emmy.mathbox.components.physics — org.mentat/emmy-viewers 0.3.1

ODE and physics-aware plotting functions using MathBox.

Comet cljs

(Comet {:keys [atom state->xyz post-fn length items size opacity color z-order
               z-index z-bias]
        :or {size 10
             opacity 1.0
             state->xyz in->out
             color 3182847
             length 16
             z-index 0
             z-bias 0
             post-fn (fn [emit x y z] (emit x y z))}})

Point that trails its historical positions out behind it in a glowing tail.

Required arguments:

• :atom: atom holding a JS array representing some state. :state->xyz will transform this into xyz coordinates to draw.

Optional arguments:

• :state->xyz: function from the contents of :atom to [x y z] coordinates.

• :length: the length of the comet tail. Defaults to 16.

• :size: size of the comet. Defaults to 10.

• :opacity: opacity of the leading point of the comet. Defaults to 1.0.

• :color: color of each curve. This can be a three.js Color object or any valid input to its constructor.

• :z-order: z-order of the comet.

• :z-index: zIndex of the comet. Defaults to 0.

• :z-bias: zBias of the comet. Defaults to 0.

ODECurve cljs

(ODECurve _)

Component that plots a curve by integrating a system of ordinary differential equations represented by f' forward from the initial input state initial-state for steps steps of dt each.

Required arguments:

• :f': function of the form (fn [[y0 y1 ...]] [<y0'> <y1'> ...]) that returns a vector of the derivatives of each input variable.

• :initial-state: the initial input vector to :f'.

Optional arguments:

• :state->xyz: function of the form (fn [[y0 y1 ...]] [<x> <y> <z>]), responsible for transforming each integrated state into a 3D point. Defaults to identity.

• :steps: the number of :dt-spaced steps for the integrator to take. Defaults to 1000.

• :dt: the distance of each evenly spaced step taken by the integrator. Defaults to 3e-2.

• :epsilon: error tolerance passed along to odex-js. Defaults to 1e-5.

• :width: width of the curve. Defaults to 4.

• :start? if true, renders an arrow at the start of the curve. Defaults to false.

• :end? if true, renders an arrow at the end of the curve. Defaults to false.

• :arrow-size: size of the arrows toggled by :start? and :end?. Defaults to 6.

• :opacity: opacity of the curve. Defaults to 1.0.

• :color: color of the curve. This can be a three.js Color object or any valid input to its constructor.

• :z-order: z-order of the curve.

• :z-index: zIndex of the curve. Defaults to 0.

• :z-bias: zBias of the curve. Defaults to 0.

PhaseVectors cljs

(PhaseVectors {:keys [f' initial-state x-idx v-idx steps dt epsilon arrow-size
                      width start? end? opacity color z-order z-index z-bias]
               :or {v-idx 2
                    start? false
                    color 3182847
                    end? true
                    dt 0.03
                    z-bias 0
                    steps 10
                    width 2
                    z-index 0
                    opacity 1
                    epsilon 1.0E-5
                    arrow-size 5
                    x-idx 1}})

In-progress attempt at a proper phase portrait component.

PhaseVectors plots a curve at each point on a grid by integrating a system of ordinary differential equations represented by f' forward from the initial input state initial-state for steps steps of dt each.

Each point is initialized by swapping out :x-idx and :v-idx in :initial-state with the $(x, \vdot{x})$ coordinates of the phase portrait.

NOTE that this is kind of weird, and only works for second-order ODEs that have been transformed. It might be that we want to allow this, but also just call :f if the user doesn't supply :v-idx, for more general ODEs.

Required arguments:

• :f': function of the form (fn [[y0 y1 ...]] [<y0'> <y1'> ...]) that returns a vector of the derivatives of each input variable.

• :initial-state: the initial input vector to :f'.

Optional arguments:

• :x-idx: index of the coordinate position in the state. Defaults to 1.

• :v-idx index of the derivative of :x-idx in the state. Defaults to 2.

• :steps: the number of :dt-spaced steps for the integrator to take. Defaults to 10.

• :dt: the distance of each evenly spaced step taken by the integrator. Defaults to 3e-2.

• :epsilon: error tolerance passed along to odex-js. Defaults to 1e-5.

• :width: width of each curve. Defaults to 2.

• :start? if true, renders an arrow at the start of the curve. Defaults to false.

• :end? if true, renders an arrow at the end of the curve. Defaults to true.

• :arrow-size: size of the arrows toggled by :start? and :end?. Defaults to 5.

• :opacity: opacity of each curve. Defaults to 1.0.

• :color: color of each curve. This can be a three.js Color object or any valid input to its constructor.

• :z-order: z-order of the phase portrait.

• :z-index: zIndex of the phase portrait. Defaults to 0.

• :z-bias: zBias of the phase portrait. Defaults to 0.