emmy.mathbox.components.plot — org.mentat/emmy-viewers 0.2.0

Higher-level mathematical plotting components built on the primitives provided by Mathbox.cljs.

AxisLabel cljs

(AxisLabel {:keys [axis position size] :or {size 16 position 5} :as opts})

Component that renders an axis label above the referenced axis.

Required arguments:

• :axis: one of :x, :y or :z.

Optional arguments:

• :label: the label to show. If label is falsey or equal to "", this component won't render.

• :position: the distance along the axis to place the label. Defaults to 5.

  NOTE: Ideally we would figure out the parent Cartesian and pick the top of the range for the axis specified as the default.

• :size: size of the label. Defaults to 16.

box-defaults cljs

Default MathBox options.

Cartesian cljs

(Cartesian & children)

Component that renders a mathematical 3d plotting scene into MathBox. Takes any number of children and nests them into a configured [[mathbox.coordinates/Cartesian]] component.

Optional arguments:

• :range: triple of the form [<x-range> <y-range> <z-range>]. Each range entry is a pair of [<min-value> <max-value>].

  Defaults to [-5 5] in each dimension.

• :scale: [<x-scale> <y-scale> <z-scale>] for tuning the relative space given to each dimension in the rendering. Each entry defaults to 1.

• :position: [<x> <y> <z>] world position of this cartesian. Defaults to [0 0 0].

• :camera: Camera position in units I don't really understand yet! Defaults to [0.5 -2 0.6].

• :axes: can be either

  • a vector like [:x :y]
  • a map of {<axis-key> <boolean-or-[[LabeledAxis]]-arguments>}

  Any axis entries missing from :axes won't be rendered.

  See LabeledAxis for more detail on allowed configuration values.

• :grids: either

  • a vector like [:xy :yz]

  • a map of {<axis-key> <boolean-or-[[Grid]]-arguments>}

  Any plane entries missing from :grids won't be rendered.

  See Grid for more detail on allowed configuration values.

DomLabel cljs

(DomLabel {:keys [tex? label size offset] :or {tex? true}})

Component that quite indulgently mounts a DOM element into the current MathBox scene.

NOTE that this is quite expensive and will slow down your updates! But when you need to show LaTeX this is where you should turn.

Required arguments:

• :label: string with the label you'd like to mount.

Optional arguments:

• :tex?: when true (default), mounts the label into the dom after processing it with katex.

• :size: size of the label. Defaults to 12, or 18 if :tex? is true.

• :offset: [<x-offset> <y-offset>] for this label on the DOM. Defaults to [0 20].

Grid cljs

(Grid {:keys [axes width opacity color z-order z-index z-bias snap divisions]
       :or {z-bias 0 z-index 0 width 0.5 opacity 1 color "#808080"}})

Component that takes a k equal to :xy, :yz or :xz and renders a grid in the specified plane into the MathBox scene.

Required arguments:

• :axes: one of :xy, :yz or :xz.

Optional arguments:

• :snap: either true, false, a single number or a 2-vector of numbers of the form [<snap-x?> <snap-y?>]. A non-vector value becomes a pair with the same value in both slots.

  "snapping" the grid means that gridlines will snap to nice numbers. false by default.

• :divisions: either a single number or a 2-vector of numbers of the form [<first-axis-divisions> <second-axis-divisions>]. A non-vector value becomes a pair with the same value in both slots.

  divisions set the number of gridlines that appear in each dimension.

• :width: width of the lines on the rendered grid.

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

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

• :z-order: z-order of the grid.

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

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

LabeledAxis cljs

(LabeledAxis {:keys [axis width opacity color z-order z-index z-bias max start?
                     end?]
              :or {z-bias 0
                   z-index 0
                   opacity 1
                   width 1
                   start? false
                   end? false
                   color "#808080"}
              :as opts})

Component that takes a k equal to :x, :y or :z and renders the equivalent axis into the MathBox scene.

Required arguments:

• :axis: one of :x, :y or :z.

