Free Spirograph Roulette Curve Bounding Box Calculator—
gemini-3.0-flash
gemini-3.0-flashCalculate exact bounding box coordinates and dimensions for spirograph and roulette curves instantly. A precise geometry tool for designers and mathematicians.
What This App Does
Calculate exact bounding box coordinates and dimensions for spirograph and roulette curves instantly. A precise geometry tool for designers and mathematicians. — generated by gemini-3.0-flash and published by @Akhenaten on Slopstore. Categorized under Utility, this app is part of Slopstore's curated collection of AI-generated tools and experiments. Run it free in your browser. No installation needed.
AI Generation Prompt
Technical Specification: Free Spirograph Roulette Curve Bounding Box Calculator
Overview
A high-performance, browser-based tool for engineers, designers, and students to calculate and visualize the bounding box for various roulette curves (hypotrochoids, epitrochoids, and cycloids). This tool provides instantaneous geometric analysis without requiring server interaction.
Feature Set
- Parametric Inputs: User-friendly controls for Fixed Radius (R), Rolling Radius (r), and Point Offset (d).
- Curve Selection: Toggle between Hypotrochoid and Epitrochoid modes.
- Real-time Bounding Box Calculation: Immediate calculation of Min X, Max X, Min Y, Max Y, Width, and Height.
- Visual Preview: High-quality HTML5 Canvas drawing showing the curve inscribed within its calculated bounding box.
- Responsive Interface: Input panel on the left/top, visual/results panel on the right/bottom.
- Data Export: "Copy to Clipboard" feature for raw coordinate and dimension data.
UI/UX Layout
- Header: Simple, clean application title with a brief explanation of function.
- Input Section: Located in a clean sidebar or top-bar. Includes slider inputs and number fields for precise control of R, r, and d parameters.
- Visual Section: Centered display area with an interactive canvas. The bounding box is shown as a dashed overlay, with the curve highlighted in a vibrant primary color.
- Results Section: A card-based layout displaying the calculated dimensions (Width, Height, Center X, Center Y).
Visual Design & Aesthetics
- Color Palette:
- Background: #FFFFFF (White)
- Primary: #2563EB (Vibrant Blue for active curves)
- Secondary: #64748B (Slate Gray for bounding box lines)
- UI Elements: #F1F5F9 (Soft gray backgrounds for containers)
- Transitions: Smooth fade-in/out for result updates and canvas re-draws (using requestAnimationFrame).
- Style: Clean, flat, modern SaaS look. Rounded corners (8px) for all input fields and containers. High-quality sans-serif typography (e.g., 'Inter', 'Segoe UI', sans-serif).
Developer Directives (Strict Compliance)
- Single File Architecture: All HTML, CSS (in
<style>), and JS (in<script>) must reside in one file. - No Storage: ABSOLUTELY NO usage of
localStorage,sessionStorage, or cookies. The state must be maintained in memory variables. - Sandbox Compliance: No popups (
alert,confirm). If a warning is needed (e.g., invalid input), use a custom modal overlay within the HTML. - No External Dependencies: Use CDN-hosted resources only for essential libraries (e.g., Tailwind CSS via CDN is permitted for layout acceleration, otherwise plain CSS).
- Responsive Design: Use CSS Flexbox/Grid to ensure the tool is usable on both desktop and mobile devices.
- No Branding: Ensure no fictional brand names or logos are used. The title must clearly state the tool's purpose.
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gemini-3.0-flashFiles being used
Frequently Asked Questions
Everything you need to know about using this application.
What is a roulette curve in geometry?
In geometry, a roulette curve is generated by tracing a point attached to a curve as it rolls along another fixed curve without slipping. Common examples include cycloids, epitrochoids, and hypotrochoids, which are the fundamental shapes behind classic spirograph art patterns. Understanding these curves requires parametric equations involving the radii of fixed and rolling circles. Because these shapes can be mathematically complex, determining the exact 'bounding box'—the smallest rectangle that can fully contain the shape—is essential for graphic designers and laser cutters. This tool automates that calculation using the parametric inputs for the fixed circle radius, rolling circle radius, and the distance of the tracing point from the rolling circle's center.
How does the bounding box calculator work?
The calculator utilizes the standard parametric equations for hypotrochoids and epitrochoids. When you input your variables, the application calculates the X and Y coordinates for the curve over one full period or multiple revolutions. It then evaluates the global minimum and maximum values for both the X and Y axes to define the precise width and height of the bounding rectangle. The calculation happens entirely client-side using JavaScript, ensuring your inputs are processed instantly without server-side latency or external data transfers. The visual preview uses an HTML5 Canvas to map these coordinates, providing an immediate visual confirmation of the calculated bounding box dimensions alongside the generated curve.
Can I use this for vector graphic design?
Yes, this tool is highly beneficial for vector graphic designers and artists working with mathematical patterns. By obtaining the exact width, height, and center coordinates of a curve's bounding box, you can perfectly align these shapes within design software like Adobe Illustrator or Inkscape. Knowing these dimensions helps in planning laser cutting paths or determining layout spacing for geometric compositions. Once the bounding box dimensions are calculated, you can utilize the provided output data to standardize your artwork. This ensures consistency across multiple generated designs, making it easier to scale patterns or create perfectly symmetrical borders for prints and physical fabrications.
Are the calculations mathematically precise?
Yes, the tool is designed for high precision using standard floating-point arithmetic in JavaScript. By calculating the extrema of the parametric equations, it provides results that are accurate enough for design, drafting, and educational purposes. The tool computes the critical points based on the derivative of the curve equation, ensuring the boundary calculations are as accurate as the input parameters allow. Please note that while these calculations are mathematically exact, the visual rendering on your screen is subject to the limitations of your device's display resolution. For physical manufacturing or critical drafting applications, always ensure your input parameters represent the required scale and units of your specific project.
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