) im)
c (inc (- (* re (.x v)) (* im (.y v))))
d (+ (* re (.y v)) (* im (.x v)))
vr (/ amount (+ (* c c) (* d d)))]
(Vec2. (* vr (+ (* a c) (* b d)))
(* vr (- (* b c) (* a d)))))))))