IntSketcher

IntSketcher is a Typst package built on CeTZ designed to visualize Riemann sums and Darboux sums. It allows you to easily draw left, right, midpoint, and trapezoidal sums, as well as lower and upper Darboux sums, for any given function.

Features

• Riemann Sums: Supports "left", "right", and "mid" methods.
• Darboux Sums: Supports "lower" and "upper" sums.
• Trapezoidal Rule: Specialized function for trapezoidal visualizations.
• Custom Partitions: Support for both uniform grids and custom tagged/untagged partitions.

Usage

First, import the package into your Typst file:

#import "@preview/intsketcher:0.5.0": intsketcher, trapezoidal

Examples

The following examples demonstrate how to use intsketcher and trapezoidal within a CeTZ canvas.

1. Left-Hand Riemann Sum

Draws rectangles based on the function value at the left of each sub-interval.

#import "@preview/cetz:0.4.2": canvas
#import "@preview/intsketcher:0.5.0": intsketcher

#canvas({
  intsketcher(
    x => calc.pow(x, 3) + 4,
    method: "left",
    start: -3.1,
    end: 3.5,
    n: 10,
    plot-x-tick-step: 1,
  )
})

2. Midpoint Riemann Sum with Custom Partition

You can define a specific partition manually for non-uniform intervals.

#import "@preview/cetz:0.4.2": canvas
#import "@preview/intsketcher:0.5.0": intsketcher

#canvas({
  intsketcher(
    x => 0.17 * calc.pow(x, 3) + 1.5 * calc.sin(calc.cos(x)),
    method: "mid",
    partition: (-3, -1.5, -0.75, -0.2, 0.8, 1.5, 2.3, 3.4),
    plot-x-tick-step: 2,
  )
})

3. Lower Darboux Sum

Visualizes the lower sum by finding the minimum value within each interval.

#import "@preview/cetz:0.4.2": canvas
#import "@preview/intsketcher:0.5.0": intsketcher

#canvas({
  intsketcher(
    x => calc.pow(x, 3) + 4,
    method: "lower",
    start: -3.1,
    end: 3.5,
    n: 10,
  )
})

4. Trapezoidal Rule

A dedicated function for drawing trapezoids instead of rectangles.

#import "@preview/cetz:0.4.2": canvas
#import "@preview/intsketcher:0.5.0": trapezoidal

#canvas({
  trapezoidal(
    x => calc.pow(x, 3) + 4,
    start: -3,
    end: 3.5,
    n: 7,
    positive-color: rgb("#210aa4"),
    plot-x-tick-step: 2,
  )
})

Parameters

intsketcher

• fn: The function to sketch (e.g., x => x * x).
• method: The calculation method: "left", "right", "mid", "lower", or "upper".
• start / end: The domain to calculate the sum over.
• n: Number of sub-intervals (for uniform partitions).
• partition: An array of x-coordinates for a custom partition.
• tags: An array of x-coordinates for tagged Riemann sums.
• sample-points: Number of sample points in each subinterval for Darboux sums.

trapezoidal

• fn: The function to sketch.
• start / end: Range of the approximation.
• n: Number of trapezoids.
• partition: An array of x-coordinates for a custom partition.

Common display parameters

Here're some display parameters. Please refer to the manual for details.

• positive-color: Color for the area above the x-axis.
• negative-color: Color for the area below the x-axis.
• dot-radius: A number (in pixels) for the radius of dots.
• size: The width and height of the plot area, given as a tuple like (5, 5).

License

This package is licensed under the MIT License. Created by Kainoa Kanter and Vincent Tam.