Optional arguments:

• :ticks: either true (default), falsey or a map of Ticks options. See Ticks for details on what's allowed.

  true will include default ticks, while false or nil will remove ticks.

• :label: either true (default) or a map of AxisLabel options. See AxisLabel for details on what's allowed.

  true will include the default label and ticks, while false or nil will remove the label.

• :width: width of the rendered axis line.

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

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

• :end? if true (default), renders the ending tick.

• :opacity: opacity of the axis (not currently passed on to ticks or labels). Defaults to 1.0.

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

• :z-order: z-order of the full labeled axis.

• :z-index: zIndex of the full labeled axis. Defaults to 0.

• :z-bias: zBias of the full labeled axis. Defaults to 0.

• :label: either true (default) or a map of options.

• :max: the maximum value reached along this axis. This is used to pass a default :position argument to the AxisLabel component if one isn't set.

NOTE this is a hack, see the comment above the component for an alternate approach.

Line cljs

(Line {:keys [coords arrow-size width start? end? label opacity color z-order
              z-index z-bias]
       :or {z-index 0 z-bias 0 opacity 1 arrow-size 6 width 4 color "#3498db"}})

Component that renders a line segment into the scene as specified by coords.

Required arguments:

• :coords: a pair of 3-vectors of the form [<x> <y> <z>] specifying the line segment's starting and ending coordinates.

Optional arguments:

• :label: either:

  • a string label,
  • a map with optional keys :start and :end
  • a vector of the form [<start> <end>]

  specifying the labels to hover over the start and end of the rendered line segment.

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

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

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

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

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

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

• :z-order: z-order of the point.

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

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

OfX cljs

(OfX {:keys [y z] :as opts})

Component that plots a function in either the y or z directions as a function of x values.

Required arguments:

• :y or :z: function of the form (fn [x] <y-or-z>), valid within the scene's x-axis range or the range specified by :range.

  NOTE that you may only supply ONE of these two! Supplying both will trigger an error.

Optional arguments:

• :samples: the number of points to use to generate the curve. Defaults to 256.

• :range: 2-vector of the form [<min-x> <max-x>] specifying the range to feed into :y or :z.

• :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.

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

• :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.

OfXY cljs

(OfXY _)

Component that plots an explicit surface defined by :z into the scene along the area specified by :x-range and :y-range.

Required arguments:

• :z: function of the form (fn [[x y]] [<z>]), valid within the area specified by :x-range and :y-range.

Optional arguments:

• :x-range: 2-vector of the form [<min-x> <max-x>] specifying the interval of the first input to f. Defaults to the scene's range.

• :y-range: 2-vector of the form [<min-y> <max-y>] specifying the interval of the second input to f. Defaults to the scene's range.

• :x-samples: the number of x samples to use to generate the surface. Defaults to 64.

• :y-samples: the number of y samples to use to generate the surface. Defaults to 64.

• :shaded? if true (default), MathBox will shade the surface.

• :opacity: opacity of the surface. Defaults to 0.75.

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

• :z-order: z-order of the surface. Defaults to 25.

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

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

Optional arguments for configuring grid lines:

• :grid-x: the number of lines of constant x to plot along the surface.

• :grid-y: the number of lines of constant y to plot along the surface.

• :grid-opacity: opacity of the grid lines. Defaults to 0.5.

• :grid-width: width of the grid lines.

• :grid-color: color of the grid lines. Defaults to a darkened version of :color.

OfXZ cljs

(OfXZ _)

Component that plots an explicit surface defined by :z into the scene along the area specified by :x-range and :z-range.

Required arguments:

• :y: function of the form (fn [[x z]] [<y>]), valid within the area specified by :x-range and :z-range.

Optional arguments:

• :x-range: 2-vector of the form [<min-x> <max-x>] specifying the interval of the first input to f. Defaults to the scene's range.

• :z-range: 2-vector of the form [<min-z> <max-z>] specifying the interval of the second input to f. Defaults to the scene's range.

