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vector.clj
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vector.clj
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;; ## n-dimentional vector utilities
;;
;; Main goal for this namespace is to provide various utility functions which operate on
;; mathematical vectors: 2d, 3d and 4d
;;
;; Concept for API is taken from [Proceessing](https://github.com/processing/processing/blob/master/core/src/processing/core/PVector.java) and [openFrameworks](https://github.com/openframeworks/openFrameworks/tree/master/libs/openFrameworks/math)
;;
;; All vectors are equipped with Counted (`count`), Sequential, Sequable (`seq`) and IFn protocols. Additionally Clojure vector is equipped with defined here `VectorProto`.
(ns fastmath.vector
"Mathematical vector operations.
### Types
* Fixed size (custom types):
* Number - 1d vector
* Vec2 - 2d vector, creator [[vec2]]
* Vec3 - 3d vector, creator [[vec3]]
* Vec4 - 4d vector, creator [[vec4]]
* ArrayVec - fixed size double array wrapper, n-dimensional, creator [[array-vec]]
* Fixed size
* doubles - double array itself
* Variable size:
* Clojure's IPersistentVector, creator `[]`
* Clojure's ISeq
[[VectorProto]] defines most of the functions.
Vectors implements also:
* `Sequable`
* `Sequencial`
* `IFn`
* `Counted`
* `Reversible`
* `Indexed`
* `ILookup`
* `equals` and `toString` from `Object`
* `IPersistentVector`
* `Associative`
* `clojure.core.matrix.protocols`
* `IReduce` and `IReduceInit`
That means that vectors can be destructured, treated as sequence or called as a function. See [[vec2]] for examples."
(:refer-clojure :exclude [abs zero?])
(:require [fastmath.core :as m]
[clojure.string :as s]
[fastmath.protocols :as prot])
(:import [clojure.lang Counted IFn ISeq IPersistentVector IPersistentCollection Seqable Sequential Reversible Indexed ILookup Associative MapEntry IReduce IReduceInit]
[clojure.core Vec]
[org.apache.commons.math3.linear ArrayRealVector RealVector]
[org.apache.commons.math3.analysis UnivariateFunction]))
(set! *unchecked-math* :warn-on-boxed)
(m/use-primitive-operators #{'abs 'zero?})
;; ## Vector definitions
(declare angle-between)
(declare normalize)
(declare div)
(defn- find-idx-reducer-fn
"Helper function for reduce to find index for maximum/minimum value in vector."
[f]
#(let [[^long midx ^long curr v] %1]
(if (f %2 v)
[curr (inc curr) %2]
[midx (inc curr) v])))
;; Add `VectorProto` to Clojure vector using map/reduce terms.
(extend ISeq
prot/VectorProto
{:to-double-array #(m/seq->double-array %)
:to-acm-vec #(ArrayRealVector. (m/seq->double-array %))
:to-vec #(apply vector-of :double %1)
:as-vec (fn
([v xs] (take (count v) xs))
([v] (prot/as-vec v (repeat 0.0))))
:fmap #(map %2 %1)
:approx (fn
([v] (map m/approx v))
([v d] (map #(m/approx ^double % d) v)))
:magsq (fn ^double [v] (reduce (fn ^double [^double b ^double x] (+ b (* x x))) 0.0 v))
:mag (fn ^double [v] (m/sqrt (prot/magsq v)))
:dot (fn ^double [v1 v2] (reduce m/fast+ (map m/fast* v1 v2)))
:add (fn [v1 v2] (map m/fast+ v1 v2))
:sub (fn [v1 v2] (map m/fast- v1 v2))
:shift (fn [v1 ^double v] (map #(m/fast+ ^double % v) v1))
:mult (fn [v1 ^double v] (map #(m/fast* ^double % v) v1))
:emult #(map m/fast* %1 %2)
:abs #(map m/abs %)
:mx #(reduce m/fast-max %)
:mn #(reduce m/fast-min %)
:emx #(mapv m/fast-max %1 %2)
:emn #(mapv m/fast-min %1 %2)
:maxdim (fn ^long [v] (first (reduce (find-idx-reducer-fn clojure.core/>) [0 0 (first v)] v)))
:mindim (fn ^long [v] (first (reduce (find-idx-reducer-fn clojure.core/<) [0 0 (first v)] v)))
:sum (fn ^double [v] (reduce m/fast+ v))
:prod (fn ^double [v] (reduce m/fast* v))
:permute #(map (fn [idx] (%1 idx)) %2)
:reciprocal #(map (fn [^double v] (/ v)) %)
:heading (fn ^double [v] (angle-between v (reduce conj [1.0] (repeatedly (dec (count v)) (constantly 0.0)))))
:interpolate (fn [v1 v2 t f] (map #(f %1 %2 t) v1 v2))
:einterpolate (fn [v1 v2 v f] (map #(f %1 %2 %3) v1 v2 v))
:econstrain (fn [v val1 val2] (map #(m/constrain ^double %1 ^double val1 ^double val2) v))
:is-zero? #(every? clojure.core/zero? %)})
;; Add `VectorProto` to Clojure vector using mapv/reduce terms.
