Plots

Mafs supports numerically plotting a number of function types by passing in plain JavaScript functions.

Functions of x and y

import { Mafs, Coordinates, Plot, Theme } from "mafs"

function FunctionsOfXAndY() {
  const sigmoid1 = (x: number) => 2 / (1 + Math.exp(-x)) - 1

  return (
    <Mafs>
      <Coordinates.Cartesian />
      <Plot.OfX y={Math.sin} color={Theme.blue} />
      <Plot.OfY x={sigmoid1} color={Theme.pink} />
    </Mafs>
  )
}

Props

<Plot.OfX ... />
NameDescriptionDefault
y*
(x: number) => number
svgPathProps
SVGProps<SVGPathElement>
color
string
minSamplingDepth

The minimum recursive depth of the sampling algorithm.

number
maxSamplingDepth

The maximum recursive depth of the sampling algorithm.

number
opacity
number
weight
number
style
"solid" | "dashed"

Props

<Plot.OfY ... />
NameDescriptionDefault
x*
(y: number) => number
svgPathProps
SVGProps<SVGPathElement>
color
string
minSamplingDepth

The minimum recursive depth of the sampling algorithm.

number
maxSamplingDepth

The maximum recursive depth of the sampling algorithm.

number
opacity
number
weight
number
style
"solid" | "dashed"

Inequalities of x and y

Inequalities represent the region less than or greater than one or two functions. Mafs allows you to plot the region between two functions, or a function and a constant. The inequality can be a function of x or y.

You cannot provide an x and a y prop to Inequality—it will throw a runtime exception. Similarly, you cannot pass conflicting inequality operators—like both < and .

import { Mafs, Coordinates, Plot, Theme, useMovablePoint } from "mafs"

function InequalitiesExample() {
  const a = useMovablePoint([0, -1])

  return (
    <Mafs>
      <Coordinates.Cartesian />

      <Plot.Inequality
        x={{
          "<=": (y) => Math.cos(y + a.y) - a.x,
          ">": (y) => Math.sin(y - a.y) + a.x,
        }}
        color={Theme.blue}
      />

      <Plot.Inequality
        y={{
          "<=": (x) => Math.cos(x + a.x) - a.y,
          ">": (x) => Math.sin(x - a.x) + a.y,
        }}
        color={Theme.pink}
      />

      {a.element}
    </Mafs>
  )
}

Props

<Plot.Inequality ... />
NameDescriptionDefault
y
{ ">"?: FnX; "<="?: FnX; "<"?: FnX | undefined; ">="?: FnX | undefined; } | undefined
x
{ ">"?: FnY; "<="?: FnY; "<"?: FnY | undefined; ">="?: FnY | undefined; } | undefined
color
string
var(--mafs-fg)
weight
number
2
strokeColor
string
var(--mafs-fg)
strokeOpacity
number
1
fillColor
string
var(--mafs-fg)
fillOpacity
number
0.15
minSamplingDepth
number
10
maxSamplingDepth
number
14
upperColor
string
var(--mafs-fg)
upperOpacity
number
1
upperWeight
number
2
lowerColor
string
var(--mafs-fg)
lowerOpacity
number
1
lowerWeight
number
2
svgUpperPathProps
SVGProps<SVGPathElement>
{}
svgLowerPathProps
SVGProps<SVGPathElement>
{}
svgFillPathProps
SVGProps<SVGPathElement>
{}

Parametric functions

import { Mafs, Coordinates, Plot, useMovablePoint } from "mafs"
import { clamp } from "lodash"

function TwistyBoi() {
  const point = useMovablePoint([0.5, 0], {
    constrain: ([x]) => [clamp(x, -1, 1), 0],
  })

  const k = point.x * 25 * Math.PI

  return (
    <Mafs viewBox={{ x: [-1, 1], y: [-1, 1] }}>
      <Coordinates.Cartesian subdivisions={4} />

      <Plot.Parametric
        t={[0, k]}
        xy={(t) => [Math.cos(t), (t / k) * Math.sin(t)]}
      />

      {point.element}
    </Mafs>
  )
}

Props

<Plot.Parametric ... />
NameDescriptionDefault
xy*

A function that takes a t value and returns a point.

(t: number) => Vector2
t*

The domain t between which to evaluate xy.

Vector2
minSamplingDepth

The minimum recursive depth of the sampling algorithm.

number
8
maxSamplingDepth

The maximum recursive depth of the sampling algorithm.

number
14
svgPathProps
SVGProps<SVGPathElement>
{}
color
string
opacity
number
1
weight
number
2
style
"solid" | "dashed"
solid

Vector fields

Vector fields take a function that is passed a point [x, y] and returns a vector at that point. Vectors are then artificially scaled down (for legibility) and plotted on the coordinate plane. You must also pass a step to indicate how dense the vector field is.

import { Mafs, Plot, Coordinates, useMovablePoint } from "mafs"

function VectorFieldExample() {
  const a = useMovablePoint([0.6, 0.6])

  return (
    <Mafs>
      <Coordinates.Cartesian subdivisions={2} />
      <Plot.VectorField
        xy={([x, y]) => [
          y - a.y - (x - a.x),
          -(x - a.x) - (y - a.y),
        ]}
        step={0.5}
        xyOpacity={([x, y]) =>
          (Math.abs(x) + Math.abs(y)) / 10
        }
      />
      {a.element}
    </Mafs>
  )
}

Props

<Plot.VectorField ... />
NameDescriptionDefault
xy*
(point: Vector2) => Vector2
xyOpacity
((point: Vector2) => number)
() => 1
step
number
1
opacityStep
number
xyOpacity === xyOpacityDefault ? 1 : 0.2
color
string
var(--mafs-fg)

Render quality

Function sampling

Plot.OfX, Plot.OfY, and Plot.Parametric use numerical methods for evaluating a function and attempting to plot it accurately. The approach works well for most functions, but it's far from perfect.

Mafs samples functions by by recursively subdividing the domain until an estimated error threshold is met (or the recursion limit limit is reached).

Sampling depth

To force more subdivisions (and therefore improve quality), the minSamplingDepth and maxSamplingDepth props can be tuned. Increasing minSamplingDepth can help when you want to ensure more subdivisions and improve accuracy, and lowering maxSamplingDepth can help improve performance.

Here's an example of a common "stress test" function for plotters, sin(1/x). This function exhibits an infinite oscillation frequency as x approaches 0, requiring theoretically infinite sampling to render perfectly.

The top plot has the default sampling depths, while the bottom has minSamplingDepth increased to 16. More samples still doesn't render the function perfectly, but it's much closer (at the cost of performance: the bottom plot has nearly 3 megabytes of SVG path data).

import { Coordinates, Mafs, Plot } from "mafs"

function SineStressTest() {
  const fn = (x: number) => Math.sin(1 / x)

  return (
    <Mafs
      viewBox={{ x: [-1/32, 1/32], y: [-3.5, 3.5], padding: 0 }}
      preserveAspectRatio={false}
    >
      <Coordinates.Cartesian />
      <Plot.OfX y={(x) => fn(x) + 1.5} weight={1} />
      <Plot.OfX y={(x) => fn(x) - 1.5} minSamplingDepth={16} weight={1} />
    </Mafs>
  )
}

If you pan this example around, you may see a considerably slow framerate. Interestingly, this slowness is happening in the browser code itself, not in JavaScript (and therefore not in Mafs). It would seem that merely rendering large SVG paths is expensive.

Vector fields

Vector field rendering quality can be tuned with the step prop. This declares the spacing between arrows, so lowering it will decrease performance.