• :x-samples: the number of x samples to use to generate the surface. Defaults to 64.

• :z-samples: the number of z samples to use to generate the surface. Defaults to 64.

• :shaded? if true (default), MathBox will shade the surface.

• :opacity: opacity of the surface. Defaults to 0.75.

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

• :z-order: z-order of the surface. Defaults to 25.

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

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

Optional arguments for configuring grid lines:

• :grid-x: the number of lines of constant x to plot along the surface.

• :grid-z: the number of lines of constant z to plot along the surface.

• :grid-opacity: opacity of the grid lines. Defaults to 0.5.

• :grid-width: width of the grid lines.

• :grid-color: color of the grid lines. Defaults to a darkened version of :color.

OfY cljs

(OfY {:keys [x z] :as opts})

Component that plots a function in either the x or z directions as a function of y values.

Required arguments:

• :x or :z: function of the form (fn [y] <x-or-z>), valid within the scene's y-axis range or the range specified by :range.

  NOTE that you may only supply ONE of these two! Supplying both will trigger an error.

Optional arguments:

• :samples: the number of points to use to generate the curve. Defaults to 256.

• :range: 2-vector of the form [<min-y> <max-y>] specifying the range to feed into :x or :z.

• :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.

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

• :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.

OfYZ cljs

(OfYZ _)

Component that plots an explicit surface defined by :x into the scene along the area specified by :y-range and :z-range.

Required arguments:

• :x: function of the form (fn [[y z]] [<x>]), valid within the area specified by :y-range and :z-range.

Optional arguments:

• :y-range: 2-vector of the form [<min-y> <max-y>] specifying the interval of the first input to f. Defaults to the scene's range.

• :z-range: 2-vector of the form [<min-z> <max-z>] specifying the interval of the second input to f. Defaults to the scene's range.

• :y-samples: the number of y samples to use to generate the surface. Defaults to 64.

• :z-samples: the number of z samples to use to generate the surface. Defaults to 64.

• :shaded? if true (default), MathBox will shade the surface.

• :opacity: opacity of the surface. Defaults to 0.75.

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

• :z-order: z-order of the surface. Defaults to 25.

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

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

Optional arguments for configuring grid lines:

• :grid-y: the number of lines of constant y to plot along the surface.

• :grid-z: the number of lines of constant z to plot along the surface.

• :grid-opacity: opacity of the grid lines. Defaults to 0.5.

• :grid-width: width of the grid lines.

• :grid-color: color of the grid lines. Defaults to a darkened version of :color.

OfZ cljs

(OfZ {:keys [x y] :as opts})

Component that plots a function in either the x or y directions as a function of z values.

Required arguments:

• :x or :y: function of the form (fn [z] <x-or-y>), valid within the scene's z-axis range or the range specified by :range.

  NOTE that you may only supply ONE of these two! Supplying both will trigger an error.

Optional arguments:

• :samples: the number of points to use to generate the curve. Defaults to 256.

• :range: 2-vector of the form [<min-z> <max-z>] specifying the range to feed into :x or :y.

• :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.

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

• :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.

ParametricCurve cljs

(ParametricCurve opts)

Component that plots a parametric curve f into the scene along the range specified by t.

Required arguments:

• :f: function of the form (fn [t] [<x> <y> <z>]), valid within the range specified by :t.

• :t 2-vector of the form [<min-t> <max-t>] specifying the domain of the parametric function f.

Optional arguments:

• :samples: the number of points to use to generate the curve. Defaults to 256.

• :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.

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

• :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.

ParametricSurface cljs

(ParametricSurface opts)

Component that plots a parametric surface defined by f into the scene along the area specified by u and v.

Required arguments:

• :f: function of the form (fn [[u v]] [<x> <y> <z>]), valid within the area specified by :u and :v.

• :u 2-vector of the form [<min-u> <max-u>] specifying the interval of the first input to f.

• :v: 2-vector of the form [<min-v> <max-v>] specifying the interval of the second input to f.