(extend IPersistentVector
prot/VectorProto
{:to-double-array #(m/seq->double-array %)
:to-acm-vec #(ArrayRealVector. (m/seq->double-array %))
:to-vec #(apply vector-of :double %1)
:as-vec (fn
([v xs] (vec (take (count v) xs)))
([v] (prot/as-vec v (repeat 0.0))))
:fmap #(mapv %2 %1)
:approx (fn
([v] (mapv m/approx v))
([v d] (mapv #(m/approx ^double % d) v)))
:magsq (fn ^double [v] (reduce (fn ^double [^double b ^double x] (+ b (* x x))) 0.0 v))
:mag (fn ^double [v] (m/sqrt (prot/magsq v)))
:dot (fn ^double [v1 v2] (reduce m/fast+ (map m/fast* v1 v2)))
:add (fn [v1 v2] (mapv m/fast+ v1 v2))
:sub (fn [v1 v2] (mapv m/fast- v1 v2))
:shift (fn [v1 ^double v] (mapv #(m/fast+ ^double % v) v1))
:mult (fn [v1 ^double v] (mapv #(m/fast* ^double % v) v1))
:emult #(mapv m/fast* %1 %2)
:abs #(mapv m/abs %)
:mx #(reduce m/fast-max %)
:mn #(reduce m/fast-min %)
:emx #(mapv m/fast-max %1 %2)
:emn #(mapv m/fast-min %1 %2)
:maxdim (fn ^long [v] (first (reduce (find-idx-reducer-fn clojure.core/>) [0 0 (first v)] v)))
:mindim (fn ^long [v] (first (reduce (find-idx-reducer-fn clojure.core/<) [0 0 (first v)] v)))
:sum (fn ^double [v] (reduce m/fast+ v))
:prod (fn ^double [v] (reduce m/fast* v))
:permute #(mapv (fn [idx] (%1 idx)) %2)
:reciprocal #(mapv (fn [^double v] (/ v)) %)
:heading #(angle-between % (reduce conj [1.0] (repeatedly (dec (count %)) (constantly 0.0))))
:interpolate (fn [v1 v2 t f] (mapv #(f %1 %2 t) v1 v2))
:einterpolate (fn [v1 v2 v f] (mapv #(f %1 %2 %3) v1 v2 v))
:econstrain (fn [v val1 val2] (mapv #(m/constrain ^double %1 ^double val1 ^double val2) v))
:is-zero? #(every? clojure.core/zero? %)})
(extend ArrayRealVector
prot/VectorProto
{:to-double-array (fn [this] (.getDataRef ^ArrayRealVector this))
:to-acm-vec (fn [this] this)
:to-vec #(apply vector-of :double (.getDataRef ^ArrayRealVector %))
:as-vec (fn
([^ArrayRealVector v xs] (ArrayRealVector. (double-array (take (.getDimension v) xs))))
([v] (prot/as-vec v (repeat 0.0))))
:fmap (fn [^ArrayRealVector v f] (.map v (reify UnivariateFunction
(value [_ v] (f v)))))
:approx (fn
([v] (prot/fmap v m/approx))
([^ArrayRealVector v ^long d] (.map v (reify UnivariateFunction
(value [_ v] (m/approx v d))))))
:magsq (fn [^ArrayRealVector v] (.dotProduct v v))
:mag (fn [^ArrayRealVector v] (.getNorm v))
:dot (fn [^ArrayRealVector v1 ^ArrayRealVector v2] (.dotProduct v1 v2))
:add (fn [^ArrayRealVector v1 ^ArrayRealVector v2] (.add v1 v2))
:sub (fn [^ArrayRealVector v1 ^ArrayRealVector v2] (.subtract v1 v2))
:shift (fn [^ArrayRealVector v1 ^double v2] (.mapAddToSelf (.copy v1) v2))
:mult (fn [^ArrayRealVector v1 ^double v2] (.mapMultiplyToSelf (.copy v1) v2))
:emult (fn [^ArrayRealVector v1 ^ArrayRealVector v2] (.ebeMultiply v1 v2))
:abs (fn [v] (prot/fmap v m/abs))
:mx (fn [^ArrayRealVector v1] (.getMaxValue v1))
:mn (fn [^ArrayRealVector v1] (.getMinValue v1))
:emx (fn [^ArrayRealVector v1 ^ArrayRealVector v2] (ArrayRealVector. ^doubles (prot/emx (.getDataRef v1)
(.getDataRef v2))))
:emn (fn [^ArrayRealVector v1 ^ArrayRealVector v2] (ArrayRealVector. ^doubles (prot/emn (.getDataRef v1)
(.getDataRef v2))))
:maxdim (fn [^ArrayRealVector v1] (.getMaxIndex v1))
:mindim (fn [^ArrayRealVector v1] (.getMinIndex v1))
:sum (fn [^ArrayRealVector v1] (prot/sum (.getDataRef v1)))
:prod (fn [^ArrayRealVector v1] (prot/prod (.getDataRef v1)))
:heading (fn [^ArrayRealVector v1] (prot/heading (.getDataRef v1)))
:reciprocal (fn [v1] (prot/fmap v1 #(/ ^double %)))
:interpolate (fn [^ArrayRealVector v1 ^ArrayRealVector v2 t f]
(ArrayRealVector. ^doubles (prot/interpolate (.getDataRef v1) (.getDataRef v2) t f)))
:einterpolate (fn [^ArrayRealVector v1 ^ArrayRealVector v2 ^ArrayRealVector t f]
(ArrayRealVector. ^doubles (prot/einterpolate (.getDataRef v1)
(.getDataRef v2)
(.getDataRef t) f)))
:econstrain (fn [^ArrayRealVector v ^double v1 ^double v2]
(ArrayRealVector. v ^doubles (prot/econstrain (.getDataRef v) v1 v2)))
:is-zero? (fn [^ArrayRealVector v] (prot/is-zero? (.getDataRef v)))})
(defn- aevery
"Array version of every"
[^doubles arr pred]
(let [s (alength arr)]
(loop [idx (unchecked-long 0)]
