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bezier.cljc
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bezier.cljc
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(ns thi.ng.geom.bezier
(:require
[thi.ng.geom.core :as g :refer [*resolution*]]
[thi.ng.geom.vector :as v :refer [vec2 vec3]]
[thi.ng.geom.utils :as gu]
#?(:clj [thi.ng.geom.types] :cljs [thi.ng.geom.types :refer [Bezier2 Bezier3]])
[thi.ng.geom.ptf :as ptf]
[thi.ng.dstruct.core :as d]
[thi.ng.math.core :as m])
#?(:clj (:import [thi.ng.geom.types Bezier2 Bezier3])))
(defn bernstein
[t]
(let [it (- 1.0 t) it2 (* it it) t2 (* t t)]
[(* it it2) (* 3 (* t it2)) (* 3 (* it t2)) (* t t2)]))
(defn interpolate
[[a b c d] t]
(let [it (- 1.0 t), it2 (* it it), t2 (* t t)]
(->> (m/* a (* it it2))
(m/madd b (* 3 (* t it2)))
(m/madd c (* 3 (* it t2)))
(m/madd d (* t t2)))))
(defn sample-segment
[seg res]
(map #(interpolate seg %) (butlast (m/norm-range res))))
(defn sample-with-res
[res include-last? points]
(let [ls (->> points
(d/successive-nth 4)
(take-nth 3)
(mapcat #(sample-segment % res)))]
(if include-last?
(concat ls [(last points)])
ls)))
;; *** Automatic curve generation
;;
;; The following two functions allow us to compute a bezier curve which
;; passes through all given points and automatically computes the
;; required control points. This only works for non-closed curves, though.
(defn- find-cpoints*
[ctor tight points]
(let [np (count points)
invt (/ 1.0 tight)
points (vec points)
c1 (m/subm (points 2) (first points) tight)
[bi coeff] (reduce
(fn [[bi coeff] i]
(let [b (/ -1.0 (+ invt (peek bi)))
c (peek coeff)
p (get points (dec i))
q (get points (inc i))]
[(conj bi b)
(conj coeff (m/* (m/- q p c) (- b)))]))
[[0 (- tight)] [(ctor) c1]]
(range 2 (dec np)))]
(reduce
(fn [delta i]
(assoc delta i (m/madd (delta (inc i)) (bi i) (coeff i))))
(vec (repeatedly np ctor))
(range (- np 2) 0 -1))))
(defn auto-spline*
[points cpoints]
(concat
(->> cpoints
(d/successive-nth 2)
(interleave (d/successive-nth 2 points))
(partition 2)
(mapcat (fn [[[p q] [dp dq]]] [p (m/+ p dp) (m/- q dq)])))
[(last points)]))
;; ** Constructors
(defn bezier2
[points] (Bezier2. (mapv vec2 points)))
(defn auto-spline2
([points]
(->> points
(find-cpoints* vec2 0.25)
(auto-spline* points)
(Bezier2.)))
([points closed?]
(auto-spline2
(if closed?
(conj (vec points) (first points))
points))))
(defn bezier3
[points] (Bezier3. (mapv vec3 points)))
(defn auto-spline3
([points]
(->> points
(find-cpoints* vec3 0.25)
(auto-spline* points)
(Bezier3.)))
([points closed?]
(auto-spline3
(if closed?