Optional arguments:

• :u-samples: the number of u samples to use to generate the surface. Defaults to 64.

• :v-samples: the number of v samples to use to generate the surface. Defaults to 64.

• :shaded? if true (default), MathBox will shade the surface.

• :opacity: opacity of the surface. Defaults to 0.75.

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

• :z-order: z-order of the surface. Defaults to 25.

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

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

Optional arguments for configuring grid lines:

• :grid-u: the number of lines of constant u to plot along the surface.

• :grid-v: the number of lines of constant v to plot along the surface.

• :grid-opacity: opacity of the grid lines. Defaults to 0.5.

• :grid-width: width of the grid lines.

• :grid-color: color of the grid lines. Defaults to a darkened version of :color.

Point cljs

(Point {:keys [label size coords opacity color z-order z-index z-bias]
        :or {size 16 z-index 0 z-bias 0 opacity 1 color color/default}})

Component that renders a point into the scene at coords.

Required arguments:

• :coords: 3-vector of the form [<x> <y> <z>] specifying the point's coordinates.

Optional arguments:

• :label: either a string label or an options map input to DomLabel. If :tex? is true in this map, the component will use katex to render the label.

  NOTE that this is computationally expensive for reasons I don't understand!

• :size: size of the point. Defaults to 16.

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

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

• :z-order: z-order of the point.

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

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

PolarCurve cljs

(PolarCurve {:keys [r range] :or {range [0 (* 2 Math/PI)]} :as opts})

Component that plots a polar curve, ie, radius as a function of theta.

Required arguments:

• :r: function of the form (fn [theta] <r>), valid within the range of theta values specified by :range.

  NOTE that you may only supply ONE of these two! Supplying both will trigger an error.

Optional arguments:

• :samples: the number of points to use to generate the curve. Defaults to 256.

• :range: 2-vector of the form [<min-theta> <max-theta>] specifying the range to feed into :r. Defaults to [0 (* 2 Math/PI)].

• :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.

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

• :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.

PolarSurface cljs

(PolarSurface _)

Component that plots a polar surface defined by :f into the scene along the area specified by :r-range and :theta-range.

Required arguments:

• :f: function of the form (fn [[r theta]] [<z>]), valid within the area specified by :r-range and :theta-range.

Optional arguments:

• :r-range: 2-vector of the form [<min-r> <max-r>] specifying the interval of the first input to f. Defaults to [0 3].

• :theta-range: 2-vector of the form [<min-theta> <max-theta>] specifying the interval of the second input to f. Defaults to [0 (* 2 Math/PI)].

• :r-samples: the number of r samples to use to generate the surface. Defaults to 64.

• :theta-samples: the number of theta samples to use to generate the surface. Defaults to 64.

• :shaded? if true (default), MathBox will shade the surface.

• :opacity: opacity of the surface. Defaults to 0.75.

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

• :z-order: z-order of the surface. Defaults to 25.

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

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

Optional arguments for configuring grid lines:

• :grid-r: the number of lines of constant r to plot along the surface.

• :grid-theta: the number of lines of constant theta to plot along the surface.

• :grid-opacity: opacity of the grid lines. Defaults to 0.5.

• :grid-width: width of the grid lines.

• :grid-color: color of the grid lines. Defaults to a darkened version of :color.

Scene cljs

(Scene & children)

Takes an optional options map and any number of children and nests them into a configured [[mathbox.coordinates/Cartesian]] component that renders a mathematical 3d plotting scene into MathBox.

Any option supported by [[mathbox.core/MathBox]] is removed and passed along to that component, after merging with box-defaults.

See Cartesian for all other supported options.

SceneAxes cljs

(SceneAxes axes)

(SceneAxes axes range)

Component that renders multiple LabeledAxis components into a scene.

axes can be either

• a vector like [:x :y]
• a map of {<axis-key> <boolean-or-[[LabeledAxis]]-arguments>}

range (optional) is a 3-vector with the rendered ranges in the x, y and z directions.