(if (< idx s)
(if (pred (aget arr idx))
(recur (inc idx))
false)
true))))
(extend (Class/forName "[D")
prot/VectorProto
{:to-double-array identity
:to-acm-vec (fn [arr] (ArrayRealVector. ^doubles arr))
:to-vec (fn [arr] (let [^Vec v (vector-of :double)]
(Vec. (.am v) (alength ^doubles arr) (.shift v) (.root v) arr (.meta v))))
:as-vec (fn ([v xs] (double-array (take (alength ^doubles v) xs)))
([v] (prot/as-vec v (repeat 0.0))))
:fmap (fn [arr f] (amap ^doubles arr idx _ret ^double (f (aget ^doubles arr idx))))
:approx (fn ([arr] (amap ^doubles arr idx _ret ^double (m/approx (aget ^doubles arr idx))))
([arr d] (amap ^doubles arr idx _ret ^double (m/approx (aget ^doubles arr idx) d))))
:magsq (fn [arr] (smile.math.MathEx/dot ^doubles arr ^doubles arr))
:mag (fn [v1] (m/sqrt (prot/magsq v1)))
:dot (fn [arr v2] (smile.math.MathEx/dot ^doubles arr ^doubles v2))
:add (fn [arr v2] (let [b (aclone ^doubles arr)]
(smile.math.MathEx/add b ^doubles v2)
b))
:sub (fn [arr v2] (let [b (aclone ^doubles arr)]
(smile.math.MathEx/sub b ^doubles v2)
b))
:shift (fn [arr v] (amap ^doubles arr idx _ret (+ (aget ^doubles arr idx) ^double v)))
:mult (fn [arr v] (let [b (aclone ^doubles arr)]
(smile.math.MathEx/scale ^double v ^doubles b)
b))
:emult (fn [arr v2] (amap ^doubles arr idx _ret (* (aget ^doubles arr idx) (aget ^doubles v2 idx))))
:abs (fn [arr] (amap ^doubles arr idx _ret (m/abs (aget ^doubles arr idx))))
:mx (fn [arr] (smile.math.MathEx/max ^doubles arr))
:mn (fn [arr] (smile.math.MathEx/min ^doubles arr))
:maxdim (fn [arr] (smile.math.MathEx/whichMax ^doubles arr))
:mindim (fn [arr] (smile.math.MathEx/whichMin ^doubles arr))
:emx (fn [arr v2] (amap ^doubles arr idx _ret (max (aget ^doubles arr idx) (aget ^doubles v2 idx))))
:emn (fn [arr v2] (amap ^doubles arr idx _ret (min (aget ^doubles arr idx) (aget ^doubles v2 idx))))
:sum (fn [arr] (smile.math.MathEx/sum ^doubles arr))
:prod (fn [arr] (areduce ^doubles arr idx ret 1.0 (* ret (aget ^doubles arr idx))))
:heading (fn [arr] (let [v (double-array (alength ^doubles arr) 0.0)]
(aset v 0 1.0)
(angle-between arr v)))
:reciprocal (fn [arr] (amap ^doubles arr idx _ret (/ (aget ^doubles arr idx))))
:interpolate (fn [arr v2 t f] (amap ^doubles arr idx _ret ^double (f (aget ^doubles arr idx) (aget ^doubles v2 idx) t)))
:einterpolate (fn [arr v2 v f] (amap ^doubles arr idx _ret ^double (f (aget ^doubles arr idx) (aget ^doubles v2 idx) (aget ^doubles v idx))))
:econstrain (fn [arr val1 val2] (amap ^doubles arr idx _ret ^double (m/constrain ^double (aget ^doubles arr idx) ^double val1 ^double val2)))
:is-zero? (fn [arr] (aevery arr #(m/zero? ^double %)))})
(defn- vec-id-check
[^long len id]
(and (number? id) (< (unchecked-int id) len)))
(defn- assert-number
[n]
(when-not (number? n) (throw (IllegalArgumentException. "Key must be a number"))))
;; Array Vector
(deftype ArrayVec [^doubles array]
Object
(toString [_] (str "#arrayvec " (if (> (alength array) 10)
(str "[" (s/join " " (take 10 array)) "...]")
(vec array))))
(equals [_ v]
(and (instance? ArrayVec v)
(smile.math.MathEx/equals array ^doubles (.array ^ArrayVec v) m/MACHINE-EPSILON)))
(hashCode [_]
(mix-collection-hash (java.util.Arrays/hashCode array) (alength array)))
clojure.lang.IHashEq
(hasheq [_]
(mix-collection-hash (java.util.Arrays/hashCode array) (alength array)))
Sequential
Seqable
(seq [_] (seq array))
Reversible
(rseq [_] (reverse array))
Indexed
(nth [_ id] (aget array (unchecked-int id)))
(nth [_ id not-found]
(let [id (unchecked-int id)]
(if (< id (alength array)) (aget array id) not-found)))
ILookup
(valAt [_ id] (when (vec-id-check (alength array) id) (aget array (unchecked-int id))))
(valAt [_ id not-found] (if (vec-id-check (alength array) id) (aget array (unchecked-int id)) not-found))
IReduce
(reduce [_ f] (reduce f array))
IReduceInit
(reduce [_ f start] (reduce f start array))
Associative
(containsKey [_ id] (vec-id-check (alength array) id))
(assoc [v k vl]
(assert-number k)
(let [^ArrayVec v v
arr (aclone ^doubles (.array v))]
(aset arr (unchecked-int k) ^double vl)
(ArrayVec. arr)))
(entryAt [v k] (MapEntry. k (v k)))
