Geomatic
A command-driven geometry studio enabled with autodiff
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What is Geomatic?
Geomatic is a minimal command-driven studio for geometric construction that allows users to define shapes, compose relationships between them, and watch everything update in real time. The tool is powered by three core technologies: reactivity (changing one geometric property instantly updates all dependent geometries), broadcasting (NumPy-style array operations that automatically propagate across multiple visual elements without manual iteration), and automatic differentiation/autograd (providing calculus capabilities in a geometric setting that unlock new possibilities like visualizing gradients and using optimization).
Key features include a slash command autocomplete interface for entering geometric commands, interactive examples gallery demonstrating concepts like cardioids, vector fields, Peaucellier-Lipkin linkage, and optimization problems, a store with ready-to-run geometric constructions for hands-on exploration, support for creating interactive articles using markdown with extended commands, and the ability to extend functionality by writing and installing custom commands or macros for specialized geometric operations and domain-specific tools.
Geomatic is designed for students learning geometry and calculus, educators creating interactive demonstrations, researchers visualizing mathematical concepts, mathematicians exploring geometric constructions, and anyone interested in hands-on exploration of geometric concepts through real-time interactive visualization. The beta tool combines geometry with calculus concepts like gradient descent, tangents, and vector fields.
Geomatic pricing
Pricing model: Freemium
Pricing details not publicly available - Geomatic is currently in BETA. The store offers ready-to-run geometric constructions but specific pricing for paid plans is not displayed on the website.
Geomatic pros
- Real-time reactive updates when changing geometric properties
- NumPy-style broadcasting for automatic propagation across visual elements
- Built-in autograd for calculus operations in geometric settings
- Slash command autocomplete for easy command entry
- No setup required - ready-to-run geometric constructions available
- Interactive examples gallery with worked demonstrations
- Support for creating interactive articles using just markdown
- Extensible with custom commands and macros
- Visualize gradients and orthogonality properties directly
- Optimization built-in for solving geometric problems without manual calculation
- Animate entire structures by animating a single parameter value
- Derive variables from single parameters for connected geometry
- Learn through hands-on exploration without explanations needed
- Demonstrates advanced concepts like vector fields and linkages
- No complex setup required for creating interactive content
Geomatic cons
- Currently in BETA stage with potential instability
- Login required to create articles
- Limited documentation beyond examples gallery
- Steep learning curve for users unfamiliar with geometry or calculus
- No pricing information publicly available yet
- Requires understanding of concepts like broadcasting and autograd
- Custom commands require programming knowledge to create
- Limited to geometric constructions - not a general-purpose tool
Frequently asked questions about Geomatic
What is Geomatic?
Geomatic is a minimal command-driven studio for geometric construction. It allows you to define shapes, compose relationships between them, and watch everything update in real time. It is powered by reactivity, broadcasting, and automatic differentiation.
How does reactivity work in Geomatic?
Reactivity means that changing a geometric property instantly updates all other geometries that depend on it. You can derive variables from a single parameter and animate the whole structure by animating just that one value.
What is broadcasting in Geomatic?
Broadcasting automatically propagates operations across multiple visual elements without manual iteration. It works like NumPy-style broadcasting, allowing you to pair arrays of different shapes to generate grids of circles or same-shape arrays for element-wise figures.
What is autograd and how is it used?
Autograd (automatic differentiation) provides calculus capabilities in a geometric setting. It unlocks possibilities like visualizing the gradient of an angle, showing that gradients point toward circumcenters, and using gradient descent for optimization problems like finding square roots or the Fermat point.
How do I get started with Geomatic?
Start with the Getting Started example in the examples gallery. It familiarizes you with how to use Geomatic, its key features, how to navigate the interface, and includes simple examples of creating and manipulating geometric objects.
Can I create my own content with Geomatic?
Yes, you can create interactive articles using just markdown with extended commands. Write your content, add interactive commands, and the system handles the rest. No complex setup is required. Login is required to create articles.
How do I extend Geomatic with custom functionality?
Geomatic is designed to be extensible. Anyone can write and install their own commands to add new functionality. You can create specialized geometric operations, custom visualizations, or domain-specific tools. Macros are also supported.
What kind of examples are available?
The examples gallery includes: cardioid visualization, vector fields (gradient and directly defined), Peaucellier-Lipkin linkage for exact straight line motion, gradient descent for square roots, Fermat point of a triangle, plotting functions with tangents, Snell's law of refraction, and optimization for geometric setup problems.
Do I need to calculate things manually before using Geomatic?
No, Geomatic allows you to use optimization to set up problems quickly without tedious manual calculation upfront. For example, you can solve geometric problems using gradient descent instead of doing manual calculations.
What operations break the reactive chain?
Operations like copy, translate, and rotate produce static snapshots that break the reactive chain. Understanding which operations maintain reactivity versus which create static snapshots is important for building connected geometric structures.