Any axis entries missing from axes won't be rendered.

NOTE: This argument is only used to fill in the :max argument to LabeledAxis for default label positioning. It should go away once we get a better strategy!

SceneGrids cljs

(SceneGrids grids)

Component that renders multiple Grid objects into a scene.

grids can be either

• a vector like [:xy :yz]
• a map of {<axis-key> <boolean-or-[[Grid]]-arguments>}

Any plane entries missing from grids won't be rendered.

threestrap-defaults cljs

Default Threestrap options.

Ticks cljs

(Ticks {:keys [axis divisions width snap? zero? start? end? labels? label-fn
               color background text-size offset z-order z-index z-bias]
        :or {text-size 16
             start? true
             snap? false
             label-fn p/format-number
             end? true
             z-bias 0
             divisions 10
             zero? false
             width 2
             z-index 0
             labels? true}})

Component that renders tick marks onto a scene, lined up with an axis.

Required arguments:

• :axis: one of :x, :y or :z.

Optional arguments:

• :divisions: the number of divisions (ticks) to generate. Defaults to 10.

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

• :snap? if true, the ticks will snap to "nice" values. false by default.

• :start? if true (default), renders the starting tick.

• :end? if true (default), renders the ending tick.

• :zero? if true, renders the tick at 0. false by default.

• :size: size of the label. Defaults to 12.

• :offset: [<x-offset> <y-offset>] for the label on each tick. Defaults to [20 0] if :axis equals :z, else [0 -20].

• :labels?: if true (default), renders a printed label underneath each tick for the :x and :y axes, or alongside the axis for :z.

• :label-fn: (fn [x] <string>) for generating the printed representation of each tick mark's value. Defaults to emmy.viewer.plot/format-number. You might also enjoy emmy.viewer.plot/label-pi.

• :z-order: z-order of the labeled axis.

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

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

Vector cljs

(Vector {:keys [tip tail] :or {tail [0 0 0]} :as opts})

Component that renders a vector into the scene with the specified tip and tail.

Required arguments:

• :tip: 3-vector of the form [<x> <y> <z>] specifying the tip of the vector.

Optional arguments:

• :tail: 3-vector of the form [<x> <y> <z>] specifying the tail of the vector. Defaults to [0 0 0].

See Line for all other supported options. All defaults are identical, except :end? defaults to true.

VectorField cljs

(VectorField {:keys [f scale x-samples y-samples z-samples x-range y-range
                     z-range arrow-size width start? end? opacity color z-order
                     z-index z-bias]
              :or {start? false
                   y-samples 10
                   color "#3090ff"
                   x-samples 10
                   end? true
                   scale 1
                   z-bias 0
                   width 2
                   z-index 0
                   z-samples 10
                   opacity 1
                   arrow-size 6}})

Component that plots a vector field defined by :f into the scene along the volume specified by :x-range, :y-range and :z-range.

Required arguments:

• :f: function of the form (fn [[x y z]] [<x> <y> <z>]), valid within the area specified by :x-range, :y-range and :z-range.

  The function should return the coordinates of the tip of a vector with origin at [0 0 0]; VectorField will translate each vector to start at [x y z].

Optional arguments:

• :scale: Optional scale factor to apply to each vector's magnitude. Defaults to 1.0.

• :x-range: 2-vector of the form [<min-x> <max-x>] specifying the interval of the first input to f. Defaults to the scene's range.

• :y-range: 2-vector of the form [<min-y> <max-y>] specifying the interval of the first input to f. Defaults to the scene's range.

• :z-range: 2-vector of the form [<min-z> <max-z>] specifying the interval of the second input to f. Defaults to the scene's range.

• :x-samples: the number of vectors to plot in the x direction. Defaults to 10.

• :y-samples: the number of vectors to plot in the y direction. Defaults to 10.

• :z-samples: the number of vectors to plot in the z direction. Defaults to 10.

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

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

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

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

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

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

• :z-order: z-order of the vector field.

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

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