emmy.mathbox.plot — org.mentat/emmy-viewers 0.3.1

Server-side rendering functions for the components declared in the emmy.mathbox.components.plot namespace.

cartesian clj/s

(cartesian & children)

Component that renders a mathematical 3d plotting scene into MathBox. Takes any number of children and nests them into a configured emmy.mathbox.components.plot/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.

• :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 labeled-axis 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.

grid clj/s

(grid opts)

Returns a fragment that takes an :axes option 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 true, false, 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.

labeled-axis clj/s

(labeled-axis opts)

Returns a fragment that takes an :axis option 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, ticks, while false or nil will remove the label.

• :width: width of the rendered axis line.

• :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), false, 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 clj/s

(line opts)

Returns a fragment 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.

of-x clj/s

(of-x opts)

Returns a fragment 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.

of-xy clj/s

(of-xy opts)

Returns a fragment 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.

of-xz clj/s

(of-xz opts)

Returns a fragment 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.

of-y clj/s

(of-y opts)

Returns a fragment 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.

of-yz clj/s

(of-yz opts)

Returns a fragment 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.

of-z clj/s

(of-z opts)

Returns a fragment 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.

parametric-curve clj/s

(parametric-curve opts)

Returns a fragment 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.

parametric-surface clj/s

(parametric-surface opts)

Returns a fragment 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 clj/s

(point opts)

Returns a fragment 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.

polar-curve clj/s

(polar-curve opts)

polar-surface clj/s

(polar-surface opts)

Returns a fragment 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 clj/s

(scene & children)

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

Any option supported by emmy.mathbox/mathbox is removed and passed along to that function.

See cartesian for all other supported options.

vector clj/s

(vector opts)

Returns a fragment 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.

vector-field clj/s

(vector-field opts)

Returns a fragment 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.