IFn
(invoke [_ n]
(assert-number n)
(aget array (unchecked-int n)))
Counted
(count [_] (alength array))
IPersistentVector
(length [_] (alength array))
IPersistentCollection
(equiv [v1 v2] (.equals v1 v2))
prot/VectorProto
(to-double-array [_] array)
(to-acm-vec [_] (ArrayRealVector. array))
(to-vec [_] (let [^Vec v (vector-of :double)]
(Vec. (.am v) (alength array) (.shift v) (.root v) array (.meta v))))
(as-vec [_ xs] (ArrayVec. (prot/as-vec array xs)))
(as-vec [v] (prot/as-vec v (repeat 0.0)))
(fmap [_ f] (ArrayVec. (prot/fmap array f)))
(approx [_] (ArrayVec. (prot/approx array)))
(approx [_ d] (ArrayVec. (prot/approx array d)))
(magsq [_] (smile.math.MathEx/dot array array))
(mag [v1] (m/sqrt (prot/magsq v1)))
(dot [_ v2] (smile.math.MathEx/dot array ^doubles (.array ^ArrayVec v2)))
(add [_ v2] (ArrayVec. (prot/add array (.array ^ArrayVec v2))))
(sub [_ v2] (ArrayVec. (prot/sub array (.array ^ArrayVec v2))))
(shift [_ v] (ArrayVec. (prot/shift array v)))
(mult [_ v] (ArrayVec. (prot/mult array v)))
(emult [_ v2] (ArrayVec. (prot/emult array (.array ^ArrayVec v2))))
(abs [_] (ArrayVec. (prot/abs array)))
(mx [_] (smile.math.MathEx/max array))
(mn [_] (smile.math.MathEx/min array))
(maxdim [_] (smile.math.MathEx/whichMax array))
(mindim [_] (smile.math.MathEx/whichMin array))
(emx [_ v2] (ArrayVec. (prot/emx array (.array ^ArrayVec v2))))
(emn [_ v2] (ArrayVec. (prot/emn array (.array ^ArrayVec v2))))
(sum [_] (smile.math.MathEx/sum array))
(prod [_] (areduce array idx ret 1.0 (* ret (aget array idx))))
(heading [_] (prot/heading array))
(reciprocal [_] (ArrayVec. (prot/reciprocal array)))
(interpolate [_ v2 t f] (ArrayVec. (prot/interpolate array (.array ^ArrayVec v2) t f)))
(einterpolate [_ v2 v f] (ArrayVec. (prot/einterpolate array (.array ^ArrayVec v2) (.array ^ArrayVec v) f)))
(econstrain [_ val1 val2] (ArrayVec. (prot/econstrain array val1 val2)))
(is-zero? [_] (aevery array #(m/zero? ^double %))))
(extend-type Number
prot/VectorProto
(to-double-array [v] (double-array [v]))
(to-acm-vec [v] (ArrayRealVector. 1 (double v)))
(to-vec [v] (vector-of :double (double v)))
(as-vec
([_] 0.0)
([_ xs] (double (first xs))))
(fmap [v f] (f v))
(approx
([v] (m/approx v))
([v d] (m/approx v d)))
(magsq [v] (m/abs v))
(mag [v] (m/sq v))
(dot [v1 v2] (* (double v1) (double v2)))
(add [v1 v2] (+ (double v1) (double v2)))
(sub [v1 v2] (- (double v1) (double v2)))
(shift [v1 v2] (+ (double v1) (double v2)))
(mult [v1 ^double v] (* (double v1) v))
(emult [v1 v2] (* (double v1) (double v2)))
(abs [v] (m/abs v))
(mx [v] v)
(mn [v] v)
(emx [v1 v2] (max (double v1) (double v2)))
(emn [v1 v2] (max (double v1) (double v2)))
(maxdim [_] 0)
(mindim [_] 0)
(sum [v] v)
(prod [v] v)
(reciprocal [v] (/ (double v)))
(interpolate [v1 v2 t f] (f v1 v2 t))
(einterpolate [v1 v2 t f] (f v1 v2 t))
(econstrain [v val1 val2] (m/constrain (double v) (double val1) (double val2)))
(is-zero? [v] (m/zero? (double v))))
(defn dhash-code
"double hashcode"
(^long [^long state ^double a]
(let [abits (Double/doubleToLongBits a)
elt (bit-xor abits (m/>>> abits 32))]
(+ elt (* 31 state))))
(^long [^double a]
(let [abits (Double/doubleToLongBits a)
elt (bit-xor abits (m/>>> abits 32))]
(+ elt 31))))
(defn- vec-throw-ioobe
[^long id len]
(throw (IndexOutOfBoundsException. (str "Index " id " out of bounds for length " len))))
;; Create Vec2 and add all necessary protocols
(deftype Vec2 [^double x ^double y]
Object
(toString [_] (str "#vec2 [" x ", " y "]"))
(equals [_ v]
(and (instance? Vec2 v)
(let [^Vec2 v v]
(and (== x (.x v))
(== y (.y v))))))
(hashCode [_] (mix-collection-hash (unchecked-int (dhash-code (dhash-code x) y)) 2))
clojure.lang.IHashEq
(hasheq [_] (mix-collection-hash (unchecked-int (dhash-code (dhash-code x) y)) 2))
Sequential
Seqable
(seq [_] (list x y))
Reversible
(rseq [_] (list y x))
Indexed
(nth [_ id] (case (unchecked-int id) 0 x 1 y (vec-throw-ioobe id 2)))
(nth [_ id not-found] (case (unchecked-int id) 0 x 1 y not-found))
ILookup
(valAt [_ id] (when (vec-id-check 2 id) (case (unchecked-int id) 0 x 1 y)))
