Sritchie/geodesic

CHANGELOG.md

@@ -2,6 +2,19 @@
 
 ## [unreleased]
 
+- #69:
+
+  - Adds
+    `emmy.mathbox.physics.{lagrangian-curve,hamiltonian-curve,routhian-curve,geodesic}`
+    to the existing `ode-curve` function.
+
+  - Adds
+    `emmy.viewer.physics.{evolve-lagrangian,evolve-hamiltonian,evolve-routhian}`
+    to the existing `evolve` function.
+
+  - Updates the `emmy.viewer.components.physics/Evolve` component to use a
+    pre-allocated JS output array instead of forcing an allocation on each tick.
+
 ## [0.2.0]
 
 - #57:

README.md

@@ -196,7 +196,7 @@ Use `plot/scene` to render multiple plots onto a 3D canvas:
 
 ![MathBox plot example](https://github.com/mentat-collective/emmy-viewers/assets/69635/3349cff0-744c-40fa-b996-1d324162b3d9)
 
-> See the [MathBox Guide](https://emmy-viewers.mentat.org/dev/examples/mafs) for 3D plotting examples.
+> See the [MathBox Guide](https://emmy-viewers.mentat.org/dev/examples/mathbox) for 3D plotting examples.
 
 Next, try clicking the 'show code' link for the examples at the top of the
 page and pasting their source into your namespace. Then visit the ["Specific

dev/emmy_viewers/notebook.clj

@@ -222,7 +222,7 @@
    :t [-10 10]
    :color :green}))
 
-;; > See the [MathBox Guide](/dev/examples/mafs) for 3D plotting examples.
+;; > See the [MathBox Guide](/dev/examples/mathbox) for 3D plotting examples.
 ;;
 ;; Next, try clicking the 'show code' link for the examples at the top of the
 ;; page and pasting their source into your namespace. Then visit the ["Specific

dev/emmy_viewers/sci_extensions.cljs

@@ -4,8 +4,6 @@
   (:require [emmy.viewer.sci]
             [examples.simulation.cylinder-flow]
             [examples.simulation.lorenz]
-            [examples.simulation.phase-portrait]
-            [examples.simulation.quartic-well]
             [nextjournal.clerk.sci-env]))
 
 (emmy.viewer.sci/install!)

dev/examples/manifold/klein.clj

@@ -5,6 +5,7 @@
    :exclude [+ - * / zero? compare divide numerator denominator
              infinite? abs ref partial =])
   (:require [emmy.clerk :as ec]
+            [emmy.mathbox.physics :as ph]
             [emmy.env :as e :refer :all]
             [emmy.leva :as leva]
             [emmy.mathbox.plot :as p]
@@ -17,17 +18,10 @@
 
 ;; # Fun with Klein Bottles
 
-(defn slider-surface [name {:keys [u v] :as opts}]
+(defn slider-surface [name {:keys [u v] :as opts} & children]
   (ev/with-let [!opts {:u (peek u) :v (peek v)}]
-    (p/scene
-     {:axes
-      {:x {:divisions 10
-           :label {:position 3}}
-       :y {:divisions 10
-           :ticks {:labels? false}}
-       :z {:divisions 10
-           :label-ticks? false}}
-      :grids []}
+    (apply
+     p/scene
      (leva/controls
       {:folder {:name name}
        :schema
@@ -37,7 +31,8 @@
      (p/parametric-surface
       (assoc opts
              :u [(first u) (ev/get !opts :u)]
-             :v [(first v) (ev/get !opts :v)])))))
+             :v [(first v) (ev/get !opts :v)]))
+     children)))
 
 ;; ## Mobius Strip
 
@@ -67,18 +62,31 @@
 
 ;; Can you find the Emmy logo hidden inside?
 
-(ev/with-let [!r {:r 2}]
+(ev/with-let [!r {:r 2 :theta_0 1 :alpha_0 0 :steps 20}]
   [:<>
-   (leva/controls {:atom !r
-                   :folder {:name "Klein Bagel"}
-                   :schema {:r {:min 2 :max 6 :step 0.01}}})
+   (leva/controls
+    {:atom !r
+     :folder {:name "Klein Bagel"}
+     :schema {:r {:min 2 :max 6 :step 0.01}
+              :theta_0 {:label (->infix 'theta_0) :min 0 :max Math/PI :step 0.02}
+              :alpha_0 {:label (->infix 'alpha_0) :min 0 :max Math/PI :step 0.02}
+              :steps   {:min 500 :max 9000 :step 50}}})
    (slider-surface
     "Klein Bagel"
     {:f (ev/with-params {:atom !r :params [:r]}
           klein-bagel)
-     :opacity 0.75
      :u [0 (* 2 Math/PI)]
-     :v [0 (* 2 Math/PI)]})])
+     :v [0 (* 2 Math/PI)]}
+
+    (ph/geodesic
+     {:x0 [(ev/get !r :theta_0) 0]
+      :v0 [(list 'Math/cos (ev/get !r :alpha_0))
+           (list 'Math/sin (ev/get !r :alpha_0))]
+      :xform (ev/with-params {:atom !r :params [:r]}
+               klein-bagel)
+      :steps (ev/get !r :steps)
+      :width 2
+      :end? true}))])
 