(conj (vec points) (first points))
points))))
;; ** Type implementations
(extend-type Bezier2
g/IArea
(area [_] 0.0)
g/ICenter
(center
([_] (Bezier2. (gu/center (vec2) (get _ :points))))
([_ o] (Bezier2. (gu/center (g/centroid _) (vec2 o) (get _ :points)))))
(centroid
[_] (gu/centroid (get _ :points)))
g/IFlip
(flip [_]
(Bezier2. (reverse (get _ :points))))
g/IVertexAccess
(vertices
([_] (g/vertices _ *resolution*))
([_ res] (sample-with-res res true (get _ :points))))
g/IEdgeAccess
(edges
([_] (d/successive-nth 2 (g/vertices _ *resolution*)))
([_ res] (d/successive-nth 2 (g/vertices _ res))))
g/IGraph
(vertex-neighbors
[_ v] (d/neighbors v (g/vertices _)))
(vertex-valence
[_ v]
(let [points (g/vertices _)]
(if-let [p (d/neighbors v points)]
(if (or (m/delta= p (first points)) (m/delta= p (peek points)))
1 2)
0)))
g/IMeshConvert
(as-mesh
[_ {:keys [res dist profile] :as opts}]
(let [points (if dist
(g/sample-uniform _ dist true)
(g/vertices _ (or res *resolution*)))]
(ptf/sweep-mesh (map vec3 points) profile opts)))
g/IProximity
(closest-point
[_ p]
(first (gu/closest-point-on-segments p (g/edges _))))
g/ISample
(point-at
[_ t] (gu/point-at t (get _ :points) nil))
(random-point
[_] (gu/point-at (m/random) (get _ :points) nil))
(random-point-inside
[_] (g/random-point _))
(sample-uniform
[_ udist include-last?]
(gu/sample-uniform udist include-last? (g/vertices _)))
g/IRotate
(rotate
[_ theta] (Bezier2. (mapv #(g/rotate % theta) (get _ :points))))
g/IScale
(scale
[_ s] (Bezier2. (mapv #(m/* % s) (get _ :points))))
(scale-size
[_ s] (Bezier2. (gu/scale-size s (get _ :points))))
g/ITranslate
(translate
[_ t] (Bezier2. (mapv #(m/+ % t) (get _ :points))))
g/ITransform
(transform
[_ m] (Bezier2. (mapv #(g/transform-vector m %) (get _ :points))))
g/IVolume
(volume [_] 0.0))
(extend-type Bezier3
g/IArea
(area [_] 0.0)
g/ICenter
(center
([_] (Bezier3. (gu/center (vec2) (get _ :points))))
([_ o] (Bezier3. (gu/center (g/centroid _) (vec2 o) (get _ :points)))))
(centroid
[_] (gu/centroid (get _ :points)))
g/IFlip
(flip [_]
(Bezier3. (reverse (get _ :points))))
g/IVertexAccess
(vertices
([_] (g/vertices _ *resolution*))
([_ res] (sample-with-res res true (get _ :points))))
g/IEdgeAccess
(edges
([_] (d/successive-nth 2 (g/vertices _ *resolution*)))
([_ res] (d/successive-nth 2 (g/vertices _ res))))
g/IGraph
(vertex-neighbors
[_ v] (d/neighbors v (g/vertices _)))
(vertex-valence
[_ v]
(let [points (g/vertices _)]
(if-let [p (d/neighbors v points)]
(if (or (m/delta= p (first points)) (m/delta= p (peek points)))
1 2)
0)))
g/IMeshConvert
(as-mesh
[_ {:keys [res dist profile] :as opts}]
(let [points (if dist
(g/sample-uniform _ dist true)
(g/vertices _ (or res *resolution*)))]
(ptf/sweep-mesh points profile opts)))
g/IProximity
(closest-point
[_ p]
(first (gu/closest-point-on-segments p (g/edges _))))
g/ISample
(point-at
[_ t] (gu/point-at t (get _ :points) nil))
(random-point
[_] (gu/point-at (m/random) (get _ :points) nil))
(random-point-inside
[_] (g/random-point _))
(sample-uniform
[_ udist include-last?]
(gu/sample-uniform udist include-last? (g/vertices _)))
g/IRotate
(rotate
[_ theta] (Bezier3. (mapv #(g/rotate % theta) (get _ :points))))
g/IScale
(scale
[_ s] (Bezier3. (mapv #(m/* % s) (get _ :points))))
(scale-size
[_ s] (Bezier3. (gu/scale-size s (get _ :points))))
g/ITranslate
(translate
[_ t] (Bezier3. (mapv #(m/+ % t) (get _ :points))))
g/ITransform
(transform
[_ m] (Bezier3. (mapv #(g/transform-vector m %) (get _ :points))))
g/IVolume
(volume [_] 0.0))