(valAt [_ id not-found] (if (number? id) (case (unchecked-int id) 0 x 1 y not-found) not-found))
Associative
(containsKey [_ id] (boolean (#{0 1} id)))
(assoc [_ k vl]
(assert-number k)
(case (unchecked-int k)
0 (Vec2. vl y)
1 (Vec2. x vl)
(vec-throw-ioobe k 2)))
(entryAt [v k] (MapEntry. k (v k)))
Counted
(count [_] 2)
IFn
(invoke [_ id]
(assert-number id)
(case (unchecked-int id)
0 x
1 y
(vec-throw-ioobe id 2)))
IReduce
(reduce [_ f] (f x y))
IReduceInit
(reduce [_ f start] (f (f start x) y))
IPersistentVector
(length [_] 2)
IPersistentCollection
(equiv [v1 v2] (.equals v1 v2))
prot/VectorProto
(to-double-array [_] (double-array [x y]))
(to-acm-vec [_] (ArrayRealVector. (double-array [x y])))
(to-vec [_] (vector-of :double x y))
(as-vec [_ [x y]] (Vec2. x y))
(as-vec [_] (Vec2. 0.0 0.0))
(fmap [_ f] (Vec2. (f x) (f y)))
(approx [_] (Vec2. (m/approx x) (m/approx y)))
(approx [_ d] (Vec2. (m/approx x d) (m/approx y d)))
(magsq [_] (+ (* x x) (* y y)))
(mag [_] (m/hypot-sqrt x y))
(dot [_ v2]
(let [^Vec2 v2 v2] (+ (* x (.x v2)) (* y (.y v2)))))
(add [_ v2]
(let [^Vec2 v2 v2] (Vec2. (+ x (.x v2)) (+ y (.y v2)))))
(sub [_ v2]
(let [^Vec2 v2 v2] (Vec2. (- x (.x v2)) (- y (.y v2)))))
(shift [_ v] (Vec2. (+ x ^double v) (+ y ^double v)))
(mult [_ v] (Vec2. (* x ^double v) (* y ^double v)))
(emult [_ v]
(let [^Vec2 v v] (Vec2. (* x (.x v)) (* y (.y v)))))
(abs [_] (Vec2. (m/abs x) (m/abs y)))
(mx [_] (max x y))
(mn [_] (min x y))
(emx [_ v]
(let [^Vec2 v v] (Vec2. (max (.x v) x) (max (.y v) y))))
(emn [_ v]
(let [^Vec2 v v] (Vec2. (min (.x v) x) (min (.y v) y))))
(maxdim [_]
(if (> x y) 0 1))
(mindim [_]
(if (< x y) 0 1))
(base-from [v]
[v (prot/perpendicular v)])
(sum [_] (+ x y))
(prod [_] (* x y))
(permute [p [^long i1 ^long i2]]
(Vec2. (p i1) (p i2)))
(reciprocal [_] (Vec2. (/ x) (/ y)))
(interpolate [_ v2 t f]
(let [^Vec2 v2 v2] (Vec2. (f x (.x v2) t)
(f y (.y v2) t))))
(einterpolate [_ v2 v f]
(let [^Vec2 v2 v2
^Vec2 v v]
(Vec2. (f x (.x v2) (.x v))
(f y (.y v2) (.y v)))))
(econstrain [_ val1 val2] (Vec2. (m/constrain x ^double val1 ^double val2)
(m/constrain y ^double val1 ^double val2)))
(is-zero? [_] (and (m/zero? x) (m/zero? y)))
(heading [_] (m/atan2 y x))
(cross [_ v]
(let [^Vec2 v v]
(- (* x (.y v)) (* y (.x v)))))
(rotate [_ angle]
(let [sa (m/sin angle)
ca (m/cos angle)
nx (- (* x ca) (* y sa))
ny (+ (* x sa) (* y ca))]
(Vec2. nx ny)))
(perpendicular [_]
(normalize (Vec2. (- y) x)))
(transform [_ o vx vy]
(let [^Vec2 o o
^Vec2 vx vx
^Vec2 vy vy]
(Vec2. (+ (.x o) (* x (.x vx)) (* y (.x vy))) (+ (.y o) (* x (.y vx)) (* y (.y vy))))))
(to-polar [v]
(Vec2. (prot/mag v) (prot/heading v)))
(from-polar [_]
(Vec2. (* x (m/cos y))
(* x (m/sin y)))))
;; Create Vec3 and add all necessary protocols
(deftype Vec3 [^double x ^double y ^double z]
Object
(toString [_] (str "#vec3 [" x ", " y ", " z "]"))
(equals [_ v]
(and (instance? Vec3 v)
(let [^Vec3 v v]
(and (== x (.x v))
(== y (.y v))
(== z (.z v))))))
(hashCode [_] (mix-collection-hash (unchecked-int (dhash-code (dhash-code (dhash-code x) y) z)) 3))
clojure.lang.IHashEq
(hasheq [_] (mix-collection-hash (unchecked-int (dhash-code (dhash-code (dhash-code x) y) z)) 3))
Sequential
Seqable
(seq [_] (list x y z))
Reversible
(rseq [_] (list z y x))
Indexed
(nth [_ id] (case (unchecked-int id) 0 x 1 y 2 z (vec-throw-ioobe id 3)))
(nth [_ id not-found] (case (unchecked-int id) 0 x 1 y 2 z not-found))
ILookup
(valAt [_ id] (when (vec-id-check 3 id) (case (unchecked-int id) 0 x 1 y 2 z)))
(valAt [_ id not-found] (if (number? id) (case (unchecked-int id) 0 x 1 y 2 z not-found) not-found))
Associative
(containsKey [_ id] (boolean (#{0 1 2} id)))
(assoc [_ k vl]
(assert-number k)
(case (unchecked-int k)
0 (Vec3. vl y z)
1 (Vec3. x vl z)
2 (Vec3. x y vl)
(vec-throw-ioobe k 2)))
(entryAt [v k] (MapEntry. k (v k)))
Counted
(count [_] 3)
IFn
(invoke [_ id]
(assert-number id)
(case (unchecked-int id)
0 x
1 y
2 z
(vec-throw-ioobe id 2)))
IReduce
(reduce [_ f] (f (f x y) z))
IReduceInit
(reduce [_ f start] (f (f (f start x) y) z))
IPersistentVector
(length [_] 3)
IPersistentCollection
(equiv [v1 v2] (.equals v1 v2))
prot/VectorProto