 ;; ## Klein bottle:
 
@@ -102,11 +110,30 @@
    (* 2/15 (sin v)
       (+ 3 (* 5 (cos u) (sin u))))])
 
-(slider-surface
- "Klein"
- {:f klein-bottle
-  :u [0 Math/PI]
-  :v [0 (* 2 Math/PI)]})
+(ev/with-let [!r {:theta_0 1 :alpha_0 0 :steps 20}]
+  [:<>
+   (leva/controls
+    {:atom !r
+     :folder {:name "Klein"}
+     :schema {:theta_0 {:label (->infix 'theta_0) :min 0 :max Math/PI :step 0.02}
+              :alpha_0 {:label (->infix 'alpha_0) :min 0 :max Math/PI :step 0.02}
+              :steps   {:min 10 :max 9000 :step 50}}})
+
+   (slider-surface
+    "Klein"
+    {:f klein-bottle
+     :opacity 0.2
+     :u [0 Math/PI]
+     :v [0 (* 2 Math/PI)]}
+
+    (ph/geodesic
+     {:x0 [(ev/get !r :theta_0) 0]
+      :v0 [(list 'Math/cos (ev/get !r :alpha_0))
+           (list 'Math/sin (ev/get !r :alpha_0))]
+      :xform klein-bottle
+      :steps (ev/get !r :steps)
+      :width 2
+      :end? true}))])
 
 ;; ## Plucker's Conoid
 

dev/examples/mathbox/color_test.clj

@@ -0,0 +1,35 @@
+^{:nextjournal.clerk/visibility {:code :hide}}
+(ns examples.mathbox.color-test
+  #:nextjournal.clerk{:toc true}
+  (:refer-clojure
+   :exclude [+ - * / = zero? compare numerator denominator ref partial
+             infinite? abs])
+  (:require [emmy.clerk :as ec]
+            [emmy.leva]
+            [emmy.env :as e :refer :all]
+            [emmy.mathbox.plot :as plot]
+            [emmy.viewer :as ev]))
+
+{:nextjournal.clerk/width :wide}
+
+^{:nextjournal.clerk/visibility {:code :hide :result :hide}}
+(ec/install!)
+
+;; # Color Testing
+
+;; ## Demo
+;;
+;; Let's make a function to try!
+
+(ev/with-let [!state {:amplitude 1}]
+  (plot/scene
+   (emmy.leva/controls {:atom !state})
+   (plot/of-xy
+    {:x-samples 128
+     :y-samples 128
+     #_#_:color "LimeGreen"
+     :z (ev/with-params {:atom !state :params [:amplitude]}
+          (fn [amplitude]
+            (fn [[x y]]
+              (* amplitude
+                 (cos (* x y))))))})))

dev/examples/mathbox/feig.clj

@@ -0,0 +1,72 @@
+;; # Feigenbaum
+
+(ns examples.mathbox.feig
+  {:nextjournal.clerk/toc true}
+  (:require [emmy.clerk :as ec]
+            [emmy.mathbox :as mb]
+            [nextjournal.clerk :as clerk]))
+
+^{::clerk/visibility {:code :hide :result :hide}}
+(ec/install!)
+
+(defn f [p x] (* p x (- 1 x)))
+
+(defn fixps [r]
+  (->> (iterate (partial f r) (rand))
+       (drop 300)
+       (take 300)
+       set
+       (map (fn [x] [r x]))))
+
+(def tree (into [] (mapcat fixps) (range 2.5 4.0 0.005)))
+(def width (count tree))
+(def boundary (Math/floor (Math/sqrt width)))
+
+(defn Feigenbaum []
+  [:<>
+   (mb/matrix
+    {:width (quot width boundary)
+     :height (mod width boundary)
+     :channels 2
+     :live false
+     :expr `(fn [emit# i# j#]
+              (apply emit# (nth ~tree (+ (* i# ~boundary) j#) nil)))})
+   (mb/point
+
+    {:color "#3090FF"
+     :size 1})])
+
+(defn axis
+  ([axis-no] (axis axis-no [0 0 0 0]))
+  ([axis-no origin]
+   [:<>
+    (mb/axis {:axis axis-no
+              :width 2
+              :color "black"
+              :origin origin})
+    (mb/scale  {:divide 10
+                :axis axis-no
+                :origin origin})
+    (mb/ticks  {:width 5
+                :size 15
+                :color "black"})
+    (mb/format {:digits 2
+                :weight "bold"})
+    (mb/label  {:color "red"
+                :zIndex 1})]))
+
+^{::clerk/width :wide}
+(mb/mathbox
+ {:container {:style {:height "1000px" :width "100%"}}}
+ (mb/camera {:position [0 0 2.1]
+             :proxy    true})
+ (mb/layer
+  (mb/cartesian
+   {:range [[2.5 4 0] [0 1 0]]
+    :scale [0.8 0.8 1]}
+   (mb/grid {:width   1
+             :divideX 10
+             :divideY 10})
+   (axis 1)
+   (axis 2 [2.5 0 0 0])
+   (Feigenbaum))))

