Calculus Mesh Viewer API

Compute volume, surface area, and generate a 3D mesh (STL) for common calculus solids.

Overview

URL: https://api.marsthelimit.com/calculate

Authentication: API Key required via header ("Authorization": "Bearer YOUR_API_KEY")

Supported format: JSON

The Calculus Mesh Viewer lets you:

• Compute volume of solids using disk, washer, or cross-section methods

• Approximate surface area

• Generate a downloadable 3D STL model

All requests are made via a JSON payload.

Request Method

POST https://calculus-mesh-viewer.p.rapidapi.com/calculus-mesh-visual

Body: JSON

Features

Disk

(disk)

Rotates a single function around a horizontal axis (y = constant) using the disk method.

Example:

1{
2  "method": "disk",
3  "function": "x",
4  "bounds": {
5    "x_min": 0,
6    "x_max": 2
7  },
8  "rotation-axis": "y=0",
9  "resolution": 100
10}

Notes

• rotation-axis is optional (defaults to "y=0")

• Function should be written in Python syntax

Multi-Region Disk

(disk-multiregion)

Use this when your solid must be built from multiple piecewise regions.

Example:

1{
2  "method": "disk-multiregion",
3  "regions": [
4    {
5      "function": "acos(x)",
6      "x_min": 0.5403023059,
7      "x_max": 1
8    },
9    {
10      "function": "log(x)",
11      "x_min": 1,
12      "x_max": 2.718281828
13    }
14  ],
15  "resolution": 100,
16  "rotation-axis": "y=1"
17}

Washer

(washer)

Rotates a region between two curves around a horizontal axis.

outer-function must be greater than or equal to inner-function over the interval.

Example:

1{
2  "method": "washer",
3  "outer-function": "x^2",
4  "inner-function": "x",
5  "bounds": {
6    "x_min": 3,
7    "x_max": 4
8  },
9  "rotation-axis": "y=0",
10  "resolution": 100
11}

Sections

(section)

Constructs solids with known cross-sections perpendicular to the x-axis.

Supported shapes:

• semicircle "semicircle"

• square "square"

• rectangle "rectangle"

• equilateral triangle "equilateral"

• isosceles right triangle (leg as base) "isosceles-right-leg"

• isosceles right triangle (hypotenuse as base) "isosceles-right-hypotenuse"

Example:

1{
2  "method": "section",
3  "outer-function": "x**2",
4  "inner-function": "0",
5  "bounds": {
6    "x_min": 1,
7    "x_max": 10
8  },
9  "resolution": 100,
10  "section-type": "rectangle",
11  "factor": 2
12}

Parameters

Common Parameters

Usage and Example

The api will return json in the following format:

1{
2  "output_url": "https://api.marsthelimit.com/tmp/models/7d5178ab-e891-400c-8caa-dfc3c7709286.stl",
3  "surface_area": 10.721228382589963,
4  "volume": 2.0438602006652666
5}

To access your 3D model, visit the link and it should automatically download. If it doesn't, please contact me or try again.

Example of an API request in Python that automatically downloads the 3D model:

1import json
2import requests
3import webbrowser
4
5# Load request body from file
6with open('data.json', 'r') as f:
7    data = json.load(f)
8
9url = "https://calculus-mesh-viewer.p.rapidapi.com/calculus-mesh-visual"
10
11headers = {
12    "Content-Type": "application/json",
13    "X-RapidAPI-Key": "YOUR_RAPIDAPI_KEY_HERE",
14    "X-RapidAPI-Host": "calculus-mesh-viewer.p.rapidapi.com"
15}
16
17# Send request
18response = requests.post(url, json=data, headers=headers)
19
20# Basic error handling
21if response.status_code != 200:
22    print("Request failed:", response.status_code)
23    print(response.text)
24    exit()
25
26# Parse result
27result = response.json()
28
29# Extract values
30url = result.get('output_url')
31volume = result.get('volume')
32surface_area = result.get('surface_area')
33
34# Open model automatically
35if url:
36    webbrowser.open(url)
37
38# Print results
39print("3D Model URL:", url)
40print("Approximate Volume:", volume)
41print("Approximate Surface Area:", surface_area)

Notes & Best Practices

• Use higher resolution for smoother meshes (100–500 recommended)

• Ensure functions are continuous on the interval

• Washer method requires outer greater than or equal to inner

• Large resolutions increase computation time

Need Help?

I'm always happy to help! Contact me at https://marsthelimit.com/contact