(to-double-array [_] (double-array [x y z]))
(to-acm-vec [_] (ArrayRealVector. (double-array [x y z])))
(to-vec [_] (vector-of :double x y z))
(as-vec [_ [x y z]] (Vec3. x y z))
(as-vec [_] (Vec3. 0.0 0.0 0.0))
(fmap [_ f] (Vec3. (f x) (f y) (f z)))
(approx [_] (Vec3. (m/approx x) (m/approx y) (m/approx z)))
(approx [_ d] (Vec3. (m/approx x d) (m/approx y d) (m/approx z d)))
(magsq [_] (+ (* x x) (* y y) (* z z)))
(mag [_] (m/hypot-sqrt x y z))
(dot [_ v2]
(let [^Vec3 v2 v2] (+ (* x (.x v2)) (* y (.y v2)) (* z (.z v2)))))
(add [_ v2]
(let [^Vec3 v2 v2] (Vec3. (+ x (.x v2)) (+ y (.y v2)) (+ z (.z v2)))))
(sub [_ v2]
(let [^Vec3 v2 v2] (Vec3. (- x (.x v2)) (- y (.y v2)) (- z (.z v2)))))
(shift [_ v] (Vec3. (+ x ^double v) (+ y ^double v) (+ z ^double v)))
(mult [_ v] (Vec3. (* x ^double v) (* y ^double v) (* z ^double v)))
(emult [_ v]
(let [^Vec3 v v] (Vec3. (* x (.x v)) (* y (.y v)) (* z (.z v)))))
(abs [_] (Vec3. (m/abs x) (m/abs y) (m/abs z)))
(mx [_] (max x y z))
(mn [_] (min x y z))
(emx [_ v]
(let [^Vec3 v v] (Vec3. (max (.x v) x) (max (.y v) y) (max (.z v) z))))
(emn [_ v]
(let [^Vec3 v v] (Vec3. (min (.x v) x) (min (.y v) y) (min (.z v) z))))
(maxdim [_]
(if (> x y)
(if (> x z) 0 2)
(if (> y z) 1 2)))
(mindim [_]
(if (< x y)
(if (< x z) 0 2)
(if (< y z) 1 2)))
(base-from [v]
(let [v2 (if (> (m/abs x) (m/abs y))
(div (Vec3. (- z) 0.0 x) (m/hypot-sqrt x z))
(div (Vec3. 0.0 z (- y)) (m/hypot-sqrt y z)))]
[v v2 (prot/cross v v2)]))
(sum [_] (+ x y z))
(prod [_] (* x y z))
(permute [p [^long i1 ^long i2 ^long i3]]
(Vec3. (p i1) (p i2) (p i3)))
(reciprocal [_] (Vec3. (/ x) (/ y) (/ z)))
(interpolate [_ v2 t f]
(let [^Vec3 v2 v2] (Vec3. (f x (.x v2) t)
(f y (.y v2) t)
(f z (.z v2) t))))
(einterpolate [_ v2 v f]
(let [^Vec3 v2 v2
^Vec3 v v]
(Vec3. (f x (.x v2) (.x v))
(f y (.y v2) (.y v))
(f z (.z v2) (.z v)))))
(econstrain [_ val1 val2] (Vec3. (m/constrain x ^double val1 ^double val2)
(m/constrain y ^double val1 ^double val2)
(m/constrain z ^double val1 ^double val2)))
(is-zero? [_] (and (m/zero? x) (m/zero? y) (m/zero? z)))
(heading [v1] (angle-between v1 (Vec3. 1 0 0)))
(cross [_ v2]
(let [^Vec3 v2 v2
cx (- (* y (.z v2)) (* (.y v2) z))
cy (- (* z (.x v2)) (* (.z v2) x))
cz (- (* x (.y v2)) (* (.x v2) y))]
(Vec3. cx cy cz)))
(perpendicular [v1 v2] (normalize (prot/cross v1 v2)))
(transform [_ o vx vy vz]
(let [^Vec3 o o
^Vec3 vx vx
^Vec3 vy vy
^Vec3 vz vz]
(Vec3. (+ (.x o) (* x (.x vx)) (* y (.x vy)) (* z (.x vz)))
(+ (.y o) (* x (.y vx)) (* y (.y vy)) (* z (.y vz)))
(+ (.z o) (* x (.z vx)) (* y (.z vy)) (* z (.z vz))))))
(axis-rotate [_ angle axis]
(let [^Vec3 axis axis
^Vec3 ax (normalize axis)
axx (.x ax)
axy (.y ax)
axz (.z ax)
cosa (m/cos angle)
^Vec3 sa (prot/mult ax (m/sin angle))
sax (.x sa)
say (.y sa)
saz (.z sa)
^Vec3 cb (prot/mult ax (- 1.0 cosa))
cbx (.x cb)
cby (.y cb)
cbz (.z cb)
nx (+ (* x (+ (* axx cbx) cosa))
(* y (- (* axx cby) saz))
(* z (+ (* axx cbz) say)))
ny (+ (* x (+ (* axy cbx) saz))
(* y (+ (* axy cby) cosa))
(* z (- (* axy cbz) sax)))
nz (+ (* x (- (* axz cbx) say))
(* y (+ (* axz cby) sax))
(* z (+ (* axz cbz) cosa)))]
(Vec3. nx ny nz)))
(axis-rotate [v1 angle axis pivot]
(prot/add (prot/axis-rotate (prot/sub v1 pivot) angle axis) pivot))
(rotate [_ anglex angley anglez]
(let [a (m/cos anglex)
b (m/sin anglex)
c (m/cos angley)
d (m/sin angley)
e (m/cos anglez)
f (m/sin anglez)
cex (* c e x)
cfy (* c f y)
dz (* d z)
nx (+ (- cex cfy) dz)
af (* a f)
de (* d e)
bde (* b de)
ae (* a e)
bdf (* b d f)
bcz (* b c z)
ny (- (+ (* (+ af bde) x) (* (- ae bdf) y)) bcz)
bf (* b f)
ade (* a de)
adf (* a d f)
be (* b e)
acz (* a c z)
nz (+ (* (- bf ade) x) (* (+ adf be) y) acz)]
(Vec3. nx ny nz)))
(to-polar [v1]
(let [^double r (prot/mag v1)
zr (/ z r)
theta (cond
(<= zr -1.0) m/PI
(>= zr 1.0) 0
:else (m/acos zr))
phi (m/atan2 y x)]
(Vec3. r theta phi)))
(from-polar [_]
(let [st (m/sin y)
ct (m/cos y)
sp (m/sin z)
cp (m/cos z)]
(Vec3. (* x st cp)
(* x st sp)
(* x ct)))))
;; Create Vec4 and add all necessary protocols
(deftype Vec4 [^double x ^double y ^double z ^double w]
Object