dev/examples/mathbox/geom.clj

@@ -7,6 +7,7 @@
   (:require [emmy.clerk :as ec]
             [emmy.leva]
             [emmy.env :as e :refer :all]
+            [emmy.matrix]
             [emmy.viewer :as ev]
             [emmy.mathbox.plot :as p]))
 
@@ -15,9 +16,28 @@
 ^{:nextjournal.clerk/visibility {:code :hide :result :hide}}
 (ec/install!)
 
+(defn basis [m]
+  (let [[x y z] (emmy.matrix/transpose m)]
+    (-> [:<>
+         (p/vector {:tip x :arrow-size 3 :color "red"})
+         (p/vector {:tip y :arrow-size 3 :color "green"})
+         (p/vector {:tip z :arrow-size 3 :color "blue"})]
+        (ev/fragment p/scene))))
+
+(ev/with-let [!size {:y 1}]
+  (p/scene
+   (emmy.leva/controls
+    {:atom !size :schema {:y {:min 0 :max 10 :step 0.01}}})
+   (basis
+    (matrix-by-rows
+     [1 0 0]
+     [0 (ev/get !size :y) 0]
+     [1 0 2]))))
+
 (ev/with-let [!size {:size 20 :pos 1}]
-  [:<> (emmy.leva/controls
-        {:atom !size :schema {:size {:min 20 :max 100 :step 1}}})
+  [:<>
+   (emmy.leva/controls
+    {:atom !size :schema {:size {:min 20 :max 100 :step 1}}})
    (p/scene
     (p/point
      {:coords [0.5 -0.5 (ev/get !size :pos)]

dev/examples/simulation/double_ellipsoid.clj

@@ -52,12 +52,11 @@
      {:threestrap {:plugins ["core" "controls" "cursor" "stats"]}}
      (leva/controls {:atom !opts})
 
-     (emmy.viewer.physics/evolve
+     (emmy.viewer.physics/evolve-lagrangian
       {:atom !state
        :initial-state initial-state
-       :f' (ev/with-params {:atom !opts :params [:m :k :x0 :a :b :c]}
-             (comp Lagrangian->state-derivative
-                   L-central-triaxial))})
+       :L (ev/with-params {:atom !opts :params [:m :k :x0 :a :b :c]}
+            L-central-triaxial)})
 
      (emmy.mathbox.physics/comet
       {:length 16

dev/examples/simulation/ellipsoid.clj

@@ -117,12 +117,11 @@
         :b {:min 1 :max 5 :step 0.01}
         :c {:min 1 :max 5 :step 0.01}}})
 
-     (emmy.viewer.physics/evolve
+     (emmy.viewer.physics/evolve-lagrangian
       {:atom !state
        :initial-state initial-state
-       :f' (ev/with-params {:atom !opts :params [:m :g :a :b :c]}
-             (comp Lagrangian->state-derivative
-                   L-central-triaxial))})
+       :L (ev/with-params {:atom !opts :params [:m :g :a :b :c]}
+            L-central-triaxial)})
 
      (plot/parametric-surface
       {:opacity 0.2

dev/examples/simulation/oscillator.clj

@@ -36,14 +36,14 @@
     (plot/scene
      (leva/controls {:atom !opts})
 
-     (emmy.viewer.physics/evolve
+     (emmy.viewer.physics/evolve-lagrangian
       {:atom !state
        :initial-state initial-state
-       :f' (ev/with-params {:atom !opts :params [:g :m :k]}
-             (comp e/Lagrangian->state-derivative L-harmonic))})
+       :L (ev/with-params {:atom !opts :params [:g :m :k]}
+            L-harmonic)})
 
      (emmy.mathbox.physics/comet
-      {:length        1
+      {:length        10
        :state->xyz    coordinate
        :initial-state initial-state
        :atom          !state}))))