# GRAPH 3D

> Plot a formula in three dimensions, then sell the same render to agents. Surfaces, parametric surfaces, 3D curves, solids of revolution, point clouds. Sliders appear for any parameter you name. 8 colour maps, contour bands, animation, 28-graph gallery. WebGL preview plus vector SVG export from the engine the priced render app-tool runs server-side (1 morsel, on EXCHANGE with ODPS v4.1). EN/FI, light/dark, no sign-in needed. Published on AIMEAT by happydude500001; served at https://graph.apps.aimeat.io. The app id is a
> filename and carries its extension — reading it off the subdomain drops the extension and every
> tool lookup for it misses.

## Documentation

- [This app](https://graph.apps.aimeat.io/): the running application
- [Agent orientation](https://graph.apps.aimeat.io/AGENTS.md): how to call this app
- [Site map](https://graph.apps.aimeat.io/sitemap.md): every document this origin serves
- [Full content](https://graph.apps.aimeat.io/llms-full.txt): this document, at the conventional full path
- [MCP Server Card](https://graph.apps.aimeat.io/.well-known/mcp.json): the server, transport and this app's tools

## Discovery

- [Tool listing](https://aimeat.io/v1/apps/happydude500001/graph.html/webmcp): every tool with its input and output schema
- [Bound skills](https://aimeat.io/v1/apps/happydude500001/graph.html/skills): what an agent can learn to use this app well
- [Node manual](https://aimeat.io/llms-full.txt): the AIMEAT node this app runs on
- [Node glossary](https://aimeat.io/v1/glossary.md): GHII, GAII, morsels and the rest
- [Get an identity](https://aimeat.io/auth.md): RFC 8628 device flow, owner-approved

## Identifiers

```
    owner:  happydude500001
    app_id: graph.html        (not "graph")
```

## Tools

- `render` — call via `aimeat_app_tool_invoke { owner: "happydude500001", app: "graph.html", tool: "render" }`
- `evaluate` — call via `aimeat_app_tool_invoke { owner: "happydude500001", app: "graph.html", tool: "evaluate" }`
- `presets` — call via `aimeat_app_tool_invoke { owner: "happydude500001", app: "graph.html", tool: "presets" }`

# GRAPH 3D

## What this is

A 3D plotter. Give it a formula and a domain and it returns a finished 3D graph as a self-contained SVG: surfaces z=f(x,y), parametric surfaces in (u,v), 3D curves in t, solids of revolution and point clouds. Rendering is deterministic and offline — no external calls, and nothing about a request is stored.

## Buy a render

app-tool `render` on happydude500001/graph.html — 1 morsel per call.
MCP: aimeat_app_tool_invoke { "app": "happydude500001/graph.html", "tool": "render", "input": { "kind": "surface", "formula": "sin(x)*cos(y)", "domain": { "x": [-6,6], "y": [-6,6] }, "colormap": "viridis" } }
The result carries `svg` (the complete image), `stats` (min/max/mean of the plotted value) and the resolved `spec`.

## Free companions

- `POST /v1/ext/graph3d/presets` — the 28-graph gallery plus the full formula grammar render accepts (kinds, variables, constants, 38 functions, styles, colour maps, limits). Read this before composing a request by hand.
- `POST /v1/ext/graph3d/evaluate` — the same formula sampled to numbers instead of pixels: the grid, min, max, mean and where the extremes sit.

## Formula grammar

Variables x y z u v t per kind, plus any name you pass in `params`, plus `time` for animation frames. Constants pi, e, tau, phi. Operators + - * / % ^ with implicit multiplication (2x, 3(x+1), sin(x)cos(y)). Functions: sin cos tan asin acos atan atan2 sinh cosh tanh exp log ln log2 log10 sqrt cbrt abs sign floor ceil round trunc min max pow hypot mod clamp step smoothstep mix sinc gauss saw tri square fract.

## Options

kind: surface | curve | parametric | revolution | points. style: solid | solid-wire | wireframe | contour | points. colormap: viridis | plasma | magma | coral | ice | terrain | fire | mono. theme: light | dark | transparent. view: { azimuth, elevation } in degrees. resolution up to 72 for surfaces, 4000 samples for curves. width/height 200-2400. format: svg (default) | dataUri | both.

## Gallery

- `ripple` (classic, surface) — Radial ripple
- `saddle` (classic, surface) — Saddle
- `egg-crate` (classic, surface) — Egg crate
- `monkey-saddle` (classic, surface) — Monkey saddle
- `paraboloid` (classic, surface) — Paraboloid
- `gaussian` (classic, surface) — Gaussian bell
- `mexican-hat` (waves, surface) — Mexican hat
- `interference` (waves, surface) — Two-source interference
- `standing-wave` (waves, surface) — Standing wave (animate t)
- `ripple-decay` (waves, surface) — Decaying ripple (animate t)
- `sinc2d` (waves, surface) — Two-dimensional sinc
- `checker-wave` (waves, surface) — Beat pattern
- `torus` (shapes, parametric) — Torus
- `sphere` (shapes, parametric) — Sphere
- `mobius` (shapes, parametric) — Möbius strip
- `klein` (shapes, parametric) — Klein bottle (figure-8)
- `shell` (shapes, parametric) — Sea shell
- `trefoil` (shapes, curve) — Trefoil knot
- `helix` (shapes, curve) — Helix
- `lissajous` (shapes, curve) — Lissajous 3D
- `vase` (shapes, revolution) — Vase of revolution
- `horn` (shapes, revolution) — Gabriel horn
- `ackley` (analysis, surface) — Ackley function
- `rosenbrock` (analysis, surface) — Rosenbrock valley
- `himmelblau` (analysis, surface) — Himmelblau
- `rastrigin` (analysis, surface) — Rastrigin
- `complex-mod` (analysis, surface) — Modulus of z² − 1
- `normal-mix` (analysis, surface) — Two-cluster density

Pass `{ "preset": "<id>" }` to render one; any other field you send overrides that preset.


## Agent affordances

- Act — WebMCP tool listing for this app: https://aimeat.io/v1/apps/happydude500001/graph.html/webmcp
- Learn — skills bound to this app: https://aimeat.io/v1/apps/happydude500001/graph.html/skills
- App catalog on this node (this app: happydude500001/graph.html): https://aimeat.io/app-catalog.html
- Register an agent on this node (RFC 8628 device flow): https://aimeat.io/auth.md