(toString [_] (str "#vec4 [" x ", " y ", " z ", " w "]"))
(equals [_ v]
(and (instance? Vec4 v)
(let [^Vec4 v v]
(and (== x (.x v))
(== y (.y v))
(== z (.z v))
(== w (.w v))))))
(hashCode [_]
(mix-collection-hash (unchecked-int (dhash-code (dhash-code (dhash-code (dhash-code x) y) z) w)) 4))
clojure.lang.IHashEq
(hasheq [_]
(mix-collection-hash (unchecked-int (dhash-code (dhash-code (dhash-code (dhash-code x) y) z) w)) 4))
Sequential
Seqable
(seq [_] (list x y z w))
Reversible
(rseq [_] (list w z y x))
Indexed
(nth [_ id] (case (unchecked-int id) 0 x 1 y 2 z 3 w (vec-throw-ioobe id 4)))
(nth [_ id not-found] (case (unchecked-int id) 0 x 1 y 2 z 3 w not-found))
ILookup
(valAt [_ id] (when (vec-id-check 4 id) (case (unchecked-int id) 0 x 1 y 2 z 3 w)))
(valAt [_ id not-found] (if (number? id) (case (unchecked-int id) 0 x 1 y 2 z 3 w not-found) not-found))
Associative
(containsKey [_ id] (boolean (#{0 1 2 3} id)))
(assoc [_ k vl]
(assert-number k)
(case (unchecked-int k)
0 (Vec4. vl y z w)
1 (Vec4. x vl z w)
2 (Vec4. x y vl w)
3 (Vec4. x y z vl)
(vec-throw-ioobe k 2)))
(entryAt [v k] (MapEntry. k (v k)))
Counted
(count [_] 4)
IFn
(invoke [_ id]
(assert-number id)
(case (unchecked-int id)
0 x
1 y
2 z
3 w
(vec-throw-ioobe id 2)))
IReduce
(reduce [_ f] (f (f (f x y) z) w))
IReduceInit
(reduce [_ f start] (f (f (f (f start x) y) z) w))
IPersistentVector
(length [_] 4)
IPersistentCollection
(equiv [v1 v2] (.equals v1 v2))
prot/VectorProto
(to-double-array [_] (double-array [x y z w]))
(to-acm-vec [_] (ArrayRealVector. (double-array [x y z w])))
(to-vec [_] (vector-of :double x y z w))
(as-vec [_ [x y z w]] (Vec4. x y z w))
(as-vec [_] (Vec4. 0.0 0.0 0.0 0.0))
(fmap [_ f] (Vec4. (f x) (f y) (f z) (f w)))
(approx [_] (Vec4. (m/approx x) (m/approx y) (m/approx z) (m/approx w)))
(approx [_ d] (Vec4. (m/approx x d) (m/approx y d) (m/approx z d) (m/approx w d)))
(magsq [_] (+ (* x x) (* y y) (* z z) (* w w)))
(mag [v1] (m/sqrt (prot/magsq v1)))
(dot [_ v2]
(let [^Vec4 v2 v2] (+ (* x (.x v2)) (* y (.y v2)) (* z (.z v2)) (* w (.w v2)))))
(add [_ v2]
(let [^Vec4 v2 v2] (Vec4. (+ x (.x v2)) (+ y (.y v2)) (+ z (.z v2)) (+ w (.w v2)))))
(sub [_ v2]
(let [^Vec4 v2 v2] (Vec4. (- x (.x v2)) (- y (.y v2)) (- z (.z v2)) (- w (.w v2)))))
(shift [_ v] (Vec4. (+ x ^double v) (+ y ^double v) (+ z ^double v) (+ w ^double v)))
(mult [_ v] (Vec4. (* x ^double v) (* y ^double v) (* z ^double v) (* w ^double v)))
(emult [_ v]
(let [^Vec4 v v] (Vec4. (* x (.x v)) (* y (.y v)) (* z (.z v)) (* w (.w v)))))
(abs [_] (Vec4. (m/abs x) (m/abs y) (m/abs z) (m/abs w)))
(mx [_] (max x y z w))
(mn [_] (min x y z w))
(emx [_ v]
(let [^Vec4 v v] (Vec4. (max (.x v) x) (max (.y v) y) (max (.z v) z) (max (.w v) w))))
(emn [_ v]
(let [^Vec4 v v] (Vec4. (min (.x v) x) (min (.y v) y) (min (.z v) z) (min (.w v) w))))
(maxdim [_]
(max-key [x y z w] 0 1 2 3))
(mindim [_]
(min-key [x y z w] 0 1 2 3))
(sum [_] (+ x y z w))
(prod [_] (* x y z w))
(permute [p [^long i1 ^long i2 ^long i3 ^long i4]]
(Vec4. (p i1) (p i2) (p i3) (p i4)))
(reciprocal [_] (Vec4. (/ x) (/ y) (/ z) (/ w)))
(interpolate [_ v2 t f]
(let [^Vec4 v2 v2] (Vec4. (f x (.x v2) t)
(f y (.y v2) t)
(f z (.z v2) t)
(f w (.w v2) t))))
(einterpolate [_ v2 v f]
(let [^Vec4 v2 v2
^Vec4 v v]
(Vec4. (f x (.x v2) (.x v))
(f y (.y v2) (.y v))
(f z (.z v2) (.z v))
(f w (.w v2) (.w v)))))
(econstrain [_ val1 val2] (Vec4. (m/constrain x ^double val1 ^double val2)
(m/constrain y ^double val1 ^double val2)
(m/constrain z ^double val1 ^double val2)
(m/constrain w ^double val1 ^double val2)))
(is-zero? [_] (and (m/zero? x) (m/zero? y) (m/zero? z) (m/zero? w)))
(heading [v1] (angle-between v1 (Vec4. 1 0 0 0))))
;;
(def ^{:deprecated "v1.3.0" :doc "Same as [[fmap]]. Deprecated."} applyf prot/fmap)
(def ^{:deprecated "v1.5.0" :doc "Same as [[vec->Vec]]. Deprecated."} to-vec prot/to-vec)
;; protocol methods mapped
(defn vec->array
"Convert to double array"
^doubles [v] (prot/to-double-array v))
(defn vec->RealVector
"Convert to Apache Commons Math RealVector"
^RealVector [v]
(prot/to-acm-vec v))
(defn vec->Vec
"Convert to Clojure primitive vector `Vec`."
[v]
(prot/to-vec v))
(defn as-vec
"Create vector from sequence as given type. If there is no sequence fill with `0.0`."
([v] (prot/as-vec v))
([v xs] (prot/as-vec v xs)))
(defn fmap
"Apply function to all vector values (like map but returns the same type)."
[v f]
(prot/fmap v f))
(defn magsq
"Length of the vector squared."
^double [v] (prot/magsq v))
(defn mag
"Length of the vector."
^double [v] (prot/mag v))
(defn approx
"Round to 2 (or `d`) decimal places"
([v] (prot/approx v))
([v d] (prot/approx v d)))
(defn delta-eq
"Equality with given absolute (and/or relative) toleance."
([v1 v2] (delta-eq v1 v2 1.0e-6))
([v1 v2 ^double abs-tol] (m/near-zero? (mag (prot/sub v1 v2)) abs-tol))
([v1 v2 ^double abs-tol ^double rel-tol] (m/near-zero? (mag (prot/sub v1 v2)) abs-tol rel-tol)))
(defn dot
"Dot product of two vectors."
^double [v1 v2] (prot/dot v1 v2))
(defn add
"Sum of two vectors."
([v] v)
([v1 v2] (prot/add v1 v2)))
(defn sub
"Subtraction of two vectors."
([v] (prot/mult v -1.0))
([v1 v2] (prot/sub v1 v2)))
(defn shift
"Add value to every vector element."
([v] v)
([v x] (prot/shift v x)))
(defn mult
"Multiply vector by number `x`."
[v x] (prot/mult v x))
(defn emult
"Element-wise vector multiplication (Hadamard product)."
[v1 v2] (prot/emult v1 v2))
(defn abs
"Absolute value of vector elements"
[v] (prot/abs v))
(defn mx
"Maximum value of vector elements"
^double [v] (prot/mx v))
(defn mn
"Minimum value of vector elements"
^double [v] (prot/mn v))
(defn emx
"Element-wise max from two vectors."
[v1 v2] (prot/emx v1 v2))
(defn emn
"Element-wise min from two vectors."
[v1 v2] (prot/emn v1 v2))
(defn maxdim
"Index of maximum value."
^long [v] (prot/maxdim v))
(defn mindim
"Index of minimum value."
^long [v] (prot/mindim v))
(defn base-from
"List of perpendicular vectors (basis). Works only for `Vec2` and `Vec3` types."
[v] (prot/base-from v))
(defn sum
"Sum of elements"
^double [v] (prot/sum v))
(defn prod
"Product of elements"
^double [v] (prot/prod v))
(defn permute
"Permute vector elements with given indices."
[v idxs] (prot/permute v idxs))
(defn reciprocal
"Reciprocal of elements."
[v] (prot/reciprocal v))
(defn interpolate
"Interpolate vectors, optionally set interpolation fn (default: lerp)"
([v1 v2 t] (prot/interpolate v1 v2 t m/lerp))
([v1 v2 t f] (prot/interpolate v1 v2 t f)))
(defn lerp
"Linear interpolation of vectors"
[v1 v2 t] (prot/interpolate v1 v2 t m/lerp))
(defn einterpolate
"Interpolate vector selement-wise, optionally set interpolation fn (default: lerp)"
([v1 v2 v] (prot/einterpolate v1 v2 v m/lerp))
([v1 v2 v f] (prot/einterpolate v1 v2 v f)))
(defn econstrain
"Element-wise constrain"
[v mn mx] (prot/econstrain v mn mx))
(defn is-zero?
"Is vector zero?"
[v] (prot/is-zero? v))
(defn zero?
"Is vector zero?"
[v] (prot/is-zero? v))
(defn is-near-zero?
"Equality to zero `0` with given absolute (and/or relative) toleance."
([v] (is-near-zero? v 1.0e-6))
([v ^double abs-tol] (m/near-zero? (mag v) abs-tol))
([v ^double abs-tol ^double rel-tol] (m/near-zero? (mag v) abs-tol rel-tol)))
(defn near-zero?
"Equality to zero `0` with given absolute (and/or relative) toleance."
([v] (near-zero? v 1.0e-6))
([v ^double abs-tol] (m/near-zero? (mag v) abs-tol))
([v ^double abs-tol ^double rel-tol] (m/near-zero? (mag v) abs-tol rel-tol)))
(defn heading
"Angle between vector and unit vector `[1,0,...]`"
^double [v] (prot/heading v))
(defn cross
"Cross product"
[v1 v2] (prot/cross v1 v2))
(defn rotate
"Rotate vector. Only for `Vec2` and `Vec3` types."
([v angle] (prot/rotate v angle))
([v angle-x angle-y angle-z] (prot/rotate v angle-x angle-y angle-z)))
(defn axis-rotate
"Rotate vector. Only for `Vec3` types"
([v angle axis] (prot/axis-rotate v angle axis))